4 Design And Typical Details Of Connections For Precast And Prestessed Concrete

/ I

DESIGN AND TYPICAL DETAILS OF CONNECTIONS FOR PRECAST AND PRESTRESSED CONCRETE Prepared by PCI Committee on Connection Details Edward R. Sturm, Chairman A. Fattah Shaikh, Consultant/Editor Alex Aswad Charles B. Baker Christian J. Birkeland Thomas J. D’Arcy Greg Force Brien N. Gibson John R. Harbage J. Scott Heuvel James A. E. King

*Paul E. Kraemer Paul Mack Joseph A. Miller Robert H. Murray Heinz Nierlich Jagdish C. Nijhawan Andrew Osborn Donald M. Schultz *A. Fattah Shaikh

Russel I R. Sneddon -Irwin J . Speyer Frederick R. Steinlein Gene R. Stevens James R. Voss Kevin B. Wall James Woodman Zenon A. Zielinski

The Committee Acknowledges these Past Members for their Contributions to this Manual William C. Arons George B. Barney James D. Brown Angelo D’Attoma Harry H. Edwards Gordon Fenton

Mark Fintel Edwin Haggard Nelson J. Hymans Sigmar Knebl Eugene A. Lamberson J e r r y McLelland

‘Past Chairmen

175 W. Jackson Blvd. Chicago, IL 60604 3121786-0300 . FAX: 3121786-0353

John Mikle Harald Nielsen William ,E. Pery *Donald W. Pfeifer Charles H. Raths Kent L. Speheger

MN L-l 23-88 Copyright G 1988 By Prestressed Concrete Institute First Edition, first printing, 1973 Second Edition, first printing, 1988 All rights reserved. This manual or any part thereof may not be reproduced in any form without the written permission of the Prestressed Concrete Institute. ISBN

0-937040-40-l

Printed in U.S.A.

PREFACE This Manual, titled “Design and Typical Details of Connections for Precast and Prestressed Concrete,” is a second edition of the former manual (l), prepared in the period 1970-1972 underthe direction of the PCI Committee on Connection Details, and published in 1973 with the title, “PC1 Manual on Design of Connections for Precast Prestressed Concrete,” MNL-123-73 Portions of the First Edition were used in preparing a chapter on connectionsforthe first edition of the PCI Design Handbook (2) which was published in 1971. A supplement to the First Edition was published in the PCI JOURNAL, May-June 1975. Since 1973, the PCI Committee on Connection Details has continued its activity in monitoring and evaluating research, code revisions, and improvements in the state-of-theart in connection design. It was particularly involved in a 1980-82 study on precast, prestressed concrete connections, sponsored by the National Science Foundation, that led to a state-of-the-art report, “Connections for Precast Prestressed Concrete Buildings including earthquake resistance,” published by PCI in 1982. In the period 1982-l 987 the Committee assembled and reviewed new material for the Manual. A. Fattah Shaikh’was then engaged as consultant/editor to complete the document and carry it through the detailed final review process. Many parts of this Manual are based on the 1982 report (3). Also extensively used in preparing this Manual is the Third Edition of the PCI Design Handbook (4). The Committee recommends that this Manual should be used inconjunction with the PCI Design Handbook Third Edition (4) to ensure proper consideration of the compatibility of connection behavior with behavior of the overall structural system.

ACKNOWLEDGMENTS It has been my privilege to have served as consultant/editor for this Manual. I appreciate the trust placed in me by the Connection Details Committee and the PCI. I also acknowledge the input and advice of the members of the Technical Activities Committee and the Architectural Precast Concrete Connections Committee. Several other individual members of PCI also provided comments on various portions of the document. Contributions by Peter Courtois, Les Martin, Alan Mattock, George Nasser and C.E. (Joe) Warnes are gratefully acknowledged. Processing of this Manual required assistance of several individuals associated with me as colleagues and students. I, particularly, acknowledge the help of Aziz Almadi Deborah Nettles and two very special associates - Christine Jacquet and Gerald Raasch: Chris undertook the tasks of word processing and document layout, while Gerry assisted In the overall management of the document as well as preparation of all sketches for Chapter 4. I thank Chris and Gerry for their dedication to this project. All other drawings were computer generated by Spectra Limited of Milwaukee using CADKEY@ software. The fine service provided by Edward Knoblock and his associates Rock Elgin, Carl Guile and Robert Sitzberger of Spectra Limited is appreciated. A close interaction on my part with Dan Jenny, PCI Technical Director, was necessary in carrying out my assignment. I am indebted to him for his guidance and encouragement. A. Fattah Shaikh Professor of Civil Engineering University of Wisconsin - Milwaukee

(iii)

CONTENTS

NOTATION..................................................................... INTRODUCTION . . .

. . . . ..*..........*..........*..............*..*.

CHAPTER 1

GENERAL CONSIDERATIONS FOR CONNECTION DESIGN

1.1 1.2 1.3

1.4

1.5 1.6

1.7

1.8

CHAPTER 2 2.1 2.2 2.3 2.4

*............

(ix)

(xv)

General.................................:.................... l-l LoadsandLoadFactors...................,..................... l - l Performance Criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . l-l 1.3.1 Strength 1.3.2 Ductility 1.3.3 Durability 1.3.4 Fire Resistance 1.3.5 Stability and Equilibrium VolumeChanges........................................... . . . . l-3 1.4.1 Volume Change Strains 1.4.2 Equivalent Volume Changes 1.4.3 Usual Design Criteria 1.4.4 Handling of Volume Changes in Connection Design Tolerances and Clearances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -1-4 Production Considerations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-7 1.6.1 General 1.6.2 Production Standardization 1.6.3 Reinforcement in Connections 1.6.4 Proper Attachment of Embedded Plates and Structural Shapes 1.65 Dimensional Considerations 1.6.6 Bulkheads and Blockouts 1.6.7 Column Base Connections 1.6.8 Hot-Dip Galvanizing Erection Considerations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1-14 1.7.1 General 1.7.2 Typical Field Considerations 1.7.3 Temporary Connections 1.7.4 Field Welding 1 . 7 5 Site-Cast Concrete Connections 1.7.6 Additional Field Considerations 1.7.7 Cold Weather Considerations Seismic Considerations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 - 1 9 1.8.1 General 1.8.2 Rational Seismic Design Methodology 1.8.3 Seismic Performance DESIGN

CONCEPTS

General................................................... .. -.. Load Transfer rams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . : :. Analysis of Potential Failure Modes. . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . .’ Stress Relief Measures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Flexibility 2.4.2 Bearing Pads 2.4.3 Slip

2-1 2-1 2-2 2-2

4.4 4.5

4.3.3 Chord Forces Bearing Pads.................................................. Member End Design for Bearing. . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plain (Unreinforced) End Bearing 4.51 45.2 Reinforced End Bearing

d-72 -

4.6

4.7 4.8 4.9 4.10 4.11

4.12 4.13 4.14 4.15 4.16

4.17 4.18 CHAPTER 5 5.1

5.2

Dapped-End Connections . .‘. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-15 4.6.1 Design Procedure Based on PCI Design Handbook(4) 4.6.1.1 Flexure and Axial Tension in the Extended End 4.6.1.2 Direct Shear 4.6.1.3 Diagonal Tension at Reentrant Corner 4.6.1.4 Diagonal Tension in the Extended End 4.6.1.5 Diagonal Tension at Undapped Beam Comer 4.6.1.6 Anchorage of Reinforcement 4.6.1.7 Other Considerations and Recommendations 4.6.2 Design Procedure Based on Truss Action and Free-Body Equilibrium BeamLedges.................................................. 4-24 Concrete Brackets and Corbels. . . . . . . . . . . . . . . . 4-26 Structural Steel Haunches. . . . . . . . . . . . . . . . . . . . : 1: : : : .* 1: 1: : : : : : : : : : 4-29 Connection Angles. . . . . . . . . . . . . . . . . . . . . . . . . . 4-31 WeldedHeadedStuds . . . . . . . . . . . . . . . . . . . . . . . :::::::::::::::::::: 4-33 4.11.1 Tension 4.11.2 Shear 4.11.3 Combined Shear and Tension 4.11.4 Plate Thickness WeldGroups................................ 4-41 Column Base Plates. . . . . . . . . . . . . . . . . . . . . . . . . . : .* .* .’ ’ * ’ * . ’ * ’ ’ ’ ’ ’ .’ :. 4-43 Moment-Resisting COnneCtiOnS. . . . . . . . . . . . . . . . . .‘.‘.’ . ’ ’ ’ ’ *.‘.‘.‘. . . 4-46 HangerConnections.. . . . . . . . . . . . . . . . . . . . . . . .‘.-.‘.‘. . . . .‘.*.‘.*.*.‘. . . . . . 4-49 4.15.1 Cazaly Hanger 4.15.2 Loov Hanger Connection of Load Bearing Wall Panels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-53 4.16.1 Vertical Joints 4.16.1.1 Hinge Connection 4.16.1.2 Grooved Joint Connection 4.16.1.3 Mechanical Connection 4.16.1.4 Keyed Joint Connection 4.16.2 Horizontal Joints 4.16.3 Structural Integrity Non-Load Bearing Wall Panel Connections. . . . . . . . . . . . 4-60 Seismic COnneCtiOnS. . . . . . . . . . . . . . . . . . . . . . . . , . . . . .‘.‘.‘.‘.‘.‘.‘.‘.‘.‘.‘.*.‘.‘.’ 4-64 TYPICAL CONNECTION DETAILS

General........................................ Structural Precast Concrete Details. . . . . . . . . . . . . . . . .: 1: ’ *.‘.*.*.‘.-.‘.*.*. 5.2.1 Column to Foundation Connections . . . . . . . . . : : . . . . : : . . . . . . . . 5.2.1 .l Column Size Base Plates 5.2.1.2 Oversized Base Plates 5.2.1.3 Socket Base 5.2.1.4 Grout-Sleeve Base 52.2 Column to Column Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2.1 Bolted Connections 5.2.2.2 Welded Plate Connections 5.2.2.3 Tube to Tube Connections 5.2.2.4 Grouted Sleeve Connections 5.2.2.5 Welded Lap Bar Connection 5.2.2.6 Tube Sleeve for Composite Beam 5.2.2.7 Post-Tensioned Splice Connection

5-1 5-l 5-l

5-7

(vii)

Girder to Column Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-l 3 5.2.3.1 Simple Welded, Bolted or Doweled Connections Hanger Connections 5.2.3.2 Composite Moment Connections 5.2.3.3 Special Applications 5.2.3.4 5.2.4 Beam to Girder Connections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-20 5.2.5 Beam to Beam Connections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-23 5.2.6 Slab to Beam Connections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-26 Hollow-Core and Solid Slab Connections 5.2.6.1 Double Tee Connections 5.2.6.2 5.2.7 Slab to Slab Connections.. . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . 5-30 5.28 Slab to Wall Connections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . * 5-33 Hollow-Core and Solid Slab Connections 5.2.8.1 5.2.8.2 Stemmed Member Connections 5.2.9 Beam to Wall Connections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-39 Beam to Wall Corbel Connection 5.2.9.1 Beam to Wall Pocket Connection 5.2.9.2 Sleeve and Dowel Beam to Wall Connection 5.2.9.3 Beam Bottom to Wall Connection 5.2.9.4 5-42 52.10 Wall to Wall Connections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Horizontal - Bolted Wall to Wall Connection 5.2.10.1 Horizontal - Welded Wall to Wall Connection 5.2.10.2 Horizontal - Sleeve Wall to Wall Connection 5.2.10.3 Horizontal - Post-Tensioned Wall to Wall Connection 5.2.10.4 Vertical - Bolted Wall to Wall Connection 5.2.10.5 5.2.10.6 Vertical - Welded Wall to Wall Connection 5-48 5.2.11 Wall to Foundation Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . Welded Wall to Foundation Connection 5.2.11 .l Bolted Wall to Foundation Connections 5.2.11.2 Moment Resistant Wall to Foundation Connections 5.2.11.3 Grouted Wall to Foundation Connection 5.2.11.4 Post-Tensioned Wall to Foundation Connection 5.2.11.5 5.2.12 Stair to Landing Connections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-53 Architectural Precast Concrete Connections. . . . . . . . . . . . . . . . . . , . . , . . . . . 5-56 5 3 . 1 Bearing (Direct and Eccentric) Connections. . . . . . . . . . . . . . . . . . . . . 5-58, 5-60 5.3.2 Tie-Back Connections (Bolted and Welded). . . . . . . . . . . . . . . . . . . . . 5-59, 5-67 5.3.3 Alignment Connections (Bolted and Welded). . . . . . . . . . . . . . . . . . . . 5-59, 5-74 5.3.4 Column and Beam Cover Connections. . . . . . . . . . . . . . . . . . . . . . . . . 5-59, 5-78 5.3.5 Soffit Hanger Connections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-59, 5-82 5.3.6 Masonry Tie-Back Connections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-59, 5-83 5.3.7 Seismic Shear Plates. . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . 5-59, 5-84 5.3.8 Unique Conditions and Solutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-59, 5-89

52.3

5.3

APPENDIX A

DESIGN AIDS

APPENDIX B

REFERENCES

APPENDIX C

CONVERSIONS BETWEEN US CUSTOMARY (USC) UNITS AND SI UNITS

NOTATION

= depth of compressive stress block

ATC

= Applied Technology Council

A”

= diagonal tension reinforcement in dapped end

Avi

= area of shear-friction reinforcement

= shear span = moment arm of concentrated load with respect to reinforcement a/d

=

A

= area of member

A,

= area of weld

= area of bar or stud

A,

= actual area overwhich load is transferred

Ail Acr

= area of crack interface

A,

A CS

= area of horizontal shear ties

= maximum area of the portion of the supporting surface that is geometrically similar to and concentric with the loaded area

Ae

= effective slab bearing area

AASHTO = American Association of State Highway and Transportation Officials

A,

= area of flexural

ACI

= American Concrete Institute

A flat

= area of the flat bottom of the truncated failure surface

AISC

= American lnstitutue

ANSI

= American National Standards Institute

Ah

= area of shear reinforcement parallel to flexural tension reinforcement

AL

= areaof ledge

A” A0

= area of reinforcement for tension force

A plate

= area of bearing plate

A Ps

= area of prestressed reinforcement

span-to-depth

ratio

reinforcement

longitudinal reinforcement in beam

= area of failure surface

AR

= reduction area, see Fig. 4.11.4

As

= area of reinforcement

A’s

Ash

ASTM = American Society for Testing and Materials A W S = American Welding Society b

= bearing length

b,b,,b,

= width of section or structure

b,

= width of member in which hanger is cast

ba bd b”

= area of reinforcement welded to steel haunch = area of reinforcement for horizontal or diagonal cracks

of Steel Construction

b” bbv

= length of anchor angle = average width of stem above dap = width of interface between precast and cast-in-place members = minimum effective web width = web width

b

= width of assumed failure surface

= auxiliary reinforcement to ensure yielding of hanger steel

BA

= bolted alignment connection

%h

BB

= beam to beam connection

A SlODe

= area of the sloping sides of failure surface

BC

= beam cover connection

=

BG

= beam to girder connection

At

Atie

= area of tie reinforcement

BT

= bolted tie-back connection

BW

= beam to wall connection

A top

= effective area of cast-in-place composite topping

C.E.

= carbon equivalent

nominal

horizontal

shear

reinforcement

C

= distance from extreme compression fiber to centroid of a section or weld group

c.g.

= center of gravity

C

= chord force

C&C, = compressive

force

C

= symbol for the element carbon

c c

= column to column connection

c c

= column cover connection

CF

= column to foundation connection

D

= spacing between beam webs

D,DL

= dead load

DB

= direct bearing connection

DT

= double tee

e

= eccentricity

ei

= center of bolt to horizontal reaction distance

e”

= eccentricity of vertical load

exgey

=

EC

= modulus of elasticity of concrete

eccentricity of load in x,y directions

Cc

= compressive force capacity of composite topping

cc

= net compressive force perpendicular to a joint

Es

= modulus of elasticity of steel

EB

= eccentric bearing connection

%

= diagonal force in corbel

ESD

= elastic strength demand

C”

= horizontal force in corbel

f

= stress

C es

= reduction coefficient for edge distance

fa

= computed axial stress

cr Cr

=

coefficient

fb

= computed bending stress

= symbol for the element chromium

f bc

= compressive stress under service loads

cu

= symbol for the element copper

fbr

= actual bearing stress

CSA

= Canadian Standards Association

fbu

= bearing stress under factored load

C”

= factored compressive force

f

= bond stress

C”

= vertical force in corbel

d

= depth to centroid of reinforcement from extreme compression fiber

reduction

d

= diameter of section

db

= diameter of reinforcing bar or stud

db, Id,,

= diameter of reinforcing bar 1,2

dbc

= diameter of cross bar

dd

= effective depth of nib

de

= edge distance in direction of load

del

~de*Jde3Bde4

= edge distances

bs

“C

= 28-day

f ‘cc

= 28-day compressive strength of composite topping

ct

= compressive strength of concrete at time of initial prestress

f Ct

= splitting tensile strength of concrete

f PS

= stress in prestressed reinforcement at nominal strength

f

= ultimate strength of prestressing steel

Pu

fr fs

compressive strength of concrete

= resultant stress on weld = design strength of steel

dh

= head diameter of stud

f S.0

= effective stress in prestressed steel

ds D

= diameter of stud shank = durometer

ft

= tensile stress

f ue

= equivalent bearing strength, Table 4.16.1

f”#f”, ,f, = shear stress

h

= total depth of a section

h

= building height

h

= depth of beam ledge

hd H

= height of dap

H

= overall height of a wall panel

HI

= horizontal load due to wind

= unit design strength of weld = combined shear and torsion stress in horizontal direction

fY

= combined shear and torsion stress in vertical direction

= overall depth of a beam

fY

= yield strength of reinforcement or structural steel

HZ

= horizontal load due to eccentricity of applied vertical load

f

= yield strength of ASh reinforcement

I

= moment of inertia

I,

= polar moment of inertia

IX’JY

= moments of inertia with respect to x and y axes

lx&

= moments of inertia of weld segment with respect to its own axes

Y=

F

= Fahrenheit

F

= connection force

CF

= greatest sum of factored anchor boft forces on one side of column = allowable axial compressive stress in absence of bending moment

Ftl

= allowable bending stress in absence of axial force

Fc

= compression force

CFc

= total compression on one side of column

F nh

= nominal horizontal shear strength

FS

= friction force

F uh

= factored horizontal shear force

Ft

= allowable tensile stress in absence of shear

CFt

= total tension on one side of column

F"

= allowable shear stress in absence of tension

Fkv FY FY

= design strength of weld

j, J

= lever arm factor, used in j,d = joint force

k

= distance from outer face of web to toe of fillet of rolled shape

Kb

= effective length factor in the plane of bending

Ke

= constant for equivalent shrinkage and creep

Kt

= constant for temperature change

4

= length of angle leg one

l,l,,l,,l 3 = length of structure Id

= development length

I dh

= development length of hooked bar

‘e

= embedment length

= seismic base shear at yield

2,

= angle leg length

= yield strength of steel

G

= projection of corbel, beam ledge, or dapped end

Ll

= horizontal shear length as defined in Fig. 4.2.2

L

= length of weld

9

= gage of angle

9

= width of joint

GC

= girder to column connection

G.C.

= general contractor

(xi)

L

= total length of weld

L,LL

= live load

L

= symbol for steel angle

L bc

= length of cross bar

M

= unfactored moment

M ep

= unfactored moment at elasto-plastic condition

Mf MT

= unfactored moment at failure of member

Mn

= symbol for the element manganese

MO

= symbol for the element molybdenum

MP

= masonry tie-back connection

= moment at plastic condition

= radius of gyration in the plane of bending

R

=

R

= resultant force

R.H.

= relative humidity

R* ROF

= reduction factor for load eccentricity

S

= distance fromfree ing

S

= spacing of concentrated loads

S

= tie, bar or stud spacing

S

= strap width of Cazaly hanger

s1's2

= span 1,2

S

= section modulus

SF

= shape factor

response modification factor

= random oriented fiber edge to center of bear-

Mt

= torsional moment

Mt

= total unfactored moment

Mu

= factored moment

SB

= slab to beam connection

Mx

= unfactored moment about x-axis

SH

= soffit hanger connection

= unfactored moment about y-axis

SI

= System International units

N

= number

SL

= stairs to landing connection

N

= unfactored horizontal or axial force

SP

= seismic shear plate connection

Ni

= symbol for the element nickel

ss

= slab to slab connection

= nominal tensile force

SW

= slab to wall connection

N”

= factored tensile force

P

= wind pressure

54 t

= section modulus of weld group

N”

$4

= grout thickness

MY

p,p,,p, =

(xii)

'b

applied load

= thickness

= nominal tensile strength of concrete

t ll

= stud head thickness

PC Fe

= symbol for plate

L

= effective throat thickness of weld

P”

= nominal strength of joint

ww2 =

PC4 P/S

= nominal tensile strength of steel = prestressed

P”

effective throat thickness of weld I,2

T,T, ,T2,T3,T4

= tensile force

T

= chord force

= applied factored load

Tb

= bond capacity

= applied forces in x and y directions

Tbr

= hook bearing capacity

px,p, r

= radius of gyration

T”

= horizontal force in corbel

r

= radius of section

Ts

= tensile design strength

TJ,, J, =

factored tensile force

W

= wind load

T”

= vertical force in corbel

W

= total load

TFE

= tetrafluorethylene, trade name - teflon

= self weight of wall panel

U

= subscript denoting factored load

wP WA

UBC

= Uniform Building Code

WF

= wall to foundation connection

ucs

= unique conditions and solutions

w-r

= welded tie-back connection

= welded alignment connection

= wall to wall connection

“,“, ,“, = unfactored vertical or shear force X

= horizontal distancefr0mc.g. of weld group to point under investigation

= nominal shear strength of concrete

X*Y

“ci

= shear at flexure-shear diagonal tension cracking

= spacing of studs in a group in x and y directions

x

= x-coordinate of centroid of a section or weld group

“cr

= contribution of concrete to shear strength of dapped-end

xc

= distance from centerline of bolt to face of column

= shear at web-shear diagonal tension cracking .

xo

= base plate projection

= nominal sliding friction resistance

Xt

= distance from centerline of bolt to centerline of reinforcement

v

= symbol for the element vanadium

“c

“cw “f

“W”H, ‘“W’“H3 = shear at horizontal joint

Y

= vertical distance fromc.g. of weld group to point under investigation

= maximum shear force

7

= y-coordinate of centroid of a section or weld group

V nh

= nominal horizontal shear strength

Y

“n

= nominal bearing or shear strength

= distance from centerline of hanger reinforcement to end face of web

YbC

= distance from bottom of section to its center of gravity

z

= the lesser of x and y spacings of studs in a group

Zs

= plastic section modulus of structural steel section

a a

= angle of assumed crack plane

4

= coefficient of thermal expansion for concrete

PI

= factor relating depth of compression block to neutral axis = angle

V int

= shear at interior support

Vmax

“r

= nominal strength provided by reinforcement

“w”, = shear at right, left support “s

= nominal shear strength of steel

“u

= factored shear force

“” “IS

= shear at vertical joint

W

= dimension

W

= uniform load

w”

= factored uniform load

=W” W

= sum of factored uniform loads

Y

= wide flange section

6,6,,6,,etc

= volume/surface ratio

= angle of reinforcement placement

= deformation

(xiii)

% %

= actual creep shortening

A “*P

=

vertical

elasto-plastic

= deformation due to compression

AVP

=

vertical

plastic

6, se c

= elastic displacement

&

= strain

= equivalent creep shortening

&f

= strain at failure condition

6

= elasto-plastic displacement

EY

= strain in steel at yield condition

6 es

= equivalent shrinkage shortening

&P

6e t

= equivalent temperature shortening or lengthening

ep

= actual shrinkage shortening = actual temperature shortening or lengthening at yield

= horizontal deformation of bearing pad

= strain in steel at plastic condition = angle of assumed vertical crack

08, se* = angle

=

shear-friction

coefficient

= structural ductility factor =

effective shear-friction coefficient

= static coefficient of friction = stress

= member deformation = total equivalent shortening due to volume changes

= stress in member at failure condition = stress in member at plastic condition

A

= prefix to denote change

Ah

= horizontal displacement

= apparent angle of friction

A he

= horizontal elastic displacement

= strength reduction factor

A hep

= horizontal elasto-plastic displacement

= curvature at plastic condition

hr

=

=

A"

Av e

(xiv)

displacement

= factor related to the unit weight of concrete

= plastic displacement

= displacement occuring

0

displacement

design

temperature

differential

= curvature

elasto-plastic

curvature

= vertical displacement

= curvature at failure

=

= curvature at yield

vertical

elastic

displacement

INTRODUCTION This Manual, “Design and Typical Details of Connections for Pre= cast and Prestressed Concrete,*’ has been prepared as a guide for consulting engineers, architects, and engineering departments of precast and prestressed concrete producers. As a second edition of the former manual (l)*, it represents a major revision and expansion. The revisions are mostly in terms of design concepts and procedures. The chapter on typical details has been greatly enlarged in number of conceptual details and in commentaryon them. Further, the details have been grouped as structural and architectural precast concrete connections. The limited amount of information available on seismic behavior of jointed structures and cyclic performance of connections in the inelastic range precludes establishment of a prescriptive code or guidelines for the seismic design of precast, prestressed concrete structures. The state-ofthe-art applicable to all seismic zones involves the use of a rational system performance design methodology based on good engineering judgment. PCI Technical Report No. 5(5) provides a simplified rational technique. Using this technique as a basis, a special section (Sect. 1.8) is included in this Manual to give a sharper focus to the design of seismic connections. The selection and design of connections are two of the most important steps in the engineering of precast concrete structures. Usually there are several alternate solutions to each connection situation and the PCI Committee on Connection Details recognizes that the design methods and details included in this Manual are not the only right ones. The information presented however is based on a comprehensive review of the state-of-theart as well as cumulative experience of the members of the Committee representing various segments of the precast, prestressed concrete industry* The Committee wishes to emphasize that this Manual is intended for the use of those with a thorough understanding of engineering fundamentals and structural design; in no case should it replace good engineering judgment. It should also be noted that various drawings included in the Manual are not the completed design details. In many details, much information is purposely omitted to illustrate with clarity only the particular aspects of connection design under discussion. The responsibility for all connections shown on the plans and specifications for a given project lies with the Engineer-of-Record. * Numbers in parentheses refer to References in Appendix B.

GENERAL CONSIDERATIONS FOR CONNECTION DESIGN 1 .I General The design of connections is one of the most important steps in the engineering of precast, prestressed concrete structures. The purpose of a connection is to transfer load and to provide stability. A single connection may be required to transfer several loads simultaneously. Each one of those loads must be considered by the Engineer in the design. In the sections which follow, various methods of transferring loads are examined and it is illustrated how some of these methods may be combined to create typical connections. A good connection combines practicality and economy with sound design and therefore requires an understanding of several factors: strength, serviceability, production, erection and economics. The purpose of this chapter is to introduce these factors and to illustrate how they influence each other in the selection and design of a connection.

1.2 Loads and Load Factors Connections are generally subjected to forces produced by many diff erent types of loads. Some of these loads are apparent, such as dead and live gravity loads, wind, earthquake, soil and fluid pressures. Others are not so obvious and are sometimes overlooked in design, often with serious consequences. For example, the forces produced by restraint of volume changes resulting from temperature variations and the creep and shrinkage of concrete are sometimes not considered. In addition to the above, consideration of other loads, such as those due to foundation settlement and the effects of gravity load eccentricities due to inelastic structural displacements which could occur during seismic activity, may be required. It is the responsibility of the Engineer to consider all applicable loads and to specify appropriate load factors and strength reduction factors. Consideration of these is necessary relative to production, erection and service states as well as in ensuring adequate design strength. With the exception of bearing pad design, the design equations in this Manual are based on strength relationships incorporating the load factors and strength reduction factors as specified in ACI 318-83(6); bearing pad design is based on service loads. Since it is undesirable for the con-

nection to be the weak link in the structure, it may be necessary to specify a load factor in addition to the load factors in ACI 318-83(6), particularly in situations where variations in dimensions of connections or in load transfer positions can cause significant changes in forces in the connectionl.

1.3 Performance Criteria Precast concrete connections must meet a variety of design criteria such as strength, ductility, durability and fire resistance. The connections must also satisfy criteria related to aesthetics, production and erection which are discussed elsewhere in this Manual. A brief discussion of the design criteria excluding special seismic considerations is given below. Discussion of the seismic considerations is included in Sect. 1.8.

1.3.1

Strength

A connection must have sufficient strength to safely transferthe forces to which it will be subjected during its lifetime. In addition to dead and live gravity loads, wind, earthquake, and soil/water pressures, attention must be given to the volume change restraint forces as well as other forces listed in Sect. 1.2. Review of distressed and failed connections in structures suggests that, most often, problems are caused by inadequate consideration of some of these forces. Most frequently overlooked are the forces caused by the restraint in the connection of volume changes, particularly those caused by temperature variations and the shrinkage of the structure. lEased on the research and performance experience gained over the past twenty years, the Committee believes that the use of a single value for this additional load factor (as the 1.3 used previously) for all connections is not appropriate. The Committee, therefore, recommends that the need and the magnitude for this additional load factor should be established by the Engineer with consideration of each individual case. In certain situations, it may not be necessary to use an additional load factor. Examples of these situations are: (a) connections which are relatively insensitive to load transfer positions, (b) where justification for adequate connection strength can be provided based on appropriate research, such as the recent PCI research (7,8,9), and (c)where an additional load factor has already been applied due to specific requirements in othercodes such as model codes, local codes and ordinances. F o r flexural members, it is recommended that the bearing connections be designed for a minimum horizontal tensile force of 0.2 times the factored dead load. 1-l

The type, frequency and magnitude of the various loads should be considered in establishing appropriate strength reduction factors, ductility and redundancy (alternate load paths) in the total structure and within the connection. 1.3.2 Ductility Ductility may be defined as the ability of a structure, a component, or a connection assembly to undergo large deformations prior to failure. In structures, ductility is usually measured by the amount of deformation between first yield and failure. Ductility in the overall structure may result from ductility of the structural members and/or their connections. In precast, prestressed concrete structures, connection ductility can be effectively used to contribute to the overall structure ductility. The connection ductility is achieved by ensuring that various load transfer elements, such as deformed bar and headed stud anchors, wire and other inserts, are adequately anchored in concrete. Adequate anchorage in concrete ensures that failure of the steel insert material (typically yield) will precede failure in concrete. In certain situations, such as where member depth is limited, where inserts are located close to concrete member edges, and/or where inserts are located close to each other, concrete failure may precede insert material failure. In such cases, consideration should be given to the feasibility of attaching connection inserts to member reinforcing steel, or providing auxiliary reinforcing steel forconfinement. Connectionfailuresresultingfrom failure in concrete are typically brittle and, as a general rule, should be avoided. 1.3.3 Durability Concrete, due to its high alkalinity, usually provides adequate corrosion protection for embedded steel elements. Caution is advised in the use of admixtures, and those containing chlorides should be avoided. Steel elements exposed to weather and/or deicing salts are particularly susceptible to corrosion and therefore should be periodically inspected and maintained. Detailing to avoid water pockets is essential. In applications where corrosion resistance is important, the exposed steel elements may be hot-dip galvanized. However, special care is necessary with this process. This is discussed in Sect. 1.6.8. 1.3.4 Fire Resistance Many precast concrete connections are not vul-

l-2

nerable to the effects of fire and thus do not require special treatment; for example, the bearings between slabs or stemmed units and beams. If the slabs or tees rest on elastomeric or other combustible material pads, protection of the pads is not generally needed because deterioration of the pads will not cause collapse. After a fire, the pads can be replaced. Those connections in which reduction in strength due to fire would result in loss of the structure’s stability should be protected to the same degree as that required for the structural frame. F o r example, an exposed steel bracket supporting a beam may be weakened enough by a fire to cause the beam to collapse. Such a bracket should be protected to the same degree as is the beam. Connections which require a fire resistance rating will usually require encasing of exposed steel elements in concrete, Other methods of fire protection include enclosing with gypsum wallboard, coating with intumescent mastic, or spraying with fire protection materials. Additional information on fire protection of connections is given in the PCI publication “Design for Fire Resistance of Precast Prestressed Concrete,” MNL 124-77(10) and in Sect. 9.3.8 of the PCI Design Handbook(4). 1.3.5 Stability and Equilibrium Problems in precast concrete structures will be minimized if proper consideration is given to stability and equilibrium of the structure and its components not only in the completed state but also during the construction phase. Liberal use of free-body diagrams showing loads and reactions required for equilibrium is recommended. A typical example is the case of a ledger or Lshaped beam as shown in Fig. 1.3.1. Because of the ecce,ntric loading, the beam is subjected to torsion and tends to roll or rotate on its supports. To prevent such rotation, appropriate end connections must be provided and the beam designed to resist resulting torsional forces. In some structures, cast-in-place concrete is used to provide restaint against torsional rotation. The cast-in-place concrete may be an integral part of topping, or used. as a separate placement in untopped floor systems. However, since this field concrete is placed after the precast members are erected, temporary connections must be provided for restraint during erection. This dual approach i.e., using temporary connections for erection and cast-in-place concrete for the completed structure requires careful planning and is often costly. It is

.

Load

Restraint Required for Stability

Support

Reaction

Fig. 1.3.1 - Equilibrium of a Ledger Beam usually better to provide permanent connections that ensure torsional stability during construction as well as in the completed structure. In most precast, prestressed concrete structures, permanent lateral stability is best provided by shear walls or cross-bracing, rather than by moment-resisting frames. To date, the most acceptable way of developing seismic frames constructed of precast, prestressed concrete members is to emulate the cast-in-place concrete systems for connections. The analytical models for such connections are well established and their behavior has been verified by tests including the recently completed PCI research (7). However, these connections tend to be congested and expensive especially when the moment-resisting frame must be designed for cyclic loads, such as those due to an earthquake. Lateral forces are typically distributed to the stabilizing elements through diaphragm action of the floor and roof units. Since the structural frame is erected before the topping is placed, temporary stability must be provided and maintained until the final connections become effective. In multi-story buildings, this may require a detailed analysis and careful planning of all construction phases. Connections are sometimes designed which will provide temporary moment resistance during erection,

and then released (by removing bolts, or cutting welds loose) when the permanent lateral stability assemblies are in place. This practice is not encouraged, because it is too easy for the Constructor to forget to release the mechanism, causing unaccounted stresses in the structure. 1.4 Volume Changes Stresses resulting from restraint of volume changes must be evaluated and considered in the design of connections. While the stresses due to loads are produced immediately upon application of Joads, the stresses due to restraint of volume changes occur over a period of time. This section provides data on volume change strains and gives recommendations for design. 1.4.1 Volume Change Strains Volume changes in concrete result from the effects of temperature variations, and creep and shrinkage of concrete. The degree of restraint to these volume changes of members determines the magnitude of the forces that must be transferred through the connections. 1.4.2 Equivalent Volume Changes If a horizontal framing member is connected such that the volume change shortening is re-

strained, a tensile force is built up in the member and transmitted to the supporting elements. However, since the deformations due to volume changes take place gradually over a period of time, shears and moments at the connections are reduced because of creep and micro-cracking of the member. For ease of design, the volume change shortening can be treated in the same manner as the short term elastic deformation by using the concept of “equivalent” shortening. Thus, the following relations can be used: 6, = “JK,

s e s = $IKe

(Eq. 1.4.1)

(Eq. 1.4.2)

where: secpses

s,,s, Ke

= equivalent creep and shrinkage shortenings, respectively = actual creep and shrinkage shortenings, respectively = a constant with values in the range 3 to 5

For typical precast, prestressed concrete members, which are generally lightly reinforced, a value of KB= 5 is reasonable. Shortening due to temperature change’ is similarly modified. However, the maximum temperature change will usually occur over a much shorter time, probably within 60 to 90 days. Thus, the equivalent shortening would be closer to the actual shortening: (Eq. 1.4.3)

set = st’Kt where: bet and I!,=

K,

the equivalent and actual temperature shortenings, respectively = a constant; recommended value = 1.5

1 Temperature change is, of course, a reversible effect;

increase causes expansion and is important in the location and design of expansion joints. Temperature differentials in roof and wall elements should also be considered.

l-4

The total equivalent shortening to be usedfordesign is: A = 6, + se, + set =

6, + 6s 6, K,

+x, (Eq.l.4.4)

When the equivalent shortenings are used in the frame analysis for determining shears and moments in the supporting elements, the actual modulus of elasticity of the member is used, rather than a reduced modulus as used in methods based on actual shortenings. 1.4.3 Usual Design Criteria The performance of actual structures indicates that only reasonable estimates of volume changes are necessary for the design of most structures even though test data on volume changes (see Tables A-l through A-7 in Appendix A) exhibit considerable scatter. The PCI Committee on Connection Details considers the use of approximate values shown in Tables A-8 and A-9 in Appendix A satisfactory for typical designs. 1.4.4 Handling of Volume Changes in Connection Design Depending on the degree of restaint, the volume change strains can result in large forces in precast members and their connections. For example, in moment-resisting frames there is always some restraint to volume changes which results in stresses in the frame members and their connections. These stresses must be considered in the design. However, it is generally preferable to design so that the volume change movements are allowed to occur without restraint. If movement is allowed, then the actual (not equivalent) volume change movement must be accounted for in detailing the connection. The PCI Design Handbook (4) Chapt. 3 gives methods for calculating volume change strains in structures. Figures A-l and A-2 and Tables A-l through A-7 in Appendix A provide data to calculate actual movements. Example 4.4.1 (Chapt. 4) illustrates bearing pad design using actual volume change strains. 1.5 Tolerances and Clearances Tolerance may be defined as the permitted variation from a specified dimension or quantity. Tolerances are specified to allow controlled leeway in fabrication of products (product or fabrication tolerances, such as variation from specified length or

width) and their installation (erection or alignment tolerances, such as deviation of a wall panel from plumbness). Clearance, on the other hand, is the space that must be provided for interfacing two items. Clearance is required to accommodate tolerances and to provide space for carrying out connection operations, such as welding and or turning of wrench for tightening bolts. The PCI “Manual for Quality Control for Plants and Production of Precast and Prestressed Concrete Products,” MNL 1 l&85(1 l), gives recommended tolerances for structural precast members. The PCI Committee on Tolerances, working closely with ACI Committee 117 on Tolerances, has published a comprehensive report in the PCI Journal(l2).

The product tolerances that interact with connections are given in Table 1.51. An important consideration is the compatibility of precast tolerances with tolerances required for other construction materials, such as the elevation of cast-inplace concrete footings and the location of preset anchor bolts. Connection tolerances must be established that are structurally as well as architecturally acceptable. Consideration should be given to the fact that normal fabrication tolerances preclude the possibility of a perfect fit in the field. The Architect-Engineer should clearly define the tolerances to be permitted in the building foundation and alignment, and the General Contractor should verify that these tolerances are being held. The tolerances shown in Table 1.52 are suggested as

Table 1.51 -- Product Tolerances Related to Connections

r

Recommended Tolerances’ (in.)

Item Field placed anchor bolts .............................................................. Elevation of field cast footings and piers ....................................... Field placed plates ........................................................................

Position of plates .......................................................................... Location of inserts ........................................................................ . Location of bearing plates ............................................................ Location of blockouts .................................................................... Length ........................................................................................... Overall depth ................................................................................ Width of stem ................................................................................ Overall width ................................................................................. Horizontal deviation of ends from square ..................................... Vertical deviation of ends from square ......................................... Bearing deviation from plane ........................................................ Position of post-tensioning ducts in precast members .................

* l/2 f1 +1

+1 zk l/2 I!I 314 fi 1 zk 314 If: l/4 f l/8 I!z l/4 f l/2 + l/8 per ft. of height f3/16 It l/2

P~chitwtwl Precast Concrete Length or width ............................................................................. Thickness ..................................................................................... Location of blockouts .................................................................... Location of anchors and inserts .................................................... Warpage or squareness ............................................................... Joint widths - specified ............................................................................... - min. and max. dimensions ................................................... ‘Other

+ l/l6 per 10 ft. but not less than of: l/8 + l/4, -l/8 + l/2 318 l/8 in 6 ft. 318 to S/8 l/4 and 314

construction materials may control tolerances selected

l-5

erection tolerances for the purposes of interfacing. Clearances should be determined with consideration of tolerances and other space requirements for making connections. If clearances are realistically assessed, they will minimize construction problems. As a rule, clearances should be as large

as possible. For example, if a 2 in. clearance can be used just as easily as a 1 in. clearance without causing structural or architectural problems, the larger clearance should be selected. Recommended minimum clearances are given in Table 15.3.

Table 1.5.2 - Erection Tolerances for Interface Design Recommended Tolerances (in.)

Item Variation in plan location (any column or beam, any location) . . . ...*~..........**‘......*..........*.......................‘...‘........ Variation in plan parallel to specified building lines . . . . . . . . . . . . . . . . . . .

Difference in relative position of adjacent columns from specified relative position (at any deck level) . . . . . . . . . . . ..**......*... ......... Variation from plumb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...I.

4 l/2 l/40 per ft., any beam less than 20 ft. or adjacent columns less than 20 ft. apart l/2, adjacent columns 20 ft. or more apart l/2 l/4, any 10 ft. of height I, maximum for the entire height

Variation in elevation of bearing surfaces from specified elevation (any column or beam, any location) . . . . . . . . . . . . . . . . . . . . .** rf: l/2 Variation of top of spandrel from specified elevation 4 l/2 (any spandrel) . . . . . . . ...‘............‘...............................‘................. Variation in elevation from bearing surfaces from lines parallel to specified grade lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .‘.‘ l/40 per ft. any beam less than 20 ft. or adjacent columns less than 20 ft. apart l/2, maximum any beam 20 ft. or more in length or adjacent column 20 ft. or more apart k 314 Variation from specified bearing length on support ................... zk l/2 Variation from specified bearing width on support ..................... l/2, maximum Jog in alignment of matching edges ..........................................

Table 1.53 - Recommended Minimum Clearances Recommended Mlnimum Clearance (in.)

Item Precast Precast Precast Precast

to precast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..‘...........f... to cast-in-place . ...‘..‘..............................‘..................... to steel ‘.......I.‘..‘............,.............‘............................... column covers . . . . . . . . . . . . . . . . . . . . . ..‘..‘............................‘.....

l/2 (1 preferred) 1 (2 preferred) 1 (2 preferred) l-1/2 (3 preferred for tall buildings)

1.6 Production Considerations 1.6.1 General In connection design, knowledge of production is essential. Understanding of the production process for the precast concrete members leads to economies in connections; it may also suggest ways in which the connection function can be improved. While several alternate connection details may be available for a particular situation, experience suggests that for greatest overall economy, the connection should be selected based on consideration of both production and erection. The following items pertaining to plant production of precast members should be kept in mind when designing connections: a. Standardize connection types. b. Avoid reinforcement and hardware congestion. c. Avoid penetration of forms where possible. d. Reduce post-stripping work. e. Be aware of material sizes and limitations. f . Consider clearances and tolerances. g. Avoid non-standard production and erection toierances. h. Standardize hardware items and use as few sizes as possible. i. Use repetitious details. j. Use symmetrical connection materials (for example, welds) to minimize errors. 1.6.2 Production Standardization Standardization of materials used in connections improves quality control in the plant and contributes to production economies. Standardization can be applied to all elements of a connection. For example, if a majority of the connection details require a 318 in. plate while in some a 5/l 6 in. plate would be adequate, all connections should be made with 318 in. plates. Similarily, in selecting reinforcing bars, if some connections require No. 6 bars and others No. 5 bars, it is better to use No. 6 bars throughout. Even more generally, where a majority of the connections on a project are required to support 80 kip loads, whereas a few are subjected to 50 kips, all connections should be designed for the 80 kip load. Standardization can also be used in dimensioning of connections. Little is gained by slight changes in dimensions, since the savings in materials may be more than offset by the extra labor involved in developing the modifications. Furthermore, if different connections vary only slightly in dimensions, there is a greater chance that an im-

proper connection may be used. With rare exception, all the materials and procedures involved in making connections should be standard to the industry and readily available in the local area. It is generally more practical to use additional quantities and even more expensive materials to achieve this type of standardization than to select items or materials that may result in delay of production or may be unfamiliar to the trade. 1.6.3 Reinforcement in Connections The diameter of reinforcing bars used in a connection area should generally be as small as possible. Large bars may be impractical due to their longer required embedment length, the difficulty in obtaining the proper bend geometry to conform to the connection hardware, or the space available within a precast member to properly contain them. Fig. 1.6.1 shows how the use of a bent bar in a corbel creates an unreinforced area of concrete nearthe edge of the corbel. It is betterto use smaller bars or, as shown in Fig. 1.6.2, welded cross bars, or deformed bar anchors. The welded headed studs and deformed bar anchors provide a convenient and reliable method of achieving positive anchorage. Their use in precast concrete connections is common. In connection design, attention must be paid to positioning of reinforcement (both prestressing strand and reinforcing bars) to allow proper casting and vibrating of concrete into the connection region. When a large numberof reinforcing bars cross each other, it may cause honeycombing of concrete in the connection area. Such problems can be minimized by checking the connection region for dimensions and clearances during the design phase. 1.6.4 Proper Attachment of Embedded Plates and Structural Shapes Proper attachment of plates, angles, and other steel shapes to the form is important. If they are not held securely in the forms, they may become misaligned or skewed relative to their planned position as shown in Fig. 1.6.3. This can result in insufficient, or uneven bearing when the connection is completed later in the field. Structural shapes, such as angles and plates, are easily held in place by providing two small size holes (say 114 in.) in the assembly for nailing or screwing to a bulkhead or location jigs. Care is also necessary in positioning of plates and angles so that proper placing and vibration of concrete under these steel sections can be

1-7

Critical Area

As Drawn

As Produced

Fig. 1.6.1 - Problems With Bending Reinforcing Bars in Critical Connection Areas

f

Welded Cross Bar

Welded Deformed Bar (shown) or Headed Stud

Fig. 1.6.2 - Solutions to Bar Bending Problems achieved. For hard to reach positions, air release holes l/4 in. to 3/4 in. in diameter should be provided through the angle as shown in Fig. 1.6.4. This procedure allows entrapped air to escape which reduces the possibility of voids under the plate or angle. The actual position of the embedment during casting must be predetermined so that the holes are drilled in the horizontal surface of the plates. Another technique for eliminating voids under plates involves placing the concrete into the form and then placing and vibrating the embedment into fresh concrete. This requires special supervision so that adequate vibration is supplied and accurate positioning measurements are taken prior to and after

the embedment is placed and vibrated into fresh concrete to avoid dislodging of the anchor and creating voids around the anchor bars. 1.6.5 Dimensional Considerations Where possible, connections should be dimensioned to the nearest 112 in. This makes it easier to detail connections and it simplifies production. Also, 112 in. increments are common in plate sizes. Dimensional considerations should include standard clearances and tolerances (see Sect. 1.5). It is neither practical nor economical to require the various pieces of the connection to be assembled to very tight dimensions. The minimum

Ej jFk$-q (a) As Shown

Jyb

Section C-C

c$lr (b) As Cast

(a) As Shown

Section D-D

Fig. 1.6.3 - Potential Misalignments Em bedded Plates

of

Center Lines of Air Release Holes I

(a) As Shown

(b) As Cast

I

(c) Detail to Prevent Honeycomb

Fig. 1.6.4 - Air Bleed Holes for Reducing Voids Under Embedments

clearance between items cast in a member should not be less than l/4 in.; 112 in. is preferred. Potential conflicts of anchorage steel within a member must be identified during detailing to avoid problems during fabrication. Reinforcing bars have deformations that add l/8 in. or more to the nominal diameter, as shown in

Fig. 1.65. This should be considered in dimensioning. The Designer must recognize that for connection details in prestressed members, the position of the prestressing strands must not interfere with the connection items. Typical situations are shown in Fig. 1.6.6 and Fig. 1.6.7.

l-9

0 t 3/16"

D + l/6”

Deformations +

Bars #3 to #8

Bars #9 to # 1 1

Fig. i .6.5 - Reinforcing Bar Deformations

Section A-A

View

Section B-B

Fig. 1.6.6 - Conflict for Space in Connection Areas Between Prestressing Steel and Connection Detail

770 0 0 c c c - - -

r Confl ict

P/S

Strands

I

5" x 3" Bearing

Section E-E

( Anchorage Steel not Shown far Clarity

1

Fig. 1.6,7 - Conflict Between Bearing Angle and Prestressing Steel at End of Beam

1.6.6 Bulkheads and Blockouts

can cause connection problems in that an uneven The majority of precast, prestressed concrete bearing can develop due to the skewed geometry in members are made in 200 to 500 ft. long beds with combination with the camber. Such members may the individual units separated by wood or steel bulkrequire bearing pads of different thicknesses to conheads. Misalignment of the bulkhead from the verform to the skew geometry. tical ortwisting out of square may influence the perBlockouts should be detailed for easy access formance of a connection. A typical case is the during production. If it is difficult to place the blocksimple end bearing of double tees on a ledger out or to secure it to the form, its position may vary beam. If the end of the tee varies from the vertical, from casting to casting. All blockouts should be this could result in a reduction of bearing length as detailed to prevent entrapment of air and resulting shown in Fig. 1.6.8. Standard variation allowed voids underthe blockouts. Air relief holes should be from square ends is +1/8 in. per foot of beam depth used in all blockouts where concrete must flow for long span building members and bridge beams. under the blockouts during the casting operation. In detailing members and setting bulkheads, the efThe non-bearing sides of blockouts should be fects of end rotation and elastic shortening caused drafted to allow for stripping of the product and to by camber and prestressing forces must be considminimize damage to areas surrounding the blockered. In deep members (24 in. or deeper) and outs. heavily prestressed, the end rotation and elastic Special attention must also be paid to dimenshortening must be determined and the bulkheads sions and position of blockouts in the end regions of skewed or set longer in order to avoid short bearing beams so that the continuous prestressing steel conditions. pattern is compatible with the blockout as shown in Long span members with highly skewed ends 1 Fig. 1.6.9.

(a) As Planned - Side View

(b) As Cast -. Side View

Ledger Beam

(c) Installed

Fig. 1.6.8 - Effect of Bulkhead Variations and Camber Induced End Rotations

6”

3 at 2"

6"

Bearing Plate and Stirrups Omitted for Clarity

(b) Preferred

Fig. 1.6.9 - Effect of Blockouts on Strand Placement 1.6.7 Column Base Connections Column base connections, although a relatively standard item of production, can greatly influence costs and production time. For example, column base plates which are larger than the cross-section of the column must extend outside the column form and thus such columns cannot be cast in long-line forms. Column-size or smaller base plates are desirable so that economical long-line forms can be utilized. Some column base connections are designed with reinforcing bars or bolts extended beyond the end. Projecting steel requires special bulkheads and their placement and alignment can be difficult. In such cases it is recommended that threaded inserts be used rather than projecting bolts. Connection elements that project out of the precast units are subject to damage. On occasion, projections may result in a product that exceeds normal limits for shipping, thus adding unnecessary cost. It is best to have all connection items internal to the members, yet accessible so that the connection can be easily completed in the field by bolting or welding. For example, reinforcing steel continuity can be achieved using products such as coil rods or posttensioning bars. Another consideration is that of the corbel pro-

1-12

jection from column faces as shown in Fig. 1.6.10. When only one corbel is required, it can be cast on the upper surface. Corbels on opposite sides of a column may require special forms, secondary pours, or welding of steel. Production problems and costs are greatly increased when corbels are required on three or four sides. It may be worthwhile to consider “mechanical” attachment of the corbels to the column faces. Such methods include casting corbels onto the column at a later time, welding structural shapes to plates cast in the columns, or bolting structural steel shapes to inserts cast in the column. 1.6.8 Hot-DIP Galvanlzlng In applications where corrosion resistance is specially important, the components of exposed connections are sometimes hot-dip galvanized. In order to ensure that the strengths of the various elements of a connection are not reduced by hotdip galvanizing, several precautions are necessary. When items of a connection assembly require welding, such as anchor bars to plates, the following recommendations by the American Hot-Dip Galvanizers Association (13) have been found to produce satisfactory results:

l ;.. .

T’

Top View

>

3

@

Side View

Single Corbel Column

jll(

Perspective

..y.

Top View

?

~ Side View

Two Corbel Column

Perspective

“

Top View

Side View

Four Corbel Column

Perspective

Fig. 1.6.10 - Forming Problems with Column Corbels 1. An uncoated electrode should be used whenever possible to prevent flux deposits. 2. If coated electrode is used, it should provide for “self-slagging” as recommended by welding equipment suppliers. All welding flux residues must be removed by wire brushing, flame cleaning, chipping, grinding, needle gun or abrasive blast cleaning. This is necessary because welding flux residues are chemically inert in the normal pickling solutions used by galvanizers; their existence will produce rough and incomplete zinc coverage.

3. A welding process such as metal-inert gas (MIG), tungsten-inert gas (TIG), or CO, shielded arc is recommended when possible since they produce essentially no slag. It should be recognized that many parts of connectioncomponents are fabricated using cold rolled steel or cold working techniques, such as bending of anchor bars. In some instances, cold working may cause the steel to become strain-age embrittled. The embrittlement may not be evident until after the work has been galvanized. This occurs because aging is relatively slow at ambient temperatures but is more rapid at the elevated temperature of the galvanizing bath. 1-13

It is known that every form of cold working reduces the ductility of steel. Operations such as punching holes, notching, producing fillets of small radii, shearing and sharp bending may cause strainage embrittlement of certain steels, particularily those with high carbon content. The following precautions are recommended by the American HotDip Galvanizers Association (13): (1)Select steel with a carbon content below 0.25% (2) Choose steel with low transition temperature since cold working raises the ductile-brittle transition temperature and galvanizing (heating) may raise it even further. (3) For steel having carbon content between 0.1% and 0.25%, a bending radius of at least three times the section thickness should be maintained. Otherwise, the material should be stress relieved at 1lOOOF for one hour per inch of section thickness. (4) Holes should be drilled, rather than punched, in material thicker than 3/4 inch. If holes are punched, they should be punched undersized and then reamed an additional l/8 in. overall or drilled to size. (5)Steel sections thicker than 518 in. and designed to carry tensile loads should be machine cut or their edges machined. (6) In critical applications, the steel should be hot worked above 1,200”F in accordance with the steel maker’s recommendations. Where cold working cannot be avoided, stress relieving as recommended in Item (3) above should be done. ASTM Recommended Practice Al43 “Safeguarding Against Embrittlement of Hot-Dip Galvanized Structural Steel Products and Procedure for Detecting Embrittlement” (14) and CSA Specifications G164 “Galvanizing of Irregularly Shaped Articles” (15), provide guidance on cold working and stress relieving procedures. Another area of concern is hydrogen embrittlement. Hydrogen released during the pickling operation, can be absorbed into the steel causing a potentially significant loss in its ductility. Even though hydrogen embrittlement is not common and the hydrogen absorbed during the pickling operation is generally expelled at hot-dip galvanizing temperatures, it is recommended that for high strength steels (ultimate strength higher than about 150,000 psi) a different method, such as grit blasting, should be used instead of acid pickling.

1-14

1 1.7 Erect Ion Considerations 1.7.1 General Consideration should be given to erection procedures when designing precast concrete connections. This is best done by consultation with the Erector early in the selection and design process. If more than one connection detail will satisfy structural requirements, the selected detail should be the one that expedites erection. Details that are best suited for field and erection conditions may require compromise of some production considerations. If possible, the same connection methods should be used throughout a project. In other words, if some spandrels are bolted to the columns, all spandrels, loadbearing and non-loadbearing, should be bolted. Also the number of different sizes of field connection hardware and connection material should be minimized. Plate sizes, weld sizes, and bolt sizes should be standardized as much as possible. Connections should also be designed so that a unit can be set and safely unhooked from the crane in the shortest possible time. The following items pertaining to erection should be kept in mind when designing connections: a. Plan for the shortest possible hoist hook-up time. b. Provide for field adjustment. c. Provide accessibility. d. Use connections that are not susceptible to damage in handling. 1.7.2 Typical Field Considerations Connection details should be planned to accommodate the possibility of bearing surfaces being misaligned or warped from the desired plane as shown in Fig. 1.7.1. Adjustments can be provided by the use of dry-pack mortar or non-shrink grout. Soft pads will usually provide the necessary adjustments at beam bearings. In establishing allowable tolerances, it must be remembered that different suppliers or subcontractors may produce the members meeting at a connection, orthatothertrades and materials (with their own tolerances) may be involved in the completion of a connection. An example of two different trades being involved in a connection is the bolting of a precast column to a cast-in-place foundation as shown in Fig. 1.7.1. Any joint that requires dry-pack or non-shrink grout for final completion should provide for at least 2 in. as the planned dimension between two surfaces. A 2-l/2 in. dimension is preferable, particularlyforgrouted base plates under precast columns.

Top of Footing or Pier

Dry-Pack

Base Plate Elevation

Fig. 1.7.1 - Base Plate Details

1.7.3 Temporary Connections During erection, loads may occur which will control the connection design. These temporary conditions can result from wind, construction loads, or impact, which may place a more severe demand on the connection than after it is completed and service loads are imposed. Also, certain elements which complete a connection, such as cast-in-place concrete, render a connection incomplete until the concrete is placed and cured. Therefore, temporary erection connections may be required to ensure stability of the structure during this phase. In fact, certain connections may be required for erection purposes only. Whenever any special or unusual erection conditions are encountered, the Engineer should identify these and determine if the connections are adequate. Fig. 1.7.2 illustrates a typical, temporary, unbalanced loading condition on an inverted tee beam which must be considered. A review of all phases of construction and erection may be necessary in order to identify required temporary connection conditions. Such a review may indicate, for example, that temporary guying, shoring, welding, bolting, or bracing the precast units is a more economical solution than requiring the connection to carry the temporary erection loads. If such temporary techniques are used, the precast member should be provided with required inserts or weld plates for attachment. Normally, the Engineer cannot anticipate the method of erection during the design phase. Thus, the Engineer should require that the erection drawings show the erection sequence. If a project

requires special erection procedures, a careful review of the drawings should be made to identify conditions which might subject the connections to loads greater than the service loads, and the Engineer should verify design for these special erection loads. 1.7.4 Field Welding Where field welding is required it should meet the procedures and qualification requirements of the American Welding Society( 16): AWS Dl .l for structural steel, AWS D1.4 for reinforcing steel and AWS Dl .l (Section 7) for stud welding. Welding through hot-dipped galvanized material requires special care(see Sect. 1.6.8). Thorough pre-removal of the galvanizing is necessary in weld zones, otherwise contaminations can occur creating poor weld quality. “Cold galvanizing” metal spray should be applied over the welded joints to replace the removed galvanizing. Where only a few field connections are to be welded, it is usually more economical to use an alternate method. When making field welded connections, the welding should be done in the down-hand position whenever possible. Welding should be avoided in confined places. This would ensure good quality welding and minimize the potential of injury due to toxic fumes. Welding should only be done as shown on the drawings. Providing more weld than shown on the plans is not necessarily better, since it may result in not only unpredictable but also undesirable behavior. When welding in cold temperatures, preheating

1-15

No Double Tee in Place Here

Plan View

Overturning

Torque

Column Top or Column Bracket

Section A-A

Fig. 1.7.2 - Effect of Erection Loads is required or special welding techniques such as thermite welding should be used. Moreover, welding in cold temperatures should be done carefully to prevent spalling of the adjacent concrete. In fact,

1-16

with welded connections, potential damage to the concrete surrounding the connections must be evaluated for possible effect on performance of the connection.

Field welding for both temporary and final connections must be specified with consideration of possible consequences. Fig. 1.7.3 illustrates a welded connection detail which may satisfy the temporary loading conditions shown in Fig. 1.7.2, but it does not provide relief of volume change forces that may build up in the beams unless the opposite ends are free to move. Unless the Engineer has fully considered the effect of field welding in restraining rotations or preventing movements of the units, welding should be avoided or temporary welds removed after erection, or the connection should be designed to yield before reaching the critical load. 1.7.5 Site-Cast Concrete Connections Connections requiring cast-in-place concrete for their completion usually provide an excellent connection method by allowing good load redistribution: with proper design they can match monolithic joints in cast-in-place concrete in ductility and performance. Where possible, the connection detail should be self-forming as shown in Fig. 1.7.4. Such details require adequate tolerances for rapid erection. When it is impractical to develop a self-forming detail, the connection should permit easy forming and easy form removal. In dimensioning such a detail, consideration must be given to the allowable tolerances in dimensions of members, possible

variations from planned positions, and completed architectural appearance. Connections completed with cast-in-place concrete are more tolerant of member fabrication tolerances. 1.7.6 Additional Field Considerations Whenever possible, the connections should be completed to permit operations to take place on the top side of erected members ratherthanfrom below where ladders or scaffolds are required. In addition, the connection details should be standardized. Repetition of the same connection improves quality control in the field. Furthermore, standardization facilitates selection and shipment of connection items to the plant and to the project, resulting in fewer delays and added economies. An advantage of standardized connections is that when erectors have experience with a typical connection, they are in a better position to expedite proper placement and connection of members. With bolted connections, 314 in. and 1 in. diameter bolts are most commonly used in the precast industry. It is important to consider the types of threads being used in bolted connections and to select those that are considered to be standard. A discussion of bolts and threaded connectors is given in Sect. 3.5. In design of connections, it should be recognized that the field adjustments may cause shift in load application positions from the design positions. An

Multi-Bay P/S Ledger Beam

Remove Weld After Erection Is Complete

Fig. 1.7.3 - Utilization of Temporary Welds for Erection Purposes 1-17

Fig. 1.7.4 - Example of Self- Forming Spaces for Cast-in-Place Concrete Connections

Ledger Beam

Fig. 1.7.5 - Effect of Erection Variations on Load Application Point on Connection

assessment of the shift must be made and the effect accommodated in design, Fig. 1.7.5 illustrates a typical situation where the actual load position on a connection has shifted due to erection tolerance conditions. Another condition to be aware of is the impact loading that mayoccurduring erection orthat may result from construction loads. Appropriate consideration of this potential impact loading should be included in the design of connections. The Engineer cannot assume that the connection will be made exactly as detailed. The Engineer

should have an understanding of how it will be made and whether the design can accommodate potential misalignments or construction irregularities without impairing the integrity of the connection.

1.7.7 Cold Weather Considerations At times when erection of precast may take place in subfreezing weather, consideration should be given to provision for drainage at the connection to prevent ice buildup which might cause damage to the joint or the product in the vicinity of the joint.

1.8

Seismic

Considerations

1. Design the system to resist “elastic strength demand” (ESD) loads. The response modification coefficient, R, is taken as 1 .O as illustrated in Ref.5 This approach may be suitable for Zones 1 and 2. 2. Design connections to be stronger than the members joined. This requires the members (rather than the connection) to develop the inelastic deformation required for energy dissipation. In most situations, a design of this type is not feasible. 3. Design the lateral load-resisting systems with a configuration which positions the connections outside the regions of the plastic mechanisms. Frame configurations in the shape of “T” or “H”, as shown in Fig. 1.8.1, provide connections in regions of smaller lateral load moments. It should be recognized that the inelastic response of the structure may dramatically accentuate the connection forces evaluated based on the elastic state of the structure. Reference18 gives a procedure for establishing loads which may be anticipated in frames. Shearwalls, as shown in Fig.l.8.2, require special consideration for seismic design. The flexural mechanism in Fig. 1.8.2(b) is the accepted behavior mode

1.8.1 General Connections located in regions of the structure where large inelastic displacements are required to develop during an earthquake are classified as seismic connections. Design of structures for Uniform Building Code (17) load levels in Zones 1 through 4 assumes energy dissipation by theformation of plastic mechanisms. When these mechanisms occur at interelement joints connected by seismic connections, energy must be dissipated through inelastic deformations of the connections. PCI Technical Report No. 5(5) provides a rational design approach and is the basis for information presented in this Manual. Earthquake engineering of structures may even be necessary in regions of low seismic intensity because significant lateral forces are generated due to the large mass of the concrete structures. Proper design of seismic connections is required to ensure satisfactory performance of most normally used lateral load resisting systems. If it is desired that non-seismic connections be provided in buildings subjected to earthquake toads, one of the following three concepts may be used:

-Q-

H - Frame

LI

-$ # Ground Level

\

Cast-In-Place with Pedestal

Footing

(a) H - Frame Configuration

(b) T - Frame Configuration

Fig. 1.8.1 - Frame Configurations to Place Connections Outside of Plastic Regions

for concrete shear walls. Sliding shear, Fig.l.8.2(c) must be avoided. Reference 18 suggests that a plastic region with height, H equal to width, W may be assumed and the moment capacity at the base taken equal to that at height H. Thus for design purposes, the area H X W is assumed to be the plastic mechanism region as shown in Fig. 1.8.2(d). If seismic connections are to be avoided, the lower portion of the wall can be cast-in-place concrete, and the section of the wall above height, H may be precast as shown in Fig. 1.8.2(e). Special care is required in the design of vertical joints to achieve effective connection of shear wall panels. Interlocking joints as shown in Fig. 1.8.3 can be readily designed to provide the load transfer capability, however the overall seismic performance of such interconnected walls, for both in-plane and out-of-plane configurations, has generally not been verified by tests. Research data on inelastic behavior of precast, prestressed concrete connections is scarce. Most bolted and welded connections have not been tested for cyclic, inelastic performance. Therefore, unless a connection is monolithic in nature or its behavior can be evaluated by using acceptable engineering techniques, the Committee recommends that the design of seismic connections should be based on appropriate tests.

Tests on typical frame connections have been conducted and the resulting information is available in Ref. 7. The use of monolithic connections, such asclosure pours, high strengthgrouted sleeves and pocket or coupling devices with mild or high strength reinforcing steel, is suitable for zones of moderate to high seismic activity. The performance of these connections is evaluated based on established cast-in-place concrete technology. 1.8.2 Rational Seismic Design Methodology The simplified rational seismicdesign procedure in Ref. 5 provides an approximate method for predicting the lateral displacement at the top of single degree of freedom structures. Figure 1.8.4 shows the “equal-energy” principle used for this estimate. New response modification values, R, are available in the Building Seismic Safety Council, National Earthquake Hazard Reduction Program provisions(19). Structure ductility, u for seismic loads is defined as the ratio of the inelastic displacement to first yield displacement at the top of the structure. Simple kinematic, post-yielding relationships, as shown for a shear wall in Fig. 1.85 are used to approximate the plastic displacement by assuming rigid-body rotations. This analytical procedure provides the inelastic deformation required to design seismic connections. Required load transfer forces for connections are calculated in an elastic load analysis for lateral base shear loads using the selected R values.

u -,I:a 4 -in f H

7

H

t---i

(a) Shear Wall

(b) Flexure

(c) Sliding Shear

(d) Plastic Mechanism

(e) Shear Wall with Cast-in-Place Bottom and Precast Top

Fig. 1.8.2 - Design Considerations for Concrete Shear Wall

I I I

Fig. 1.8.3 - Vertical Joints in Shear Walls

ATC-3 Elastic Strength Demand ( i.e. : R = 1 ) Design Yield Strength of Elasto-Plastic System -- 1.4 X UBC Load

Lateral

Generalized Plastic Displacement

Response

Displacement cture

i_:-isep

Modification

Factor

Ductility

Factor

6 P =6ep

RJSD FY

A, = A,

Y

‘0, 1111 11. pJ% 2

6, =sy(+J)

Fig. 1.8.4 - Equal Energy Principle for Estimating Maximum Seismic Displacements of an Elasto-Plastic System 1-21

Connection loads are then modified by the appropriate load factor to determine the design load for the seismic connection. The design load is assumed to correspond to the threshold of yielding for the connection and any additional deformation to occur without increase in the load. In reality, strain hardening of the yieldingcomponents of the seismic connections may occur and could be considered. Other connections, as well as the members in the lateral load resistant system, including the diaphragm, can also be designed using strength design principles and a factor which accounts for the actual strain hardened capacity of the yielding component. Two factors which must be considered are the stability of the gravity support system when displaced to the inelastic level, and the redundancy of seismic connections. 1.8.3 Seismic Performance Types of seismic connections, their design strengths, and the required inelastic deformation capacity are discussed in Sects. 1.8.1 and 1.8.2. In addition, cyclic inelastic performance is a consid-

eration in selecting appropriate seismic connections. Reference 5 provides a table for estimating the range of cycles for seismic connections for different building periods, and the response modification coefficients. As an illustration of the design using the concepts discussed, Fig. 1.8.6 schematically shows two welded wall panel to foundation seismic connections which are designed for different load levels. A detailed numerical example is given in Sect. 4.18. The two connections shown in Fig. 1.8.6 resist tension or compression which develops from the seismic overturning moment. For each, the angles were selected as the component of the connection to yield. Welds and embedded plates were designed to resist the strain hardened plastic capacity of the angle. High strength grout provides a uniform bearing surface to transfer the compressive loads. The inelastic deformation capacity of the angle was checked to ensure that the required inelastic displacement at the top of the shear wall was provided.

"PLASTIC HINGE" lumped at base of wall.

Vertical displacement equals predicted sum of plastic elongations across horizontal joints which yield.

Wall assumed to rotate about corner.

Fig. 1.8.5 - Kinematics of Isolated Wall Undergoing Plastic Deformation

l-22

. . d =- 1 ” f o r S h ims & Grout

Foundation Wall

Td arm

” (a)

DT Leg

DT Flange

Fig. 1.8.6 - Two Base Connections

1-23

CHAPTER 2 DESIGN CONCEPTS

2.1 General This chapter discusses several concepts which are useful in visualizing connection behavior and in testing validity of the design. Because forces converge on connections and also because many connection design equations are empirical in nature, it is importantthat the Engineer focuson those mechanisms which transfer the loads; to do this the Engineer must first identify the path of load transfer. 2.2 Load Transfer Paths The purpose of a connection is to transfer load from one precast member to another, or from a precast member to another element of the structure. In most cases, the load will be transferred through several elements of the connection by various mechanisms. As an example, considerthe steel bracket shown in Fig. 2.2.1. To avoid penetration of the form, the exterior portion of the bracket was welded after the column was removed from the form. The load, w is transferred to the column by the mechanisms de-

C o l u m n b.. . A

scribed below: 1. Beam to bearing area by shear in the beam. 2. Bearing areato bracketthrough compression of the pad. 3. Bracket to steel plate through shear and flexure in the steel bracket. 4. Through the plate via welds to embedded steel shape. 5. From embedded steel shape to column concrete through bearing. The tensile force, T caused by restraint of volume change shortening follows these paths: 6. Concrete beam to reinforcing bars by bond. 7. Reinforcing bars to bearing angle through weld. 8 . Bearing angle to steel haunch through friction on top and bottom of the bearing pad. Most of the volume change force is then relieved through deformation or slipping of the pad. 9. A small amount of tensile force is transmitted through the welds to the steel plate, and then to the embedded structural shape. 10. Forces transmitted to the embedded shape are then resisted by bearing on the projecting studs.

B e a m

0I",-. 0 '. .,

'.

Projecting Studs

Fig. 2.2.1 - Load Paths on Connection 2-1

Each of these load transfer mechanisms yields the forces to be used for designing the corresponding element of the connection. It is usually more economical to use a connection alternate with the fewest loadtransfers. Also, thefewerthe number of load transfers, the less the chance for error. 2.3 Analysis of Potential Failure Modes In a manner analogous to consideration of the load transfer paths, the Designer must examine each potential mode of failure in the connection including its component parts. In some of the simple connections, the critical failure mode will be quite apparent. In others, it may not be as obvious, and laboratory testing may be required to determine behavior. An excellent example of a connection where one of several potential failures is possible is that of the dapped-end of a beam. The PCI Design Handbook(4) lists five potential failure modes which must be investigated in designing the dapped-end. The causes of these are described below and the typical cracks are shown in Fig. 2.3.1. 1. Flexure (cantilever bending) and axial tension in the extended end --potential crack@. 2. Diagonal tension emanating from the reentrant corner -- potential crack@. 3, Direct shear at the junction of the dap and the main body of the member -- potential crack@. 4. Diagonal tension in the extended end -potential crack@. 5. Diagonal tension in the beam -- potential crack@. Bearing on the extended end should also be checked. Recent PCI funded research (8) on dappedends has generally confirmed the need for addressing the five types of cracks discussed above (Fig.

2.3.1). This research dealt with diff erent reinforcing schemes of dapped-ends in thin web stemmed members such as double tees. Typical cracks observed in the tests carried out under this study are shown in Fig. 2.3.2. Comparison of Figs. 2.3.1 and 2.3.2 show that, except for crack@ there is good correlation between the assumed failure modes for design and the observed cracking in the tests of Ref. 8 specimens. Previous experience supplemented by this recent research suggests that, by attention to member size proportions and proper detailing, some of the potential failures can be prevented. Design is then limited to considerationof the remaining potential failure modes. For example, by limiting the average shear stress in the extended end, failures related to cracks@ and @can be prevented. Also, extending the horizontal leg of the hanger reinforcespecifieddementadistanceof 1.7timestheACl(6) velopment length, as shown in Fig. 2.3.2, ensures development of the hanger reinforcement yield strength and prevents occurrence of premature failure due to the critical diagonal tension crack. The force in the hanger reinforcement based on its yield strength may then be used in conjunction with the “~~JSS analogy”or the “free-body” equilibrium to provide additional design information. A brief discussion of the truss analogy and the free-body diagram concepts is given in Sects. 2.8 and 2.9. 2.4 Stress Relief Measures In most cases, as long as structural integrity is ensured, the connections that allow some relative movements between precast members are preferable to those that impose considerable restraint. The forces due to restraint can be quite large and may add significant premium to the design of connections and members. The relief of restraint is

Fig. 2.3.1 - Possible Failure Modes in a Dapped-End

2-2

Nib Inclined Crack

Branch Crack Over Rebar

Nib Flexure Crack

Re-Entrant Corner Crack

Critical Diagonal Tension Crack ,,bWeb

Flexural Bond Cracks

CracksHanger

Flexure

Reinforcement

Fig. 2.3.2 - Typical Cracks in Dapped-End (Ref. 8) particularly desirable for loads due to volume changes and earthquakes. Extreme care is necessary in designing connections which provide restraint relief but which must also resist lateral loads. In general, it is desirable to rigidly connect to no more shear walls or frames within the system than absolutely necessary to resist the lateral loads. All otherconnections should be designed to provide relief of restraint. 2.4.1 Flexibility Designed-in flexibility of selected components, which allows elastic and inelastic deformations to take place, is also a useful concept for achieving relief of stress. For example, in Fig. 2.4.1, because of the arrangement of welds the connection at the top of the beam would be effective in resisting torsional rotation, but the angles would deform enough under gravity loads so that a large negative moment would not be produced. 2.4.2 Bearing Pads To relieve restraint of volume changes and to minimize local spalling due to nonuniform bearing conditions, flexible pads are recommended between beams and stemmed deck members, and their supports. These pads relieve restraint by either deforming readily within their thickness or by allowing slippage. There are several materials and combinations of materials that are suitable as flexible bearing pads. These are discussed in Sect. 3.11.

2.4.3 Slip Stress buildup can also be prevented if portions of the connections are allowed to slip to accommodate volume changes. Some types of bearing devices are designed with slip characteristics. The most common are thin plastic or hardboard bearing strips used under slabs. Tetrafluorethylene (TFE trade name Teflon) beating devices are also used where very low friction is desired. It is common practice to use slotted holes in clip angles as shown in Fig. 2.4.2. When properly placed, these allow some horizontal movement but will restrain torsional rotation. However, since the slot is also used forfield adjustment during erection, care is required so that the bolt does not bear against the end of the slot, thus disallowing further movement in one direction. There is also a tendency for the erection personnel to tighten the bolt too much. If the purpose of the slot is to relieve restraint, erection instructions should clearly indicate this. Care must also be exercised in the design and fabrication to prevent rust buildup which can progress to the point that the joint may become “frozen.” A smooth slip surface, such as the lowfriction washer shown in Fig. 2.4.2, should be provided at the interfaces of a slotted connection. 2.5 Expansion Joints The term “expansion joint” is applied to joints which extend completely through the building, effectively separating it into two or more structures. The PCI Design Handbook(l), Sect. 3.3.3, contains

2-3

Low-Friction Washer

Column

Fig. 2.4.1 - Flexible Top Connection a discussion of the expansion joints in precast, prestressed concrete structures. A true “expansion joint” is only required if the movements resulting from temperature rise are greater than the shortening caused by creep and shrinkage. In precast concrete buildings, this rarely happens, except in exposed components such as wall panels, or structures such as parking garages. Instead, joints that permit contraction are needed to allow the shortening caused by the additive effects of temperature drop, creep, and shrinkage. There are differences of opinion regarding the spacing of expansion joints. These joints are sources of frequent problems and require maintenance. Thus it is desirable to have as few expansion joints as possible. The National Academy of Sciences publication, “Expansion Joints in Buildings”(20), providesguidelines for expansion joint spacing and design. The recommendations in that report are based on a study of government buildings and elastic analytical study of the effects of uniform temperature change on typical two-dimensional frames. The report lists several parameters that must be considered in the design and spacing of expansion joints. These parameters are: 1. Framing materials -- concrete, steel. 2. Configuration of the building -- rectangular, L-shaped, T-shaped.

2-4

Fig. 2.4.2 - Slotted

Corbel Below

Connection

3. Whether or not the building is heated and/or air conditioned. 4. The base fixity condition of the columns. 5. The relative stiffness against lateral displacement along the length of the building. The report does not address precast concrete buildings with “soft” connections, i. e. those which employ bearing pads or other restraint relieving measures. Experience has shown that if all or most connections are “soft,” the distance between joints can be substantially increased over those recommended in Ref. 20.

2.6 Friction The static coefficients of friction for various interface conditions commonly used in connections are given in Table 2.6.1. These values, which are maximums, should be used for assessing the undesirable effects of friction, such as the restraint of volume changes. Friction may be depended upon to resist temporary construction loads. In that case however, the coefficients of friction shown in Table 2.6.1 should be divided by five. Friction may also be depended upon to contribute to the resistance to design loads in specific situations where appropriate analysis and/or testing justifies its use. One such situation is the horizontal joints of precast concrete wall panels.

Table 2.6.1 Static Coefficients of Friction of Dry Materials’ Material

ps

Elastomeric to steel or concrete . . . . . . . . . . . . . . . . . . . Concrete to concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . Concrete to steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Steel to steel (not rusted) . . . . . . . . . . . . . . . . . . . . . . . TFE to stainless steel . . . . . . . . . . . . . . . . . . . . . . . . . . . Hardboard to concrete . . . . . . . . . . . . . . . . . . . . . . . . . Multimonomer plastic (non-skid) to concrete . . . . . . . . Multimonomer plastic (smooth) to concrete . . . . . . . . .

See Fig. 4.4.2

0.8

0.4 0.25 See Fig. 3.11.3 0.5 1.2 0.4

A reduction of 20% is recommended for wet conditions. The total resistance to lateral wind or seismic loads may be obtained by adding the sliding friction resistance at the interfaces, and the shear resistance of the connectors through the joint. The sliding friction resistance is calculated as: w, = @ yc,

(Eq. 2.6.1)

where: 5 = nominal value of sliding friction resistance. hi = appropriatecoeff icient of friction obtained by tests. For non-platform type joints’, a value of 0.6 and for platform type joints’ with plastic strips a value of 0.4 may be used. c, = The net compression force perpendicular to the joint. This net compression force should be evaluated based on all applicable loads and appropriate load factors. In addition to the gravity loads, including those transferred from any intersecting walls, the effects of post-tensioning, overturning moment, and vertical seismic accelerations must be considered in evaluating the net compression force. o = strength reduction factor = 0.65

1 Platform type joints are typically used with hollow core slab units wherein the hollow core is set on plastic bearing strips and the space between the ends of the hollow core units is filled with grout. If bearing strips are not used, as in double tees bearing directly on ledges or in blockouts, the joint is refered to as the non-platform type.

This sliding friction resistance (Eq. 2.6.1) added to the shear resistance of the connection inserts in the joint yields the total shear resistance available at the joint. A minimum amount of connection inserts or ties must be provided through the joint even where the sliding friction resistance exceeds the applied lateral shear force. This minimum tie requirement ensures integrity of the structural system by providing tension continuity (see Sect. 4.16.3). As recommended by the PCI Committee on Bearing Wall Buildings (21), the minimum amount of ties should be such that, based on yield, their design strength in tension is equal to a force of 3000 lb per lineal f oot of wall. 2.7

Shear-Friction Shear-frtction is an extremely useful tool in connection design and in certain other applications in precast, prestressed concrete structures. Use of the shear-friction concept is recognized in ACI 31663(6) which states that “provisions of Sec.1 1.7 are to be applied where it is appropriate to consider shear transfer across a given plane, such as: an existing or potential crack, an interface between dissimilar materials, or an interface between two concretes cast at different times.” A basic assumption used in applying the shearfriction concept is that concrete within the direct shear area of the connection will crack. Strength is maintained by placing reinforcement across this anticipated crack so that the tension developed by the reinforcing bars will produce a compressive force normal to the crack. The normal force in combination with friction at the crack interface provides the shear resistance. The shear-friction analogy can be adapted to designs for reinforced concrete bearing, corbels, daps, composite sec-

2-5

Table 2.6.1 Static Coefficients of Friction of Dry Materials* ................... oncrete to concrete. . . . . . . . . . . . . . . . . . . . . . . . . . . Concrete to steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Steel to steel (not rusted) . . . . . . . . . . . . . . . . . . . . . . . TFE to stainless steel . . . . . . . . . . . . . . . . . . . . . . . . . . . Hardboard to concrete . . . . . . . . . . . . . . . . . . . . . . . . . ........

The total resistance to lateral wind or seismic loads may be obtained by adding the sliding friction resistance at the interfaces, and the shear resistance of the connectors through the joint. The sliding friction resistance is calculated as: Wf

= 4wsc,

(Eq. 2.6.1)

where: Y = nominal value of sliding friction resistance. = appropriate coeff icient of friction obtained k by tests. For non-platform type joints’, a value of 0.6 and for platform type joints’ with plastic strips a value of 0.4 may be used. c, = The net compression force perpendicular to the joint. This net compression force should be evaluated based on all applicable loads and appropriate load factors. In addition to the gravity loads, including those transferred from any intersecting walls, the effects of post-tensioning, overturning moment, and vertical seismic accelerations must be considered in evaluating the net compression force. $I = strength reduction factor = 0.85

1 Platform type joints are typically used with hollow core slab units wherein the hollow core is set on plastic bearing strips and the space between the ends of the hollow core units is filled with grout. If bearing strips are not used, as in double tees bearing directly on ledges or in blockouts, the joint is refered to as the non-platform type.

0.8 0.4 0.25 See Fig. 3.11.3 0.5

This sliding friction resistance (Eq. 2.6.1) added to the shear resistance of the connection inserts in the joint yields the total shear resistance available at the joint. A minimum amount of connection inserts or ties must be provided through the joint even where the sliding friction resistance exceeds the applied lateral shear force. This minimum tie requirement ensures integrity of the structural system by providing tensioncontinuity (see Sect. 4.16.3). As recommended by the PCI Committee on Bearing Wall Buildings (21), the minimum amount of ties should be such that, based on yield, their design strength in tension is equal to a force of 3000 lb per lineal foot of wall. 2.7

Shear-Friction Shear-friction is an extremely useful tool in connection design and in certain other applications in precast, prestressed concrete structures. Use of the shear-friction concept is recognized in ACI 31883(6) which states that “provisions of Sec.1 1.7 are to be applied where it is appropriate to consider shear transfer across a given plane, such as: an existing or potential crack, an interface between dissimilar materials, or an interface between two concretes cast at different times.” A basic assumption used in applying the shearfriction concept is that concrete within the direct shear area of the connection will crack. Strength is maintained by placing reinforcement across this anticipated crack so that the tension developed by the reinforcing bars will produce a compressive force normal to the crack. The normal force in combination with friction at the crack interface provides the shear resistance. The shear-friction analogy can be adapted to designs for reinforced concrete bearing, corbels, daps, composite sec-

2-5

tions, and other connections. The shear- friction method given in Sect. 11.74 of the ACI Code(G) is based on a simplified model which results in conservative designs. Other models which result in closer predictions of shear transfer strength to experimental information are available and may be used. Two such methods mentioned in the Commentary to the ACI Code(G) are the modified shear friction method(22,23) and the effective shear friction method of the PCI Design Handbook(4). It has been previously shown(24) that these methods result in comparable designs. A recent article(25) notes that the above two methods yield somewhat conservative results for low reinforcement ratios and/or high concrete strengths (5,000 - 9,000 psi range), and presents alternate equations for improved accuracy. The PCI Design Handbook method(4) uses the procedure given in Ref. 24. It is described below: An “effective” shear-friction coefficient, p,, may be used when the concept is applied to precast concrete connections. The shear-friction reinforcement nominally perpendicularto the assumed crack plane can be determined as:

1000 h.A,,u I$ = Vu x

= 1 .O for normal weight concrete P (f,(6.7)/ c ) for sand-lightweight or allIightweigM concrete. lf f,* is unknown: h = 0.85 for sand-lightweight concrete and 0.75 for all-IightweigM concrete = splitting tensile strength of concrete, psi fct P = value from Table 2.7.1 AC, = area of the assumed crack interface, sq. in. When axial tension is present, additional reinforcement should be provided: A,

=

N u @‘Y

(Eq. 2.7.3)

where: A” = area of reinforcement required to resist axial tension, sq. in. NU = applied factored horizontal tensile force nominally perpendicular to the assumed crack plane, lb. = 0.85 (Note: Q, = 0.85 is used for consis$ tency with Eq. 2.7.1)

(Eq. 27.1) where: $ = 0.85 A,, = area of reinforcement nominally perpendicular to the assumed crack plane, sq. in. = yield strength of Ati, psi (equal to or less fY than 60,000 psi) v u = applied factored shear force, parallel to the assumed crack plane, lb. (limited by the values given in Table 2.7.1)

s values in Table 2.7.1 (Eq. 2.7.2)

All reinforcement should be properly anchored on both sides of the assumed crack by providing adequate development length (with or without hooks), or by welding to angles or plates.

able 2.7.1 Shear-Friction Coefficients Recommended CL

Maximum k

Maximum V, (I VU/ @ ), lb

1. Concrete to concrete cast monoHthically

1.4X

3.4

0.30 3L 2 f’c A,, s 1000 X 2 A,,

2. Concrete to hardened concrete with roughened surface

1.0X

2.9

0.251i2f’,A,

3. Concrete to concrete

0.6 3,

2.2

0.20 h 2f’c A,, s 800 h 2 Acr

4. Concrete to steel

0.7 h

2.4

0.20 3c 2f*c A,, s 800 h 2 Acr

Crack Interface Condition

2-6

slOOOh”A~

2.8 Truss Analogy Truss analogy has been well established as a basis for design of cracked concrete beams loaded in bending, shear, and torsion. It has also been successfully used to provide at least qualitative information for design of many connections in precast, prestressed concrete. If avalid truss model for a connection can be developed, then the design of that connection would involve use of fundamental principlesof equilibriumandcompatibility,thuseliminating the need for much of the current empiricism in connection design. The appropriate truss models can be developed using analytical methods, such as the finite element method, or may be based on laboratory tests. For

example, from photoelasticity tests(26) the stress trajectories in a corbel and dapped-end are shown in Figs. 2.8.1 and 2.8.2, respectively. The corresponding truss analogies are shown in Figs. 2.8.3 and 2.8.4. Another example of a truss model is given in Fig. 2.8.5 for a dapped-end with one of the reinforcement schemes in Ref. 8 study. Recently, generalizations of the truss analogy have been proposed(27) in theformof stmt-and-tiemodels. These models have the potential to lend themselves to design applications in regions of structures where discontinuities or load concentrations exist, as in the connections of precast, prestressed concrete structures.

Tensile Trajectories/

lressi o n ector ties

Fig. 2.8.1 - Corbel Stress Trajectories

//// 0 q Fig. 2.8.2 - Dapped-End Stress Trajectories Ineffective

Area

/-

N”

II V”~ - Tension -ct-

Fig. 2.8.3 - Corbel Truss Analogy

Compression

Fig. 2.8.4 - Dapped-End Truss Analogy 2-7

Fig. 2.8.5 - Assumed “Truss-Action” in Nib for a Double-Tee Dapped-End (Ref. 8) 2.9 Free-Body Diagram The concept of free-body diagram should be used liberally to provide information regarding stability and equilibrium of the connection with respect to the overall structure. It should also be used in conjunction with equations of statics to evaluate and check forces in various components of a connection.

As an illustration of the use of a free-body diagram, Fig. 2.9.1 shows the free-body diagram of a double tee dapped-end with respect to the reentrant comer crack identified in Fig. 2.3.2, This free-body diagram can be used to calculate the tension forces, T and F, and the concrete compression force, C.

C

Corner Crack

""

T = A&

Fig. 2.9.1 - Free-Body with Respect to the Re-Entran Crack (see Fig. 2.3.2)

2-8

CHAPTER 3 CONNECTION MATERIALS

tion hardware, their anchorage, and other related considerations are discussed in this chapter.

3.1 General A variety of hardware including deformed bar and headed stud anchors, plain wire and coil inserts, structural shapes, bolts and threaded rods and other materials is in use in connections of precast concrete structures; in order to achieve specified strength, these must be properly anchored in the concrete. The anchorage is achieved by bond and/or bearing between the insert and the adjacent concrete. For ductility, it is preferable to have the failure initiate in the steel ratherthan in the surrounding concrete. Consequently, anchorage to concrete is a major consideration in connection design. Some of the more commonly used connec-

3.2 Reinforcing Bars Reinforcing bars used in connections usually conform to ASTM A615 or ASTM A706 specifications although those conforming to ASTM A61 6 and A61 7 are also occasionally used. Reinforcing bars are anchored usually by bonding to the concrete. When there is insufficient length available to anchor the bars, supplemental mechanical anchorage is required. Thiscan be accomplished by using hooked bars, or by welding to structural steel shapes such as plates and angles. Use of a welded cross bar to achieve anchorage, as shown in Fig. 3.2.1, is also common practice. Load transfer between bars may be achieved by lap splicing, welding, orwith various types of couplers. The development lengths, lap splice require-

Welded Cross Bar

Fig. 3.2.1 - Anchorage with Welded Cross Bar

3-1

men&, and material properties for reinforcing bars are given in Tables A-l 0 through A-12 in Appendix A. A brief discussion of couplers, dowels, and welding of reinforcing bars is given below. 3.2.1 Couplers A variety of couplers, mostly proprietary in nature, is available for use in precast concrete connections(2629). Typical examples are shown in Fig. 3.2.2. Some are suitable for compression splices only, while otherscan be used fortension splices as well. Most of the couplers available are not suitable for connecting dowels projecting from adjacent precast members. Designs using these devices should be based on the manufacturers’ recommendations. ACI 318-83(6) requires couplers to be

capable of developing 125% of the specified yield strength of the bars. 3.2.2 Dowels Reinforcing bars or steel rods are frequently used as dowels to connect precast concrete components. These dowels may be cast in one member, and field placed and grouted into a preformed orpredrilled hole in another member, orthey may be field placed in both members. In many applications, these dowels are placed vertically and used only for alignment or to resist nominal shear loads, and thus may not require full tension strength development. Occasionally, a dowel will be required to resist tension. In this case, the bar must be anchored to develop the required tension strength. However,

Thread-Deformed Nan-Shrink

Bar

Coupler

-Tap

Hole

Grout

Cold-Swaged Steel Coupler

t- Reducer Insert

Metal-Filled

Wedge-Locking

Sleeve

Coupler Tapered-Threaded

Coupler

Fig. 3.2.2 - Mechanical Couplers

3-2

Extruded Steel Coupler

the bond of the grout to the concrete may control the embedment length. For most situations, ordinary sand-cement grout in drilled holes is unreliable under direct tension loads. Therefore, larger preformed sleeves or special grouts such as epoxy mixtures are required. 3.2.3 Reinforcing Bar Welding Welding of reinforcing bars is covered by AWS Dl.4-79, “Structural Welding Code-Reinforcing Steel”(l6). Weldability of steel is determined by its chemical composition which is typically expressed in terms of carbon equivalent given by the following formula: C.E. =%C+~+~+~+~-~-~ (Eq. 3.2.1) where C.E. = carbon equivalent The last three elements usually appear only as trace elements, and thus are often not included in the mill reports. For bars that are to be .velded, the carbon equivalent should be requested from the mill with the purchase order. AWS D1.4-79 indicates that most reinforcing bars can be welded. However, the preheat and other quality control measures that are required for bars with high carbon equivalent are difficult to achieve. Unless the welding quality control procedures are well established and meet AWS D1.4-79, it is recommended that carbon equivalent be limited to 0.45% for No. 7 and larger size bars, and 0.55% for No. 6 and smaller size bars. Most reinforcing bars which meet ASTM A615 Grade 60, will not meet the above chemistry specifications. A615Grade 40 bars may or may not meet the above specifications. Bars which meet ASTM A706 are specially formulated to be weldable, and are now available in most parts of North America. Fig. 3.2.3 shows the most common welds used with reinforcing bars. Full penetrationgroove welds can be considered to develop the same strength as the nominal strengthof the bar. Thedesign strength of other types of welds can be calculated using values from Table A-13 in Appendix A. The design strength of the weld is given by: F,= fwtvfw

(Eq. 3.2.2)

where: Fvl = 1, = & = L =

design strength of weld unit design strength from Table A-13 length of weld effective throat thickness of weld (Note: the t, values for ffare-V-groove and flare-bevel-groove shown in Fig. 3.2.2 are applicable when the weld is filled flush to the solid section of the bar.) Table A-14 gives strength of commonly used sizes of fillet welds and Tables A-15 through A-17 show welding required to develop the full strength of reinforcing bars. Reinforcing bars should not be weldedwithin 2 bardiameters, nor less than 2 in., of a bar bend. The welded cross bar detail shown in Fig. 3.2.1 is not included in AWS D1.4-79. However, it has been validated by tests(30) and successfully used in numerous structures. Table A-18 in Appendix A gives design strength of connection with welded cross bar. AWS D1.4-79 prohibits use of tack welds unless authorized by the Engineer. Where authorized, these should be made using the same preheat and quality control requirements asthe permanent welds. 3.3 Welded Headed Studs - ASTM A108 Stud welding is a semi-automatic process of welding certain types of fasteners. It is an efficient and economical method by which anchorage of steel shapes (plates, angles, etc.) to concrete can be achieved. The process is schematically shown in Fig. 3.3.1. Most precast concrete manufacturing plants have stud welding capability. The most common type of fastener available for use with this process is the headed stud. Headed studs are made from low carbon steel with a tensile strength of approximately 60,000 psi. The anchorage to concrete is provided by concrete bearing under the head of the stud. Several typical details of application of the headed studs are shown in Fig. 3.3.2. Table A-19 in Appendix A, contains information on sizes commonly available, and Chapt. 4 ineludes examples of connection designs using headed studs. 3.4 Deformed Bar Anchors - ASTM A496 Deformed bar anchors are made from the same type of steel as headed studs. They are welded to steel plates and other shapes by the same semiautomatic process that is used for headed studs. Anchorage to concrete is achieved by deformations

3-3

45 o - 60’

45O - 6O0

Single-V-Groove

Weld

Double-V-Groove

Weld

Full Penetration Welds Nate:

As shown for

#9 and larger bars.

#El

and

smaller

bars

require

appropriate

backing.

Fillet Welds

t, = 0.3d, db/2

I

Bars Same Size

Flare-V-Groove

Welds

-3

db

Flare-Bevel-Groove

I 3-4

t, = 0.2db

Welds

Fig. 3.2.3 - Typical Reinforcing Bar Welds

I

The stud tip is placed against the work surface. When the trigger A welding arc burns off surface is pulled, the stud is raised. contamination, melts the stud tip and a small area on the work surface. The stud is forced into the molten area and is instantly welded to the surface.

Fig. 3.3.1 - Stud Welding Process

Fig. 3.3.2 - Applications of Headed Studs on the bar similar to reinforcing bars, except that the deformations are indentations rather than projections. Bond properties of deformed bars are similar to those of reinforcing bars. Table A-20 in Appendix A lists the development lengths for commonly used sizes of deformed bar anchors. Fig. 3.4.1 shows typical applications. Substitution of reinforcing bars for deformed bar anchors should not be allowed. Their weldability characteristics are usually different, and also their strengths may not be the same. 3.5 Bolts and Threaded Connectors Various types of bolts and other threaded connectors are used in connections in precast concrete. The primary advantage of these devices is that they facilitate quick assembly and erection. The

primary disadvantage is that close tolerances are required for the placement of the connector and its receptacle. In most connections, the bolts are shipped loose to the site and are threaded into receptacles cast into the concrete. Occasionally a precast concrete member will be cast with a threaded connector projecting from the face. This is undesirable because these items are vulnerable to damage during handling. Also, unless the projection is from the top of the member as cast, stripping forms is usually difficult. A majority of the connections of precast, prestressed concrete structures tends to be of the bearing-type, wherein the load transfer is achieved with fasteners acting essentially as dowels. On the other hand, in the friction-type connections the load

3-5

Fig. 3.4.1 - Applications of Deformed Bar Anchors

transfer is provided by the friction between the interconnected parts. The friction resistance capability is produced by the normal compressive force, which in turn is due to tensioning of the threaded fasteners. When threaded fasteners are tightened against concrete, there is the likelihood of minor crushing of the concrete. For this reason, and also because of the creep of concrete, there is a degree of uncertainty regarding the actual tension in the fasteners, and thus the resulting friction resistance. Therefore, the friction-type connections are not commonly used in precast concrete construction. The types of threaded connectors commonly available are: 1) standard bolts; 2) high-strength bolts; 3) threaded steel rods; 4) coil bolts and coil rods. Other proprietary connectors are also available. 3.51 Standard Bolts Standards bolts are defined here as those conforming to ASTM A307 specifications. Threads comply with the “Coarse Thread Series” specification of ANSI B1.1(31), as detailed in Table A-21 in Appendix A. Standard bolts are designed in accordance with the AISC Specifications(32). The AISC design method is based on controlling stresses produced by unfactored loads i.e., the working stress design method. If it is desired that connection design be based on factored loads, i.e., the strength design method, a reasonable approximation of the strength of standard bolts is obtained by multiplying the AISC allowable stresses by a factor of 1.65. The tension and the shear maximum service

3-6

loads as well as the nominal design strengths of standard bolts are listed in Table A-22 in Appendix A. These values are applicable when the tension or the shear loads act alone. For bolts under simultaneous tension and shear loads, adjustment in the values shown is required. This may be done in accordance with the AISC(32) procedure which is based on a straight line approximation of experimental data. Alternatively, an elliptical interaction curve, which correlates with the experimental data more closely, may be used. This elliptical interaction, which is the same as the one used for design of headed studs in this Manual (Sect. 4.11) except in terms of stresses instead of forces, is given below for bolts in bearing-type connections: (g

+ (+.o

(Eq. 3.51)

where: f, f” Ft F,

= = = =

nominal tensile stress due to applied loads nominal shear stress due to applied loads allowable tensile stress in absence of shear allowable shear stress in absence of tension.

3.5.2 High-Strength Bolts High strength bolts (ASTM A325 or A490) were developed primarily for friction-type connections between structural steel members. They have more than two times the tensile strength of A307 bolts. Their application requires controlled tensioning of the fastener to develop sufficient force to

prevent slipping of the connected parts. The tensioning is done using calibrated torque wrenches or load indicating washers(32). As noted previously, because of the creep of concrete and the likelihood of crushing of concrete due to bolt tightening, the friction-type connections are not commonly used in precast concrete construction. Furthermore, since for economy the high strength bolts require tensioning, their use in the bearing-type connections is generally not necessary. The overall resuft is that high strength bolts are used only infrequently in precast concrete connections. 3.5.3 Threaded Steel Rods Threaded steel rods of various sizes are also used in precast concrete connections. The most common application is for anchor bolts at column bases. Allowable loads for rods of ASTM A-36 steel are given in Table A-22 in Appendix A. 3.5.4 Coil Bolts and Rods Coil bolts and continuously threaded coil rods (Fig. 3.5.1) are popular items for both temporary and permanent connections of precast concrete. The threads are designed to fit the contour and diameter of a helically wound wire coil insert. Because the threads are very coarse, they are not easily clogged or damaged. Coil bolts and coil rods are anchored by threading into the wire coil insert which is embedded in concrete. The coil rod can also be anchored directly to concrete with threads serving the same function as deformations on reinforcing bars. The development length of coil rods is assumed to be the same as that for deformed reinforcing bars, however, this

Coil Bolt

have beenvalidated assumptiondoes not appearto by tests. Coil bolts and coil rods (lengths up to 20ft.) range indiameterfrom l/2 in. to l-1/2 in. and are available from several concrete accessories suppliers. Since coil bolts and rods are not covered by standard specifications, it is suggested that the manufacturers’ recommendations should be used in design. Manufacturers’ catalogs give maximum allowable working load values which are based on strength tests under static loads, and typically a factor of safety of 4 to 5. 3.55 Post-Tensioning Rods Post-tensioning rods (usually conforming to ASTM A-722 specification) are also used to connect precast members. They can be used simply as bolts, or preferably prestressed to resist uplift and/ or shear forces created by lateral loads. The prestressing is usually done by casting conduits into shearwalls andvertically tensioning the shearwalls to the foundations. 3.6 Inserts A large variety of inserts are commercially availableforuse in precast concrete construction. Some are intended for transfer of design loads. Their strengths and application procedures are generally well defined. For the purpose of discussion here, these are referred to as primary inserts. Othertypes of inserts are used for temporary conditions, such as lifting and handling, or light loads, such as various shelf angle inserts including the commonly used wedge insert. These are labeled here as secondary inserts. Only a few examples are discussed and illus-

Threaded Coil Rod

Fig. 3.51 - Coil Bolt and Coil Rod 3-7

trated in this Manual. Reference to manufacturers’ catalogs is suggested for many others that are available in the market. 3.6.1 Primary Inserts Basically these inserts include a receptacle to engage a connector, such as a bolt, and an element, such as a wire loop, for anchorage to concrete. Examples of these inserts are shown in Figs. 3.6.1 and 3.6.2. These inserts use one of the following three basic types of receptacles (see Fig. 3.6.3): (a) Standard coil: A helically wound coil of wire which forms a “nut” into which a coil bolt or rod is threaded. (b) Tapped coil: The standard coil may be tapped to accept standard machine bolts. Such tapped coils will also accept coil bolts. Because of the dual thread, care is needed in starting the coarse threaded coil bolt to prevent “cross-threading.” Due to difficulties inherent in the tapping process, the cost

of tapped coils tends to be high. Thus, their use is infrequent. (c) “Ferrule” or “Weld nut”: This is for use with bolts or rods with standard threads. The nuts are weldable and are of sufficient length to ensure design load transfer to the anchor wires. The wires provide for the anchorage to concrete. Design strengths of machine bolts are shown in Table A-23 in Appendix A. For higher strength connections, the weld nuts may be welded to plates rather than wires. The anchorage to concrete is achieved by wetding high capacity anchors, such as headed studs, to these plates. The anchorage of the wire inserts to concrete is achieved by engagement of the loop in concrete (loop type inserts - Fig. 3.6.1) or by bond with concrete (open wire inserts - Fig. 3.6.2). Failure of an insert may be due to either concrete failure, or due to the insert material failure. The lesser of the two is taken as the in-place strength for design. If the insert is adequately anchored into the

Fig. 3.6.1 - Loop Type Wire Inserts

3-6

Fig. 3.6.2 - Open Wire Inserts

Standard

Coil

Tapped Coil

Weld Nut (Ferrule)

Fig. 3.6.3 - Receptacles for Wire Inserts

concrete and the anchorage wires are properly welded to the receptacle, the in-place strength of the insert is governed by the strength of wires or the receptacle capacity. Again, it is desirable to have the boltorthewiresgoverntheconnectionstrength, because such failures are more predictable and ductile. Strengths of the wires typically used in inserts are shown in Table A-24 in Appendix A. For the open wire inserts, manufacturers’ data including the recommended safety factors should be used in design. The loop type inserts may also be designed using manufacturers’ data. Alternately, the loop type inserts can be investigated in a manner similar to that for the welded headed studs, wherein the strength governed by concrete failure is based on the shear cone shown in Fig. 3.6.4 (see Refs. 4 and 33 and Sect. 4.11).

3.6.2 Secondary Inserts A variety of inserts have been devised for lifting and handling of precast members, suspension of ceilings and for attachment of shelf angles. These inserts are intended for temporary loads or for supporting light permanent loads. Their use for structural applications in primary connections is not recommended. Because of the large variety available, it is not feasible to include a comprehensive coverage in this Manual. Reference to manufacturers’ catalogs is recommended for the various types and their applications. It is also recommended that manufacturers’ data should be used in estimating their load carrying capabilities and for installation procedures. One of the more commonly used inserts in this group is the wedge insert. It is discussed here as an

3-9

/

example to point out the care necessary in the use of many of the secondary inserts. The wedge inserts (two types are shown in Fig. 3.6.5(a)) are used for attaching shelf angles to precast members to support light loads. A typical installation schematic is shown in Fig. 3.6.5(b). The insert includes a wedge shaped track and an integral device for anchorage to concrete. The wedge shaped track allows for vertical adjustment of the skew head bolt as shown in Fig. 3.6.5(c). The successful use of wedge inserts depends on the full engagement of the skew bolt head in the wedge, the snug tightening of the nut and the full fit of the nut with the wedge surface. Otherwise, the potential stress concentrations at the bolt head would result in unpredictable behavior. The concrete surface surrounding the wedge insert must be smooth and flat to ensure that the connection angle will bear against the concrete. To achieve this, it is recommended that the wedge insert body be recessed l/8 to l/4 in. below the concrete surface. Care must be taken to prevent overtightening of the bolt so that the lips of the wedge do not tear, and in installation of the wedge inserts in the right-side up position. Considering the above requirements, and the limitations related to sensitivity of the connection strength to over and undertightening of the bolt and

Concrete

its unsuitability for cyclic loads, it is recommended that their use be restricted to light loads only. Primary connections of cladding elements to the support structure should not be made with wedge inserts. 3.7 Expansion Inserts Expansion inserts are devices placed into holes drilled in hardened concrete. The insert develops tensile and shear capacity when expanding parts of the insert are forced against the sides of the hole. This is usually done by tightening the connector bolt into the insert. All expansion inserts are proprietary. Examples are shown in Fig. 3.7.1. The manufacturers have established the tensile and shear strengths of their devices by testing. Typical ranges of tensile and shear strengths, taken from manufacturers’ catalogs are shown in Table A-25 in Appendix A. At the minimum recommended embedment depth, the tensile capacity agrees well with the “shear cone” concept. However, because of slip of the anchor in the hole, deeper embedment does not proportionally increase the capacity. For small edge distances and grouping of expansion bolts, reduction factors similar to headed studs may be used. The upper limit of the capacity of the expansion inserts is the strength of the connector bolts, which are usually

Surface

Surface Area

Fig. 3.6.4 - Shear Cone Development for Loop Inserts 3-l 0

(a) Two Types

(b)

Installation Schematic

(c) Bolt Adjustment

Fig. 3.6.5 - Wedge Inserts standard bolts. Since the expansion inserts thrust against the sides of the installation hole producing lateral pressures, the spacing between inserts and location with respect to edge(s) of the member are critical factors in their load carrying capability. Manufacturers’ recommendations should be used in this regard. The advantage of expansion inserts is that they can be placed in exactly the right position after the precast members are in place. They are often used as corrective measures when cast-in inserts are misplaced or left out. Proper performance of the inserts is largely dependent on workmanship. The holes must be drilled straight, deep enough and of the proper diameter and must be cleaned out. The bolts must be tightened to the recommended torque, sometimes requiring pneumatic impact wrenches. Design of connections employing expansion inserts is usually based on the working strength values given by the manufacturers. Typically, a working strength value not to exceed one-fourth of the test strength value is recommended. It should, however, be noted that the test strength values usually correspond to monotonic load tests in uncracked concrete. Cyclic loads and the extent of cracking in concrete have been shown (34,35) to cause significant reduction in the strength of these anchors. Manufacturers’ recommendations should be sought in such applications.

3.8 Resin Capsule Anchors Resin capsule anchors or “epoxy” anchors are also used for attachment to hardened concrete. Like expansion inserts (Sect. 3.7) they are placed in holes drilled in the hardened concrete. A resin capsule anchor consists of two parts: 1. A sealed glass capsule containing premeasured amounts of an aggregate suspended in synthetic resin and a separate vial within the capsule containing the catalyst/hardener. 2. A threaded rod stud with washer and nut. During installation the capsule is inserted into a pre-drilled hole and the stud is driven into the capsule thus breaking it. The resulting chemical reaction between resin, aggregate, crushed glass, and hardener forms a thick synthetic mortar which bonds stud to the concrete. Since the pull-out strength is developed by resistance along the entire depth of the anchor, the strengths of these anchors are typically higher than the strengthsof similarsize expansion inserts shown in Table A-25 in Appendix A. Also, because of the full depth bonding, the resin capsule anchors are less likely to %ork loose” under shock or vibration conditions than the expansion inserts. The synthetic resin is practically unaffected by water or corrosives and thus protects the stud. Like other epoxy compounds discussed in Sect. 3.12.3, the resistance and creep information is not well established for these anchors.

3-11

Fig. 3.7.1 - Typical Expansion Inserts 3.9 Structural Steel Structural steel plates, angles, wide-flange beams, channels, tubes, etc. are often used in connections. When designed using factored loads, it is appropriate to use plastic section properties and yield strengths. Plastic section moduli and shape factors are given in Table A-26 in Appendix A. The shear yield strength of structural steel is commonly taken as 0.55 times the yield strength in tension. 3.9.1 Welding of Structural Steel Welding of steel plates, angles, and other shapes should follow AWS Dl .l-86(16). Nearly all struc-

3-12

tural steel used in precast concrete connections is ASTM A-36, and thus is readily weldable with standard equipment and procedures. Stainless steel plates are weldable to other stainless steelelementsorto low carbon steel. Forthese cases, the general procedure for welding low carbon steel should be followed. Consideration of the stainless steel characteristics that differ, such as higher thermal expansion and lower thermal conductivity, is necessary (see Sect. 3.9.2). Reference 16 contains detailed information on weldability of stainless steel. Welding design procedures have been devel-

oped in conjunction with design of steel structures, and are presently based on working stress levels. However, precast concrete structures, including the connections, are usually designed basedon strength design using factored loads. To facilitate connection design using factored loads, the weld strength values based on working stress may be adjusted using recommendations of either the AWS(16) or the AASHTO Specifications(36). In the AWS Code(l6), the weld strength for use with factored loads (i.e., the nominal strength) is taken as two times the weld strength for use with working loads. When a strength reduction factor, o is considered for concrete design and given a value of 0.85, the resulting multiplier (which includes I$ factor) is 1.7. suggest a net multiThe AASHTO Specifications(36) plier (which includes a o factor) of 1.67. Table A-13 in Appendix A gives the allowable working stress and the design strengthvalues. Thedesign strength values are basedon theAASHT0 Specifications(36) multiplier of 1.67. Various types of welds are shown in Fig. 3.2.3. The most commonly used are fillet welds and full penetration welds of either the V-groove or bevelgroove type. Properly made full penetration welds are stronger than the base metal. Fillet welds are usually made assuming a 45” fillet. Table A-14 in Appendix A gives strength of fillet welds using these assumptions, and Sect. 4.12 contains an example of weld group design. 3.9.2 Cracking In Concrete Around Welded Connections When welding is done on components that are embedded in concrete, thermal expansion and distortion of steel may destroy bond between steel and concrete, or cause cracking or spalling in the surrounding concrete. Occasionally stainless steel plates and assemblies are used for exposed connections to minimize corrosion. Since stainless steel requires higher heat for welding, a great deal of care is necessary in its field welding to manage the increased expansion and the resulting potential cracking of anchorage concrete. The extent of cracking anddistortiondepends on the heat generated during welding and the stiffness of the steel member. Heat may be reduced by: I) use of low-heat welding rods of small size, 2) use of intermittent rather than continuous welds, or 3) use of smaller welds in multiple passes. Distortion can be minimized by using thicker steel sections--a minimum of 3/8 in. thickness is recommended for plates. Providing space around the metal on the surface, and filling with sealing

foam, weather stripping or thick tape, also reduces damage. 3.10 Post-Tensioning Steel Post-tensioning is often used in connections, particularly those which are subjected to high tensile forces, such as the connections in momentresisting frames. The post-tensioning is done using either 7-wire strand (ASTM A416) or bars (ASTM A722). The tensile strength of strand is either 250,000 or 270,000 psi, while for bars, it ranges from 150,000 to 160,000 psi. Table A-27 in Appendix A lists selected design data for commonly used sizes of prestressing strand and bar. In accounting for the effect of prestressing on connections due to post-tensioning, a reliable measurement of the prestressing force is necessary. Typically, 15 to 20 ft. length is desirable for this purpose, although shorter lengths can be used where anchor set is well defined and considered in prestress loss calculations. Some designers discount the effect of prestressing when short tendons are used and consider only the ductility and the tensile strength aspects of post-tensioning steel. 3.11 Bearing Pads Bearing pads are used to provide for a more uniform distribution of loads overthe bearing areas, and to allow limited horizontal and rotational movements (see Fig. 3.11.1) to provide stress relief. Their use has proven beneficial, and is often necessary for satisfactory performance of precast concrete structures. A general discussion is presented here and the design is covered in Sect. 4.4. Reference to PCI Technical Report No. 4, “Criteria for Design of Bearing Pads” (37), and a recent PCI Journal article(38) dealing with selected elastomeric bearing pads is recommended. Several materials are available and commonly used in bearing pads: 1. AASHTO-grade chloroprene pads are made with 100 percent chloroprene (neoprene) as the only elastomer, and conform to the requirements of the AASHTO Standard Specifications for Highway Bridges(36). Inert fillers are used with the chloroprene and the resulting pad is black in color and of a smooth uniform texture. While allowable compressive stresses are somewhat lower than other pad types, these pads allow the greatest freedom in movement at the bearing. NOTE: chloroprene pads which do not meet the AASHTO Specifications are not recommended for use in precast concrete structures. 3-13

Fig. 3.11.1 - Deformations Corresponding to Shear (a), Compression (b), and Moment (c)

2. Pads reinforced with randomly oriented fibers (ROF) have been used successfully in recent years. These pads are usually black, and the short reinforcing fibers are clearly visible. The reinforcement increases the vertical load carrying capacity, however these pads offer somewhat greater resistance to rotations and horizontal movement than the chloroprene pads. Some ROF pads possess different properties in different directions in the plane of the pad. Therefore, unless proper planning and care is used in their installation, it may be desirable to specify those pads that have been tested to exhibit similar properties in different directions. There are no national standard specificationsforthismaterial. Manufacturers have developed appropriate design and performance documentation. 3. Cotton-duck fabric reinforced pads are generally used where a higher compressive strength is desired. These pads are often yellow-orange in color and are reinforced with closely spaced, horizontal layers of fabric, bonded in the elastomer. The horizontal reinforcement layers are easily observed at the edge of the pad. A discussion of this material is included in the AASHTO Standard Specifications for Highway Bridges (36). 4. Chloroprene pads laminated with alternate layers of bonded steel or fiberglass are often

3-14

used in bridges, but seldom in building construction. The AASHTO Specification(36) also covers these pads. 5. A multimonomer plastic bearing strip is manufactured expressly for bearing purposes. It is a commonly used material for the bearing support of hollow core slabs, and is highly suitable for this application. The material has a higher compressive strength than that of concrete typically used in precast construction. 6. Tempered hardboard strips are also used for bearing of hollow core slabs. These pads should be used with caution when moisture conditions exist. In addition to the progressive deterioration of the pad, staining of the precast units may occur. 7. TFE (trade name Teflon) coated materials are often used in bearing areas where large horizontal movements are anticipated, for example at “slip” joints or expansion joints. The TFE is normally reinforced by bonding to an appropriate backing material, such as steel. Fig. 3.11.2 shows a typical bearing detail using TFE, and Fig. 3.11.3 shows range of the friction coefficient that may be used for design. Typical allowable stress is about 1000 psi for virgin TFE and up to 2,000 psi for filled material with reinforcing agents such as glass fibers.

tion areas will be heavily congested with reinforcement, thus it is advisable to use small size coarse aggregate and concrete with relatively high workability. Additional discussion on this topic is included in Sect. 1.7.5 and design examples are covered in Chapt. 4.

3.12 Other Load Transfer Materials 3.12.1 Cast-in-Place Concrete Many connections of precast structures are completed in the field with cast-in- place concrete. It is an effective way of providing for transfer of compressive and shear forces. Tension force transfer capability can also be achieved by using properly anchored reinforcement in the connection area in conjunction with the cast-in-place concrete. This scheme enables design of connections forductilemoment-resistingframes,diaphragmconnections for lateral load transfer and, in general, achieving composite members. The generally accepted practice of mixing and placing cast-in-place concrete should be used for field-cast concrete for connections. Often, connec-

3.12.2 Grout Many connections require the use of grout. It may be required for fire or corrosion protection, or for cosmetic purposes. In other situations, it is required to transfer compressive forces; in such cases, use of non-shrink grout (see Sect. 3.12.2.3) is recommended. 3.12.2.1 Sand-Cement Grout and Dry-Pack Most grout used in connections is a simple

Stainless Sliding Surface

TFE Backing

Bond

I

Steel

Fig. 3.11.2 - Typical TFE Bearing Pad Detail

s

0.30

-E x IL

0.20

6 E .w 0 E

0.10 0.08

t? 0 0 *t;i ti

0.04 0.02 0.01 10

20

50

100

200

500

1000

2000

Pressure, psi

Fig. 3.11.3 - TFE Friction Coefficients 3-15

mixture of portland cement, sand, and water. Proportions are usually one part cement to 2 to 3 parts sand (by volume). The amount of water required depends on the sizes of spaces to be filled, and the method of placement. Masonry mortar is sometimes substituted for grout indiscriminately. In mortar, about one half of the portland cement is replaced with lime. This improves its bonding characteristics but reduces its strength. Thus, the Engineer is cautioned not to allow the use of mortar in place of grout in a structural connection. If compressive forces are to be transmitted by the grout, then it should have a minimum compressive strength equal to that of the concrete. Shrinkage of the grout, as it cures, can impede the ability of the connection to transfer compressive forces. Thus, the grout should be kept as dry as the placement procedures will permit. Quality control of grout is as important as that of concrete. Often this is not the case in practice. Sitemixed grout should be made and tested at regular intervals according to ASTM C-1019 which parallels ASTM C-39 for testing of concrete. Dry-pack is the common term for a very stiff sand-cement mix. Dry-pack is used when forming or other confinement is impractical, for example under column base plates and horizontal panel joints. Compaction is attained by hand tamping with a blunt instrument. 3.12.2.2 Flowable Grout Flowable grouts are high-slump mixesused to fill small size voids that are either cast into the precast member or formed in the field. Since the watercement ratio is relatively high (typically about 0.50), such grouts have low strength and high shrinkage. These grouts also exhibit a tendency for the solids to settle, leaving a layer of water on the top. Special admixtures or treatments are typically used to improve these characteristics, but add to the cost. For very small spaces in confined areas, grouting is sometimes done by pumping or the pressure injection method. The confinement, such as ducts for post-tensioning must be of sufficient strength to resist the pressures produced by these methods. 3.12.2.3 Non-Shrink Grout Shrinkage can be reduced, or more appropriately, compensated for by the use of commercially available non-shrink, pre-mixedgrout. These mixes expand during the initial hardening to offset the subsequent shrinkage of the grout. Since the non-

3-16

shrink grouts are primarily proprietary, their chemical composition is usually not available to study their potential effects on the interfacing materials, such as reinforcement and inserts in the connection. Thus, it is advisable that manufacturers’ recommendations should be carefully followed. For a general reference on the characteristics and methods of testing of non-shrink grouts, the Army Corps is suggested. of Engineers Specification(39) 3.12.2.4 Epoxy Grouts Epoxy grouts are mixtures of epoxy resins and a filler material, usually sand. These are used when high strength is desired, or when improved bonding to concrete is necessary. Reference 40 is a comprehensive report on the subject by Committee 503 of the American Concrete Institute. The physical properties of epoxy compounds vary widely. Also, the epoxy grouts behave very differently than the sand-cement grouts. For example, the thermal expansion of an epoxy grout can be as much as 7 times the thermal expansion of sand-cement grout. It is therefore important that use of these grouts be based on a good base of experience and/orappropriate tests. Recommended tests and methods are given in Ref. 40. Several railroad agencies have used a different method for epoxy grouting of shear keys in bridges. Instead of a pre-mixed mortar, awell-graded aggregate is placed in the keyway, and then a lowviscosity epoxy resin is poured on top. This results in a higher aggregate to epoxy ratio and is thus more economical. It is also easier to place and clean up. The coefficient of thermal expansion is somewhat more compatible, although still about twice that of concrete. 3.12.3 Epoxy Compounds Epoxy compounds are generally formulated in two or more parts commonly designated as A and B. Usually, Part A is the portion containing the epoxy resin and Part B is the hardener system. The epoxy compounds can be used to bond hardened concrete or other construction materials to hardened concrete. They can also be used for grouting or pressure injection of cracks to restore the tensile strength of concrete and other materials. Epoxy resins specially formulated to be moisture insensitive can be used to bond plastic concrete to hardened concrete orto repair concrete in wet condition. ASTM has a specification for epoxy bonding systems(41). The specification divides the systems into types, grades, and classes. Type I is to be used

for bonding hardened concrete and other materials to hardened concrete. Type II is for use in bonding freshly mixed concrete to hardened concrete. The term “Grade” is used to define viscosity. Grade 1 is low viscosity and is used to fill fine cracks. Grade 2 is medium viscosity and Grade 3 has a non-sagging consistency. The Class determines setting time, which is affected by ambient temperature. Class A is to be used in applications below 40°F, Class B between 40” and 60” F, and Class C is intended for use above 60° F . Epoxies are often considered, but sparingly used

in precast concrete connections, except for grouting anchor bolts or dowels into pre-drilled holes. They have also been used for repair or modification of connections in the field. Care is advised in the use of epoxies since their properties including strength and deformation as well as fire resistance are not well established. Also, many of the epoxies degrade due to creep at temperatures in the 140 “to 1 50°F range. Such temperatures are readily experienced in warm climates particularly in facade panels with dark aggregates.

CHAPTER 4 DESIGN PROCEDURES AND EXAMPLES 4.1 General The preceding chapters of this manual have been devoted to general considerations, design concepts and materials for connections. In this chapter, that information is used in conjunction with applicable parts of ACI 318-83 (6) and current industry practice to developconnection design procedures for a variety of commonly used connections. Numerical examples are included to illustrate the application of the design procedures. 4.2 Horizontal Shear Transfer in Composite Members Composite behavior of a precast member and cast-in-place topping requires transfer of horizontal shear forces at the interface between the two. The mechanism by which the horizontal shear transfer is achieved depends on the magnitude of the shear force that must be transferred. ACI 318-83 (6) permits design of horizontal shear transfer by two alternate methods. One method (given in ACI Sect. 17.5.2) uses the factored vertical shear force as the basis for design, while the other method (given in ACI Sect. 17.53) is based on the horizontal shear force calculated from the actual change in compressive or tensile force in a beam segment. Both methods are described below and either one may be used. However, because of its more direct nature, the method based on ACI Sect. 17.5.3 is preferred by the PCI Committee on Connection Details. This method is illustrated with a numerical example. Design Method 1 (AC1 318.83 (6), Sect. 17.5.2) Design Basis: VU I Q V, where: V” = factored shear force at the section considered V,, = nominal horizontal shear strength @ = 0.85 For V,,, two threshold values are given which determine the type of interface preparation and amount of shear transfer reinforcement required.

These values are: V“,, = 80 bvd (pounds), and V“,,, = 350 b,d (pounds) where: b, = width of in-place d =distance centroid

interface between precast and castmembers, in. from extreme compression fiber to of tension reinforcement, in.

Case 1: Vu I I$ (80 b,d) No ties are required if the precast beam top surface is intentionally roughened, otherwise minimum ties (ACI Sect. 17.6) must be provided. Case 2: $ (80 b,d) c I’, 5 e (350 b,d) The precast beam top surface must be intentionally roughened to a full amplitude of approximately l/4 in. and minimum ties (ACI Sect. 17.6) must be provided. Case 3: VU > i$ (350 b,d) Design for horizontal shear must be done using shear-friction analogy (ACI Sect. 11.7). Note: The design for this case is the same in both design methods and is developed as part of Design Method 2. Design Method 2 (AC1 318-83 (6), Sect. 17.5.3) Design Basis: F,, I cp F,, where: F“,, = factored horizontal shear force F“,, = nominal horizontal shear strength Q = 0.85 Note: In using this method, it is more convenient to carry out design directly in terms of the nominal horizontal shear force, F,. Thus, calculation of the facfored horizontal shearforce, F,,, is not required. The nominal horizontal shearforce, F,,, is calculated from the change in compressive or tensile force as shown in Fig. 4.2.1 The effective width of the cast-in-place topping is calculated in accordance with ACI Sect. 8.10. The design using this method follows the same steps as in Method 1 except that, in the nominal horizontal shear strength values, the term b,d is

Positive Moment Section:

’

~~h”~~~~-~~-~~-~~

0

e-

c

,

Alo,, = effective area of the cast-in-place topping Cc = Compressive force of the topping = 0.85 f’ccA,OP = total compressive force C T

Case 1:

Case 2:

c c cc F, = C = T

c>c, F nh=CccT

= total tensile force I A,f, + A,,f,,

f’cc = compressive strength of the topping F nh = nominal horizontal shear force

Negative Moment Section: 0

I

0

l

4T

3

-Ic :

‘~ ;

Fnh=T=C

Fig. 4.2.1 - Horizontal Shear in Composite Members

-

w $$Continuous

Simple Span Member I

Moment Diagram

Moment

I- 2Ch -

Fig. 4.2.2 - Shear Transfer Length 4-2

Member

1

Diagram

replaced with the area of the crack interface, A,,. This area is equal to the width of the interface, b,, (see Fig. 4.2.1) times the horizontal shear length, It, (see Fig. 4.2.2). Thus: Case 1: F”h 5 80 Uh No ties are required if the precast beam top surface is intentionally roughened, otherwise minimum ties (ACI Sect. 17.6) must be provided. Case 2: 80 bJ,,, < F,, I 350 b&,,, The precast beam top surface must be intentionally roughened to a full amplitude of approximately l/4 in. and minimum ties (ACI Sect. 17.6) must be provided. Case 3: F”h ’ ml w v h Design of horizontal shear ties based on shearfriction analogy is required. The design procedure, based on ACI Sect. 11.7 and the effective shear friction coefficient discussed in Sect. 2.7 of this Manual, is given below: The area of horizontal shear ties required in length I,,,, may be calculated by:

where f’c is the lesser compressive strength of the precast member and the composite topping. Section 17.6.1 of ACI 318-83 (6) also requires that ties, when required, should be spaced no more than fourtimes the least dimension of the supported element, nor 24 in., and meet the minimum shear reinforcement requirements of Sect.1 1.553. (Eq. 4.2.4)

Example 4.2.1 - Horizontal Shear Design of a Composite Beam Given: An inverted tee beam with composite topping as shown.

(Eq. 4.2.1)

where: Acs = area of horizontal shear ties, sq. in. F = nominal value of horizontal shear force fynh = yield strength of horizontal shear ties &I = effective shear-friction coefficient as defined in Section 2.7 1000 hA,,u = Vu For composite deck members, u = 1 .O h , and A,, = b,i$,, thus: 1000 L*b:&., < 2 9 P* =

+Fnh

-

(Eq. 4.2.2)

*

(See Table 2.7.1 for u and maximum y values.) The value of F,, is limited to: F,,(max) = 0.25 h 2 f’,b,I,,, I 1000 X2 bJvh (Eq. 4.2.3)

Span length . . . . . . . . . . = 20’-0” (simple

span)

Precast concrete, P, . . . . = 5000 psi (normal weight) Topping concrete, f’, . . . = 3000 psi (normal weight) Shear tie steel, f . . . . . . = 60 ksi Prestressing St&d, f,, . . = 270 ksi, (14)-l/2” diameter Strand stress at nominal strength, f, = 246 ksi (Note: f, can be determined by strain compatibility or by Eq. 18-3 of ACI 318-83 (6)) Problem: Determine the tie requirements to transfer horizontal shear force using Design Method 2.

4-3

Solution: b” = 12 in.

Acr

= b+,,,, = 12(120) = 1440 sq. in. Atae= 3(60) + 2(12) = 204 sq. in. cc = 0.85f’, A,, = 0.85(3)(204) = 520.2 kips T = A,,f,s = 14(0.153)(246) = 527.0 kips > 520.2 Therefore, F",, = 520.2 kips From Eq. 4.2.3: F,,(max) = 0.25 X2ff6 A,, I 1000 h2A,, = 0.25(l)2(3)(1440) = 1080.0 kips > 520.2 (Notes: f’, is lesser of the strengths of precast member and the composite topping; 0.25f’, u 1000, ok; for normal weight concrete, h =1 .O)

80 AC, = 80(1440)/l 000 = 115.2 kips < 520.2 Therefore, at least minimum ties are required. 350 A,, = 350(1440)/l 000 = 504.0 kips < 520.2 Therefore, more than minimum ties are required. From Eq. 4.2.2: 1000 h2Acl 1000(1)2(1440) I$ = = 0.85(520.2)(1000) +F”h = 3.26 z 2.9, use 2.9 (see Table 2.7.1) From Eq. 4.2.1:

6 = 3.0 sq. in.

Check minimum requirements: From Eq.4.2.4: A, (min) = 7 =w = 1.2 sq. in. < 3.0 9 Y For #4 ties: area per tie, A,, = 2(0.2) = 0.4 sq. in.; spacing, s = Z+,,A,JA, = 120(0.4)/3.0 -15.9 in.; max. tie spacing (AC1 Sect. 17.6.1) = 4(5) = 20 in. < 24 Use #4 ties at 15 in. ox. (Note: Ties must be fully anchored into interconnected elements in accordance with ACI Sect. 12.13.)

4.3 Diaphragm Design Horizontal loads from wind or earthquake are usually transmitted to shearwallsor moment-resisting frames through the roof and floors acting as horizontal diaphragms. 4.3.1 Method of Analysis The diaphragm is analyzed by considering the roof or floor as a deep horizontal beam, analogous to a plate girder or l-beam. The shear walls or structural frames are the supports for this analogous beam and the lateral loads are transmitted to these supports as reactions. As in a beam, tension and compression are induced in the chords or “flanges” of the analogous l-beam as shown in Fig. 4.3.1. When precast concrete members which span parallel to the supporting shear walls or frames are used forthe diaphragm, the shear in the analogous beam must be transferred between adjacent members and also to the supporting elements. The ‘web” shear must also be transferred to the chord elements. Thus, the design of a diaphragm is essentially a connection design problem. 4.3.2 Shear Transfer between Members In floors or roofs without composite topping, the shear transfer between deck members is usually accomplished by weld plates or grout keys depending on the member. Weld plates may be analyzed as illustrated in Fig. 4.3.2. In addition to the hardware details shown, many others are used by precast concrete manufacturers. For members connected by grout keys, a typical value of 80 psi is used for the design strength of the grouted key. Excessive shrinkage may cause degradation of the grouted key effectiveness. In that case, or when higher shear transfer strength is required, reinforcement placed as shown in Fig. 4.3.3 can be used to transfer the shear. This steel is designed by shear-friction principles discussed in Sect. 2.7. In floors or roofs with composite topping, the topping itself can act as the diaphragm if it is adequately reinforced. Reinforcement requirements can be determined by shear-friction analysis. It should be noted that the connections between members often serve functions in addition to the transfer of shear due to lateral loads. For example, weld plates in flanged members are often used to adjust differential camber and the grout keys facilitate distribution of concentrated loads.

Lateral Load, W = wl

Max. Shear

Weld Plates Designed for Shear Force

Chord Force C = Mi b

= Chord Force

Typical Double Tee Roof

Typical Hollow-Core Roof Section A-A Shear on Diaphragm

Moment on Diaphragm

Fig. 4.3.1 - Analogous Beam Design of a Diaphragm

with a t: 45” and

Plan

Plan

Section

Section

Fig. 4.3.2 - Typical Flange Weld Plate Details

Grouted Shear Key -Ir

Static friction as discussed in Chapt. 2 can be used to transfer wind loads to walls. The static coefficients of friction (Table 2.6.1) should be divided by 5 when used for this purpose. In bearing wall buildings higher than 3 stories, a minimum amount of perimeter reinforcement is recommended for resistance to “abnormal loads.” When design for abnormal loads is required by the building code or owner, these minimum requirements may be sufficient to resist the chord tension. Example 4.3.1 -Design of Typical Connections in a Roof Diaphragm Glven: A roof system as shown in Fig. 4.3.1 consisting of 258’~0” double tees and an inverted tee beam. b = 70ft. s, = 30 ft. s2 = 40 ft. 1 = 200 ft. Building height, h = 30 ft. Wind pressure, p = 15 psf Load factor for wind = 1.3 Concrete, f’c = 5000 psi (normal weight)

Fig. 4.3.3 - Perimeter ShearFriction Steel Connections which transfer shear from the diaphragm to the shear walls or moment-resisting frames are analyzed in the same manner as the connection between diaphragm members. 4.3.3 Chord Forces Chord forces may be calculated as shown in Fig. 4.3.1 I For roofs with intermediate supports as shown, the shear stress is carried across the beam with weld plates or bars in grout keys as shown in Section A-A. Bars are designed by shear-friction. Stresses are usually quite low, and often minimum reinforcement is required. In flanged deck members, the chord tension at the perimeter of the building is usually transferred between members by the same type of connection used for shear transfer. Between connections, the tension must be taken by lapped reinforcement within the member flange unless the concrete tensile strength is adequate with $I = 0.65.

4-6

Problem: Design roof diaphragm connections. Solution: 1. Design flange-to-flange connection between tees: w = pN2 = (15/1000)(30)/2 = 0.225 kips/ft W = w(Z) = 0.225(200) = 45.0 kips V, = V, = 45.012 = 22.5 kips Maximum shear between members: v max = @a lf W,) . = (2 x 92/200)(22.5) = 20.7 kips Note: a = Z/2 -width of one tee = 20012 - 8 = 92 ft. Try 3 connections in the 30 ft. long tees and 4 connections in the 40 ft. long tees. Number of connections, N=7 V /connection = V,, /N = 20.7/7 = 2.96 kips VU /connection = V/connection x Load factor = 2.96(1.3) = 3.85 kips Try #4 Grade 40 bars bent at 45O (see Fig. 4.3.2) @Vn =10.2 kips z 3.85 kips, ok

Use R l/4” x 4” x 4”

7 connections are adequate (Note: The bars must be of adequate length to ensure their development.) 2. Design connection at end of tees for chord forces:

Design weld - plate to plate: From Table A-l 4, design strength of 3/l 6” fillet weld using E70 Electrode is 4.64 k/in d, = T”/Capacity = 20.9/4.64 = 4.5 in. Use 5 in. weld each end of connector plate.

K

2-#4 Gr 60 Weldable

\\

c

-------< --------

b

”/.

---------

Note: Temperature changes and shrinkage of concrete produce stresses in the plate and may cause minor cracking in concrete near the joint. This likelihood of cracking should be checked. Debonding of bars for about 12 in. on each side of the joint usually alleviates this problem. 3. Design connection at beam and column line near center of building:

vc

Plan

Plan

Section M = wZ*/8 = 0.225(200)*/8 = 1125 k-ft M” = L. F. x M = 1.3( 1125) = 1462.5 k-ft T, = C, = MU/b = 1462.5170 = 20.9 kips A,(w) = T, / + f, = 20.9/(0.9x60) = 0.39 sq. in. Use 2-#4 bars, Gr 60,1.7$ = 20 in. (Table A-12) if lapped wlth other reinforcement.

Section

From Table A-l 7, minimum $, using E70 Electrode is l-3/4 in. Weld size is d,/5 = 0.5/5 = 0.10 in.

Shear at interior support, Vint = chord force(C, or TJ = 20.9 kips (Note: See basis for Design Method 2 in Sect. 4.2.)

Use 3/W x 2”weld on both sides of each bar.

This total shear force must be transfered in one half of the building length. Assume one connection per tee: Vu/connection = V,,/(No. of tees/2) = 20.9/(25/2) = 1.67 kips

Design connector plate (A-36 steel): A,@4 = T, 4 f, = 20.9/(0.9x36) =0.65 sq. in. Assuming a 4” wide plate, t = 0.65/4 = 0.16 in.

4-7

f&allowable) = o(0.55)f, = 0.85(0.55)(36) = 16.83 ksi > 2.23, ok Design plate in tee leg:

Mu

= 1.67(4.5) = 7.52 k-in V,(direct)/stud = VU/N = 1.67/2 = 0.84 kips VJmoment)/stud = M, /s = 7.52/2 = 3.76 kips Resultant VU/stud From Table A-36(Appendix A),Case 5: x = b*/(2b + d) = 42/(2(4) + 3) = 1.45 in. I, = (8b3 + 6bd2 + d3)/1 2 - b4/(2b +d) = [8(43)+ 6(4)(3*) + 33]/12 - 44/(2(4) + 3) = 39.64 in4/in MU= V, x e = 1.67(3.05) = 5.09 k-in = 1.67/l 1 -t 5.09 fY = VU/L + MUc/I, (2.55)/39&l = 0.48 k/in fX = MUc /I, = 5.09(1.5)/39.64 = 0.19 k/in f, =

= 0.52 k/in

From Table A-14, design strength of 3/l 6”fillet weld using E70 Electrode is 4.64 k/in > 0.52.

Therefore a 3/W fillet weld is adequate. Design connector plate: Mu = 5.09 k-in Z,W4 = M, / $ fy = 5.09/(0.9x36)

Use R 114” x 3” x 9”

4-8

=v(O.84)*

+ (MJs)~ + (3.76)2 = 3.85 kips

From Table A-35, for f’, = 5000 psi, h=l.O,andd,=4in. 3/8 in. diameter headed studs have capacities as follows: Concrete: V, = 5.3 kips Steel: Vs = 5.0 kips Steel strength controls. 5.0 kips > 3.85 kips, ok

Use (2) 318 in. diameter x 4 in. long headed studs 4.4 Bearlng’Pads

= 0.16 in3

Z, = td*/4 = t(s)*/4 = 2.25 t (Table A-26) 2.25t = 0.16, therefore, t = 0.07 in.

Check shear in plate: f, = V,/td = 1,67/(0.25x3)

=-&V,,/N)2

= 2.23 ksi

The bearing pads provide for a more uniform distribution of load over the bearing area and also facilitate relief of restraint. Recent research (37) indicates that much of the stress relief provided by the elastomeric bearing pads (see Sect. 3.11, items 1 through 4) is due to slip ratherthan the pad deformation. Other recent research (38) has shown that pads with randomlyorientedfibers maintain their integrity for cyclic loads even under simultaneous

high shear displacements (up to 0.7times the thickness) and high compressive stress with up to 0.03 radian pad rotation. Both studies (37,38) also show that the coefficient of lateral resistance (i.e., ratio of shear to compressive stress) reduces significantly under slow cyclic movements, such as those produced by temperature variations. The following recommendations, and Figs. 4.4.1 and 4.4.2 can be used to design bearing pads: 1. Use unfactored loads (i.e., service loads) for design. * 2. Under the maximum allowable compressive stress, instantaneous vertical strains of 10 to 20% can be expected. This strain may double if the bearing surfaces are not parallel. In addition, time-dependent creep strains may add another 25 to lOO%, depending on the magnitude of the sustained load. 3. The length and width of unreinforced pads should be at least five times the thickness for stability. 4. A minimum thickness of l/4 in. for joists and double tee stems, and 318 in. for beams is recommended. 5. Shear stress has been shown to be a function of slip in the chloroprene and random fiber reinforced pads (see Fig. 4.4.2). 6. It is preferable to size the bearing pad to be within the covered beating surface. In any case the portion of pad outside of the covered bearing surface should be neglected in calculating pad stresses and movements. 7. Shape factors, S, for unreinforced pads should be greater than 2 when used under tee stems, and greater than 3 under beams. 8. The sustained dead load compressive stress on unreinforced pads should be limited to the range of 300 to 500 psi. 9. The volume change strains used in Sect. 1.4 may be reduced by one half when calculating horizontal movement because of compensating creep and slip in the bearing pad.

Example 4.4.1 - Bearing Pad Design Given: A lightweight concrete double tee with 3 in. normal weight concrete topping for a parking garage roof as shown in sketch(a). Temperature profile on a hot summer day is shown in sketch(b)

and bearing conditions are shown in sketch(c). Span = 60’-0” Precast dead load = 0.408 Mt Topping dead load = 0.375 k/ft Sustained load = 0.783 kIft(11.75 k/leg) Live load (for stress and strength analyses) = 0.40 wft(6.0 k/leg) Live load (realistic estimate for deformation calculation) = 0.180 Mt(2.7 Meg)

Problem: Determine if the l/4” x 4.5” x 4.5”, random fiber reinforced bearing pad is satisfactory.

Solution: Memberstress, strength and deformation analyses may be carried out using procedures given in the PCI Design Handbook(4). Use of Refs. 42 and 43 is also suggested. In typical applications, experience suggests that only reasonable estimates of member end rotations are required for bearing pad design. The parameters and results pertinent to the bearing pad consideration are: Axial shortening’ per half span (30 ft.) after erection, 6, = - 0.290 in. End rotation’ at release, 0, = +0.012 rad. End rotation at erection, 9, = +O.OlS rad. End rotation at 10 years(final), 6, = +0.005 rad. Instantaneous rotation of the composite section under 0.18 k/ft load, 6, = - .0021 rad. End rotation corresponding to the temperature gradient of 45’ (i.e. 125O - 80°, see sketch(b)), 8, = 0.007 rad. Coefficient of thermal expansion of concrete, oc = 6 x lu6 in/iWF Values needed to check design are: 1. Change in end rotation between final (10 years)and erection conditions: %-% = -0.014 rad. 2. Displacement due to end rotation change: 62 = (02 - B,)Y, = 0.014(21 .13) = +0.296 in. 1 Outward displacement (i.e., corresponding to elongation), and clockwise rotation of the beam right end are taken as positive.

4-s

v Shape Factor = S = * 2(w + b)t

7

D = Durometer (Shore A hardness)

/I ~

A = Design horizontal movement at end of member

cwj/,

Allowable Compressive Stress (psi)

Pad Material

Shore A Hardness D

Recommended Minimum Thickness

Recommended Maximum Rotation’

50 through 70

1.4A

0.3t borw

Unreinforced Chloroprene or Rubber (AASHTO Sect. 25)

4DS I800

Random-Fiber Elastomeric

1000 + 100s < 1500

8OklO

1.4A

0 3t b

5 2000

9OklO

Data Not Available

0.31 borw

Reinforced

Cotton-Duck Fabric Reinforced ;AASHTO 2.10.3 (L))

1 Movement and rotation that occur after erection. For movement or rotation in two directions, use the higher value. The values in the table are based on sliding criteria. If sliding is not critical or testing indicates more advantageous conditions, thinner pads may be used.

Fig. 4.4.1 - Single Layer Bearing Pads

‘B

250

3 g

200

tf 0 z E 2 2

On Concrete -

si5 z cr”

On Steel - -

150

T ‘- Random-Fiber Reinforced -------FL_/--- c - - - - -

100

e ,) - 4-y _-----

0

3

-

50

- - -

ccc .-. 0 0

200

400

600

800

1000

-

-

-

-

-

.----

17 Chloroprene 1

1200

1400 1600 1800 2000

Compressive Stress, psi 1 Average values based on tests at 70% shear and slippage strain

Fig. 4.4.2 - Shearing Resistance of Bearing Pads

3. Displacement due to live load (0.18 Mft) end rotation: 6, = 04 Yh = 0.0021(21.13) = +0.044 in.

7. Allowable compressive stress (Fig. 4.4.1):

4. Displacement due to temperature change: 6, = 0, ybc + ~,U /2)( A -f-l = -0.007(21.13) + 6 x 10+x 360 x 4 5 = -0.148 + 0.097 = -0.052 in.

8. Recomended

e mar

5. Max. uniform compressive stress under service load: f bc = (11,750 + 6,000)/(4.5 x 4.5) = 877 psi 6. Shape factor (Fig. 4.4.1): sx

(4.5)(4.5) wb 2(w + b)t = (2)(4.5 + 4.5)(0.25)

(‘Jmex

= 4.5

Design

=1OOO+lOOS=145Opsi max. rotation (Fig. 4.4.1):

= e = 0.3(0.25) 4.5

= 0,017 rad.

Checks:

1. The maximum displacement is: 6, = 0.052 in. (Note: The net creep and shrinkage effect, 6, + 6, = 0.006 in., is negligible. The displacement due to 0.18 k/ft live load, S3 = 0.044 in. is smaller than and opposite to 8,)

/- 3” Topping / fc----, r ----‘- - - - c.g. Composite 27 ybc = 21.13” b 1 b L--

120”

(a) Roof Section

(b) Temperature Profile

l

Random Fiber Reinforced Elastomeric Pad

Bearing Pad

(c) Bearing Pad Geometry

4-11

From Fig. 4.4.1: Min. pad thickness = 1.4 A = 1.4 6, = 1.4(0.052) = 0.073 in. < 0.25, ok

I I---e-I c / I I ‘45” k

::.i#+::.zi ,$fi., Ci:;:.i,:;:. . fb :I :.:.‘y+‘$x::..‘ : j:..,>::..i:),:.. I II n I

2. The maximum rotation is: %-- 0, = 0.014 rad. < 0.017, ok (Note: The rotation is less than 0.03. Therefore pad will maintain integrity under cyclic ioads(38)) 3.

Compressive stress: 877 psi c 1450, ok

‘I-+‘,;

Thus l/4” x 4.5” x 4.5” bearing pad is ok Note: The resistance to horizontal movement at contact surface can be obtained from Fig. 4.4.2. Since in this case, the double tee stem includes a steel bearing plate, the lesser of values of the “on concrete” and “on steel” conditions is appropriate. Thus, for a compressive stress of 877 psi, the resulting contact shear stress is 80 psi. A tension force equal to 80 x 4.5 x 4.5 = 1.62 kips must be considered in designing the double tee. 4.5 Member End Design for Bearing it is preferable that member ends include at least a nominal amount of reinforcement for load transfer in the bearing areas. However, in situations where the bearing is uniform and the bearing stresses are low -- as is typical in hollow core and solid slabs -members without end reinforcement usually perform satisfactorily. in thin stemmed members with bearing area smaller than 20 sq. in., some reinforcement should be provided for control of accidental spailing or cracking of the member end. The recommended amount of reinforcement (with one No. 3 bar as minimum) is: (Eq. 4.51) where: NU = factored horizontal force at the bearing fY = yield strength of steel 4 = 0.9 4.5.1 Plain (Unreinforced) End Bearing The design bearing strength of plain concrete (Fig. 45.1) may be calculated as:

4-12

I I

Plan

l---l

Fig. 4.5.1 - Bearing on Plain Concrete +V,, = + C,(0.85f’c A,)*, I 1.2f’, A, (Eq. 4.5.2) where: @In = design bearing strength mT = ---0.70

c,= -fg ( >

NJv”

= 1 .O when reinforcement is provided in the direction of NU in accordance with Sect. 4.5.2, orwhen NU is zero. The quantity “SW” should not be greater than 9.0 sq. in. A, = loaded area A, = maximum area of the portion of the supporting surface that is geometrically similar to and concentric with the loaded area.

Example 4.5.1 - Plain (Unreinforced) Member End Design for Bearing Given: (Refer to Fig. 4.51) Vu = 70 kips; N, = 14 kips = 5 in.; b x 8 in.; w = 6 in. ‘, = 5000 psi: normal weight concrete Problem: Determine if reinforcement for bearing is required. Solution: S W = 5(6) = 30.0 sq. in. > 9.0, Use 9.0

Vu N” A, = A, + A, = - + 4+Jy WY

SW N” JVu cr =-z%i ( > =

A, A,

19 1 200

14170

shows that the assumption of 9 = 0” corresponds to a more probable failure mode. A procedure based on this model has been successfully used by several precast and prestressed concrete manufacturers in the Colorado area for several years. The procedure is given below: 1. Assume the vertical crack at 6 = 0”. 2. Use an additional load factor of 1.15. This load factor is in addition to ACI 318-83(6) load factors and primarily accounts for uncenainties related to the effects of load eccentricity and concentration of reinforcement across the shear transfer interface. 3. Calculate the nominally horizontal reinforcement, A, as:

= 0.54

= 6(8) = 48 sq. in. = (6 + 4)(8 + 4) = 120 sq. in.

From Eq. 4.5.2: QV” = oCJO.85 ‘:A,)\/-, = 0.7(0.54)(0.85)(5)(48)~ = 121.9 kips Maximum $Vn = 1.2 f’c A, =1.2(5)(48) =288kips>121.9,ok Since +Vn > V, (Le. 121.9 kips 3 70), no bearing reinforcement is required. 4.5.2 Reinforced End Bearing If the factored shear force in the bearing area, V, exceeds the design bearing strength, eV, as calculated by Eq. 4.52, reinforcement for bearing is required in the member end. The reinforcement, calculated using shear friction analogy, is provided to intercept the potential vertical and horizontal cracks shown in Fig. 4.5.2. The PCI Design Handbook(4) uses a 20” orientation (i.e, 6 = 20°in Fig. 4.5.2) fortheverticalcrack. While this assumption produces reasonable design results, laboratory tests (44) have shown that the cracks at the reinforcement location form in a more nearly vertical position (i.e., 0 = 00). A parametric study (45) of the analytical equation based on exact statics of the bearing end also

(Eq. 4.5.3)

where: At = nominally horizontal reinforcement for shear force (A,) and direct tension (A,). (Note: Inclinationof this reinforcement up to 15’with the horizontal produces negligible error.) = factored shear force vu = factored tension force N” lOOOhA,,u I values in Table 2.7.1 P* = Vu AC, = area of the vertical creek plane = bh b = average width of the beam web h = height of the beam fY = yield strength of A, reinforcement = 1.4 (See Table 2.7.1) = 0.85 for A,, 0.9 for A, 4. Calculate reinforcement, A,,, for the horizontal crack: (Note: Field experience suggests that that occurrence of the horizontal crack is unlikely. However, until analysis or tests conclusively validate this experience, reinforcement calculated based on Eq. 4.5.4 should be provided). A

At fy sh= I$

(Eq. 4.5.4)

where: Ash = vertical reinforcement across the potential horizontal crack

4-13

h

Fig. 4.5.2 - Reinforced A, = nominally horizontal reinforcement from Eq. 4.5.3 Ire= YS

=

Au = 4 = b = P =

lOOOhA,,u I values in Table 2.7.1 Af t Y yield strength of A,, reinforcement 1.7 $, b, sq. in. development length of A, bars, in. width of beam at the potential horizontal crack location, in. 1.4 (see Table 2.7.1)

(Note: stirrups or mesh used for diagonal tension reinforcement can be considered to act as Ash reinforcement.) 5. Ensure proper anchorage of A, and A,, reinforcements on both sides of the corresponding cracks. 6. Members subjected to bearing stresses in excess of the limits indicated in Sec. 10.15 of ACI 318-83(6) may require confinement reinforcement in all directions. Behavior of member ends with such high stresses is not well understood.

Concrete

Bearing

Example 4.5.2 - Reinforced End Bearing Given: PCI standard rectangular beam 16RB28 “” = 115 kips NU = 25 kips (based on all load factors) Bearing Pad = 4” x 14 ” fy (all reinforcement) = 40,000 psi f’c = 5000 psi (normal weight concrete) Check of Eq. 4.5.2 indicates that reinforcement is required. Problem: Design reinforcement for bearing. Solution: Check ACI 318-83(6), Sect. 10.15: (““LAX = o”” = $J (0.85flc A,) = 0.7(0.85 x 5)(4 x 14) = 166.6k> 115, ok With reference to Fig. 4.5.2: For 6 = O*, A,r = bh = 16(28) = 448 sq. in.

4-14

Calculate A, reinforcement (Eq. 4.5.3): p

e

=

1OW4WU

.4

= 5 g4>

115(1000) * Use 3.4 (See Table 2.7.1)

.

3 4

’

“” 115 A,, = ~ = = 0.99 sq. in. 0.85(3.4)(40) Q cl, ‘y

An

= 0.69 sq. in.

Therefore, A, = 0.99 + 0.69 = 1.68 sq. in. Use 4- #6 (At

q

1.76 sq. in.)

Calculate A,, reinforcement (Eq. 4.5.4): From Table A-l 2: 1.7 Z,for#6 bar=31(2/3)(1.68/1.76)= 19.7in. > 24d, and 12 in. , ok AC, = 1.7 Zd b = 19.7(16) = 315.2 sq. in. P, = ’ ooo(315*2)(1 e4) = 6.6 > 3.4, Use 3.4 1.68(40,000) Ash = m = 0.49 sq. in. Use 2 - #4 stirrups (A,,, = 0.8 sq. in.) (Note: Anchorage of A, and A,, must be ensured.) 4.6 Dapped-End Connections Precast and prestressed concrete beams are often dapped at their ends to reduce overall depth of floors and roofs. However, dapping of the beam end results in a complex force transfer mechanism necessitating consideration of several possible failure modes. These possible failure modes are discussed in Sect. 2.3 and form the basis for the design procedure in the PCI Design Handbook(4). As noted in Sect. 2.3, there is a reasonable correlation between these failure modes and the typical cracks found in test specimens of PCI Research Study(8). However, the Ref. 8 study has brought into focus some additional considerations which are taken into account in the design procedure given here in Sect. 4.6.1. Reference 8 study covered five different reinforcing schemes (Table 4.6.1) suitable for thin stemmed members such as double tees. Design methods based on truss action and free-body equi-

librium concepts are developed and their use illustrated in the report(8). Since these concepts offer good potential for improvement in the state-of-theart of connection design, it seems appropriate to include a design procedure based on these concepts and its application in this Manual. Reinforcing scheme 1 and the corresponding design procedure from Ref. 8 is selected for this purpose and covered in Sect. 4.6.2. 4.6.1 Design Procedure Based on PCI Design Handbook(4) The provisions of this section are appropriate for cases where shear span-to-depth ratio (a/d in Fig. 4.6.1) is not more than 1 .O. The Committee plans to develop provisions for dapped-ends in which a/d exceeds 1.0. In the interim, use of Ref. 46 is suggested. The design equations for this procedure are based on consideration of various potential failures associated with the dapped-end. These potential failure modes (shown as resulting cracks) and the reinforcement required for each are listed below and shown in Fig. 4.6.1. 1. Flexure (cantilever bending) and axial tension in the extended end. Provide reinforcement, As, consisting of At (for flexure) and A, (for axial tension). 2. Direct shear at the junction of the dap and the main body of the member and axial tension. Provide reinforcement, A,, consisting of a part (2/3) of A,, (for shear-friction) and An (for axial tension). Note: The remaining A, must be distributed across crack @ and is automatically considered in the requirement for A,, reinforcement given in step 4 below - See ACI Commentary(G), Sect. 11.9 for derivation. 3. Diagonal tension emanating from the reentrant corner. Provide reinforcement, A,,. 4. Diagonal tension in the extended end. Provide reinforcement composed of A, and A”. 5. Diagonal tension in the undapped portion. This is carried for by A’,, reinforcement in combination with A, reinforcement. 6. Bearing of the beam at the dapped-end must also be checked - See Sect. 4.5. Each of these potential failure modes should be considered separately. However, the reinforcements required for modes 1 and 2 are not additive i.e., A, is taken as the greater of that required for considerations 1 and 2.

’

4-15

4.6.1.1

Flexure and Axial Tension in the Extended End The horizontal reinforcement is determined as: A, = A, + A,

4.6.1.2 Direct Shear The potential vertical crack, crack @ in Fig. 4.6.1, is resisted by a combination of A, and A,. This reinforcement can be calculated by Eqs. 4.6.2 through 4.6.5.

= + [Vu (f) + N, (:)I (Eq. 4.6.1) A, = where: $ = 0.85 (use of I$= 0.85 compensates for use of d in place of j,d.) a = shear span, in., measured from load to center of A,,, h = depth of the member above the dap, in. d = distance from top of beam to center of the reinforcement, A,, in. = yield strength of the flexural reinforcement, fY psi

2V” 3 4 $ I-+ + A”

(Eq. 4.6.3)

A,, = O.S(A, -An)

= 0.85 1”, = yield strength of A,, A,, A,,, psi 1000hbhu I values in Table 2.7.1 h= ,v U (Eq. 4.6.5)

/T;J

I

VU -

-

a

Note: Flexure and‘shear reinforcement for claritv

omitted

Fig. 4.6.1 - Reinforcement in Dapped-End Connections

4-16

(Eq. 4.6.4)

where:

Vua + N&h -d)

Welded Anchor 4l

(Eq. 4.6.2)

The shear strength of the extended end is limited by (see Table 2.7.1): V, I 0.3 X2 f’,bd < 1000 h* bd (Eq. 4.6.6) The reinforcements from Eqs. 4.6.1 and 4.6.2 are not additive; only the greater of the two should be provided. 4.6.1.3 The tension can be

Diagonal Tension at Reentrant Corner reinforcement required to resist diagonal cracking starting from the reentrant corner calculated from: V (Eq. 4.6.7) Ash=g

2.

3.

where:

+ =o.as

4.

VU = applied factored load, lb f, = yield strength of A,,, psi

5.

4.6.1.4 Diagonal Tension in the Extended End Additional reinforcement is required in the extended end, as shown in Fig. 4.6.1, such that: eVn = o (At, + AhfY + 2 X’& bd)

(Eq. 4.6.8)

At least one half of the reinforcement required in this area should be placed vertically. Thus:

(A,)m,n = + [ + - 2 k< bd ] (Eq. 4.6.9) Y

4.6.1.5 Diagonal Tension at Undapped Beam Corner The vertical reinforcement, ASh may be bent and extended at the bottom of the beam to ensure its development and thus guard against failure due to crack@. Abetteralternative, however, isto provide separate horizontal reinforcement, A’,, (as shown in Fig. 4.6.1). The amount of the AShreinforcement must be at least equal to the A,, reinforcement. Thus: !sh ’ ‘sh

(Eq. 4.6.10)

4.6.1.6 Anchorage of Reinforcement With reference to Fig. 4.6.1: 1. Horizontal bars A, should be extended a

minimum of 1.7 L, past the end of the dap and ld past crack@ , and anchored at the end of the beam by welding to cross bars, angles or plates. Horizontal bars A, should be extended a minimum of 1.7 Zd past the end of the dap and anchored at the end of the beam by hooks or other suitable means. The extension at the beam bottom of the bent hanger reinforcement, A,,, or the separate horizontal reinforcement, A’,,, must be at least 1.76 beyond crack@. The A’,, reinforcement may be anchored on the dap side by welding it to a cross bar (as shown in Fig. 4.6.1) or to an angle. Vertical A, bars should be properly anchored by hooks as required by ACI 31683(6). Welded wire fabric in place of bars may be used for reinforcement and should be anchored in accordance with ACI 31683(6).

4.6.1.7 Other Considerations and Recommendations 1. The depth of the extended end should not be less than one-half the depth of the beam, unless the beam is significantly deeper than necessary for other than structural reasons. 2. The hanger reinforcement, Ash, should be placed as close as practical to the reentrant corner. This reinforcement requirement is not additive to other shear reinforcement requirements. 3. If the flexural stress, calculated for the full depth of section using factored loads and gross section properties, exceeds Se immediately beyond the dap, longitudinal reinforcement should be placed in the beam to develop the required flexural strength. 4. In Ref. 8 study, it was found that, due to formation of the critical diagonal tension crack (crack@ in Fig. 4.6.1), it was not possible to develop a full depth beam shear strength greater than the diagonal tension cracking shear in the vicinity of the dap. It is therefore suggested that for a length of the beam equal to the overall depth, H, of the beam, the nominal shear strength of concrete, V,, should be taken as the lesser of Vci and V, calculated at H/2 from the end of the full depth web.

4-17

2. Direct shear: 1OOOhbhu = 1000(1)(16)(16)(1.4) v 100,000 u = 3.58 > 3.4, Use 3.4 (Table 2.7.1)

Example 4.6.1 - Dapped - End Design

b=

Given: The 16RB28 beam with a dapped-end as shown. 5 = 100 kips N,= 15 kips ‘:: = 5000 psi (normal weight) 1, for all reinforcement = 60 ksi (weldable)

By Eqs. 4.6.2 and 4.6.3: A, =

Problem: Determine the required reinforcements, A,, A,,, A,,, A’s,, and A,.

=

N”

2(100) 3(0.85)(60)(3.4)

+

15 0.85(60)

= 0.38 + 0.29 = 0.67 sq. in. c 1.10, Use 1.10 sq. in.

Solution: Assume: Shear span, a = 6 in., d = 15 in. 1. Flexure in extended end (Eq. 4.6.1):

2v”

WyPe + -q-

Provide 445, A, = 1.24 sq. in. By Eq. 4.6.4: A,, = 0.5(A, -A”) = 0.5(1.10 - 0.29) = 0.41 sq. in.

As = $- [V” ($1 +%($I ] Y

Use 2-##3 U-bars, A,, = 0.44 sq. in. Check shear strength, Eq. 4.6.6: V, = (1000h2bd) = (1000)(1)2(16)15/1000 = 240 kips

* = 1.10 sq. in.

l-

1

d= 15”

H - 2’-4

sh

/

/

lexural

Reinforcement 8 I

4-18

1

oVn = 0.85(240)

= 204 kips > 100, ok

Ash bars(#4): 1.7 I, = 20 in. (say 24 in. beyond dap).

3. Diagonal tension at reentrant comer: By Eq. 4.6.7: V = 1.96 sq. in. A =-u= 100 0.85(60) sh + fy Use 5#4 closed ties, A, = 2.00 sq. in. Use A’, =lO-#4 4. Diagonal tension in the extended end: Concrete ca acity = 2 h q bd 5000 (16)(15)/1000 = 33.9 kips = 2(l) + By Eq. 4.6.9: (Av),,,in = 5 [ f - 2 hsCi;, bd ] Y

m - 33.9 ) = 0.70 sq. in. = & 0( . 8 5 Try 2-#4 = 0.80 sq. in. for A,, and 2-#3 = 0.44 sq. in. for A,, Check Eq. 4.6.8: +vn = Cp (AJy + A,f, + 2 hflc bd) = 0.85[0.80(60) + O&(60) + 33.91 = 92.1 kips < 100, ok Change A,, to 2-#4 % = 110.4 kips > 100, ok 5. Check anchorage requirements: A, bars: From Table A-l 2: for f, = 60,000 psi, f’c = 5000 psi, #5 bars c = 15 in. past 45” diagonal crack from corner Total = 28 in. - 15 in. + $, = 28 in., or 1.7 Zd = 26 in. beyond dap A, bars:

4.6.2 Design Procedure Based on Truss Action and Free-Body Equilibrium(8) As noted previously, the PCI research on dapped-ends (8) included testing of five different reinforcing schemes (Table 4.6.1) suitable for thin stemmed members. Based on results of these tests, the report(8) gives design procedures for each of the five schemes. These procedures use a combination of modeling of the dapped-end as a truss and free-body equilibrium. Even though the design procedures are “reinforcing scheme specific”and there are some differences between them, the general ideas follow the same methodology. Therefore, only one of the reinforcing schemes (Scheme 1) and the corresponding design procedure is covered in this section. The details of the specimens using reinforcing scheme 1 are shown in Fig. 4.6.2 and the correis shown in Fig. sponding truss action4assumed) 4.6.3. By reference to these figures, the following design procedure is established: 1. General Requirements: (a) Use an additional load factor of 1.15 i.e., additional to ACI 318-83(6) load factors. (b) The inclination of the hanger reinforcement to the vertical must be within 28” and 45O. The centerline of the hanger reinforcement should be as close to the centerline of the web as possible. (c) The shearspan-to-depth ratio (a/d) should not exceed 1 .O. (d) Requirements 1 and 3 of Sect. 4.6.1.6 and requirements 2 and 4 of Sect. 4.6.1.7 also apply. (e) It is recommended that, if at all possible, at least one half the prestressing strands should pass through the nib (i.e., portion of the beam above dap). Ref. 8 study found that the test specimens which met this requirement exhibited considerably improved serviceability because of the reduced extent of cracking and the width of cracks.

From Table A-l 2 for #4 bars: 1.7 Z,, = 20 in. beyond dap

4-19

Tahla AR I Ct~mmarv nf . Tact Prnnram__ \-, 181 .UY*-7.“. I VY,..**,Ya, -. w-s . . ‘3---

Specimen Type

/ I

Bar B

2. Calculate V, and N,: “” = 1.15VJ i$, N, = 1.i5NU/~ (Eq. 4.6.11) Where, VU and NU are calculated using ACI 31883(6) load factors. The nominal shear strength is limited’ to: For normal weight concrete: (Eq. 4.6.12a) V, I 0.2f’,b,d, I 800b,d, For sand-lightweight concrete:

4-20

I

V, I (0.2 - 0.07 a/d,)f’,b,d, < (1000 - 350a/d,)b,d,

(Eq. 4.6.12b)

1 The difference in the maximum nominal shear strength, Vn,values between this procedure and the one based on the PCI Design Handbook procedure should be noted. The PCI Design Handbook procedure uses the “effective shear-friction” model and the limits for V, are consistent with that model (see Table 2.7.1). The limiting values for V, used here are the same as given in Ref. 8 which forms the basis for Sect. 4.6.2 design procedure.

I’ Specimen

I

-d--5/8"

Length L

Bars A

- -

1A

2-#4

13"

1B

l-#4+ 1-U

22-114"

1C

l-#4+1-#3

1

22-114"

Fig. 4.6.2 - Details of Specimens Using Reinforcing Scheme 1 I

- c l e w -

*

;

:

d’

A /-s

Bar

where: b, = length of the upper anchorage angle b, = average width of nib See Fig. 4.6.3 for other terms 3. Calculate A,,, choose bar size and calculate “y” (see Fig. 4.6.3): V A s h =” (Eq. 4.6.13) f, cosa 4. Assume a value for “x” and calculate “e”:

Y

e=Z,+y/cosa -(h,-x)tana

(Eq. 4.6.14)

5. Calculate A,:

Fig. 4.6.3 - Assumed “TrussAction” in Nib For all-lightweight concrete: V, I (0.2 - 0.07 a/d&b,d, I (800 - 280a/d,)b,d,

A, =

V,e + N&h, - x)

(Eq. 4.6.15)

fy (dd - x) 6. Calculate ‘k” and compare with assumed value in step 4. Iterate if necessary,

(Eq. 4.6.12~)

% ‘= 1.7f’,b,

(Eq. 4.6.16)

4-21

where: C, = A& + A,,f,sin a - N,

Solution:

7. Calculate tan y and compare with 0.15:

1. Assume: (a) 3/8 in. thick bearing plate (b) #4 reinforcing bar for A,, therefore d, = 7.38 in. (c) Distance from the centerline of hanger reinforcement to end face of web, y, is 1 .O in.

(Eq. 4.6.17)

tan y = e/(d, - x) a. If tan y

c

0.15, design is satisfactory

b. If tan y > 0.15, provide a cross bar, diameter d,,, length L,, welded to bearing plate, so that: 0.85f’,d,L, 2 V,e/(d, - x).

Example 4.6.2 - Dapped-End Design Based on Truss Action and Free-Body Equilibrium (Ref. 8)

2. Calculate nominal forces from Eq. 4.6.11: 4 = 1.15 VU/o = 1.15(15)/0.85 = 20.3 kips N, = 1.15 N,/o = 1.15(4)/0.85 = 5.4 kips Check maximum V, from Eq. 4.6.12a: Since 0.2f’, = 1000 psi > 800, ok V” I 800 bddd I 800(5.3)(7.38)/l 000 = 31.3 kips > 20.3, ok 3. Calculate A,, (Eq. 4.6.13):

Given: Dapped-end for a double tee(8DT20) in Fig. A.

as shown

A sh

Vi7 LXQ- = 0.39 in* = fy = 6O(cos30”)

Use 2-#4, Grade 60 (weldable) IX

4. Determine horizontal extension of A,, in beam: Id for #4, (Grade 60, f6 = 5000 psi) = 12 in. 1.7 Z,, = 20.4 in. (Alternately from Table A-l 2, 1.7 Id = 20.0 in.)

------__ Stranc ______._ StGha 4 - - - e - - eStrandz-----

Extend A., bars 21 in. as shown in Fig. B 1

i

i

I

1

)2.0:“{

4.5”---+ 5.77’ Ij20.27’ HQ =

j lo.07

i

i

t

x

Fig. A - Dapped End of 8DT20 f’c = 5000 psi (normal weight concrete)

5. Calculate A,: With 3/4 in. cover to #4 bar, distance y (Fig. 4.6.3) = 1 .O in. Assuming distance x = 0.7 in., from Eq. 4.6.14: e = ZP + y/cos a - (hd - x)tan a = 4.5 + l/cos30° - (8.0 - 0.7) tan30° = 1.44 in. From Eq. 4.6.15: A, =

f sB = 150 ksi (transfer length = 36 in.) Yl = 15 kips/web N” = 4 kips/web average width of stem above dap, b, = 5.3 in. Problem: Design reinforcement for the dapped-end - reinforcing scheme 1 (see Fig. 4.6.2). 4-22

V,e .+ N,( h, - x) f, (dd - xl

= 20.3(1&I) + 5.4(8.0 - 0.7) 60(7.38 - 0.7) = 0.17 sq. in. Verify x (Eq. 4.6.16): C, = A& + A,,f,sin a - N,

4 314”

x

6”

x

318”

c l-y-- 21*-----l

’

Fig. B - Example Design Using Reinforcing Scheme 1

= (0.17)(60) + 0.39(60)sin30° = 16.5 kips X

- 5.4 I

16.5 = 0.65 in., =1.7(5)(3)

close to and less than assumed value, ok Use 2-#3 for A, (0.22 sq. in.) 6. Determine extension of A, in beam: As should project into the beam web the further of: (a) 1.7 td beyond the reentrant corner (b) distance from end face of nib equal to transfer length of strand

Use #&I cross-bar, 3 in. long (L,d,, = 1.5 sq. in.) Provide lineal total of l/4 in. E70 flare bevel groove weld to attach cross bar to bearing plate. Weld to carry 0.216(20.3) = 4.4 kips. 8. Determineupperanchorageof ment:

hangerreinforce-

For a 2 in. vertical leg, the length of anchorage angle is: bcl = C, /(0.85f’,(2)] = 16.5/[0.85(5)(2)] = 1.94 in. Use L 2 x 4 x 114 in., length = 3 in.

(a) For #3, 60 ksi, f’, = 5000 psi, Zd = 12 in., 1.7 Zd = 20.4 in. (b) For transfer length of 36 in., and nib length of 6 in., projection beyond reentrant corner is30 in. Use 30 in.

Weld #4 hanger bars to opposite faces of 1-314x 3-314 x 5/8 in. plate welded inside the anchor angle. Length of 114 in. E70 flare bevel groove weld between each bar and the 5/8 in. plate (See Table A-l 7) = l-314 in.

Providel-1/4of3/16In.E70flarebevelgroove weld to attach each #3 bar to 6 x 3/8 x 4-3/4 in. bearing plate.

Length of 114 in. E70 fillet weld between plate and angle: L,,, = C, /(weld strength/in.) = 16.5/6.19 (Table A-14) = 2.7 in.

7. Calculate tan y (Eq. 4.6.17): tan y = e/(d, - x) = 1.44/(7.38 - 0.7) = 0.216 > 0.15, therefore cross bar is needed. Minimum Lbcdbc = [V,e/(d, - x)]/(0.85f’,) = (20.3)(0.216)/(0.85)(5) = 1.03 sq. in.

Provide l-1/2 in. of 114 in. fillet weld each side of plate.

4-23

4.7 Beam Ledges The design of ledger beams, in particular the spandrel ledger beams, continues to be a controversial topic in the precast prestressed concrete industry. There is no uniformly accepted procedure for design of such members particularly for the design of the beam end, the beam ledge, and attachment of the ledge to the web through hanger steel. While the design of the overall member is outside the scope of this Manual on connections, procedure for design of the beam ledges is given in this section. This procedure, which is the same (with some additional recommendations given here) as included in the PCI Design Handbook(r)), has generally proven satisfactory. However, to address the still remaining uncertainties with respect to design of the hanger steel, the PCI Committee on Connection Details recommends use of an additional load

factor of a minimum of 1.3 for its calculation’ (see Eq. 4.7.5). The design shear strength of continuous beam ledges supporting concentrated loads, as shown in Fig. 4.7.1 can be determined as: For s > b + h, use lesser of Eqs. 4.7.1 and 4.7.2 values: +V, = 3 $Afic h(22, + b + h)

(Eq. 4.7.1)

+V, = @Cc h(2i$ + b + h + 2dJ

(Eq. 4.7.2)

For s < b + h, and equal concentrated loads, use the lesser of Eqs. 4.7.la, 4.7.2a, and 4.7.3 values: @In = e 1.5 hflc h(2\ + b + h + s) (Eq. 4.7.la) @In = ~+kfi~ h(b + y+ d, + s) (Eq. 4.7.2a)

1 Recent PCI funded research(g) indicates that the current PCI Design Handbook procedure may be unconservative for certain ledge configurations. The additional load factor of 1.3 recommended here for the design of hanger steel is judged to address this mntern. Alternatively, the design procedure given in Ref. 9 may be used.

where: h. = I, = b = S =

depth of the beam ledge, in. ledge projection, in. width of bearing area, in. spacing of concentrated loads, in.

Note:

,

-I

d,+ y L-

Cb+hJ

’

Fig. 4.7.1 - Design of Beam Ledges 4-24

Main reinforcement for L-Beam not shown. Closed ties required when torsion is critical.

d, =distancefromcenterof load to the endof beam, in.

the

If the ledge supports acontinuous load or closely spaced concentrated loads, the design shear strength is: @I,, = (b24h “c

(Eq. 4.7.3)

If the applied factored load exceeds the strength asdetermined by Eqs. 4.7.1,4.7.2,4.7.3, the ledge should be designed in accordance with Sect. 4.6. Flexural reinforcement, A, computed by Eq. 4.7.4 should be provided in the beam ledge, and hanger steel, A,,, computed by Eq. 4.7.5 should be provided in the beam web. These equations are given below:

(Eq. 4.7.4) (Eq. 4.7.5)

where: + = 0.85 (Note: Use of o = 0.85 rather than 0.9 in Eq. 4.7.4 compensates .for using d in place of the actual lever arm j,d). = yield strength of the particular reinforcefY ment See Fig. 4.7.1 for other terms. The flexural steel, A, and the hanger steel, A,, may be uniformly spaced over a width of 6h on either side of the bearing, but not to exceed l/2 the distance to the next load. Bar spacing should not exceed the ledge depth, h, or 18 in. No less than one half of the A,, reinforcement should be placed within the width of the assumed failure surface (b + h). A,, need not be additive to shear and torsion reinforcement designed in accordance with Sect. 4.3 and 4.4 of the PCI Design Handbook (4). Longitudinal reinforcement, calculated by Eq. 4.7.6 should be placed in both the top and bottom of the ledge portion of the beam (see Fig. 4.7.1): A, =(200Z,d)/fY

(Eq. 4.7.6)

Example 4.7.1 - Design of a Beam Ledge Given: 8 ft. wide double tees resting on a standard Lbeam similar to that shown in Fig. 4.7.1. Layout of tees is irregular so that a stem can be placed at any point on the ledge. V, per stem = 18 kips N, per stem = 3 kips h = 12 in., b = 3 in., s = 48 in., d = 11 in., I p= 6 in. “C = 5000 psi (normal weight) = 40 ksi fY (Note: The loads V, and N, are based on ACI 318-83(6) load factors.) Problem: Investigate shear strength and determine reinforcement for the ledge. Solution: Min. d, = b/2 = 1.5 in. Since s > b + h and d, < (22,, + b + h), use Eq. 4.7.2: eVn=oh+~h(2$+b+h+2d,) = 0.85(l)- (12)[2(6)+ 3 +12 e 2(1.5)] /1000=21.6kips>18 Shear span, a = 31,/4 + 1.5 = 3/4(6) -I- 1.5 = 6.0 in. By Eq. 4.7.4: A, = A, + A, =&pq$)+%($-)] Y

= o 8;(40)

[18(6/l 1) +3(12/l

111

= 0.39 sq. in. 6h=6ft.>s/2=2ft. Therefore distribute reinforcement avers/2 side of the load. (s/2)(2) = 4 ft. Maximum bar spacing, h = 12 in.

each

#I3 @ 12 in. = 0.44 sq. in. in each 4 ft. Place 2 additional bars at the beam end to provide equivalent reinforcement for stem placed near the end.

By Eq. 4.7.5: As h = +&= %%& = 0.69 sq. in.14 ft. Y

-

Provide 743 in every 4 ft. width, with 4-#3 in a width b + h = 15 in. Note: For placing convenience, the fabricator may elect to place A, at the same spacing as Ash. By Eq. 47.6: A, = 200$ d ify = 200(6)(11) = 0.33 sq. in.

/40,000

Use 2 -##4 top and bottom = 0.40 sq. in. Note: Also check shear and torsion requirements, per Sects. 4.3 and 4.4 of the PCI Design Handbook(4).

4.8 Concrete Bracket3 and Corbels Concrete brackets and corbels are short cantilevers with shear span-to-depth ratios (a/d in Fig. 4.8.1) less than unity. The failure mechanisms of such members are usually different than cantilevers with a/d larger than unity. Therefore, ACI 318-83 (6)‘ based on references 30 and 47, includes special provisions in Sect. 11.9 for the design of brackets and corbels. The design procedure given below follows these recommendations in conjunction with use of the effective shear friction analogy of PCI Design Handbook (4) and the following limitations (see Figs. 4.8.1 and 4.8.2): 1. aIds 2. NusVu 3. e = 0.85 for all calculations 4. Anchorage at the front face of the corbel must be provided by welding or other positive means. 5. Concentrated loads on continuous corbels may be distributed as for the beam ledges in Sect. 4.7.

A, (Main Reinf.) /A,, (Stirrup Reinf.)

Free-Body

Force

Reinforcement

h/2

11

L Anchor Bar Hanger Fieinf . A, (Main Reinf.) Panel

Free-Body

Force

Reinf.

Reinforcement

Fig. 4.8.1 - Corbel Force Diagrams and Typical Reinforcement

4-26

2/3d (Max.)

ith Deformed Bar

Deformed

Bar

Alternate Anchorage

Fig. 4.8.2 - Design of Concrete Corbels The area of primary tension reinforcement, A, is the greater of (A1 + .A”) as calculated below, or (2A,/3 + A”) where AVr is the shear-friction reinforcement discussed in Sect. 2.7: A, =

VUa + N&h - d) @ fyd

(Eq. 4.8.1)

(Eq. 4.8.2)

(Eq. 4.8.3)

For convenience, the equations can be rewritten so that A, shall be the greaterof Eq. 4.8.4 and4.8.5, but not less than (A&, from Eq. 4.8.6: A, = + [v”(f) + N”($)]

(Eq. 4.8.4)

As

=k’

2v, 1 3y +N” 1

(A&” = O.O4(f’,/f,)bd

(Eq. 4.8.5)

(Eq. 4.8.6)

Additional reinforcement, A,, calculated by Eq. 4.8.7 is also required and, as shown in Fig. 4.8.2, it should be placed within 2d/3 of the primary tension reinforcement, A,. A,, 2 0.5(A, - An)

(Eq. 4.8.7)

The nominal shear strength of a corbel is limited’ by (see Table 2.7.1): 1 The difference between the limiting value of nominal shear strength given here and the ACI 318-83 (Sect. 11.9) is noted. The value given here (Eq. 4.8.8) is consistentwith useof the”effectiveshear-friction” model discussed in Sect. 2.7.

4-27

V, I 0.3 X2 f’,bd I 1000 h* bd

(Eq. 4.8.8)

Table A-28 in Appendix A lists design shear strength values for a wide range of corbel sizes.

By Eq. 4.8.6: (AJtnin

= O.O4bd(f’,/f,) = 0.04(14)(13)(5/60) = 0.61 sq. in. < 1.04

Provide 247 bars = 1.20 sq. in. Example 4.8.1 - Reinforced concrete corbel Given: A concrete corbel similar to that shown in Fig. 4.8.2 V, = 80 kips Nu=15kips fY = Grade 60 (weldable) “C = 5000 psi (normal weight) Bearing pad: 14 in. x 6 in. b = 14 in.; ZP = 8 in. h = 1.0; f.l=l.4 Problem: Determine corbel depth and reinforcement. Solution: Try h = 14 in., d = 13 in. Assume load Vu eccentricity, a = 3/4 $ = 6 in. By Eq. 4.8.4:

A, = & /j’,(2)+ Nu(ff)] = : [80(G) + 15(g) ] 0.85(60)

for h = 14 in., the come1 would have a strength of 89 kips with A, = 2 - #7.) By Eq. 4.8.7: A, = 0.5(A, - An) = 0.5[1.04 - 15/(0.85(60)] = 0.37 sq. in. Provide 2 - #3 closed ties (A,, = 0.44 sq. in.) in top (2/3)d = 8.7 in. of corbel. Check maximum shear strength of corbel: From Eq. 4.8.8: 0.3 h*f’,(bd) = 273 kips 1000 h2(bd) = 182 kips V A.-- 80 = 94.1 kips c 182.0, ok I$ 0.85 Design anchorage of A, reinforcement: (Note:The size of the welded cross bar used for anchorage should be the same or somewhat larger than the size of the bars to be anchored) Force to be developed in one #7 bar

= 1.04 sq. in.

= e (O.S)(SO) = 31.2 kips

By Eq. 4.8.5: %3=

(Note: The AS reinforcement could also be estimated from Table A-28 in Appendix A: For b = 14 in. and ‘, = 8 in., the table shows that

1000 h bh u ,1000(1)(14)(14)(1.4) v 80,000 U

= 3.43 > 3.4, Use 3.4 (Table 2.7.1)

1

+ N”

From’Table A-l 8, it is seen that it would require a cross bar larger than #lo. Try 3-#7 for A, to reduce the force to be developed in each bar. Force to be developed = ?$

(0.6)(60)

= 20.8 kips

From Table A-18, #I9 cross bar provides a design strength = 22.3 kips> 20.8, ok = 0.60 sq. in. < 1.04 Use 3-#7 for A, with 1-#9 welded cross bar (E90 electrode)

4-28

4.9 Structural Steel Haunches Structural steel shapes, such as wide flange beams, double channels, tubes and vertical plates are frequently incorporated in precast concrete columns to serve as haunches or brackets. Design of the steel shapes is done in accordance with accepted methods of structural steel design. The concrete strength including contribution of any reinforcement welded to the embedded shape and appropriately developed in the concrete may be calculated using principles of statics supplemented by guidelines given in this Manual and ACI 31883(6). The design procedure given below is based on Ref. 48. Using the relationships and assumptions shown in Figs. 4.9.1 and 49.2:

(Eq. 4.9.2) Vr (the nominal strength of reinforcement welded to steel section; A’s = A, is assumed) (Eq. 4.9.3)

e = a + lJ2

a = shear span 4 = embedment depth b = effective width of compression block S = distance between A’, and A, 4.1 = 0.85

1. The concrete based design strength is: 2. The design strength of the steel section is: (Eq. 4.9.1)

fvf,= 4wc+Vr)

Based on flexure: where: Vc (the nominal strength of concrete)

4 qy wn = a + VU/(0.85f’Cb)

(Eq. 4.9.4)

h e

$/2 x-9 0

h

”

VA L-,-l

---A Xl

Strains

%; ‘I-

0.003

-ri

f - - q - J

-:

$ o.oo3

PIXb -I Stresses ~ +fj r, 5

(a) Pure Shear

r -i 0.85 f:

7

(b) Pure Moment

JPXY

af’c7- nm &f: -T(c) General Loading

Fig. 4.9.1 - Stress-Strain Relationships - Steel Haunches 4-29

for Moment on Embedded Section

Column Reinforcement

7

1 cc-s-4

---/ bs2.5w L

Fig. 4.9.2 - Assumptions and Notations-Steel Haunch Design Based on shear:

4%

= $ (0.55fyh t)

where: 2, = plastic section modulus of the steel section (see Table A-26) fY = yield strength of steel h,t = depth and thickness of steel section web, respectively 0 = 0.9 (Note: Plastic design criteria for structural steel do not require the use of o factor. However, the load factors used are 1.7 (D + L). Therefore, when using plastic steel design with concrete load factors (1.4D + 1.7L), the use of 9, = 0.90 is suggested in order to provide approximately the same overall factor of safety.) The design strength, o V, is taken as the least of the values obtained from Eqs. 4.9.1, 4.9.4 and 4.95, and the design based on cp V, 2 VU. The following recommendations should be used in conjunction with the design procedure given above.

4-30

1. In a column with closely spaced ties above and below the haunch, the effective width, b, can be assumed as the width of the confined region, or 2.5 times the width of the steel section, whichever is less. 2. For thin-walled members, such as the tube shown in Fig. 4.9.2, the inside should be filled with concrete to prevent local buckling. 3. When the supplemental reinforcement, A, and AS, is anchored both above and below the members, as in Fig. 4.9.2, it can be counted twice. 4. The critical section for bending of the steel member is located a distance V,/(0.85f’Cb) in. from the face of the column. 5. If the steel section projects from both sides, as in Fig. 4.9.1(a), minimum eccentricity corresponding to e/g = 0.5 is recommended in Eq. 4.9.1. 6. Horizontal forces, NU, are resisted by bond on the perimeter of the section. If the bond stress resulting from factored loads exceeds 250 psi, headed studs or reinforcing bars can be welded to the section.

Example 4.9.1 - Design of structural steel haunch Given: The structural steel haunch shown.

I I I I .I I

For A, = 2 - #4, anchored 2 sides, I = 10 in., V, = 2(14) = 28 kips

I f

I

I i

Column

8”

i--

Problem: Check whether the design shown is adequate. Solution: Effective width is lesser of b = confined area (8 in.) or 2.5~ = 2.5(4) = 10 in. Use b = 8 in.; e=4+10/2=9in. From Eq. 4.9.2: 0.85 f’CbZ, = OW5)(8)(10) 1 + 3.6 e/ii, 1 + 3.6(9)/( 10)

t

80.2 kips

Since the A, bars are anchored above and below, they can be counted twice. A, (2 - #4) = 2(2)(0.2) = 0.80 sq. in. From Eq. 4.9.3:

vr =

2A,f 2(0.80)(60) X , + WM1O) 6el2, I+ 4.8(slZ,) - 1 4.8(7/l 0) - 1

= 29.2 kips

W” = oVC + $Vr = 68 + 0.85(28) = 92 kips Steel shear capacity: From Eq. 4.9.5: +V” = C$ (0.55f,ht) = 0.9(0.55)(36)(6)(2)(0.5) = 106.9 krps Steel flexure capacity(Table A-26):

Reinf.

Vu = 85.0 kips “c = 5000 psi f, (reinforcement) = 60,000 psi (weldable) f,, (structural steel) = 36,000 psi

vc =

Alternate solution using Tables A-29 and A-30: For b=8 in., a = 4 in., il, = 10 in., CpV, = 68 kips

4”X6”X l/2” Steel Tube

--i

From Eq. 4.9.1: @In = 0.85(80.2 + 29.2) = 93.0 kips

+ql+y) (,-L/i)‘] = 17.25 in.3 For V, = 85 kips, V, i0.85f’C b = 2.50 in. From Eq. 4.9.4: + q, W” = a + VJ(0.85f’,b)

= 0.9(17.25)(36) 4 + 2.50

= 86.0 kips Design Strength Summary: @V, (concrete) = 93.0 kips $V, (steel) = 86.0 kips Steel flexure controls. Since 41 Vn :, VU (i.e., 86.0 kips B 85.0), the design is adequate.

4.10 Connection Angles Angles used to support precast members can be designed by statics as shown in Fig. 4.10.1. in addition to the applied vertical and horizontal loads, the design should include all loads induced by restraint of relative movement between the precast 4-31

(b) Bolted With Gusset

(a) Bolted Without Gusset

(c) Welded

Note: 2 s 1 for all cases. I

Fig. 4.10.1 - Design Parameters for Connection Angles member and the supporting member. The minimum thickness of non-gusseted angles loaded in shear as shown in Fig. 4.10.2 can be determined by: (Eq. 4.10.1)

(See Table A-31 for values)

where: I) = 0.90 b = net length of the angle taking into account holes design e, o actual 8, + l/2 in. (Note: For welded angles (see Fig. 4.10.1 (c)), design e, may be taken as actual 8, - k) The tension on the boit can be calculated by: (Eq. 4.10.2)

r See Fig. 4.10.1

For angles loaded axially, Fig. 4.10.3 either in tension or compression, the minimum thickness of non-gusseted angles can be calculated by: (Eq. 4.10.3) (See Table A-32 for values) The tension on the boit can be calculated by: Surface of P r e c

C&-l a

s

t

Unit--j

Connection to the 1%fppo;ructure

Fig. 4.10.2 - Vertical Load on Angle

P” = N”(l + $)

(Eq. 4.10.4)

where: 6) = 0.90 g = gage of the angle (see Fig. 4.10.3) b P net length of the angle

I,-cl With e, = 2 - -6- =2- 2 =1.67in. 6

r See Fig. 4.10.1 /-Low-Friction Washer

6.00 kips

7 Vert. Slot 1 2 1125

Example 4.10.2 -Connection Angie Design for Horizontal Load Given: Surface of 1 Precast Unit-H Pu = NJ1 + g/e,)

I

Connection to the Support .Structure not Shown

Fig. 4.10.3 - Horizontal Load on Angle

(see Fig. 4.10.3) N, = 4 kips; g = 3 in.; f, = 36 ksi angle size = 5” x 4” x v-5” 5/8” bolt hole

Problem: Determine the angle thickness required.

Solution: b = 5 - 0.625 = 4.375 in.

Example 4.10.1 -Connection Angie Design for Vertical Load

From Eq. 4.10.3:

Given: (see Fig. 4.10.2) VU = 4 kips; e, = 2 in.; f, = 36 ksi angle size = 4” x 4” x w-4” 543” bolt hole, g = 2 in.

Problem: Determine the angle thickness required.

Solution: Design e, = 2 + 0.5 = 2.5 in. b = 4 - 0.625 = 3.375 in. From Eq. 4.10.1:

= 0.582 in.

Use L 5” x 4” x 518” From Table A-32; fort = 5/6 in., L,= 5 in., g = 3 in. oNn ZI 1055 lb/in. > 4w = 914, ok Tension in the bolts (From Eq. 4.10.4) with ei -2-t =1.67in:

P” = N”

(1 +$> =4(1 + l$&)=11.20kips

4.11 Welded Headed Studs use L 4” x 4” x 38” From Table A-31 ; for t = 5/8 in., e, = 2.5 in., I@/, = 1266 Jb/in of width > E5 =1185, ok Tension, P, in the bolts is calculated using Eq. 4.10.2:

Welded headed studs are designed to resist direct tension, shear or a combination of the two. Either the strength of the concrete or of the steel may be critical, and both must be checked. The design procedure given below and also used in the PCI Design Handbook(4) is based on Ref. 33 and is applicable to studs which are previously welded to steel plates or members and embedded in unconfined concrete. Confinement of the concrete, either

4-33

I

from ment due tions

applied compressive loads or from reinforceis known to increase the capacity however, to limited research, acceptable design equawhich include confinement are not available.

4.11 .l Tension The design tensile strength governed by concrete failure is: (PP, = 41 A&2.8 3L K)

of aconcrete member, Eq. 4.11.4 should be applied twice, once for each edgedistance. Table A-33 lists design tensile strength values. For a group of studs, the concrete failure surface may be along a truncated pyramid, as shown in Fig. 4.11.2 rather than separate shear cones.

(Eq. 4.11.1)

where: @ = 0.85 A,= areaoftheassumedfailuresurfacewhich, for a single stud not located near a free edge, is taken to be that of a45” truncated cone as shown in Fig. 4.11 .l

Fig. 4.11.2 - Truncated Failure

Pyramid

For this case, the design tensile strength is: #PC = G-& WA,,,, + 4AAat 1

Surface Area: A,=%l,(I,+d,)

Fig. 4.11.1 - Shear Cone Failure Using the45O cone area and o = 0.85, Eq. 4.11 .l may be written as: oPc = 10.72&l, + d,,) V+&

(Eq. 4.11.2)

Or, for simplicity, conservatively neglecting the diameter of the head: (PP, = 10.71** h fit

(Eq. 4.11.3)

For a stud located closer to a free edge than the embedment length, 1 e, the design tensile strength given by Eqs. 4.11 .l, 4.11.2 or 4.11.3 should be reduced by multiplying it with C,: C

*s

3 Ie

11.0

(Eq. 4.11.4)

where, de is the distance measured from the stud axis to the free edge. If a stud is located in the corner 4-34

(Eq. 4.11.5)

where: Aslope = area of the sloping sides A+,at = area of the flat bottom of the truncated pyramid For stud groups in thin members, the failure surface may penetrate the thickness of the member as shown in Fig. 4.11.3. This type of failure is likely when the thickness of the member is less than a certain minimum thickness, h,i,, given in Fig. 4.11.4 and tabulated inTable A-34 in Appendix A. The pullout strength corresponding to h c h,i, is then based on area of the sloping sides only. Nominal pull-out strengths for both conditions (i.e., h 2. h,i, and h c h,,,J for different edge vicinity cases aregiven in Fig. 4.11.4. The values obtained fromFig.4.11.4equationsshould becomparedwith the sum of the strengths based on separate cone failures and the lesser of the two used for design. Figure A-3 in Appendix A can be used to calculate design strength values for the six cases in Fig. 4.11.4 corresponding to both h 2 h,i, and h c h,,,i, conditions. The design tensile strength per stud as governed by steel failure’ is: 1 The minimum tensile strength of steel for studs, f, is typically 60,000 psi. The yield strength in tension may be taken at 0.9 f, and the yield strength in shear may be taken at 0.75 f,.

Section A-A

Fig. 4.11.3 - Pull-out Surface Areas for Stud Groups in Thin Sections +Ps = $A& = A,(O.gf,) = 54,000 A, (Eq. 4.11.6) where: 4 = 1.0 f, = 60,000 psi Table A-33 lists the design strength values from the above equation. 4.11.2 Shear The design strength governed by concrete failure should be taken as lesser of the values given by the following equations: $V, = +800A, hflc, if d, 2 1 Od,

2. Strength based on the d, of the weakest row of studs times the number of rows, and 3. Strength based on the d, of the row of studs farthest from the free edge. (Note: The above conditions were developed by consensus within the PC/ Committee on Connection Details due to lack of research data. Currently, research under two PCI Fellowships is being carried out. The results of these studies may suggest changes in this recommendation and other aspects of concrete based design strength calculations.) The design shear strength per stud as governed by steel failure’ is:

(Eq. 4.11.7) +V, I cp%fY = A&0.75f,) = 45,00OA,

rjN,=~2zd,*Xfl~, ifd,
(Eq. 4.11.9)

where: 4 = 1.0 The design strength values determined from Eq. 4.11.9 are listed in Table A-35. 4.11.3 The tension action

Combined Shear and Tension design strength for studs under combined and shear should satisfy the following interequations:

Concrete: l-[(!Ly+(xL)‘]

11.0 (Eq. 4.11 .lO) 4-35

Case 1:

Not Near a Free Edge’

h 2 h,,,,“*

i$ P, * q 4 n-q (x + 21,) (y + 2tJ

h < hnl,”

~P,I~~~~~[(x+~~,)(~+~Z,)-A,~I

Case 2:

Free Edge on One Side

t) P, I I$ 4 1% (x + 1, + d,,) (y + 21,)

h ’ hmin

4~ P, - Q 4 “q [(x +l, + de,) (Y + 21,)

h < hinin

Case 3:

- A, 1

Free Edges on 2 Opposite Sides

3 01bx4ci 02 I-h ’ hrnin

h < hnll”

@ f’, - Q, 4 Aflc (x +d,, + d,J (Y + 2V + P, - cp 4 nGc W +d,, + d,J (Y + 21,) - A, I

1 Near a free edge implies d, < t,. 2 hmin = (t + 2&)/2, where t is lesser of x and y (see fable A-34) 3 AR e (x c 25 - 2h)(y + 2$ - 2h)

Fig. 4.11.4 - Design Tension Strength of Stud Groups

4-36

4

t-x-4 I d 02 d 81

Fig. 4-l 1.4 - Design tension Strength of Stud Groups (C

where: t$ = 0.85

d, > $, d, = 6 in., d, > $ Thus effects of vicinity to two edges apply (Case 4 in Fig. 4.11.4).

Steel:

t[(%,‘+(%J] yfq 4,, ,,) . . .

where: I$ El.0 P, and Vu are the factored tension and shear loads. 4.11.4 Plate Thickness Thickness of plates to which studs are attached should be at least 2/3 of the diameter of the stud. Bending in plates anchored with headed studs should also be investigated whenever moments are induced in them.

Example 4.11 .l - Tension strength of a stud group Given: A base plate with four headed studs embedded in corner of a foundation slab.

1

4”

2. Check for member thickness (see Fig. 4.11.4 or Table A-34): h & = (2 + 21,)/2 where z is lesser of x and y h,i, = [8 + 2(8)]/2 = 12 in. (Note: Same result can be read from Table A-34.) Since h (= 10 in.) c hmin, failure surface is likely to penetrate through the slab. 3 . Calculate tension strength based on concrete for the studs as a group: (Note: For this purpose, Equation in Fig. 4.11.4 (Case 4, h c h,,J or Fig. A-3 in Appendix A may be used. The latter is illustrated here.) With reference to Fig. A-3 (p. A-30): k, = (x + d,, + de21 = (16+4~8)=28 (Note:d,,>I,,thus d e2 = l, = 8 in.) (Y + d,, + de4) = (8 + 6 + 8) = 22 (Note: de4 > Z,, thus

kz? =

t- 16”,---

d 84 = Z, = 8 in.) k’, = (x + 21e - 2h) = 116 + 2(8) - 2(10)] = 12 k; = (y + 2Z8 - 2h) = [8 + 2(8) - 2(10)] = 4 I

2

I I

(4)-3/4 in. diam. headed studs embedment, Ze = 8 in. slab thickness, h = 10 in. “c = 4000 psi (normal weight) Problem: Determine the tension (pull-out) strength of the stud group. Solution: 1. Check for edge effect: For the given problem (see Fig. 4.11.4): x = 16 in., y = 8 in., d,, = 4 in., 4-38

From Fig. A-3, for k, = 28, 4 122, h = 1 .O, and r, = 4000 psi:

+pc,

= 138 kips

and for k’, = 12, k; = 4, h = 1 .O, and fpc = 4000 psi:

@PC2

= 18 kips

Thus, oPc = $Pc, - eP& = 138 - 18 = 120 kips 4. Checksum of individual stud concrete failure capacities: For no edge effect, stud capacity is obtained from Eq. 4.11.2, or Table A-33. Using Eq. 4.11.2:

opt

= 10.7 Z& + d,,) Xpc

where: d, = diameter of stud head = 1.25 in. 10.7(8)(8 + 1.25)(l) v4000 /lOOO = 50.0 kips

w, =

Adjusting for edge Stud 1: $P, = Stud 2: #PC = Stud 3: i$P, = Stud 4: @P, =

effects (Eq. 4.11.4): 50.0(4/8)(6/8) = 9.8 kips 50.0(6/8) = 37.5 kips 50.0(4/8) = 25.0 kips 50.0 kips

Thus, total capacity is: @PC = (9.8 + 37.5 + 50.0 + 25.0) = 122.3 kips > 120; stud group failure is more likely.

Section A-A

5. Check capacity based on steel failure: From Table A-33, for 3/4 in. diam. stud: 4q = 23.9 kips/ stud

(lO)- 1/2"4l

Studs

Total $Ps = 4(23.9) = 95.6 kips < 120

Thus the tension strength of the group = 95.6 kips

Example 4.11.2 - Shear strength of a stud group

Given:

A plate with studs embedded in a column subjected to shear.

“c = 5000 psi (normal weight),

h = 1 .O = 60,000 psi fs (10)-l/2” diameter studs, A, = 0.20 sq. in./stud, 10d = 5.0 in.

Problem:

Determine the shear strength of the group.

Solution:

ForRowl,d,=3”<10d=5”, useEq.4.11.8: $Vc = i$2 xd,* lific = 0.85(2)(3.14)(3*)(1~/1000 = 3.40 kips/stud

Section B-B For Row 2, d, = 6”> 10d = 5, use Eq. 4.11.7: f$vc = $800A, n?(vc = 0.85(800)(0.2)(l)+%% /lOOO = 9.62 kips/stud useEq.4.11.7: For Row 3, d, =9”>lOd=5, @I, = ct, 800A, Xc = 9.62 kips/stud Maximum capacity of the group (based on concrete): 1. Strength of the weakest stud times no. of studs: QVc = 3.4(10) = 34.0 kips 2. Strength of the weakest row times no. of rows: $V, = 3.4(4)(3) = 40.8 kips, or +V, = 9.62(2)(3) = 57.7 kips 3. Strength of the row of studs farthest from free edge: eVc = 9.62(4) = 38.5 kips

4-39

Condition (1) controls concrete strength, (pV, = 34.0 kips

Vu = 75 k, N, = 12 k (all load factors included) column size 16 in. x i 6 in.

Check steel strength, use Eq. 4.11.9: oVs = (0.75f,AJ = (0.75)(60)(0.2) = 9.0 kips/stud

Problem: Determine if the studs are adequate for the connection.

For 10 studs: oVs = 1 O(90.0)

Solution: = 90.0 kips

The plate studs shear capacity by the concrete strength: QV” = 34.0 klps

Is governed

Example 4.11.3 - Design of headed studs for combined loads Given: A plate with headed studs for attachment of a steel bracket to a column as shown in the figure. Assumed railure Surface

t--'6"l

\ -F---i

l--+-T-

1. Strength based on concrete: a. Tension (group of top six studs) (1) Strength based on individual cones (Eq. 4.11.2 and 4.11.4): 0 PC = 10.71,( Ze + d,,) h qc (d&J = 10.7(6)(6 + 1.25)($5)(5/6) = 27.4 k/stud (Alternately, the value may be obtained from Table A-33) For six studs: oP, = 6(27.4) = 164.4 kips (2) Strength based on truncated pyramid failure (Fig. 4.11.4): hmi, = (3 + 2(6))/2 = 7.5 in. < 16 Use Case 3 in Fig. 4.11.4 corresponding to h > hmi,. 4q = $4 X q (x + d,, + d,,Ny + 2!J ?a 0.85(4)(1 .O)N5000 )(6 + 5 + 5) (3 + 2(6))

= 57.7 kips or, P, = 57.710.85 = 67.9 kips

l- 518” Studs

(3) Required tension strength, P, for group of top six studs: Direct tension, N, = 12 kips Tension due to moment: MU = 75(6) = 450 k-in. >T,(j”d) = TJd - (a/2)] = 450 T,d -

T”

0 . 8 5 flcb(2)

= 450

T2 Tu (“*‘) - 0.85(5;(10)(2)=

T” “c =

5000 psi (normal weight), h = 1 .O (12)- 5/8 in. diam. studs; %/stud = 0.307 sq. in. 4 = 6 in. d, = 1.25 in. fs = 60,000 psi 4-40

450

= 42.9 kips

Therefore, P, = T, + N, = 42.9 + 12.0 = 54.9 kips b. Shear (all 12 studs) From Eq. 4.11.7 (de > 1 Od): 4% = 0.85(800)(0.307)m)I1000 = 14.7 k/stud

(same value is obtained from Table A-35 ford, 2 9 in.) For the 12 studs: I@/, = 12(14.7) = 176.4 kips or, V, = 176.410.85 = 207.6 kips

(a) Shear and Torsion

c. Combined tension and shear Using Eq. 4.11.10: $[(?):(+)‘I

s1.0

(b) Torslon

& [(~S+(&ji-j”] = 0.92
(c) Shear and Bendlng

Fig. 4.12.1 - Eccentric Loads on Weld Groups

c. Combined tension and shear Using Eq. 4.11 .l 1: ast into Column

&i [(E>: <%>‘3 I 0.51 < 1 .O ok

Thus the connection Is adequate. 4.12 Weld Groups

Welds in groups are more efficient than line welds in resisting bending and torsional moments produced by eccentric loads. Examples of this type of loading are shown in Fig. 4.12.1. Design of weld groups may be done as given below with nomenclature shown in Fig. 4.12.2. The combined shear and torsion stresses in horizontal and vertical directions are given by Eqs. 4.12.1 and 4.12.2 respectively:

Fig. 4.12.2 - Welded Bracket Connection 4-41

(Eq. 4.12.1)

n

Embedded Plates

(Eq. 4.12.2)

The resultant stress on weld is given by:

f, =qlpqF

(Eq. 4.12.3)

where: P, = applied force in x direction P, = applied force in y direction Y = vertical distance from c.g. of weld group to point under investigation = horizontal distance from c.g. of weld group X to point under investigation I,v = polar moment of inertia = I, -I. I, = I: I,, + cAj* + c l,, + cAwy2 (Eq. 4.12.4) M, = torsional moment = P,eY + Pyex t, = effective throat thickness of weld A,= area of weld = weld length x t, w,, = moment of inertia of weld segment with respect to its own axes For computing nominal stresses, the locationsof the lines of weld are defined by edges along which the fillets are placed, rather than to the center of the effective throat. This makes negligible difference, since the throat dimension is usually small. By treating the welds as lines with t,,, = 1, the physical properties of weld groups are simplified. The most commonly occurring weld groups are listed in Table A-36 along with their section moduli and polar moments of inertia. The equations given above are for elastic section properties, which is inconsistent but conservative when used with factored loads and design strength of weld material. The plastic section propertiesoftheweldgroupcan becalculatedor, if a less conservative solution is acceptable, the properties may be derived from the appropriate “shape factor’ from Table A36. Methods given in Ref. 32 may also be used. Example

4.12.1 - Design of a weld group

Given: Corner angle connection as shown Angle size = 4” x 4” x l/2” x l’-2” 4-42

Connection Angle 1

F, = 36 ksi, E70 electrodes Factored load, VU = P, = 49.8 kips Problem: Determine required weld size. Solution: Find c.g. of weld group: ‘jl=:

2(2)(1)

+

14to)

14+2(2)

= 0

22

in

*

*

by symmetry, ‘jT = 7 in. A,= [2(2) + 141 t,,, = 18 t, Polar moment of inertia (Eq. 4.12.4): IP

= Cl,, + XAj 2 + Cl,, + wl,Y’ =2[tJ2)3/1 2 + 2tw(0.78)2

+ 2(tJ3/1 2 + 2(t,J7)2]

+ t,( 14)3/1 2 + 1 4(t,J3/1 2 + 1 4(t,J(0.22)2 = 429.j t, + 1 .50(tw)3 Since second term is small, it may be neglected. Alternatively, using Table A - 36, case 5: b = 2 in., d = 14 in. x = b2/(2b + d) = 4(4 +14) = 0.22 in. For f- 1.0: I, = 8b3 + f;bd2 + d3 b4 2b +d

24 = 8(2)3 + 6(2)(14)* + l43 _ 12 2(2) + 1 4 = 429.1 in4/in e = 1 + 4 - 0.22 = 4.78 in. ir = P e = 49.8(4.78) = 238 in-kips X = 2y- 6.22 = 1.78

where: 0 = 0.90 xc, b from Fig. 4.13.1 fY = yield strength of the base plate CF=greatest sum of anchor bolt factored forces on one side of the column If the analysis indicates the anchor bolts on one or both sides of the column are in tension, the base plate thickness is determined from:

From Eq. 4.12.2:

fY +! +!)f P

W

= 49.8/l 8t, + 238( 1.78)/429.1 (t,,,) = 2.77/t,,, + 0.99/t, = 3.76/t,

fx ++!p

Under loads which occur at service, the base plate thickness may be controlled by bearing on the concrete or grout. In this case, the base plate thickness is determined from:

P

= 0 + 238(7)/429.1(L)

(Eq. 4.13.2)

where: x, from Fig. 4.13.1

From Eq. 4.12.1:

W

t =

=3.88/t,

From Eq. 4.12.3: f , = ‘/(fx)* + (f,)* = ‘/(3.88&J* + (3.76/t,)* = 5.40/t, or t, = 5.401 f, From Table A-l 3: design strength of E70 weld = 35 ksi = 5.40/35 = 0.154 in. tW For a 45O fillet weld: leg size = 0.154/0.707

= 0.218 in.

Use l/4 in. fillet weld (E70 electrode) 4.13 Column Base Plates Column bases must be designed for both erection loads and loads which occur in service; the former often are more critical. Several examples of column to foundation connections are included in Chapter 5 (Sect. 5.2.1). Two commonly used base plate details are shown in Fig. 4.13.1 although other details are also frequently used. When all the anchor bolts are in compression (typically the case under erection loads prior to placement of the grout under the plate), the base plate thickness required for bending can be determined from: t =:

(Eq. 4.13.1)

(Eq. 4.13.3) where: x, from Fig. 4.13.1 f bu = bearing stress on concrete or grout under factored loads I$ (0.85 f’J, where o = 0.7. See ACI 318-83(6) -- Sect. 10.15. Table A-37 may be used for base plate design. Nominal base plate shearing stresses should not exceed 0.55 fy. The anchor bolt diameter is determined by tension or compression on the area of the threaded portion of the bolt. Anchor bolts may be either ASTM A307 bolts or threaded rods of ASTM A36 steel. In most cases, both base plate and anchor bolt stresses can be significantly reduced by using properly placed shims during erection. When the bolts are near a free edge, as in a pier or wall, the buckling of the bolts before grouting may be aconsideration. Confinement reinforcement, as shown in Fig. 4.13.1, should be provided in such cases. A minimum of 4 No. 3 ties at about 3 in. on centers is recommended for confinement. The in-place tension strength of the bolt should be taken as the lesser of the strengths calculated based on concrete failure and steel failure (typically yield). The calculation of concrete based strength

4-43

2” Min. Grout Space

(a) Oversized Base Plate

2” Min.

I-----l

(b) Flush Base Plate

Fig. 4.13.1 - Column Base Connections

4-44

’

will depend upon the type of anchor bolt used. F o r anchor bolts with headMasher of adequate stiffness, similar to headed studs, the strength can be determined by assuming a shear cone pull-out failure described in Sect. 4.11. Otherwise, and for hooked anchor bolts, the strength should be determined by adding the bond resistance of the bolt shank and the bearing resistance of the bolt head or the hook. If necessary, the bearing area of the bolt head can be increased by welding a washer or steel plate. Nominal bond stress on smooth anchor bolts should not exceed 250 psi. The confined bearing stress on the hook or bolt head should not exceed cp (0.85 f’,) q as per ACI 318-83(6) -- Sect. 10.15. Typically,$@, will be larger than 2.0 in such cases, thus the limiting value for design bearing strength of 0.7(0.85 f’J x 2.0 = 1.2 P, may be used. The bottom of the bolt should be a minimum of 4 in. above the bottom of the footing, and also above the footing reinforcement.

Solution: From Eq. 4.13.1: = 1.24 in.

t

Use Rl-114” x 16” x 16” Note: Compression on anchor bolts during erection can be substantially reduced by the use of steel shims. The required area of the shims can be determined by the concrete allowable bearing stress.

Example 4.13.2 - Column base plate - anchorbolts in tension Glven: A 16 in. square column as shown. 16" x 16" Column

Example 4.13.1 - Column base plate - anchor bolts in compression

T

Given: A 16 in. square column as shown.

Total tension on one side of column, XF = 50 kips. f’,=4ksi, b=l6in., x,=3in. 1, = 36 ksi (bolt and base plate) Allowable bond stress on bolt, f, = 250 psi P, = 200 kips Compression on one side of column, ZF = 100 kips b=16in.,x,=2in.,fY=36ksi Problem: Determine the required base plate thickness, 1.

Problem: Determine the following: 1. Required base plate thickness, t 2. Size (diameter) of anchor bolts, D 3. Embedment length of bolt, c 4-45

P, = 400 kips “c = 5 ksi (concrete or grout) fY = 36 ksi, x, = 4 in.

I.

t =dT =dx =l.O8in. Use RI-l@ x 16” x 16” 2. t/bolt = 50/2 = 25 kips From Table A-22, select l-114 in. diameter A-36 rod @T, = o(34.88) = 0.9(34.88) = 31.4 kips @ threads > 25, ok 3. Hook bearing capacity, $T,,r= (dia.)(length)( 1.2f’J =I (1.25)(4)(1.2 x 4) = 24.0 kips Remaining capacity to be developed by bond. +Tb = +$ - 4$ x 31.4 - 24.0 = 7.4 kips Using a bond stress, f,, of 250 psi, T,/in. = f,(x)(dia.) = 0.25(3.14)(1.25) = 0.98 k/in $T,/in. = 0.7(0.98) = 0.69 k/in Embedment length, Ze = oT,,/($T,/in.) = 7.4/0.69 = 10.7 in. Use 1’ - 0” embedment Example 4.13,3 - Column base plate - bearing on concrete or grout Given: A 16 in. square column as shown. Yl6”x 16” Column

4-46

Problem: Determine the required base plate thickness, t. Solution: f

b”

P = u s2s = 0.694 ksi A Plate

(fbu)rnax

= +(0.85 “J = 0.7(0.85 x 5) = 2.98 ksi > 0.694, ok

From Eq. 4.13.3:

UseRl**x24”x24”

4.14 Moment-Resisting Connections When lateral stability of precast, prestressed concrete buildings is achieved by frame action or by a combination of shear wall and frame action, the connections to develop frame action must be designed for appropriate moment transfer capability. The tension force for the moment resistance within a connection can be provided by properly anchored headed studs, deformed bar anchors, orothertypes of inserts. Post-tensioning can also be used to develop moment resistance at joints between interconnected members. Where a high degree of moment resistance and ductility are required, compos‘ite construction is frequently used to achieve connections that are similar to monolithic joints in their behavior. Several examples of connections with varying potentials of moment resistance are included in Chapt. 5. The composite connections are shown in Sect. 5.2.3.3and the post-tensioned connections in Sect. 5.2.3.4. Achieving “fully rigid” connections can be costly. In most cases, it may not even be desirable to buildin a high degree of fixity, since the restraint of volume changes could result in large forces in the connections and the members. It is therefore preferable that the design of moment-resisting connections be based on the concept of “partial fixity”, wherein the desired moment resistance is achieved

with some deformation/rotation at the connection. The deformation should be controlled to provide for the desired ductility. While the moment-curvature analysis of precast and prestressed concrete members is readily done based on established analytical methods, connections generally require testing for their behavior. Recently completed PCI Funded Research (7) and other previous research (49), as well as considerable research in progress, are expected to lead to adequate knowledge base on moment-resisting connections and enable formulation of rational analytical procedures. In this section, a scheme is proposed and illustrated which may be used to assess the moment resistance and curvature of partially fixed connections. While the scheme is given with reference to a beam-column connection, the methodology is general and may be used for other types of connections: With reference to Fig. 4.14.1 (the numerical values in Fig. 4.14.1 pertain to Example 4.14.1): 1. Draw moment-curvaturediagramforthe beam

60.0 ,

I

with varying levels of end fixity including the limiting conditions of “full fixity - zero rotation” and “zero fixity - maximum possible rotation”. 2. Select a connection scheme and draw moment-curvature diagram of the connection. 3. Obtain the allowable moment capacity of the connection and the corresponding end rotation by reading coordinates of the point of intersection of the two curves obtained in steps 1 and 2. 4. The allowable moment capacity obtained in step 3 must exceed the actual connection moment calculated from frame analysis, but must be less than the beam-end moment strength. This check should be made for both the service load and the factored load states. 5. The end rotation values corresponding to the allowable moments should be used in assessing the connection ductility. The above scheme is used in Example 4.14.1 related to a beam-column connection.

I

0:001

I 0:002 0.00182

I

I 0:003 0.0028

I

01004

END ROTATION (rad)

Fig. 4.14.1 -

Moment-Rotation

Diagrams

(The Numerical Values Shown are for Example 4.14.1)

4-47

Solution: M = w&l2 where, w = D + L = 0.5 + 1.5 =2kKt = 2( 14)2/l 2 = 32.67 k-ft

Example 4.14.1 - Beam-column moment connection Given: 8RB16 Beam clear span,Z = 14 ft. 16 in. square Column “C = 5000 psi (normal weight) Reinforcement, f, = 60 ksi E, = 4.3 x 1 O3 ksl; E, = 29.5 x lo3 ksi D= 0.5 Wft, Applied service loads: L=lSWft

MU= ~$12 where, w, = 1.40 + 1.7L = 1.4(0.5) + 1.7(1*5) = 3.25 Wft = 3.25( 1 4)2/12 = 53.08 k-ft Design moment strength based on yield strength of top bars, e”” = $ P,f,d) = 0.9(2 x 0.44)(60)(14)/l 2 = 55.44 k-ft

Problem: Determine moment capacity of the beam-column connection shown in the figure.

Grout

Pocket-\

I

Determine end rotation, 0, @ + M, = 55.44 k-ft 8 = (A H)/d = [(f,lE,)(Z )] /d where: A H = elongation of the top bars at yield. Assuming fixity of bars at column center line, 1 =8+0.5+4=12.5in. 9 = 60(12.5)/(29.5 x lo3 x 14) = 0.00182 rad.

L-l’

Note: In the above calculation, it is assumed that the beam will rotate about the bottom weld. In reality, the location of pivot point will depend on the relative stiffness of connecting parts.

I 6"x 16"~ 14'-0"

Maximum beam end rotation, 9, assuming zero fixity is: 13, = wl 3/24E,l where: w = 2.0 wft I = pd3/1 2 = 8( 1 6)3/l 2 = 2 7 3 1 in4

0,

= 2(14)(14 x 12)2/(24x = 0.0028 radians

4.3 x lo3 x 2731)

Plot “gM, vs 9” curve (connection), and “M vs 8” and “M, vs 0” curves (beam) - see Fig. 4.14.1 Calculate allowable service and ultimate moments for the connection: 0.0028 = 23.62 k-ft 0 00182 ( 55.44 +32.67 o*oo28 > 23.62 k-ft c 32.67 k-ft, ok M(allow)=

. ,.,,,’ .. . . . I 4-48

Mu (allow) =

0.0028 ( O.OO1 55.4482

foilows(Fig. 4.15.2(b)): 1. The cantilevered bar is usually proportioned so that the interior reaction from the concrete is 0.33 VU. The hanger strap should then be proportioned to yield under a tension of 1.33 VU.

= 32.76 k-ft

+53.08 0.0028 >

32.76 k-ft < 53.08 k-ft, ok Note: The rotations corresponding to the above moments can be readily determined and adjustments can be made to ensure desired design ductility.

As

1.33v =u +‘Y

(Eq. 4.15.1)

where: Design welds: Top: To ensure ductility, design weld to develop the strength of a #6 Grade 60 reinforcing bar.

fY = yield strength of the strap material t$ = 0.90 2. VU may be assumed to be applied 0.5 in. from the face of the seat. The remaining part of the moment arm is the width of the joint, g. It is therefore important that the joint width used in analysis is not exceeded in the field.

From Table A-17, minimum length required for E70 electrode is 2 l/2 in. for angle leg thickness of 5/16 in. or larger. Bottom: C, = MU/d = 55.44(12)/l

4 = 47.52 kips

I

From Table A-14, the design strength of l/4 in. fillet weld is 6.19 k/in. Weld length required, & = C, /strength = 47.526.19 = 7.67 in.

where: fY = yield strength of the bar material @ = 0.90 Other notation is shown in Fig. 4.15.2(b)

Notes: a. It is desirable to have the top and bottom welds in the same vertical plane to minimize shear forces on top anchorages, thus minimizing the possibility of theirpremature yielding in flexure. b. If there is transfer of moment through the column, it will cause shear in the connection. The connection then must be designed for both tension and shear.

If the bar is proportioned to carry this moment at the yield stress, but using elastic section properties, the shear and tensile forces can usually be neglected. 4. The bearing pressure creating the interior reaction may be calculated as in Sect. 4.5. If the width of the member in which the hanger is cast = b,, then: I

4.15 Hanger Connections Hangers are similar to dapped ends, except that the extended or bearing end is steel instead of concrete. They are used when it is desired to keep the structural framing depth small. Four examples of hanger connections are included in Chapter 5, and are reproduced in Fig. 4.15.1 for convenience of reference.

4.15.1 Cazaly Hanger(50) The Cazaly hanger has three basic components (Fig. 4.15.2(a)). Design assumptions are as

3. The moment in the cantilevered bar is then given by: MU = V&O.5 + g + 0.375s) (Eq. 4.152) I $fybd2/6

f ,,” = $0.85 Q&i6

(Eq. 4.15.3)

where: 4 = 0.7 The bearing length, &, is then given by: v t3

b =b$-bu

(Eq. 4.15.4)

The exterior cantilever should have a minimum length of (g + 1) in. Most hangers in practice have cantilever lengths of 2 l/2 to 3 l/2 in.

4-49

GC17

GC18

BG3

SB7 Fig. 4.151

Cantilever

- Hanger Connections

Cantilever Bar

Bar

(a) Basic Components

(b) Design Assumptions

Fig. 4.152 - Cazaly Hanger 4-50

5. To maintain the conditions of equilibrium assumed, the interior cantilever must have a length: 2 = (1.5 + 3g + s + 0.5$ ) in. 6. The minimum total length of bar is then: Z,,,i, = (2.5 + 4g + 2s + 0.5&) in. (Eq. 4.155) 7. Longitudinal dowels, A,, are welded to the cantilevered bar to transmit the axial force, N,: (Eq. 4.15.6) where: fy = yield strength of the dowel (I = 0.90

Design weld, strap to cantilever bar: From Table A-14 for E70 electrode, design strength for 3/l 6 in. weld is 4.64 k/in 1 .33vu I 3.44 ii. I, = S(d esign strength) al.330 2(4.64) Weld 2 In. across top 3/4 In. down sides, Weld length = 3.5 in. By Eq. 4.15.2: Mu = Vu(0.5 + g + 0.375s) = 24(0.5 + 1 + 0.375(2)) = 54 k-in z

MU wd. =

8. The lower dowel, A,,, and the area confined within the strap can be conservatively proportioned using shear-friction described in Sect. 2.7: (Eq. 4.15.7) where: @ = 0.85 fY = yield strength of lower dowels, psi h?= 1000 ”1 bh u I value in Table 2.7.1 (Eq. 4.15.8) U

Example

4.15.1 - Design of a Cazaly Hanger

Given: Hanger similar to that shown in Fig. 4.15.1 fSB7) “c = 5000 psi (both member and support) fy (reinforcing bars) = 60 ksi f, (structural steel) = 36 ksi VU = 24 kips; N, = 4 kips b, = 6 in., g = 1 in. (see Fig. 4.15.2) Problem: Size the hanger components. Solution: Determine area of strap (Eq. 4.15.1): 1.33v = ‘.33(24)= 0.99 in2. A, (strap) = U ef 0.9(36) Y

54 =1.67in3 =.b$!

c =

Try 2 in. wide bar: d =dv = 2.24in. Use 2 x 2 114 in. bar By Eqs. 4.15.3 and 4.154: fbu - -1$O.S5f’~v= (0.7)0.85(5)

%$= 5.15 ksi

2413 = 0.78 in. =2(5.15)

JU I3 k

b fbu Min. interior cantilever length =1.5+3g+s+o.52, = 1.5 + 3(l) + 2 + 0.78/2 = 6.89 in. Min. total length (Eq. 4.15.5) =2.5+4g+2s+o.51, = 2.5 +4(l) + 2(2) + 0.5(0.78) = 10.89 in. Use bar 2 x 2 l/4 x 12 in. By Eq. 4.15.6: N

AlI ‘“‘&c) 4t

= 0.07 sq. in.

Use 1 - #3 dowel; provides 0.11 sq. in. From Table A-l 2: 1.7 Zd = 15 in. Try h = 16 in.; by Eqs. 4.15.7 and 4.158: k3=

1000 h bh u JOOO(1)(2)(16)(1.4~ v 24,000 U

= 1.87 < 3.4, ok A, r\/U,

j Use l/4 x 2 in. strap; A, = 0.25(2)(2) = 1.00 in2

0.9(36)

0

‘y

&3

24 = 0.25 sq. in. 0.85(60)( 1.87)

4-51

Use 1 - #5 dowel; A, = 0.31 sq. in. Alsocheckdowelwelding A-l 7.

(Eq. 4.15.10)

requirementsperTable where: I$ = 0.90 f* = yield strength of A,

4.152 Loov Hanger(51) The hanger illustrated in Fig. 4.15.3 is designed using the following equations: (Eq. 4.15.9) where: I) = 0.85 fY = yield strength of As,,

The steel bar is proportioned so that the bearing strength of the concrete is not exceeded and to provide sufficient weld length to develop the diagonal bars. Bearing strength is discussed in Sect. 4.5. However, if the bar is at the top of the member as in Fig. 4.153, there is no “geometrically similar” area larger than the edge of the bar, and with o = 0.7: f, P o 0.85 f’C = 0.6 f’C

7 Steel Bar

(a) Basic Components

,tana+N,

(b) Design Assumptions

Fig. 4.15.3 - Loov Hanger

4-52

(h d-al2

(Eq. 4.15.11)

The connection should be detailed so that the reaction, the center of compression and the center of the diagonal bars meet at a common point, as shown in Fig. 4.15.3(b). The compressive force, C, is assumed to act at a distance a/2 from the top of the bearing plate. Thus: (Eq. 4.1512)

By Eq. 4.15.11: f bu = 0.6 f’c = 0.6(5)= 3.0 ksi C = V,,tan a = 24 tan 30” = 13.9 kips Assume b, = 1 in. a = & = 13.9 = 4.66 in. l(2.98) al2 = 2.33 in.

where:

Min. weld length, #5 bar, E70 electrode (Table A17) = 2-l/4 in. Use 2-l/2 in.

C =V,tana+

t(ha;z) -

(Eq. 4.1513)

For most designs, the horizontal bars, A,, are placed very close to the bottom of the steel bar. Thus, the term (h - d) can be assumed equal to zero, simplifying Eqs. 4.1510 and 4.1513. Tests have indicated a weakness in shear in the vicinity of the hangers, so it is recommended that stirrups in the beam end be designed to carry the total shear.

Provide end bearing plate as shown below.

2”x5”xl”

\

R

---

Example 4.152 - Design of a Loov Hanger Glven: Hanger similar to that shown in Fig. 4.153. Design for the same data as in Example 4.15.1 a = 30”. Problem: Size the hanger components.

End of Member

Solution: By Eq. 4.15.9: A

Vu 2 sh = $f,coSo? = 0.65(6Oy!ios 30” = 0.54 sq. in.

Use 2 -#5 bars, A,, = 0.62 sq. in. Detail A, so it is near the bottom of the steel bar i.e., h - d = 0 By Eq. 4.1510:

A, +A y

0.9(60)

= 0.07 sq. in.

Use l- #3 dowel, A, = 0.11 sq. in.

4:16 Connection of Load Bearing Wall Panels Connections for load bearing wall panels are an integral part of the structural support system: care in their design is essential in ensuring the overall stability of the structure. In addition to the weight of the panels, the connections must resist and transfer dead, live, wind and earthquake loads, and effects of volume changes. Erected load bearing walls may have both horizontal and/or vertical joints across which forces must be transferred. Fig. 4.16.1 indicates, for separate cases, the principal exterior forces and the resulting joint forces. In buildings, all forces and various combinations of panel and joint assemblies must be considered.

4-53

Distribution of lateral forces to shear walls depends largely on adequate connections of floors to walls. In addition to the transfer of vertical shear forces due to lateral loads, vertical joints may also be subject to shear forces induced by differential loads on adjacent panels. Joint and connection details of exterior bearing walls are specially critical since the floor elements are usually connected at this elevation and a waterproofing detail must be incorporated. 4.16.1 Vertical Joints Vertical joints may be designed so that the wall panels form one structural unit, or act independently. 4.16.1.1 Hinge Connection A hinge connection transfers compression and tension forces but not moments. This is usually done at floor levelsthroughfloordiaphragms and tie beams. The joint between floor levels usually is “open” so the panels resist lateral loads independently according to their relative rigidity (Fig. 4.16.2).

Sound and waterproofing details may also have to be considered. 4.16.1.2 Grooved Joint Connection Grooved joints are continuous and usually filled with grout. The minimum groove dimension should be 1 l/2 in. deep and 3 in. wide (Fig. 4.16.3). The joint strength can be evaluated by shear-friction even if shrinkage, creep, and temperature movements have caused a crack at the wall-grout interface. 4.16.1.3 Mechanical Connection Mechanical connections consist of anchorage devices cast into the wall panels and steel sections (plates, angles, bars, etc.) crossing the joint. The strength is usually controlled by the capacity of the cast-in anchorage (Fig. 4.16.4); connection of the steel section to the anchorage device can be made by bolting, welding, or grouting. Tie beam connections at floor levels may patticipate with the mechanical connections. The relative participation in resisting applied forces depends on

Vertical Shear at Vertical Joint 0 I V” I Vrigid

Reaction at Horizontal Joint ‘v = “ r i g i d

(a) Lateral Loads in Plane of Walls

Fig. 4.16.1

(b) Lateral Loads out of Plane of Walls

(c)

Differential Loads

- Exterior Forces and Joint Force Systems

Gravity

(a) Angle-Bolt

(b) Plate-Bolt

Fig. 4.16.2 - Wall to Wall Hinge Connections at Floor Levels (c) Thru-Bolt

t-(hi”., 1

.---” w--w- -----“~yLT- --= :‘,I

0’1

t

-----.-A-/L.---,,,’ - ----,s-----. -.t-

(d) Direct Welding

Y m--w--. -m----v, 4 7 ~.#z~~= TV= v --------. se- - ---. ”h

Fig. 4.16.3 - Grooved Joint Connections

-

their force-deformation characteristics. The ultimate capacity is the sum of the strength of the tie beams and the mechanical connections. Once the connection forces have been established, evaluation of connection strength is made using appropriate strength of the materials and the principles developed in other sections of this Manual. 4.16.1.4 Keyed Joint Connection Keyed joints can either be reinforced or nonrein-

(e) Welding with Make-up Pieces

Fig. 4.16.4 - Mechanical Connections forced (Fig. 4.16.5). Test results indicate substantially similar load-deformation behavior, but also show that the reinforced joints are stronger and possess higher ductility. Reinforcement is required in high seismic zones. As shown in Fig. 4.16.6, the resistance of a keyed joint can be limited by: (a) cracking of grout parallel to joint, (b) diagonal cracks across joints, (c) crushing of key edges or joint concrete at key edges, or (d) slippage along contact area. 4-55

J>R

J< R

Fig. 4.16.5 - Keyed Joint Connections

For (a) the shear-friction concept applies (Sect. 2.7). For (b),(c) and (d), the strength of the connection is usually a function of the compressive strength of the grout, the bond strength of the grout to the precast concrete, and the profile of the keys. As shown in Fig. 4.16.5, the vertical shear force can be resolved into tension and compression components with o as the apparent friction coefficient and a the angle of the key. Depending on the number of keys per floor, the unit forces per key resulting from the vertical shear force V are: J = V sin a C = Vcos a The joint force J is resisted by the shear-friction force R developed in the plane of J, with: R =Ctano Assuming a conservative value of tan o = 0.60, sliding along J will not occur if: R>J which is the case for a 530”. For a z 30” and R <J, a tension force T develops which must be taken by horizontal reinforcement in the joint. According to Fig. 4.16.5: A T ;osBa _ AJ _ cos a

V(s’n

= V(tan a - tan o)

t-Compression

I

Section A

’

(a) Diagonal Tension

;lill~~~/IB!I

(b) Shearing

(c) CrushingShearing

(d) Dislocation

Fig. 4.16.6 - Forces in Keyed Joint 4-56

*;;;

a

tan

o)

(Eq. 4.16.1)

The sum of the unit tension forces at each floor level can be taken by horizontal ties or by uniformly distributed horizontal reinforcing bars protruding from the wall. 4.16.2 Horizontal Joints Horizontal joints in load bearing wall construction occur at floor levels and at the foundation or transfer beams. The principal forces to be transferred are vertical and horizontal loads from panels above and from the diaphragm action of floor slabs. The resulting forces are: (a) normal to joint - compression or tension, (b) horizontal to joint - horizontal shear, (c) vertical to joint at face - vertical shear, and (d) perpendicular to joint - compression or tension from floor to diaphragm (Fig. 4.16.7). Because of the limited frame action that can be developed perpendicularto awall, moment stresses in the joint are normally only of minor importance. The following procedure, based on Ref. 52, may be used to design for axial load transfer through horizontal joints: Fig. 4.168 shows three joint details used in multistory load bearing buildings with hollow core slabs used for the floors. For the condition of Fig. 4.16.8 (a), the joint strength is:

e = eccentricity of load(occurswhenfloorspans or loads on either side of wall are unequal, and at end walls) h = slab thickness “C = design concrete strength of slab ij = 0.7 When the space between slab ends is grouted, load is shared by the slab ends and grout columns according to their stiffnesses. The splitting strength of the wall may also limit the joint capacity. The effect of grout flowing solidly into the slab ends is to confine the grout column. If the space between slab ends is less than about l-1/2 in., an unconfined grout column will add little strength. The strength of the connection can be determined by: (Eq. 4.16.3)

4P” = cb t, lfueR* where:

= grout thickness = length of joint (parallel to wall) being considered f = equivalent bearing strength from Table ue 4.16.1. Accounts for distribution of load between grout column and slab ends = 1 - (2e/h) Re iI 1

Fig. 4.16.7 - Typical Interior Horizontal Joints oP, = (PO.85A$‘,R,

Table 4.16.1 - Equivalent bearing strength, fueW)

(Eq. 4.16.2)

where: P, = nominal strength of the joint A, = effective slab bearing area = 2 w b, w = bearing length (Fig. 4.16.8) b, = net web width of slab R, = reduction factor for eccentricity of load = 1 - (2e/h)

Grout strength, psi 3000 4000 5000 Slab cores not filled 4.5 5.9 5.9 Slab cores filled

5.8

6.5

7.1

Valid for slab f’, = 5000 psi or higher with slabs supported on multimonomer plastic bearing strips. For other conditions see Ref. 52.

Fig. 4.16.8 - Typical Joints in a Bearing Wall Building 4-5’

Example 4.16.1 1 Design of grouted horizontal joint Given: An I&story bearing wall building with cast concrete walls and 8 in. hollow-core roof. Floor slabs span 28 ft and bear on omer plastic bearing strips. V&precast concrete) = 5000 psi Loads: Roof: DL = I5 psf; LL = 30 psf Floors: DL = IO psf ; LL = 40 psf Hollow core = 60 psf Walls = 800 plf/story No LL reduction

8 in. prefloors and muitimon-

\

28[1.4(60 + 15) + I .7(30)1/I 000 4.37 klf 28[1.4(60 + IO) + 1.7(40)1/I 000 4.65 kif 1.4(800)/l 000 = 1. I2 klf/story

Accumulate loads above floor noted:

4-58

= 0.7(0.85)(3 + 3)(0.3 x 12)(5)(1 = 64.26 kips/ft

- y )

Adequate for floors 8 through roof.

Problem: Find grouting requirements for interior joint. Solution: Loads: Roof: W” = = Floors: wU 2: = Walls: w, =

Evaluate capacity of ungrouted joint: Assume the ratio of webwidth to total width of the slab = 0.3; from Eq. 4.16.2: P” = 4)0.85A$‘,(,,,$,

Floor

w”

CW”

I8 17 16 I5 I4 I3 I2 II IO 9 8 7 6 5 4 3 2

4.37 + I.I2 4.65 + I.I2 5.77 5.77 5.77 5.77 5.77 5.77 5.77 5.77 5.77 5.77 5.77 5.77 5.77 5.77 5.77

5.49 II.26 17.03 22.80 28.57 34.34 40.1 I 45.88 51.65 57.42 63.19 68.96 74.73 80.50 86.27 92.04 97.81

Evaluate capacity of grouted joint: Try f’, of grout = 3000 psi use t, = 2 in., R, = I .O as above From Table 4.16.1: Slab cores not filled, fue 2: 4.5 ksi From Eq. 4.16.3: 4Pn = + t, 1 fueR, = 0.7(2)(12)(4.5)(I) = 75.6 kips/ft Adequate for floors 6 and 7. Slab cores filled, fue = 5.8 ksi $P, = 0.7(2)(12)(5.8)(I) = 97.4 kips = 97.81, say ok (may choose to specify a slightly higher grout strength.) Notes: I. Typical examples of other connections through horizontal joints are shown in Chapter 5. 2. When forces are concentrated at a few points, they must be redistributed into the panels above and below. 3. The connection should have more ductility and strength than the vertical ties fastened to it. 4.16.3 Structural integrity(21) For precast concrete load bearing wall structures higher than 3 stories, minimum tensile ties should be provided at the joints to resist the following forces (Figs 4.16.9 and 4.16.10): T, u 2 1500 Ib/ft x span of floor slabs (ft) -- cross tie T2 u 116,000 lb -- peripheral tie Ts’” 1 2 l/2% of service load on wall ’ 11500 ib/ft x length of wall (ft) -- iongitudinai tie T4 u 2 3000 Ib/ft x length of wall (ft) -- vertical tie where subscript u denotes factored load.

.

/

/ T*

Fig. 4.16.9 - Recommended Tie Forces in Precast Concrete Bearing Wall Buildings

Fig. 4.16.10 - Typical Tie Arrangement

4.17 Non-Load Bearing Wall Panel Connections The design of connections of non-load bearing architectural wall panels follows the same principles as structural connections, except the loads are generally lighter. Usually, the connections are detailed to minimize the volume change forces and thus, are primarily designed for the self-weight of the panel and lateral loads. Example 4.17.1 illustrates use of this scheme in the design of load bearing and tie-back connections for an architectural wall panel. Attention to details and proper protection of any exposed hardware are most important to ensure satisfactory performance of the connections for the service life of the structure. Several examples of typical details are shown in Chapt. 5 (Sect. 5.3).

- 3 314” /-

Knife

Plate

Tie-Down Plate

r

Example 4.17.1 - Design of Architectural Wall Panel Connections

2'-10"

Given: 6” x 7-O” x 20*-O” long architectural panel There are two load bearing and two tie-back connections per panel Distance between connections = 14-O” Estimated volume change strain = 0.0003 Wind load = 30 psf Plates: fy = 36 ksi; Anchors: fy = 60 ksi; Reinforcement: f, = 60 ksi (weldable) Concrete: f’, = 5000 psi (normal weight) Beam width: b = 8 in. Problem: Design load bearing (at top) and tie-back (at bottom) connections -- See Fig. A Solution: It is noted that the connection reactions (see Fig. B) are statically indeterminate and the exact solution would require consideration of the rigidity of various components including weld sizes and configurations. In typical situations however, such exact solution is not necessary. By making simplifying assumptions, a conservative but reasonable solution can be obtained. For this problem, the following assumptions are made (see Fig. B). 1. The tie-down plate is thin and flexible, thus M = 0. 2. For design of the tie-down plate, the holddown force, T, is applied at the outside edge where most of the weld is located. However, for overall equilibrium purposes, the force T

Fig. A will be assumed at center of the tie-down plate since the plate is assumed to be thin. 3. In calculation of the horizontal reaction, H,, it is assumed that the shim reaction is zero. This would produce the largest value of reaction H, under wind suction and panel dead load. It will also produce the largest compression force on the tie-back connection under wind pressure and panel dead load. The shim reaction C, however, is calculated and considered in the design of knife plate. Using the above assumptions, the reactions shown in Fig. B are calculated as follows:

the shims as well as the knife plate are rigid and the shims are installed tightly. With these assumptions, the tie-back connection will carry only the wind load and thus, He = 1.05 kips. Using Fig. B and summing moments about the bottom of the tie-down plate: (0.03)(10)(7)(18) - C(2.5) = 0

J

m--

He=H,-Hz

+ 6.82(10) - 1.05(36)

C = 27.3 kips Therefore, T = 27.3 - 6.82 = 20.48 kips 2. Design Knife Plate and its Anchorage: With reference to the knife plate free body diagram in Fig. C, and summing moments about the left end:

n wP Fig. B 1. Determine Loads: (a) Horizontal load due to wind per connection: H, = (20)(7)(.030)/(4) = 1.05 kips (b) Horizontal load due to panel eccentricity: W,,= panel weight/connection = (1.3)[(20)(7)(.075)/2)] = (1.3)(5.25) = 6.82 kips (Note: 1.3 load factor is used in the above calculation recognizing the sensitivity of the connection to tolerances with respect to the gravity load. (c) Horizontal reactions due to eccentric panel weight are obtained by summing moments about the bottom of the tie-down plate (M = 0, c = 0): 6.82 (10) - H,(36) =O H, = 1.89 kips Thus, the maximum horizontal reactions are: HA=H,+H,=1.05+1.89=2.94kips He = 1.05 kips (tension) and = 2.94 kips(compression) (d)The shim reaction, C, and the hold-down force, T, are determined as follows: Note: The maximum reaction C would occur underwind pressure and underthe assumption that

Fig. C M + 2.94(2.5) + 27.3(4.5) - 20.48(7) = 0 M = 13.16 k-in Maximum moment in the plate: M max = 6.82(4.5) + 13.16 = 43.85 k-in Try 1” x 4” Knife Plate: A = 4 sq. in. S = (1)(4)*/S = 2.67 in3 (a) Checkfortension and bending (Ref. 32,Sect. 1.6.1):

where: f&l = 2.9414 = 0.74 ksi f b = (43.85)/2.67 = 16.4 ksi 0.6 F, = 0.6(36) = 21.6 ksi 0.66 FY = 0.66(36) = 23.76 ksi 4-61

Thus0.-/4 +a=0.72<1.0, ok ’ 21.6 23.76 (b) Check volume change forces: Volume change at each end, 6 = 20(12)(.0003)/2 = 0.036 in/end Corresponding force, p = 3EI (6) i3 where: E =29x103ksi I = (4)(1)3/12 = 0.33 in4

Required area of steel,

As=*

= 16.4/0.9(60)

= 0.30 sq. in. Use 2-#3 on each side of plate (Refer to Table A-17 for welding requirements) A, (provided) = 2(0.1 l)(2) = 0.44 sq. in. (Note: Since the bars are provided both above and below the plate, they are counted twice - see Sect. 4.9.)

Therefore, P = [(3)(29 x 10’)(0.33)(0.036)] = 3.0 kips

/(7)3

Stress in plate (assumingfixity at panel face and neglecting any horizontal reaction at shim), f = M/Z = 3(7)/[(1/4)(4)(1)*] = 21 .O ksi e 36, ok

3. Design of Tie-Down Plate: Assume a 314” x 5” x 5” plate. A = (3/4)(5) =3.75 sq. in. S = (0.75)(5)*/S = 3.125 in3 (a) Check plate for bending and tension: Summing moments about the plate centroid (see Fig. E),

(c) Design anchorage of knife plate: Taking moments about F, (see Fig. D):

II

20.4ak Tie-Down Plate

13.16 in-k

Fig. E

Fig. D

FJ3.75) = 6.82(4.5) + 13.16 Therefore, F, = 43.85/3.75 = 11.7 kips With ACI 318-83(6) load factor of 1.4: (F,)” = (F2)” = 11.7(1.4) = 16.4 kips

4-62

M = 20.84(0.75) - 2.94(2.5) = 8.01 k-in f a = 20.4813.75 = 5.46 ksi 1, = 8.01/3.125 = 2.56 ksi f 5.46 2.56 fI.J a - +23.76 0.6 FY +mFy = 21.6 = 0.36 < 1 .O, ok (b) Design weld to knife plate (See Fig. F, Sect. A-A) A,,, = 9.0 sq. in./in

Fillet Weld

Fillet Weld -,

Section B-B Fig. F SW= [(4)* + (2)(4)]/(3) = 8.0 in3/in f “, = 20.4819.0 = 2.28 Win f = 2.94/9.0 = 0.32 k/in fL* = 8.01/8.0 = 1 .O Win f reqd = d (1 .O + 0.32)* + (2.28)* = 2.82 Win

Bearing Reinforcement

Shims

Use l/4 in., E70 Electrode Max. allowable stress (Table A-14)

= 3.71 k/in > 2.82, ok

(c) Design weld to plate embedded in supporting structure (See Fig. F, Sect. B-B) f “, = 20.4819.0 = 2.28 Win f v 2 = 2.94/9.0 = 0.32 Win f reqd = X/ (2.28)* + (0.32)* = 2.30 Win Use l/4 in., E70 Electrodes 4. Design Embedded Plate in Supporting Structure (see Sect. 4.5): With reference to Fig. G: Vu = 1.15(1.4)(C) = 1.15(1.4)(27.3) = 44.0 kips = N” 1.15[0.75(1.4 H, + 1.7 H,)] = 1.15[0.75( 1.4( 1.89) + 1.7( 1.05))] = 3.82 kips (Note: The load factor of 1.15 is recommended in Sect. 4.5 as an additional load factor) CL,=

‘Ooo A v U

Acr

p = lOOO(l.O)(8)(34)(1.4) 44.0

= 9.7 > 3.4 (Table 2.7.1)

Fig. G

Use p, = 3.4

A,=/!L=

44.0 0.85(60)(3.4)

4 fyhl = 0.25 sq. in.

3 82 =-=~=0.07sq.in. 0.9(60)

AS =AvfiAn= 0.25 + 0.07 = 0.32 sq. in. Use 2-#4, A, = 0.40 sq. in. For tension in the vertical direction: Pu = 1.4(T) = 1.4 (20.48) = 28.7 kips From Table A-33: ford, = 2”, f’c = 5000 psi, b = 6 in., Select (3) - l/2 in. diameter x 6 in. studs

4-63

Pull-out capacity = 3( 10.6) = 31.8 kips > 28.7, ok 5. Design of Tie-Back Connection at Bottom:

4.18 Seismic Connections Special considerations related to strength and ductility requirements for seismic connections are discussed in Chapt. 1 (Sect. 1.8). The following example illustrates use of that methodology in the design of a non-load bearing wall panel to foundation connection for a building located in a region of low seismicity. Review of Ref. 5 is suggested for additional information and design examples.

Example 4.18.1 - Wall Panel to Foundation Seismic Connection

Fig. H With reference to Fig. H: M = (2.94)(2) = 5.9 k-in S reqd. = 5.910.66 f, = 5.9123.76 = 0.25 in3 Use L 4” x 6” x 3/8” x V-4” Toallowforpanel movementforvolumechanges, provide oversize hole in the angle. Use 112 in. diameter A-307 bolt with standard washer and nut. From Table A-22: Capacity = 2.84 kips > 1.05, ok Design weld: f = 2.9414 = 0.73 Win fI’= 5.9/[(2)(1)(3)2/6] = 1.97 Win f reqd. = d(0.73)2 + (1 .97)2 = 2.10 Win Use 3/16 in. E70 weld From Table A-l 4: capacity = 2.78 Win > 2.10, ok

Given: 1. Aone-story warehouse with non-load bearing 8 ft. wide double tee wall panels (see Fig. A). The vertical connections between wall panels are for alignment only. Thus eachdouble tee panel may be assumed to act independently to resist lateral loads. 2, The total dead load of the warehouse is 2770 kips. The wall panel dead load is38 psf, or DL = 6.38 kips per panel. There is a total of 32 wall panels. 3. Using a response modification factor, R = 5.5 (Ref.fj), the lateral seismic shear is calculated to bel.42 kips per panel. 4. The same connection is provided between each double tee stem and the foundation. 5. Use ACI 318-83(6) load factors. Problem: Perform the following five tasks: 1. Design the seismic connection at the foundation to yield in tension. 2. Check the connection to determine if it will deform inelastically providing the structural energy dissipation required for the assumed response modification factor. 3. Check stability of the building under inelastic dynamic P-A effects. 4. Determine the controlling ultimate shear in the wall and the ultimate tensile force necessary to design the elastic components of the foundation connection. 5. Design weld and the stiffeners for the vertical leg of the erection angle to remain elastic for the load in task 4 above. Solution: 1. Design the seismic connection at the foundation to yield in tension:

4-64

of the angle under a tensile load of 7.0 kips. Using k = 1 in. (See Fig. C): M” = T&4.0 - k) = 7.0(4.0 - 1 .O) = 21 .O k-in For f, = 36 ksi, 2, = 0.25bt2 and b =6 in, M, = f,(Z,) = fY(0.25bt2) = 21 .O k-in

c==J V

Therefore,

HP

t=l/$GY =vzG 19’-6”

= 0.624 in (say, 5/8 in) Use L 4” x 4” x 58” x 0’6”

v I

1 -Concrete Footing

cr-D-4

x 4” x t x 6” Long

k

Fig. A - Wall Panel Elevation From ACI 318-83(6) Sect. 9.2.3, Load factor = 1.1 x 1.3 t 1.43 Factored tension load per connection: i” = 1.43V(H/D) - 0.9(DU2) = 1.43( 1.42)( 19.5/4) - 0.9(6.38/2) = 7.0 kips For the connection shown in Fig. B, the thickness, t of the angle is determined based on yielding

-,;a\I

II 7-

F

- 8DT12 Wall Panel

-f

F

o

o

t

Fig. B - Foundation

a T”

In--/ &3.---d

Fig. C - Forces on Angle 2. Check the connection to determine if it will deform inelastically providing the energy dissipation required for the assumed response modification factor. Use the conservative equal energy approach. , (a) The required structural ductility (see Fig. 1.8.4) P = (R2 + 1)/2 = (5S2 + 1)/2 = 15.6

I I” Grout

Stiffener f

=

*Concrete 1i n g

Sectlon

where: P = structural ductility factor (Fig. 1.8.4) R = response modification factor (b)The lated as:

wall displacements (see Fig. D) are re-

All = A “H/D = A “( 19.514) = 4.9 A v (c) Using the idealized stress-strain diagram in Fig. E, determine the corresponding moment -curvature diagram (see Fig. F). The calculations required are given below:

4-65

H Curvature ($I) Table Point/Momentlvature

Fig. II - Kinematic Mechanism for Wall Panel

14.1 k-in k-in k-in

1 2 3

1C o m m e n t -

0.00384 0.00575 0.64

21.1 21.1

First Yield Full yield Fracture

-

Fig. F - M-4 Diagram

/ Strain (E) Table

- - - -

Fig. E - Idealized Stress-Strain Diagram for A36 Steel S = bt2/6 = (6.0)(0.6252)/6 Z, = bt2/4 = (6.0)(0.6252)/4

= 0.391 in3 = 0.586 in3

At point 2: Moment: MY = fyZ, = 36.0(0.586) = 21.1 k-in Curvature: 3 = SF($) = 1 .5( .00384) = 0.00575 in-’ At point 3 (see idealized curve in Fig. F): Moment: M, = fyZ, = 21.1 k-in Curvature: 4+= E, /(t/2) = 0.2/(0.625/2) = 0.64 in-’ (d) For calculation of the vertical displacement of the angle, the horizontal leg of the angle is modeled as a cantilever beam of length = 3 in. (see Fig. G), i.e., the plastic hinge is assumed to initiate at a distance’%” from the angle heel. The vertical displacement of the angle and the corres$onding horizontal displacements at the top of the wall (A,, = 4.9A,) are estimated as: Max.

elastic:

A “* = $,( Z2/3) = 0.00575(3.02/3)

= 0.0173 in.; (A,,, = 0.0847 in.) The shape factor, S, = f = m= 1.5 Max. plastic (Ref. 18): At point 1: Moment: M, = fyS = 36.0(0.391) = 14.1 k-in Curvature: $, = &y/(t/2) = 0.0012/(0.625/2) = 0.00384 in-’

4-66

A “p = ($ - 4p)U - w

= (0.64 - 0.00575)(0.625)(3.0 - 0.625/2) = 1.07 in.; (A,,P = 5.22 in.) Total A

elastoplastic: hep

=

‘he +

‘hp

= 0.0847 + 5.22 = 5.30 in.

is evident from the pinching of hysteresis loops in laboratory tests. Reduction factors to account for the loss in energy absorption capacity, particularily for precast connections, have not been well defined. For this connection with yielding in the angle leg, a range of 2 to 5 for the reduction factor would be considered reasonable. Since the structure is located in a region of low seismic activity, the margin on structural ductility (62.6versus 15.6) is assessed to be adequate. 3. Check stability of the building under inelastic dynamic P-A effects: (a) Angle Leg

The stability of the building may be checked by considering one wall panel and the model from Ref. 54 shown in Fig. H.

(b) Idealization

--I

0.65"

Fig. H - P - A Moment Structural Stability

(c) Moment

,1

0.64

in-’

Dead load of the building per wall panel: P = (2770)/32 = 86.5 kips A,.,*= 0.0847 in. sH = 19.5 ft. Vu = 1.43 (V) = 1.43(1.42) = 2.03 kips

0.00575

in-’

(d) Curvature Fig. G - Cantilevered Horizontal Leg of the Erection Angie The corresponding maximum structural ductility is 5.3/0.0847 = 62.6. This is much larger than 15.6 required for R = 5.5. However, it should be noted that members subjected to inelastic cyclic loads progressively lose capacity to absorb energy. This

The stability coefficient(54): 0 = P&J /Vu U-4

86.5(0.0847) =2.03(19.5

x 12)

xo 0154 .

If 8 I emax, no amplification is required. where: =0 . 0 5 8

may

R-0.4

(Note: The 6,,, value is obtained by simplifying Ref. 54 equations)

4-67

0

max

therefore, The

=

0.05 = 0.0098 < 0.0154, 5.5 - 0.4

amplification

amplification

is

required.

factor,

ad = 1 + 2(R - 1)e = 1 + 2(5.5 - 1)(0.0154) l-0 1 - 0.0154

M, = fyZ, + S@, - by) = 30.4 + 0.5625(58 - 36) = 42..8 k-in M/My = 42.8130.4 = 1.4 Tension: T, = 1.4(8.59) = 12.0 kips Shear: V, = [Tu + O.S(DL)](D/H) = [12.0 + 0.9(6.38/2)](4.0/19.5) = 3.05 kips

= 1.16 i.e. Tu = 12.0 kips, Vu = 3.05 kips

Use thisfactorto revisethe reponse modification factor and Tasks 1,2 and 3. Since calculations are based on the equations used previously, only the important results are given below:

5. Determine weld and the stiffeners for the vertical leg of the erection angle to remain elastic for the load determined in Task 4 above. (a) Weld size:

R(new) = R (s) = 4.75 Use the weld configuration shown in Fig. I: V&new) = V&1.16) = 2.03(1.16) = 2.35 kips for task $= Mu= t =

A = 3(2) + 6 = 12 in*/in

1: 8.59 kips 24.7 k-in 0.68 in.

yt,=

for task 2: u(new) = 11.8 My= 30.4 k-in $‘= 0.0048 in-’ 4j = 0.533 in-’ 4, = 0.0648 in. = 4.85 in. >:p = 4.85 + 0.0648 + 4.92 in. Structural

Ductility,

4 92 = 75.9 > 11.8, ok = L ’ 0.0648 for task 3: 8 = 0.010, 6,,, =O.O12>6,ok 4. Determine the controlling ultimate shear in the wall and the uftimate tensile force necessary to design the elastic components of the foundation connection: Design forces for the elastic components of the foundation connection including strain-hardening effects are:

4-68

2(3)(1.5) + 6(3) =L 2 25 in DAY cA= 12

-yT = 3 -ys = 3 - 2.25 = 0.75 in. I = l/l2(2)(l)(3)3 + 2(3)(2.25 - 1.5)* + (6)(3 - 2.25)2 = 11.25 in4/in

Use L 4 x 4 x 314 x W-6”

Maximum

Section properties of the weld are:

s,=

-=& =$j-$j-

=5.0in3/in

S, = +- = ‘g = 15.0 in3 /in

Shear stress in the weld due to T,: f, =*

T 2 =y = l-Ok/in

Tension stress in the weld due to Mu: Mu = Tu(3.5) = (12.0)(3.5) = 42.0 k-in.

Resultant stress in the weld: f m a x = Y/m = v(l .O)* + (8.4)* = 8.46 k/in

(a) Weld Configuration

(b) Free-Body Diagram

Fig. I - Weld Configuration and Free-Body Diagram Use 3/8” fillet weld, E70 From Table A-14, design strength = 9.28 Win > 8.46, ok (b) Vertical stiffeners: Try 3/4” x 1-l /2” x 0’4” stiffeners: Section properties for the vertical leg with two stiffeners are (see Fig. J):

r Vertical

Stiffener

A = 6(0.75) + 2(0.75)(1.5) ‘iT, =

6(0.75)(0.75/2)

= 6.75 in*

+ 2(0.75)(1.5)(1.5) 6.75

= 0.75 in. iq = 1.5 in. I = (6)(0.75)3/12+ 2(0.75)(1.5)3 /12 + 6 (0.75)(0.75/2)* + 2.25(1 Z/2)* = 2.53 in4

S, = -& = oT = 3.38 in3 S,= k= e=1.69in3 Maximum compressive stress,

= 23.1 ksi c 36.0, ok Maximum tensile stress,

= 14.2 ksi < 36.0, ok Fig. J - Stiffener Details

Use (2) 3/4” x l-1/2” x V-4” Stiffeners

4-69

CHAPTER 5 TYPICAL CONNECTION DETAILS

. Column to Foundation. . . . . . Column to Column. . . . . . . . . . Girder to Column . . . . . . . . . . . Beam to Girder. . . . . . . . . . . . . Beam to Beam.. . . . . . . . . . . . Slabto Beam.. . . . . . . . . . . . . Slab to Slab.. . . . . . . . . . . . . . Slabto Wall.. . . . . . . . . . . . . . Beam to Wall.. . . . . . . . . . . . . Wall to Wall . . . . . . . . . . . . . . . Wall to Foundation . . . . . . . . . Stairs to Landings. . . . . . . . . l

5.1 General This chapter includes examples of connection details for structural as well as architectural precast, prestressed concrete products. The details included are neither exhaustive nor necessarily the best possible arrangements. The purpose in including these details is to present ideas and show some common schemes. The Connection Details Committee hopes that these ideas and schemes would lead to yet other ideas and schemes’ to enhance the state-of-the-art of precast, prestressed concrete connection technology. Selection of a connection detail for a particular situation requires consideration of strength requirements and load transfer paths. It should also include consideration of production, erection, serviceability and durability. Chapters 1,2 and 3 of this Manual cover details related to these considerations. Common practice by precast, prestressed concrete manufacturers in a given area may also influence the final selection of details on a particular project. Consistent with the purpose of this chapter, which is to present ideas and possibilities, detailed design information is not given on the sketches. Sizes of components such as, plates, bars, welds, and other details such as, joint spaces, bearing pad thicknesses have been purposely omitted. 5.2 Structural Precast Concrete Details The following sections present several typical structural details. These particular details were selected by the PCI Committee on Connection Details from a large inventory on the basis of their more common use. A sufficient variety is included to illustrate the various concepts discussed in previous chapters. The details are arranged in groups according to the products they are designed to connect. Within each category, the description of the details, including features and disadvantages, is given followed by sketches for the details. The details included cover the following categories: 1To facilitate recording of different ideas and details, a

blank page is provided at the end of details shown within each category of connections.

CF CC GC BG BB SB SS SW BW WW WF SL

5.2.1 Column to Foundation Connections (CF) There are four basic types of column to foundation connections: Column Size Base Plates . Oversize Base Plates . Socket Base Grout-Sleeve Base ;ypically, these connection details are concealed by placing them below the finished floor level. The selection of a particular connection detail for a given project usually depends upon whether the column is: (a) prestressed or non-prestressed; (b) cast individually or in a long-line form; and (c) pinned or restrained. l

5.2.1 .l Column Size Base Plates (CFl, CF2 and CF3) The column is cast with pockets and a base plate the same size or slightly smaller than the column. Pockets may be either in the corners (CFl), centered in the sides of the column (CF2), or on two sides (CF3). The column is erected over anchor bolts protruding from the foundation. The pockets and space between the column and foundation are filled with dry-pack or non-shrink grout. Temporary support and leveling are accomplished by tightening down on the nuts with the column resting on a center stack of shims or by a double nut arrangement as shown in the sketches. Features: 1. Corner pockets allow easy wrench access. 2. Side pockets allow comer column bars to be welded to the base plate. 3. Holes in base plates are oversized to minimize tolerance problems. 5-.

4. Column size base plate does not require form penetration and permits use of thinner base plates. 5. Pocketed anchor bolts are concealed and protected from corrosion after grouting. 6. Bolting allows quick and easy erection in any weather. 7. Column can be prestressed with tendons passing through holes in the base plate. Disadvantages: 1. Difficult to achieve moment resistance. 2. Corner pockets prevent attachment of column comer reinforcing bars to base plate. 3. Individual side pockets (CF2) restrict wrench movement and provide less effective placement of anchor bolts for moment resistance. 4. Projecting bolts are susceptible to damage. 5.2.1.2 Oversized Base Plates (CF4, CF5, CF6 and CF7) The common characteristic of these column bases is the oversized plate which has at least one dimension larger than the corresponding column’s dimension. The base plate may be cast with the column as one unit or the oversized plate may be attached by welding later. Typically, four anchor bolts are used to connect the column to the foundation and may be located in the corners or at the centers of the sides of the column. Column reinforcement is sometimes welded to the base plate, but it is more common to lap deformed bar anchors with the main column reinforcement. Features: 1. Wrench movements are not restricted. 2. Column corner reinforcing bars can be welded to the base plate for anchorage. 3. The larger base plate increases effective bearing area and, with stiffeners on base plate, large moment resistance can be achieved. 4. Oversized holes in base plates help minimize tolerance problems. 5. Bolting allows quick easy erection in any weather. Disadvantages: 1. Oversized base plates are usually thicker than column size base plates and thus are more expensive. 2. Connection may not be concealed or protected from corrosion. 3. When cast with concrete as one unit, the

5-2

plate has to penetrate column form or project beyond end of form. Thus, the connection is rarely used when columns are prestressed or cast in long-line forms. 4. Stiffeners may have to be installed after casting. 5. Projecting bolts are susceptible to damage. 5.2.1.3 Socket Base (CF8) The socket base connection involves setting a column into a relatively rigid base and filling spaces between the column and the base socket with structural grout. The socket may be formed above the foundation or into the foundation. Shims and wedges are typically used for temporary support and alignment. The connection is much stiffer than the steel base plate type connections and can be designed to provide substantial moment resistance at the column base. Features: 1. Quick, easy erection in any weather, however follow-up grouting is weather sensitive. 2. Moment resistance at column base. 3. The socket connection results in simplified column casting with minimum tolerance problems. Disadvantages: 1. The socket connection requires expensive foundation work. 2. It is difficult to ensure good grouting in the socket under the column. 3. It is difficult to achieve tension reinforcement continuity between the column and the foundation.

5.2.1.4 Grout-Sleeve Base (CF9, CFl 0, CFll and CF12) Grout-sleeve connections require special care during layout due to close tolerance requirements. Grout-sleeves can be cast into the column or the foundation. The sleeves fit over reinforcement projecting from the mating part. Sleeves are grouted and reinforcing bars are developed by bond strength. The gap under the column is filled with dry-pack or non-shrink grout. Features: 1. Moment resistance at column base can be readily achieved. 2. Connection is concealed after grouting. 3. Can be used for architectural columns where base is exposed.

4. Difficulties due to close tolerance requirements are minimized by using larger sleeves. Disadvantages: 1. Sleeve length for larger bars can be quite long and special commercial high strength couplers (typically proprietary) might be necessary. 2. Requires temporary bracing during grout curing. 3. Protruding reinforcement, either in the column or the foundation, is susceptible to damage before column is placed or during erection. 4. Weather can affect grouting process. 5. Precautions must be taken to keep sleeves free of water and debris.

5-3

5-4

CFI

CF2

CF3

CF4

CF5

CF6

52.2 Column to Column Connections (CC) Selection of the appropriate connection is based upon: (a) column reinforcement (prestressed or conventionally reinforced); (b) the degree of moment transfer required; (c) final exposure of connection; and (d) required erection sequence. The most common column to column connections are: . Bolted . Welded Plates . Tube to Tube Grouted Sleeves . Welded Lap Bars . Tube Sleeves . Post-Tensioned Splice l

5.2.2.1 Bolted Connections (Ccl, CC2 and CC3) Thecolumniscast inoneofthreeways: (a) flush, or slightly undersized base plate with four corner pockets; (b) flush, or slightly undersized base plate with four side pockets; (c) dapped sideswith angles; the angles are anchored by welded bars. The column is then set over anchorbolts protruding from the column below. The space between the columns is filled with dry-pack or non-shrink grout. Temporary support and leveling are accomplished by tightening the nuts with the column resting on a center stack of shims, or by use of double (leveling) nuts. Features: 1. Oversized holes for bolts reduce tolerance problems. 2. Connection is concealed and protected from corrosion after the pockets are grouted. 3. Boning allows quick, easy erection in any weather. Disadvantages: 1. Due to limited moment capacity, the connection is suitable for locations near inflection points. 2. For the connection with angles (CC3), more grouting is required. Also, the axial tensile strength is limited by the thickness of the angle. 3. Projecting bolts are susceptible to damage. 5.2.2.2 Welded Plate Connections (CC4 and CC5) Welded plate connections are commonly used when moment transfer is required. The columns are match cast with top and bottom plates which are welded during erection.

Features: 1. Moment resistance can be provided. 2. Field fitting problems are minimized if car-rectly match cast. 3. Immediate full bearing results, so erection can proceed to upper levels without delays for grouting. 4. The connection is protected from corrosion after concealment. Disadvantages: 1. Match casting requires special care in the plant. 2. A significant amount of welding is required. 3. Crane must support column until welding is done. 5.2.2.3 Tube to Tube Connections (CC6) Tube to tube connections minimize field adjustmentsand are suitable where limited moment transfer is required. The tubes, which may be round or square, are in a male-female arrangement with the smaller tube extending either from the bottom or the top column. The columns are match cast and the tubes may be grouted when erected. Features: 1. Field fitting problems are minimized if correctly match cast. 2. The connection is concealed and protected from corrosion. Disadvantages: 1. Tubes must be very accurately placed in the plant. 2. Correction of errors can be diff icutt. 3. Entire column must be stripped as a unit. 5.2.2.4 Grouted Sleeve Connections (CC7, CC8 and CC9) Sleeves are placed in either upper or lower column to accept projecting reinforcement from the mating column. After alignment, the sleeves are grouted. The space between the column sections is filled with a non-shrink grout. Temporary support and leveling must be provided by guying or other means until the grout in the sleeves is cured. Features: 1. Moment transfer can be achieved through the connection. 2. Concealed connection when grouted. 3. Tolerance parameters can be adjusted by changing sleeve size.

5-7

Disadvantages: 1. Sleeve length for large bars can be quite long. 2. Requires temporary bracing during grout curing. 3. Good weather or auxiliary heating is required for grouting. 4. Main reinforcement may require bending to accommodate sleeves. 5. Protruding bars are susceptible to damage during handling. 6. Sleeves must be kept free of water and debris. Several proprietary devices for splicing bars are available in the market and have received increasing acceptance. Many of these devices include special features to aid in placement and erection (see CC9). Leveling is accomplished by shims or by use of a bolt in threaded insert. With some systems the grout is pumped into the lower part of the sleeve until it comes out the top part. In others, the bars project from the upper column section and the grout is then placed in the sleeves and the shim space, prior to placing the top column. Features: 1. Moment transfer capability is achieved. 2. Special installation devices reduce tolerance problems, and no post-erection grouting is required. Disadvantages: 1. Additional means of bracing must be provided until grout in sleeves has set. 2. Proprietary devices may add to the cost. 5.2.2.5 Welded Lap Bar Connection (CClO) This connection is only used when full moment transfer is desired in large, heavily reinforced columns. Both column sections are cast with reinforcement protruding from the ends. The reinforcement is welded together during erection. Temporary support and leveling are accomplished by resting the column on a center stack of shims and welding only selected bars. After proper alignment is achieved, the remaining bars are welded and the connection is grouted. Features: 1. Moment resistance is developed at the connection with relatively short lap lengths. 2. The connection is concealed and protected from corrosion after grouting.

5-8

Disadvantages: 1. Reinforcement must be placed accurately to accomplish welding. 2. Reinforcement must be of a weldable grade steel. 5.2.2.6 Tube Sleeve for Composite Beam (CC1 1) This connection may be used when fully continuous, composite ductile frames are required. It allows the placement of column ties for confinement. Beam reinforcement is placed through the joint and the assembly is completed with cast-inplace concrete. If required, temporary support is provided by a sleeve-in-sleeve connection. A pipe or tube (structural) protruding from the upper section fits into a slightly larger pipe or tube in the lower section. A small weld holds the assembly in place. No weld is required if the fit is snug. Features: 1. Moment transfer capability is achieved for both beam and column. 2. The connection has good ductility. 3. The connection is concealed. 4. With proper design, the next level can be erected before concrete is placed. Disadvantages: 1. Sleeves must be accurately placed. 2. The connection is congested, so care is necessary to avoid honeycombing in cast-inplace concrete. 3. Requires much field labor. 5.2.2.7 Post-Tensioned Splice Connection (CC1 2) This system uses post-tensioning bars for the column reinforcement and for splicing column sections. Post-tensioning ducts are cast in the columns at the plant. The tendons (usually bars) are attached to an anchor (at the bottom floor) or a coupler (at intermediate floors). The upper column is then threaded over the next lift of bars. The bars are tensioned and anchored, leaving enough projection toattachacouplertoreceivethe barsforanotherlift. Features: 1. Provides aductile, moment resisting connection. 2. Post-tensioning reduces drift in high-rise buildings.

3. Good corrosion protection with dry-packed or grouted pockets. Disadvantages: 1. Erection procedure is more complex and requires special inspection. 2. Alignment of post-tensioning ducts is critical. 3. Requires supplemental reinforcement or pretensioning for handling. 4. Post-tensioning is an added operation. 5. Vertical post-tensioning ducts may be required to be grouted.

I I

CC6 5-10

I I

5.2.3 Girder to Column Connections (GC) Since girder-column framing in precast concrete structures is very common, there are many and varied types of connections for joining these elements. The type of connection that is appropriate for a particular application depends primarily upon load and geometry conditions. Some other considerations are: .

Girder bearing condition: At roofs, girders may bear directly on column tops, or the column may extend to the top of the girder. I n the latter case, and also at floors, the girders usually bear on corbels protruding from column faces.

.

Floor and ceiling heights: Building height consideration may necessitate dapping of girder ends, use of knife or other hidden corbels, or use of hanger connections.

.

Lateral force resistance: If the frame is to resist lateral loads, the connections must be capable of the required moment transfer. On the other hand, if a shear wall is incorporated in the structure as the primary lateral load resisting element, flexible connections may be used between girders and columns.

.

Load type and magnitude: Corbel sizes and girder bearing plates depend on vertical and horizontal (e.g. volume change) forces. Eccentric loading may necessitate torsion restraint in the connection. Special situations, such as a cantilever girder, may require the girder to pass through the column thereby requiring special connections.

In addition to the above considerations, local plant preferences may dictate welding, bolting, doweling, grouting, or field concreting and post-tensioning. 5.2.3.1 Simple Welded, Bolted or Doweled Connections (GCl - GC16) The girder usually sits on a bearing pad which provides uniform bearing and permits small movements for accommodating the effects of shrinkage, creep and temperature changes. The top connection transfers horizontal forces between the girder and column, provides erection stability, and braces the column, but may not provide rotational restraint. Welding of girder bottom to the column requires utmost care. If the girder bottom is welded at both

ends to the support, the forces resulting from restraint to volume changes can be quite large. Welding of girder bottom at one end only can also cause problems particularly where curvature caused by the thermal gradients is restrained. When welding is used, the top connection should allow some rotation to minimize negative moments at the girder ends. Thus, when the angle connection is used, only the toes are welded. A flat bar can be used if the joined plates in the column or girder are designed to flex, or the bar itself is sufficiently flexible. In order to prevent restraint when using the dowelsleeve system, the bottom of the sleeve should be filled with compressible material such as sand, vermiculite, or asphalt. The remainder is then filled with grout. It should be noted that vermiculite could intermingle with very wet grout. In the dowel-sleeve method, a sleeve in the end of the girderfits over a dowel which is threaded into either an insert in the support or a ferrule welded to the underside of the bearing plate. To prevent damage in handling, the dowel is inserted just prior to erection. The sleeve should be 3 or 4 times the size of the dowel to minimize field tolerance problems. The schematics show several variations of connections which use structural steel members projecting from the column to support the girders. In general, steel corbels are smaller in size than concrete brackets which can be an important consideration when head room is critical. Fireproofing may be necessarywhen projecting steel shapes are used. Several methods of dapping and pocketing are shown to reduce depth of structure. Features: 1. These connections allow quick, easy erection with few tolerance problems. 2. Volume change restraint is minimized. 3. Steelcorbelsprovide reducedstructuraldepth compared with concrete corbels. 4. Clean looking, concealed connections are possible. Disadvantages: 1. Limited moment capacity and limited torsional restraint. 2. Dowel-sleeve connections provide no lateral restraint until sleeves are grouted. They can be weather sensitive and the sleeve can fill with water or debris during erection. 3. Many of the steel embedments in columns require form penetrations causing production problems in the plant. Alignment of hard-

5-13

ware during casting is critical. 4. Exposed steel may require encasement for fire and corrosion protection. 5. Some hidden connections require dapped girder designs. Pocketing can necessitate field grouting. 5.2.3.2 Hanger Connections (GC17 and GC18) Two variations of hanger connections are shown in the schematics. Hanger connections are stable upon erection, although without a bottom stop, may “roll” when loaded eccentrically. Hanger connections are acceptable for special situations where head room is limited. They are not commonly used in typical precast construction. Features: 1. They provide quick, easy erection with various degrees of erection stability. 2. Volume change restraint is minimized. 3. Connection is generally concealed and protected after topping is placed. Disadvantages: 1. Connection hardware is expensive and more difficult to cast properly in the product. 2. Welding of reinforcement is critical. 3. Alignment of the embedded corbel is critical. 4. Girder rolling can occur without proper stops. 5.2.3.3 Composite Moment Connectlons (GC19 - GC20 also CC1 1) Composite connections are most commonly used in moment resisting frames. In some versions, the girders bear on a hammerhead column. Other versions require the girders to be shored in place until field concreting is cured. Continuity of girder reinforcement is attained by lapping, welding, or hooking depending on dimensions available. The negative moment steel is often placed through sleeves in the column or adjacent to the column in composite topping. In soffit girder designs, it is sometimes possible to provide sufficient strength so that shoring is not required. Features: 1. Full moment resistance at the connection can be achieved. 2. Field adjustments can be easily accommodated. 3. Good ductility and performance. 4. In some variations, multi-story columns can be used with economy. In these instances, the next floor can be erected before cast-in5-14

place concrete work is completed. 5. Connections are concealed. Disadvantages: 1. Temporary shoring may be required. 2. Routing negative reinforcement steel through the column can cause alignment problems. 3. During construction, connections may be weather sensitive. 4. Conflicts can arise between precaster and field concreting personnel. Who does and provides what? 5.2.3.4 Special Applications (GC21 - GC24) Post-tensioning can be used to provide negative moment resistance as shown in GC21 and GC22. A post- tensioning tendon is fed through a duct in the girder and an oversized sleeve in the column. An anchorage plate is attached in the pocket and the tendon is tensioned from the other end and anchored in the recessed pocket provided. The pockets should be sized to accomodate jacks. Prior to tensioning, the space between the girder and column is filled with dry-pack grout. In other applications, post-tensioning strands or bars can be used to develop continuity of columns where the columns are interrupted to allow the girder to pass through (GC23 and GC24). The girder is erected over post-tensioning tendons which have been placed in conduits in the column and coupled to the tendons from the lower level in the pocket provided. The girder is set on shims and then grouted underneath. When the grout has set, the tendons are tensioned and anchored. The next column is then erected and grouted. Features: 1. Moment resistance at connection is achieved for negative moment. 2. Girders or columns can pass through uninterrupted. 3. Connection is concealed and protected from corrosion after grouting. Disadvantages: 1. Anchorage bearing stresses must be considered in the girder and/or column design. 2. There is no erection connection until tendons are jacked. Other means of bracing may be necessary. 3. Post-tensioning requires special erection and inspection procedures. 4. Possible alignment problems can occur with conduits.

GCl

GC7

GCIO

GC9

‘7 GCII 5-16

-J GC12

GC13

GC17

GC14

SC18 5-l i

5-18

READER’S IDEAS

52.4 Beam to Girder Connections (BG) These types of connections are required when precast beams are supported by girders. They may be used for framing openings and other special applications. The first two (BGl and BG2) depict cases where the beam sits on a bearing pad on a ledge in the lower portion of the girder. Depending upon the relative depths of the beam and girder, the beam may need to be dapped as well (See BG2). The beams and girders are often used in conjunction with a floor system having a composite topping. If there is no topping, a top connection may be required. Connection BG3 shows a hanger connection concept similar to those shown in the beam to column connections. The dowel-sleeve joints (BG4) are also used when there is sufficient depth to allow placement of beams on top of the girders. Features: 1. Girders with ledges to support beams allow quick, easy erection with a minimum of volume change restraint. Beams have immediate stability and crane time is short. 2. Grouted sleeves allow quick erection with a positive connection. When the beams are placed on top of girders the full section of the girder is effective. Disadvantages: 1. The dowel system, with beam placed on top of the girder, increases height of the building. 2. Dowel alignment is critical and sleeves must be protected from water and debris. Cold weather precautions are needed for grouting. 3. Dapped ends cause congestion of reinforcement and increase fabrication time. Only limited moment capacity is available in the connection. 4. Some of the connections are not easy to conceal and protect from corrosion or fire.

5.2.5 Beam to Beam Connections (BB) These types of connections are used in special framing where it is desired to have the connection away from the column. Examples are tree columns with drop-in beams, cruciform beam-columns with connections at mid-span, or systems which use story-high columns and continuous beams. The first illustration (BBl) requires dapping of ends on both beam segments. Modifications of hanger connections shown in the beam to column section can also be used. The top connection should be designed to allow longitudinal movement to prevent volume change force buildup. The second example of beam to beam connections (BB2) utilizes embedded steel supports forming a cradle. Bearing pads and top connections are required and the hardware can be recessed and grouted if desired. The connection BB3 shows the use of special splice sleeves to achieve beam connection. Continuity of reinforcement is achieved which facilitates moment transfer. Features: 1. Longer clear spans can be achieved, allowing greater flexibility in framing. 2. Beam to beam connections allow quick, easy erection with minimum volume change restraint. Beams have immediate stability and crane time is short. Disadvantages: 1. Dapped ends cause congestion of reinforcement and increase fabrication time. 2. Some of the connections are not easy to conceal and protect from corrosion or fire.

5-23

BBI

BB3

BB2

52.6 Slab to Beam Connections (SB) These connections are most frequently made to join floor or roof members to precast concrete beams (inverted tee, ledger, rectangular), or steel beams. Often, the slab functions as diaphragm and the connections must transmit diaphragm shear and chord forces. In cases where cast-in-place topping is planned, it may be necessary to provide connections to ensure stability during erection. 5.2.6.1 Hollow-Core and Solid Slab Connections (SW-SB6) Precast slabs (voided or solid) bear on high density plastic, hardboard or neoprene bearing strips. Connection choice depends upon: (a) the magnitude of lateral forces in the diaphragm, and (b) whether or not the member has composite topping to transfer the forces. Some types of hollowcore are produced with extruding equipment that will not permit plates or other hardware to be cast integrally into the product. In these cases, the hardware must be installed subsequently. Features: 1. When a mechanical tie from slab to support is not required: a. Quick easy erection is accomplished with adequate tolerances. b. Volume change restraint is minimized. 2. When a mechanical tie from slab to support is required: a. A positive connection to the beam is achieved for shear transfer or torsion restraint. b. When welding is used, cast-in-place concrete may not be required. Disadvantages: 1. When a mechanical tie from slab to support is not required: a. Without topping, there is no positive tie to beam for shear transfer or torsion restraint. 2. When a mechanical tie from slab to support is required: a. When cast-in-place concrete is used to complete the connection, placement of longitudinal bars along top of beam requires threading through the beam stirrups. Also, there is no positive tie until joints are grouted and field concrete is cast and cured. b. When welding is used, accurate preplanned placement of beam hardware (embedded plates) is necessary. 5-26

5.2.6.2 Double Tee Connections (SB7-SB12) Tee stems are suspended (SB7) or sit on bearing pads and a top connection is made as shown. Although one top connection per double tee end will usually suffice for erection stability and diaphragm forces, two may be required in some situations. Experience has shown that in most stemmed members, a welded top connection will not cause volume change restraint problems if the bottom of the stem is not restrained. It is recommended that fhebottomofteestemsnotbe wekfedatthebearing to their supporting strf.cture. Features: 1. The connection provides erection stability and shear transfer capability. 2. Connections are simple and allow adequate tolerances. 3. Usually, there are no volume change restraint problems unless the stem bottom is welded at the bearing. 4. When hangers are used to minimize structural depth, there is no need for pockets or ledges on beams. Disadvantages: 1. Embedded plate locations in beams require pre-planning and accuracy. 2. Hangers are limited in load capacity and hardware may be expensive and thus they should be used only when other solutions are not feasible.

SBI

SB2

SB3

SB5

SB6

SB7

SB8

SB9

SBII

SB12

5.2.7 Slab to Slab Connections (SS) Adjacent slabs are connected to transfer diaphragm shear loads, for vertical load distribution, and for alignment purposes. Slab thicknesses vary from 2 in. for double tee members to 12 in. and greater for hollow-core or solid slabs. The standard connection used between the hollow-core slabs and the solid slabs is the grouted shear key (SSl). The size and shape of the key vary with the product type. The key is usually filled with a sand-cement grout. This connection distributes vertical loads and provides horizontal shear transfer for moderate loads for the deck to function as a diaphragm. Mechanical connections use anglesorflat plates with deformed bar anchors and/or headed anchor studs embedded in the concrete (SS2 - SS6). These connections can be recessed if the slab is thick enough to accommodate the hardware. A plate or bar is welded to the embedded items to complete the connection. If topping is used in the flooror roof system, the connections are hidden and protected from corrosion. Features: 1. There are no embedded items required in the grout key, thus no corrosion. 2. Properly spaced connections distribute vertical loading and transfer diaphragm forces. The connections can help the erector even out differential camber. 3 All connections are simple and allow quick, easy erection. Disadvantages: 1. Grout keys are susceptible to damage from debris and freezing of water. 2. Mechanical connections must be carefully located during detailing. 3. If reinforcing bars are used, they must be weldable. 4. Connections in 2 in. double tee flanges have limited capacity to resist vertical forces. Their effectiveness in evening out differential camber between adjacent slabs is also limited.

5-30

L’-------y,,

ss3

5.2.8 Slab to Wail Connections (SW) Flat or stemmed slabs interface with several types of walls. Some walls can be hollow (masonry), others are solid (precast shear walls or castin-placefoundationwalls), andstillothersareribbed or stemmed (double tees). Connections joining the slabs and walls may require load transfer for bearing or diaphragm action, or they may require movement accommodation such as needed when long roof members are joined to non-load bearing walls. 5.2.8.1 Hollow-Core and Solid Slab Connections (SW1 - SW4) Precast slabs are erected on high density piastic or hardboard bearing strips, leaving a 2 to 3 in. gap end to end. If the wall is concrete masonry, the cores are filled in the last 2 or 3 courses and vertical reinforcing bars are embedded at approximately 32 in. on center. Longitudinal reinforcement is added in the joint to tie the connection together. A composite topping, reinforced with welded wire fabric, is placed and the next level of wall is constructed. A regular masonry bond beam can be used in lieu of the filled courses. Bars or strands are located in grout-key spaces to satisfy minimum tie requirements. In end bearing conditions, the bars in the grout keyscan be welded to plates in the exterior walls. Threaded inserts can also be used. Features: 1. Tolerance problems are minor because of the wider grout joints inherent in hollow-core and solid slab construction. 2. Diaphragm forces can easily be accommodated and transferred to the walls. 3. Usually, there are no embedded items, thus eliminating corrosion problems. 4. Grouted shear key operations are not complicated and do not require extensive training. Disadvantages: 1. Placement of concrete topping may delay wall construction and precast erection. 2. Dowels embedded in masonry must be aligned with notches or joints in slabs. 3. Coordination is required to clarify which trade is responsible for providing the hardware. 4. Often, multiple move-ins are necessary for the precast concrete supplier because of the slower masonry construction.

5.2.8.2 Stemmed Member Connections (SW5 SW1 2) Normally, double tee walls are arranged with their stems placed outward from the walls so that the flange provides a smooth wall inside the structure. Occasionally however the double tees will be placed with stems inside the building. The wall panel has either a continuous reinforced concrete ledge or individual corbels. The roof or floor tee sits on a bearing pad and has a top connection which can take a variety of configurations. In roofs usually a top connection over each stem is used while in floors one top connection midway between stems is used. When roof slabs cantilever over the wall panels, the stem of the wall panel is blocked back and the flange notched so that the roof tee may pass through. The roof member bears on a pad on the top of the stems and cantilevers out. A plate cast in the bottom of the stem of the roof member iswelded to an angle at the Again, welding at bearing should be support. avoided, unless relief of restraint is provided for by other means, such as in SW7 where the flexibility of the wall provides the relief. in non-load bearing applications (SW8), a loose angle with avertical slot is bolted into an insert in the panel and welded to a plate in the slab. The slot allows for vertical movement, but enables transfer of diaphragm forces. Features: 1. Quick, easy erection is accomplished, and the slabs brace the wall panels. 2. Connections are protected when roofing or topping is placed. 3. When slabs cantilever over wall panels, no haunch is required. 4. Adequate strength can be developed to resist diaphragm shear and chord forces. Disadvantages: 1. Special forming is required for a continuous ledge or corbel. 2. Wide tee slabs do not align with narrow panel tees which necessitates a continuous ledge. It is preferred that the roof tee width matches the wall panel width. 3. When wall panel stems are turned inside, detailing is more difficult and the quality of the exterior building finish is limited to as-cast top surface unless additional finishing is used. Also, the top connection is exposed and may require protection. Eccentricities are larger and extra reinforcement may be required.

Finally, the narrowness of the wall panel stems may limit the types of connections that can be used. 4. Cantilevered roof panel connections may require overhead welding. Such connections are difficult and may require workers to operate on ladders which can be a safety hazard. Wall panel flanges require additional reinforcement when stems are blocked out. 5. The bolt sometimes hangs up in the slotted connection used in non-load bearing conditions. Also, flatness of embedded plates is critical to avoid binding of the bolted connections. Stemmed roof and floor members also commonly bear on masonry or solid walls (SW9 SW1 2). Precast tees are set on bearing pads with flanges blocked back when walls need to continue through. Either filled masonry cores or bond beams are necessary to resist member loadings. Care must be taken to avoid loading the face shell of bond beams as this will cause spalling or cracking of the block to occur. Longitudinal and vertical reinforcement in the wall is routine. Diaphragm forces are easily transferred to walls through dowelsorwelded top connections at tops of tee stems. Again, cafe is necessary when considering welding of tee stem bottoms. In general, it should be avoided.

SW1

-

SW2

SW6

SW5

A

5-36

SW8

SW11

SW12 5-3:

5.2.9 Beam to Wall Connections (BW) Various types of beam to wall connections in common use are: . On corbel with top connection . In pocket . With sleeve and dowel . With bottom connection All of the connections in this group are intended forvertical load transferonly and are not suitable for resisting moments. The beams shown are rectangular but the connections can be used with other shapes. Different wall construction, such as precast double tees, cast-in-place concrete and masonry are illustrated but, in some cases, the connections are interchangeable. 5.2.9.1 Beam to Wall Corbel Connection (BWl and BW2) The beam sits on a bearing pad suppoited by a concrete or steel corbel, projecting from the wall panel. The top connection transfers horizontal shear forces between the beam and panel, provides erection stability and braces the panel. Features: 1. Quick, easy erection. 2. Few tolerance problems. 3. Braces the wall panel. Disadvantages: 1. No moment capacity. 2. Special forming required for corbel. 3. Design of wall must consider eccentricity of the loads. 5.2.9.2 Beam to Wall Pocket Connection (BW3) A pocket iscast into thewall to receive the beam. The beam sits on a bearing pad inside the pocket. A top connection may be used. Axial shortening of the beam due to volume change should be considered when designing depth of the recess. This connection is more commonly used with cast-inpace walls, but can also be used with precast panels. Ample tolerances are required.

beam can “swing” into place. It is recommended that this connection not be used at both ends of a beam. 5.2.9.3 Sleeve and Dowel Beam to Wall Connection (BW4) A sleeve in the end of the&earn fits over a dowel protruding from the bearing, shown as a bond beam or grouted masonry core. The sleeve should be 3 or 4 times the size of the dowel to minimize field tolerance problems. In order to prevent restraint, the bottom few inches of the sleeve should be filled with a compressible material such as sand, vermiculite, or asphalt. The remainder is filled with grout. Features: 1, Quick, easy erection. 2. Volume change restraint is minimized. 3. Provides shear resistance and some torsional restraint after grouting. Disadvantages: 1. No lateral connection until sleeves are grouted. 2. No reliable moment capacity. 3. Sleeve can fill with water during erection and freeze and crack the beam, unless precautions are taken. 5.2.9.4 Beam Bottom lo Wall Connection (BW5 and BW6) This connection is used primarily when the beam is required to provide lateral restraint to the wall. This detail requires bearing plates installed in the wall. Features: I. Positive tie to the wall. Disadvantages: 1. Requires close coordination with masonry trades. 2. Level placement of bearing plate difficult. 3. Volume change shortening of the beam must be considered in design of the wall.

Features: 1. Minimum of embedded hardware for light loads. 2. Clean, concealed connections. Disadvantages: 1. Pocket dimensions must be planned so that 5-39

BW3

5-40

5.2.10 Wail to Wail Connections (WW) There are two configurations of wall to wall connections: horizontal joints, usually in combinationwithfloorconstruction,andverticaljoints. These can be further identified as:

,

, Horizontal - bolted . Horizontal - welded . Horizontal - sleeve Horizontal - post-tensioned . Vertical - bolted . Vertical - welded l

The connections from wall to wail are primarily intended to position and secure the walls although, with proper design and construction, they are capable of carrying loads from uplift, shear wall or frame action. Solid wall panels are shown but many of the connections could also be used with double tee or hollow-core wall panels. 5.2.10.1

Horizontal - Bolted Wall to Wail Connection (WWl) A threaded bolt or continuous rod extends out of the top of the lower panel and bolts through a member cast in the bottom of the upper panel. The strength of the elements in the connection can be developed by bond and lap with panel reinforcement or by continuity through the panel. Proper vertical elevation is obtained with shims or leveling nuts. The joint is later dry-packed or filled with nonshrink grout.

welded to shim inserted between the two plates. During erection, the panel is shimmed to the proper elevation and the joint dry-packed after the connection is completed. Features: 1. Positive connection between walls. 2. Connection is concealed and protected after grouting. 3. Continuous vertical tie through connection. Disadvantages: 1. Plate alignment in the walls is critical. 5.2.10.3

Horizontal - Sleeve Wail to Wail Connection (WW4) The sleeve connectors shown receive reinforcing bars and are later filled with a non-shrink grout to achieve continuity. The sleeves are capable of developing full strength of the bars. Features: 1. Continuity through the connections. 2. Connection is concealed and protected. Disadvantages: 1. No connection between wails until splice sleeves or ducts are grouted. 2. Sleeve connections and sleeve grout may be proprietary. 3. Hardware placement is critical.

5.2.10.4 Features: 1. No welding required. 2. Connection is concealed and protected after grouting. 3. Vertical uplift capacity can be developed. Disadvantages: 1. Requires accurate placement of hardware. Cast-in connection should include oversized hole or slot. 2. if projecting bolts are used, they are susceptible to damage. 5.2.10.2 Horizontal - Welded Wail to Wail Connection (WW2 and WW3) The upperwall is cast with an embedded plate in a recessed pocket. The lower wall is cast with an angle. A plate or round bar is then welded to the embedments in both the upper and lower walls. Alternately, the lower wall may also incorporate an embedded plate and the two wall panel plates are 5-42

Horizontal - Post-Tensioned Wail to Wail Connection (WW5 and WW6) Vertical post-tensioning bars are field installed in ductscast in the wall panels. The bars may be made continuouswith a couplerand post-tensioned (WW5) or they may be simply connected with a threaded coupler (WW6). Features: 1. Vertical post-tensioning can be used to withstand uplift forces. 2. Connection is hidden and protected. 3. Welding is not required. Disadvantages: 1. Duct and hardware placement in walls is critical. 2. Connection is not developed until tensioning is completed.

5.2.10.5 Vertical - Bolted Wall to Wall Connection (WW7 and WW8) Inserts, or bolts welded to steel plates are cast into panels. The loose plate or angle has slots in opposite directions on each side to allow both vertical and horizontal adjustment. If properly placed, the bolts will allow some movement for volume changes. If a rigid connection is desired, the plates can be later welded. Features: 1. Quick erection. 2. Volume change movement is accomodated. 3. When recessed, connectioncan beconcealed and protected. Disadvantages: 1. Limited field adjustment. 2. Shear transfer between panels unreliable without welding. 5.2.10.6 Vertical - Welded Wall to Wall Connection (WW9 - WWl2) Plates or angles are cast in the wall panels and are anchored with studs and/or welded reinforcing bars. A loose plate, angle or bar is welded across the joint. Features: 1. Ample adjustment allowance. 2. When recessed, connectioncan be concealed and protected. 3. Good shear transfer. Disadvantages: 1. Rigid, unyielding connection. 2. Possible volume change problems except in WW12.

s-44

WWI

ww2

ww3

ww4

ww5

WW6

ww9

WWII

5.2.11 Wail to Foundation Connections (WF) The types of wall to foundation connections commonly used are: . Welded . Bolted . Grouted . Moment Resistant . Post-Tensioned Ail of the types can be used with double tee wall panels, hollow-core wall panels or solid wall panels with the exception of vertical post-tensioning which is suitable for solid wails only. The wall panels may be load bearing or non-load bearing. Combination of welding, bolting, etc. is also used in some connections. 5.2.11.1

Welded Wail to Foundation Connection (WFl) The wall panel and the foundation have weld plates cast into them. The wall panel is set on shims. Loose angles or plates are welded to the embedded plates. Generally, two connections per panel are provided. The space under the wall is usually filled with dry-pack or non-shrink grout. Features: 1. Connection allows quick, easy erection. 2. There are few tolerance problems. 3. When the footing is not wide enough, the bottom leg of the angle can be turned under the panel. 4. When the face of the panel is in line with the face of the foundation, or grade wail, a plate can be welded between vertical plates in the wail and foundation. Disadvantages: 1. When the connection is below grade, the welding may be difficult. 2. if the connection is on the exterior face of the panel, it is susceptible to corrosion unless protected with mastic or grout. 5.2.11.2 Bolted Wail to Foundation Connections (WF2 - WF4) in WF2 and WF3, an angle or plate is attached to the wail panel and foundation wail. A cast-in insert is commonly used in the wall panel and a drilled-in expansion bolt may be used in the foundation. The wall panel is set on shims and two connections per panel are made. in place of shims, round head leveling bolts (WF4) can be used for panel align-

5-48

ment and the bolt heads welded to a plate cast in the foundation wall. The space under the panel is usually filled with dry-pack or non-shrink grout. Features: 1. A commonly used variation of this type includes the connection angle or plate bolted to the foundation and welded to the wall panel. 2. Bolting allows quick easy erection in any weather. 3. Drilled-in expansion bolts eliminate the need for any hardware to be accurately located in the foundation. Disadvantages: 1. Anchorage of the cast-in insert near the bottom of the wail panel may be difficult. 2. if not installed properly, drilled-in expansion bolts are not as reliable as cast-in inserts. 5.2.11.3 Moment Resistant Wall to Foundation Connections (WF5 and WF6) These connections are used when cantilever moments must be developed. One type develops moment resistance at the base with a welded and/ or bolted connection on each face of the wall panel. Another type includes a connection to the foundation and a connection to the interior floor slab. The floor slab connection can be made with coil rods threaded into inserts in the wall panel and cast into the floor slabs. An alternate uses the strand lifting loops in conjunction with bent reinforcing bars to accomplish the tie to the floor slab. Features: 1. Moment resistance at the base is provided. Disadvantages: 1. Par base connection, anchorage within wall panel is critical. 2. For base connection, moment must be resisted by the foundation. 3. For slab connection, location of insert vertically is critical. Moment resistance is not developed until slab connection is complete. 4. For slab connection, slab construction requires care to ensure that the bars are properly embedded and that there is no slab settlement.

5.2.11.4 Grouted Wall to Foundation Connection (WF7) The foundation is cast with corrugated steel sleeves to receive projecting reinforcing bars from the wall panel. The sleeves are filled with grout just prior to erection of the panels, which are shimmed to correct elevation and later dry-packed underneath. Features: 1. Quick, easy erection. 2. No tolerance problems. 3. Shear resistance perpendicular to wall is achieved. Disadvantages: 1. No connection for wall panel during erection. 2. Projectingdowelsfromwallpanelscancause difficulties during fabrication. 5.2.11.5 Post-Tensioned Wall to Foundation Connection (WF8) Vertical post-tensioning bars are installed in the foundation and continue through ducts in the wall panels. The bars may be coupled at the top of the foundation depending on erection considerations. Features: 1. Vertical post-tensioning can be used to resist uplift forces. 2. Moment resistance is achieved. Disadvantages: 1. Bar, duct and hardware placement accuracy in foundation and wall panels is critical. 2. There is no positive connection until the bar is tensioned.

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WFI

WF3

5-50

WF7

5.2.12 Stair to Landing Connections (SL) Precast concrete stairs can be produced with integral landings orthey may require separate landings. When landings are integral with the stairs, connections from the landing to supports are necessary. Generally, the support is a bearing wall, either precast or cast-in-place. Embedments or corbels are provided in the wall and attachment hardware is cast into the edge of the landing (SLlSL2). Connections are designed to minimize crane setting time and are completed with field welding. A thin topping may be placed to obtain a good walking surface. When landings are separate, they must be joined to the stair sections. The top stair may be recessed so that connections will be hidden when a topping slab is cast (SL3SL4). The bottom stair usually rests on a footing so that the stair is simply set on shims with no welding required (SL5). When the lower floor slab is cast, the stair is securely positioned. Features: 1. Quick, easy erection is attained, tolerances are adequate. 2. Joints can be located either at wall junctions or on continuous walls. Disadvantages: 1. Connections are exposed to view from underneath unless special grouting is done. Fireproofing may be required. 2. Plate locations in supporting structure are critical. 3. A thin topping may be necessary. 4. Stairs with integral landings require special formwork.

TOP OR BOTTOM LAND

SL2

TOP OR BOTTOM LANDING AT WALL JOINT

TOP OF STAIR AT SEPARATE LANDING

SL4

BOTTOM OF STAIR AT SEPARATE LANDING

BOTTOM OF STAIR AT FOOTING OR LANDING

5.3 Architectural Precast Concrete Connections The versatility of architectural precast concrete has led to its rapid growth, not only as an enclosure material (cladding) where shape and finish are of primary consideration, but also as a structural material where attractive appearance is combined with load bearing function. It has also been effectively used as shear walls for resisting lateral loads and as beam struts between lateral load resisting elements. Regardless of whether an architectural precast element is used in a load bearing or a non-load bearing function, various forces must be considered in its design. In non-load bearing applications, a cladding panel must resist its self weight and all other appropriate forces, such as earthquake forces, forces due to restraint of volume changes and support system movement, as well as forces due to wind, snow and construction loads. If the panel is load bearing, then in addition to the above, it must also resist and transferdead and live loads imposed on it by the supported structural members. These forces are transferred by the architectural precast element through its connections to the supporting structure. Once the loads are established and load transfer path identified, the design of the connections is based on concepts and design procedures given in earlier chapters of this Manual. However, there are several considerations which are unique to the design of architectural precast concrete connections. Thus, even though there is some duplication of previously covered material, a general discussion is given in the following paragraphs which attempts to bring together the various items pertinent to the architectural precast concrete connections. This general discussion is followed with typical details for various applications. These applications include the following broad categories: . Bearing (Direct and Eccentric) - DB, EB . Tie-Back (Bolted and Welded) - BT, WT . Alignment (Bolted and Welded) - BA, WA . Column and Beam Cover - CC, BC . Soffit Hanger - SH . Masonry Tie-Back - MT . Seismic Shear Plate - SP Unique Conditions and Solutions - UCS Some of the fundamental points that should be considered in the design of architectural precast concrete connections are: (1) Provide for a simple and direct load transfer

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path with a minimum number of connections per panel, and a minimum number of load transfer mechanisms within a connection. A connection system which renders the panel to be statically determinate is preferable because the forces can be reliably calculated. It also facilitates accomodation of volume change movements. A discussion of load transfer mechanisms within a connection is given in Chapt. 2 (Sect. 2.2). (2) Provide sufficient ductility in the connections to preclude brittle failures. (3) Recognize the interdependency of behavior of panel connection and the supporting frame. (4) Standardize connection details as much as possible. Standardization not only facilitates production and erection but also reduces the chance for error. (5) Protect connections from corrosion and fire. (6) Provide for adequate tolerances and clearances (see Sect. 1.5). (7) Plan for the shortest possible crane hook-up time. These design requirements pose aconsiderable challenge in that all of these must be considered separately as well as interactively to arrive at the best possible solution. It is not uncommon that a great deal of attention is paid to the consideration of loads while other factors, such as volume change, compatibility with frame movements, ductility and tolerances receive inadequate attention. In high seismic areas, the most common application of architectural precast concrete is as cladding panels. The Uniform Building Code(17) requires that “Precast or prefabricated non-bearing, non-shearwallpanelsorsimilarelementswhichare attached to or enclose the exterior shall be designed to resist the forces and shall accommodate movements of the structure resulting from lateral forces or temperature changes.” For seismic forces, the Uniform Building Code requires that the body of the connector be designed for a force equal to 1.33 times the required panel force and that it be ductile. Furthermore, to ensure that failure would initiate in the body of the connector and thus be ductile, the Uniform Building Code requires that all fasteners of the connection system be designed for a force equal to four times the required panel force. Design for such elevated loads requires careful consideration of anchorage of the connectors to concrete to avoid premature and sudden failures. This generally leads many Designersto specify confining hoops (such as shown

in detail UC%), deformed bar anchors, or reinforcing bars welded to plates rather than headed studs or other similar inserts. Headed studs can be used, however the Designer must ensure that sufficient anchorage is provided to preclude concrete failures. In certain situations, such as when studs are near an edge of concrete and loaded toward that edge, auxiliary confinement steel may be necessary. It is preferable that the architectural precast be connected to the structural frame with the fewest possible connections. If the connection scheme supports the precast element in a staticallydeterminate mode, the connection forces are easily and accurately determined. Furthermore, the fewer the connections, the easier it is to provide for the various movements required to accommodate volume changes, drift, etc. If a connection scheme renders the supported element statically indeterminate, it is generally not feasible to determine with certainty individual connection forces and thus all connections may need to be designed for higher loads to overcome uncertainties. It is recommended that the weight of the precast panel be carried by no more than two load bearing connections. That would facilitate accurate calculation of connection forces as well as provide for ease of design for movement accomodation. On the other hand, if a wall panel had a load bearing connector at each corner and one at the center, depending on howitwasshimmed,theweightofthe panel could be shared by the three connectors, or almost the entire weight could be carried at the center. Additional connections could be provided to carry subsequent loads, such as wind or earthquake, but the gravity load typically remains on the initial connections. If leveling bolts are used, such as in EBl, the final weld plates are proportioned for all lateral loads. The leveling bolt is usually left in place and carries the vertical load. If shims are used instead of leveling bolts and lateral loads are to be carried, a weld plate is recommended since welding of shim edges is usually unreliable for transmitting significant forces. Use of shims or bolts for leveling is a matter of individual preference; properly used, both work well. In cladding steel frame structures, it is generally preferable that the cladding panels are supported either directly on the columns or at the centerline of perimeter steel beams. In many cases however, the wall panels are mounted to the steel frame with outriggers off the frame or long panel brackets. In these cases, weight of the panels is eccentric with respect to the steel beam causing torsion in the

beam. This torsion must be considered in the design of the beam and may require use of stiffeners and/or beam bottom flange braces. For seismic forces in the plane of the panel, anchorage of the bracket to the panel can become quite difficult as the seismic forces must be combined with gravity loads. If a shear transfer plate is added to the system, such as in detail SPl, the bracket anchorage becomes more manageable. When possible, it is advantageous to arrange concrete anchor studs so that the same ones that carry tension due to gravity do not have to carry tension due to seismic forces. For example, if the horizontal leg of the angle bracket in EB6 and EB7 were welded (via shear plate) to the structure plate to carry seismic load perpendicularto the panel, the bracket/stud arrangement of EB7 would be preferred. In detail EB6 the lower studs would be in tension due to gravity loads as well as seismic forces while in detail EB7, the lower studs would carry the gravity tension and the upper studs the seismic tension. Shear would be carried by all studs in either case. In considering movement accommodation in connections, the “story drift” allowance can be 2 in. or more from one floor to the next and may present greater challenge than the forces. Spandrel panels usually have load bearing connections at the floor level with the tie-back (also known as push-pull or stay) connections located below, attached to the same floor beam. In this instance, the tie-backs are not affected by drift since the top and bottom of the floor beam move together. In the case of floor to floor wall panels or column covers, if the panel is wide it is usually rigidly fixed to and moves with the floor beam nearest the panel bottom. In this case the upper attachments become isolation connections to prevent the building movement forces from being transmitted to the panel thus the panel translates with the load supporting beam. Some designers prefer to support the panel at the top and put the isolation connections at the bottom. The isolation (movement) is facilitated by the use of slots, or more often with long rods which flex. The rods usually have to be designed to also carry tension and compression, in addition to the induced flexural stresses. If the panel or column is narrow, the connection system is sometimes selected to have both the top and bottom of the element move with their respective floors and force the panel to rotate on one of the two load bearing connections. Since the movement occurs in both directions, each load bearing connection must have the capacity to carry the full

5-57

weight of the element and also not become a tie down. Vertical movement must be allowed, for example with slots, as the panel rocks back and forth. These movement capabilities must not be compromised with the need for adequate production and erection tolerances. If combined tolerances were +1 in. and drift allowance were +2 in., a slot length of 6 in. plus the bolt diameter would be required. It is essential that the types of movement (e.g., translation or rotation) be studied and coordinated not only with the connection system but also with the wall joint locations and joint widths. For example, if a rotating column cover is between translating spandrel panels the joint width must accommodate the amount of rotation that would occur in their common height. Such considerations may govern the connection system or the location of the wall joints. At the isolation connections, movement must be available. If it is to be accomplished with sliding, matching surfaces must not lockupdue tocorrosion or binding. This can sometimes be prevented with low-friction washers, or sleeves slightly longer than the slotted receiver. Long or medium length rods or bolts can bind when load is applied at the far end. If nuts are used at sliding connections, they must be prevented from tightening or loosening with movement. This can be done with, for example, jamb nuts, patent nuts, punched threads, or by tack welding the nut to the tie-back rod (not at the stressed side), to a square plate washer large enough to have its rotation limited by an adjacent return or to a separate stub bar which would hit a stop if it turned too far. Long rods which flex with drift are more reliable and thus more commonly used. A conscious recognition of the difference between required adjustment for tolerance, and the need to prevent or allow subsequent movement is necessary. This sometimes appears to present conflicting requirements, but they can be provided for when treated individually. For example, adjustment can be accomplished with an oversized hole and then movement controlled with a plate washer welded over it. If the washer is slotted, it can take load on one axis and allow movement on the other. The washer could be welded under the piece with an oversized hole to reduce bending in the bolt. A hole off center both ways in a plate washer allows maximum adjustment in a minimum space since it can be rotated as necessary. Washers used for these purpose can usually be welded on any two sides.

5-58

For economy, the connection scheme selected should provide for rapid release of the crane hook during erection. In most situations this can be accomplished by using temporary ties for stability connections after final and completing permanent alignment. In some cases this course of action is even necessary since adjacent panels may have to be aligned simultaneously. The following pages show a number of typical details of some of the commonly used connections for cladding panels, and certain other connections that may be useful in special applications. The details should not be considered as “standard,” but are presented as ideas on which to build. Also, two or more details may have to be combined to accomplish the intended purpose. For example, DBl and DB2 are often combined. As noted previously, detailed design information, such as component sizes, weld sizes and details of anchorage, etc., is purposely omitted. The details included in this section were selected by the Architectural Precast Concrete Connections Committee which elected to have the text/ commentary incorporated side-by-side with the corresponding schematics. Thus, only a brief description of the various categories is given below followed by compilation of the schematics. 5.3.1 Bearing (Direct and Eccentric) Connections ( DB, EB) Bearing connections are intended to transfer vertical loads to the supporting structure or foundation. Bearing is provided at two points per panel either directly in the plane of the panel along the bottom edge or eccentrically located by casting integrally with the panel a continuous or localized corbel, or by anchoring a rigid structural steel section into the panel. Lateral load transfer capability can be provided by various tie-back arrangements. Tolerances in the support system generally necessitate the use of shims, leveling bolts, bearing padsand oversized or slotted holes. Direct bearing connections are used primarily for panels resting on foundations or rigid supports where movements are negligible. This includes cases where cladding panels are stacked and selfsupporting for vertical loads with tie-back connections to the structural frame to resist forces perpendicular to the panel. Eccentric bearing connections are usually used for panels above the first support level where movements of the support system are possible. Cladding panels are fastened to and/or supported by a structure located in a different plane. Practically all loads

from the cladding react eccentrically on the support structure. According to the type of connection and load transfer details, bending, combined tension and shear, and torsion must be resisted by the connection. 5.3.2 Tie-Back Connections (Bolted and Welded) W, WT) Tie-back connections keep the precast panel in a plumb position as well as resist wind and seismic loads perpendicular to the panel. Nearly every precast panel requires tie-back connections in addition to the bearing (support) connections. The important characteristic of tie-back connections is their ability to carry tension and/orcompression forces perpendicular to the panel. They may take forces or allow movement both vertically or horizontally in the plane of the panel. 5.3.3 Alignment Connections (Bolted and Welded) (BA, WA) Alignment connections are used to adjust relative position with respect to adjacent elements and do not usually transfer design lateral loads. Out-ofplane alignment of panels is often necessary, especially if they are very slender, or if prestressing or storage has caused warping or bowing. 5.3.4 Column and Beam Cover Connections (CC, BC) Precast concrete panels when used as covers over steel or cast-in-place concrete columns and beams are generally supported by the structural column or beam, and are themselves designed to transfer no vertical load otherthan their own weight. The vertical load of each length of column or beam cover section is normally supported usually at one elevation, and the panel is tied back at top and bottom for lateral load transfer and stability. Connections need sufficient adjustability to compensatefordeviations of the structural system. Column cover connections are, by their location, off en diff icult to reach and once made, difficult to adjust. When access is available, consideration should be given to providing an intermediate connection for lateral support and restraint of bowing. “Blind” connections made by welding into joints between the precast elements are sometimes used to complete the final enclosure of these elements. 5.3.5 Soffit Hanger Connections (SH) Any of the tie-back connections previously discussed could be modified to become soffit hanger connections. However, if flexible long hanger ele-

ments are used, a lateral brace in the form of a tieback or cross brace to the support structure is necessary to provide horizontal stability. 5.3.6 Masonry Tie-Back Connections (MT) Concrete cladding panels covering masonrywalls commonly use direct tie connections with an adjustable anchorage element cast into the panel and a bolt or strap anchor mortared or grouted into the masonry 5.3.7 Seismic Shear Plates (SP) In many cases, use of long cantilevered eccentric bearing connections to transfer both vertical and horizontal loads results in difficult embedments and proves to be costly. In such cases, use of weld plates (or angles) is usually a better solution. Although weld plates primarily serve as shear plates to resist forces in the plane of the panel, they also carry loads perpendicular to the panel and thus act as tie-back connections. Since seismic force is the most common in-plane force, these plates are often refered to as seismic shear plates. Details SPI throughSP4 illustrate the use of these plates. 5.3.8 Unique Conditions and Solutions (UCS) UCSl through UCS7presentsolutionsforunique connection situations. Since each of these is a special situation, description of each is given along with the corresponding detail.

Direct Bearing (DB) Design . simple l lateral restraint not provided Production l simple Erection l simple l does have large tolerance l joint may be caulked or dry-packed

4

.

.Q

Shim Stack \

.

.

b h

*

2 shim stacks / panel

DBI Design l more detailing 9 provides lateral restraint l shims must be placed to hold vertical alignment until grouting or dry packing is done l realignment is not possible once connection has been completed Production 0 more measuring l reasonable tolerance each way Erection 0 wet placement requires care l grout problem in cold weather l may be best to field drill oversized hole into foundation

or Sleeve

Variation . grout could be injected through tubes allowing more time for alignment Shim stacks occur at 2 points per panel adjacent to connection

DB2 5-60

Direct Bearing (DB) Design . preferable for bracket to be on contract drawing and shop installed l may require restraint for shim stack Production l cost substantially more if column bracket field installed Erection l reasonable, if column bracket already there l layout crew required if bracket not shop installed Variation l leveling bolt may be used in lieu of shims

. 4

*

. . *

DB3

Eccentric Bearing (EB) Design l weld all around may not be required 0 keep bearing at centerline of beam to avoid torsion l safety and sequence may dictate blockout to embed bracket in floor slab Production l simple l substantial shop fabrication l leveling bolt is costly Erection l simple l leveling bolt saves time Variations l different tieback connection may be used in lieu of weld plate l shims may be used in lieu of leveling bolt l location and configuration of weld plate may vary

EBI Design l hardware layout drawing required for G.C. l consider torque on projecting element if unsymmetrical section used Production l simple l requires early coordination with G.C. l requires additional space for storage and shipping Erection 0 simple Variations l W, I, channel, ST, flat bars, angle or TS may be used

5-62

Eccentric Bearing (EB) coordination drwg. for G.C. consider anchorage in concrete . preferable for column bracket to be on contract drwg. and shop installed l accommodates column size variation with same size panel bracket l

l

Production l simple l requires early coordination with G.C. l requires additional space for storage and shipping Erection l simple l layout crew required if bracket not shop installed Variations l leveling bolt can be used by providing two projecting bars and welding a coupling nut between bars or at end of bracket l panel bracket may be W,I channels, TS or ST

Works with column rotated 90'

hardware layout drwg. required for G.C. eliminates or reduces moment in panel 0 simple reinforcement l l

Production l simple l requires early coordination with G.C. Erection l difficult l requires layout crew before erection l panel must be removed to change shims

.)

.

*

~a .

.A ,. . . . . *.

Variations l bracket may be another structural shape *

. ..*’

‘.

. l-1/2"

Minimum

EB4

Eccentric Bearing (EB) Design l hardware layout dtwg. required for G.C. l complex haunch reinforcement Production l involved l extra forming, or haunch made separately and set in form l proper location of reinforcing steel in haunch is critical l requires early coordination with G.C. Erection l simple Variation l plate or angle may be used in haunch l welded plate or insert is optional l haunch may be continuous or intermittent l plate washer may require welding for seismic load conditions

rdware layout drwg. required for G.C. Production l simple l requires early coordination with G.C. Erection . simple Variations l leveling bolt may be used in lieu of shims l weld plate may be used in lieu of Separate tieback connection

5-64

Oversize Hole or Vertical Slot

.

:, . . .*

Eccentric Bearing (EB)

l

confinement steel around studs in panel may be required

Production l simple l requires early coordination with G.C. Erection l simple

,: ** ,. .I.

Variations tieback connection

l

important for shaped panels; can eliminate overturning moment from dead load when centerline of shim is at c.g. of panel

Production l complex forming especially if location of haunch changes Erection l simple Variations l forming made easier by substituting a bolt-on steel bracket especially if haunch location changes

5-6

Bolted Tie-Backs (BT) l

slenderness ratio must be considered for compression load

Production

Erection

lease from crane Variations l if threaded insert is used, the in-plane movement may be achieved by flexibility of the rod, or by an oversized hole at the opposite end l field weld angle to structure 0 bolt angle to structure

Design . simple l edge distance must be considered \ Production l simple Erection l simple l must coordinate with steel in foundation l accommodates large tolerance with exp. anchor Variations . if pre-set insert is used in place of exp. bolt, a slotted hole is necessary in the horizontal leg of the angle

Threaded

Insert

Bolted Tie-Backs (BT) Design l slotted hole or oversized hole may be used to accommodate erection tolerance and any required movement l consider clearances Production l simple Erection

l

not be overtightened shims may be required

Variations

l

5-68

be achieved by another connection use threaded rod as in BTl

Welded Tie-Backs (WT) l

l

l

volume change of panel a n d live load deflection of steel beam must be considered consider staggering studs to minimize magnification of the force on headed stud due to misalignment of plate rigid connection

Production l simple Erection

l

b e achieved by another connection ample adjustment allowance

Design . rigid connection l possible volume change restraint problems l connection is difficult to inspect Production l simple Erection l requires bracing until welded; bracing may be achieved by another connection l ample adjustment allowance l alignment and welding must be completed before panel above is erected

Welded Tie-Backs (WT) Design l if strap is used, volume change restraint in the plane of panel must be considered * slenderness ratio must be considered for compression load Production l simple Erection l requires bracing until welded; bracing may be achieved by another connection l threaded rod should not be overtightened if future movement at slotted insert is expected

.

a..

Plain rod with thread at one end or strap

WT: Design l live load deflection of superstructure must be considered l if bracing angle is designed as axial member, then the vertical component of force must be accounted for in the design of other connections on the same panel Production l simple . Erection 9 slots and bolts are used for temporary erection connection l weld after final alignment

’

*

.

* . .

WT4 5-70

Welded Tie-Backs (WT) Design l good solution to avoid problems caused by superstructure deflection Production l simple Erection . if hardware is assembled prior to erection, oversized holes and plate washers are required Variations l use stiffervertical members and eliminate the diagonal

Oversized

Hole

WT5 Design l a minimum bolt penetration into insert should be specified and ensured Production l simple Erection 9 quick l adjustment allowance limited by ferrule and bolt lengths l must have adequate clearance for welding Variations . weld may not be required if connection transfers only compression . could be reversed

Welded Tie-Backs (WT) l

good for seismic parallel and perpendicular forces

Production . simple Erection l tolerances require various diameter rods Variations l angle in panel may be used for ease of welding l anchorage of plates may vary .*

-. b’.

Design l good for seismic parallel forces l hardware layout drwg. required for G.C. Production . simple l requires early coordination with G.C. Erection l simple l considerable adjustment Variations l forseismicpetpendicularforces,maychange weld plate to angle

5-72

. .

*

*

Bolted Alignment (BA) Design l can also serve as a tie-back connection for light loads Production l simple l requires close thickness tolerances Erection l quick

l

not be overtightened may require horseshoe shim spacers

Slotted

Plate

Design . volume change relief is provided unless necessary to weld plate washers for specific loads ..a. ... .Q.,’ .:

Production 0 simple Erection l quick l good adjustment allowance l to avoid volume change restraint bolts should not be overtightened

’

I

5-74

BA2

Welded Alignment (WA) Design l can also serve astie-backconnectionfor normal load

light

Production l simple l face of panel to face of plate dimension is critical Erection l quick l good solution when connection is not accessible after erection

may be governed by this connection

WA1 Design l good shear transfer l rigid connection l possible volume change restraint problems Production l simple l face of panel to face of plate dimension is critical Erection l quick, easy . ample adjustment allowance Variations . various embedded plates or shapes may be welded together l one side could be bolted with slotted or oversized hole

WA2

Welded Alignment (WA) Design l rigid connection l possible volume change restraint problems Production l simple and relatively inexpensive l unusual mounting or attachment to side forms l inexpensive hardware Erection l quick l requires close joint tolerance l different size bars required to accommodate different joint widths Variations l angles may be eliminated and field weld made directly to U shaped panel bar as shown

Variation

I 5-76

WA:

/

Column Cover Connection (CC) Design . provides a rigid connection between column cover segments can be used where connection to column Or beam would be difficult due to limited access WI” minimum joint size is recommended l

l

Production allows reasonable tolerance for alignment if the column section is thin, placement and coverage of plate is difficult l

Plate Cast in Column Cover

l

Erection . panel joint must be sufficient to allow forwelding 0 care must be taken in preventing welding stain on exterior concrete care must be taken not to apply excess heat that would crack the concrete l

can carry horizontal tie back forces requires sufficient clearance between column and cover . preferable for bracket to be on contract drwg. and shop installed

l l

Production inserts must be attached to the back form for casting accuracy l

Erection alignment must be done when erecting first column section oversized holes allow for adjustment and alignment l

l

Variations can be used on any shape column covers . can be used for connecting both half column covers if near top and accessible l

Threaded Rod or Coil Rod with Nut and Washer Inserts Cast in Panel

5-78

*.

:

Column Cover Connection (CC) Design l can be used only at top of column cover where access is available for welding l used for lateral stability and alignment Production l the weld plates must be placed on the end form

M

r *

Erection l need access to top of column cover to make connections Variations l can be used on any shape column cover l can be changed to bolted

Typical

. . b. * . *

.

*

. * . * . 4 -+ . . .

.

cc3 Design . can be used for both vertical and tie-back loads with welded washer l can be used where access is difficult Production l requires that the angle bolt assembly be cast in a manner so as to keep the bolt parallel to the face of the panel Erection l requires bracing until welded l requires that the panel be properly aligned and set prior to welding and setting of the panel above

Plan View

Varlatlons l use insert and bolt in lieu of bolt welded to angle * use bolt cast close to C.G. of panel instead of bolt welded to angle Section

View

cc4 5-79

Beam Cover Connection (BC) Design l beam must be designed to prevent excessive rotation during erection l rigidity provided by welded connections must be considered

,-

Production l requires careful casting to match finishes on faces l requires a close casting tolerance on the doweled connections for the cap piece

Place 3rd

S e e DB2--/

Erection l requires that the erector place pieces in proper sequence l may require a combination of bolting, welding and grouting l care must be taken to prevent staining of exposed surface during welding Variations l alternate top conditions are shown but only one type should be used Notes l refer to EBl ,BTl and CC1

- Place 2nd

7-k

L- P l a c e 1 s t

BCI 5-80

Soff it Hanger (SH) Design . allows for adjustment and movement l may require additional bracing for lateral loads

Oversized holes with plate washers and nuts

Production l ease in casting inserts into panel Erection l allows for final alignment after panel is released l may be difficult to get to areas requiring bolting Variations l angles or other shapes maybe used instead of threaded rods

Precast Soffit Panel

SHI

5-82

Masonry Tie-Back Connection (MT) l

the masonry may need to be reinforced

Production erance Erection

l

braced prior to layup of masonry temporary bracing is required

Variations slots may be used in lieu of strap anchors

5-83

Seismic Shear Plate (SP) Design l normally one used at centerline of panel l takes seismic force parallel to panel to minimize lateral load on bearing connections l assume fixed at beam, pinned at panel l particularly advantageous when panel to beam dimension is large l also takes force perpendicular to panel l thin plate allows some vertical movement Production 0 panel plate tolerance large Erection l welding required l cannot be installed until panel fully aligned 0 large tolerance Variations l connection to panel can be made with angle and slot perpendicular to panel to allow movement perpendicular to panel l is sometimes accomplished with a pair of angles or flat bars l could be changed to bolted fastenings . simplest version is small rectangular plate to floor slab embedment when panel is close to slab edge

SPI 5-84

Seismic Shear Plate (SP) Design l similar to SPl except combined with bearing connector rather than separate l takes seismic force parallel and normal to panel to minimize requirements on bearing connector l also takes perpendicular force so bearing connector need not be welded l see also SPl Production l panel embedment serves dual purpose: so an additional one is not required Erection l since shear plate cannot be installed until panel is fully aligned, a temporary safety tieback may be required during erection l welding required l large tolerance Variations l could be welded to outstanding arm of bearing connector

SP2

Seismic Shear Plate (SP) Design l at mid-height of column covers to eliminate inertial overturn . if not welded to column, must be used in pairs and column cover rotates in plane of wall with story drift so bearing connections must allow lift off l if welded to column, the column cover translates in plane of wall which otherconnections must tolerate l items above require careful integration of entire connection system and panel joint widths for interstory displacements Production l panel plate tolerance large Erection l welding required l large tolerance l can not be installed until panel fully aligned

SP3 5-66

Seismic Shear Plate (SP) Design l shims carry full panel weight l shims should be immediately adjacent to welded angle l can not be installed until unit fully aligned so temporary tie may be required during erection l orientation of angle provides maximum capacity both parallel and perpendicular to wall Production l simple l large tolerance l separate embedment may be required for temporary tie

,t-Temporary Ti

Erection l can not be installed until panel fully aligned Variations l any type of plate, angle or T may be used for field plate l leveling bolt could be recessed in sill for ease of alignment in lieu of shims

I--

Shim

SP4 5-87

Unique Conditions & Solutions (UCS) Design l shims transferweight to bottomof vertical run in stacked panel situations l weld can only be achieved on upper part of bolt head - see variation l creep (including of shims) will transfer some indeterminate load to bolt Production l dimension from face of panel to embedded angle is critical Erection l alignment can not be adjusted after upper panel is placed l shims must be placed in joint l requires care, not safe to install shims with fingers Variations l shop weld a plate to bolt head forgreaterfield weld length . provide through bolt from wall insert and grout face pocket to eliminate weld Note l

this is an example of how connections can be combined (WT6 and WAl) and adapted to different conditions

Blind Multi-Story Cladding Connection

Unique Conditions & Solutions (UCS)

I

Design l requires oversize hole in beamwebandangle l use to limit unsupported length of rod 0 preferable for angle and holes to be on Contract drwgs. and shop installed l may have to allow for beam deflection

Tie-Back @ Limited Access Around Beam

b*

Erection

4.

.

*

allow reaching around beam flange to install nut at web

Design l use when tie-back well above beam bottom l requiresoversize hole in beamweb and channel l preferable for channel to be on contract drwg. and shop installed . I

Production . insert location and beam bracket can be held at constant distance to floor (greater panel standardization) Erection panel Variations l use MC, L or split TS

Tie-Back with No Access Between Panel & Beam

Unique Conditions & Solutions (UCS)

l

uires oversize hole in beam web and angle preferable for angle to be on contract drwg. and shop installed

Between Panel & Beam

Production l insert location must vary with beam depth Erection l use where no access between beam flange and panel Variations l use MC,C or TS

l l

s very high load capacity when it engages and confines panel reinforcement good for dynamic loads, i.e. seismic size variability makes it adaptable to many panel configurations

Production l expensive fabrication but alternates for equal capacity may be more costly iariations l bearing lug may be desirable to reduce shear on loop anchors

Embedment

Anchorage

Unique Conditions & Solutions (UCS) lesign l need for blind connection to precast panel l allow for tolerance l requires lay-out drawing to be provided to G.C. l face of panel needs no patching 3’oduction l no special production problems frection l requirestemporary bracing if angle notwelded until after alignment l simple, welded slotted tie-back connection

Cast-In-Place or Masonry Wall P/C Panel -

h :. ” . * . *q-*-. . *

. .

* * D * . . * . b *. * .. .I .

a.-. .2 . . - * : ’* . ** . 9 :.’ ‘Pa ’ * . . * 'b . . ’ .b . . * . ..*

lariations . insert could be slotted

Angle with Oversized Hole and Plate Washers

5-92

Unique Conditions & Solutions (UCS) Design l tolerates high seismic drift without complications of sliding or flexing of rod l intermediate length rods often bind rather than slide l length/diameter ratio of rod may not take adequate compression or allow sufficient flexing l wave washer flattens under nominal movement; prior to that rod is pinned both ends, subsequently pinned left end only

Articulated Tie-Back -

Production . simple l economical flat bar embedment Erection l fast; carries load immediately yet allows subsequent alignment l wave washer (spring, etc.) must be installed on side which is not loaded under dead load only but should not be over tightened l wave washer is standard off the shelf hardware l ample tolerance

Pre-Welded to Beam or Column

Variations l forfull pivot at beam end, seevariation sketch. l coil spring or neoprene washer could be substituted for wave washer l compression capacity can be increased with loose pipe over rod since it limits rod buckling

Detail Flat Bars

Section A-A

ock Nut or Tack Weld to Allow Pi oting

Variation

ucs7 5-93

APPENDIX A DESIGN AIDS Figures A-i - Maximum seasonal climatic temperature change, deg. F. . . . . . A-2 A-2 - Annual average ambient relative humidity, percent. . . . . . . . . . . . . . A-2 A-3 - Design pull-out strength of stud groups (including edge and member thickness effects). . . . . . . . . . . A-30 Tables A-i - Creep and shrinkage strains (millionths) . . . . . . . . . . . . . . . . . . . A-3 A-2 - Correction factors for prestress and concrete strength (creep only) A-3 A-3 - Correction factors for relative humidity. . . . . . . . . . . . . . . . . . . . . A-4 A-4 - Correction factors for volume/surface ratio . . . . . . . . . . . A-4 A-5 - Design temperature strains (millionths) . . . . . . . . . . . . . . . , . . . A-4 A-6 - Volume change strains for typical building elements (millionths) . . , . A-5 A-7 - Volume change strains for typical building elements (millionths) . . . . A-5 A-8 - Equivalent volume change strains for typical continuous building frames (millionths) . . . . . . . . . . . . . A-6 A-9 - Equivalent volume change strains for typical continuous building frames (millionths) . . . . . . . . . . . , . A-6 A-l 0 - Reinforcing bar data . . . . , . . . . . . A-7 A-l 1 - Required embedment length for standard end hooks on Grade 60 bars . . . . . . . . . . . . . . . . . . . . . . . . A-8 A-l 2 - Required development and lap lengths for Grade 60 bars . . . . . . . A-9 A-l 3 - Allowable working stress and design strength of welds . . . . . . . . A-10 A-14 - Strength of fillet welds for building construction . . . . . . . . . . . . . . . . . . A-l 0 A-15 - Size of fillet weld required to develop full strength of bar, welded onaside . . . . . . . . . , . . . , . A-l 1

A-l 6 - Size of fillet weld required to develop full strength of bar, welded both sides . . . . . . . , . . . . . A-l 2 A-l 7 - Minimum length of weld to develop full strength of bar, weld parallel tobar....................... A-13 A-18 - Design strength of connection with welded cross bar(kips) . . . . . . . . . A-14 A-19 - Dimensions of headed studs. . . . . A-15 A-20 - Development length for deformed bar anchors . . . . . . . . . . . . . . . . . . A-l 5 A-21 - Screw thread, bolt head and nut standards . . . . . . . . . . . . . . . . . . . . A-l 6 A-22 - Strength of bolts and threaded rods A-l 7 A-23 - Nominal strength of machine bolts in “ferrules” or “weld nuts” . . . . . . A-17 A-24 - Strength of wires/rods used in concrete inserts . . . . . . . . . . . . . . . A-l 7 A-25 - Range of expansion bolt strengths (from manufacturers’ catalogs) . . . A-17 A-26 - Plastic section moduli and shape factors . . . . . . . . . . . . . . . . . . . . . . A-l 8 A-27 - Prestressing steel (ASTM A41 6) properties and allowable design loads. . . . . , . . . . . . . . . . . . . . . . . A-19 A-28 - Design strength of concrete brackets, corbels, or haunches . , . A-20 A-29 - Design strength of structural steel haunches - concrete . . . . . . . . . . A-25 A-30 - Design strength of structural steel haunches - reinforcement . . . . . , . A-26 A-31 - Shear strength of connection angles . . . . . . . . . . . . . . . , . . . . . . A-27 A-32 - Axial strength of connection angles. . . . . . . . . . . . . . . . . . . . . . A-27 A-33 - Tensile strength of welded headed studs and bolts (see Fig. 4.11 .l) . . A-28 A-34 - Stud groups: Minimum thickness of member for truncated pyramid failure. . . . . . . . . . . . . . . . . . . . . . . A-29 A-35 - Shear strength of welded headed studs and bolts . , . , , . . . . . . . . . . . A-31 A-36 - Properties of weld groups treated aslines(t,=l) . . . . . . . . . . . . . . . A-32 A-37 - Column base plate thickness requirements . . . . . . . . . . . . . . . . . A-33

A-l

75

A-2

Table A-l -Creep and shrinkage strains (millionths) Concrete Release Strength q 3500 psi Average Prestress = 600 psi Relatfve Humidity = 70% Volume/Surface Ratio = 1.5 in.

T-

Creep Time Ways)

Normal Weight

Lightweight

Shrinkage Accelerated Cure

Moist Cure

1

29

51 65 76 86

76 97 114 127

10 29 47 63 79

14 40 64 85 104

10 20 30 40 50 60 70 80 90 100

90 118 137 150 161 169 177 183 188 193

133 176 204 224 239 252 263 272 280 287

86 149 198 236 267 292 314 332 348 361

113 185 235 272 300 322 340 355 367 378

200

222

331

439

434

1 Yr

244

363

487

465

3 Yr

273

407

533

494

5 Yr

283

422

544

500

Final

315

468

560

510

3 5 7 9

43

I

Table A-2 - Correction factors for prestress and concrete strength (creep onl! Release Strength, f’,l (psi) Avg. PIA (psi) 0

2500 0.00

200 400 600 800

0.39 0.79 1.18 1.58

1000

1.97 2.37 2.76

1200 1400 1600 1800 2000 2200 2400 2600 2800 3000

3000 0.00

6000 0.00

0.36 0.72 1.08 1.44

0.25 0.51 0.76 1.02

1.80 2.16 2.52 2.88 3.24

1.27 1.53 1.78 2.04 2.29 2.55 2.80 3.06 3.31 3.56 3.82

Table A-3 - Correction factors for relative humidity Avg. Ambient R. H. (from Fig. A-2) 40 50 60 70 80 90 100

Creep

Shrinkage

1.25 1.17 1.08 1.00 0.92 0.83 0.75

1.43 1.29 1.14 1.00 0.86 0.43 0.00

Table A-4 - Correction factors for volume/surface ratio ShrinkaQe

Creep Time Idays

v ;

V/S 4

5

6

1

2

3

4

5

6

0.49 0.50 0.51 0.51 0.52

0.32 0.33 0.33 0.34 0.35

0.21 0.22 0.23 0.23 0.24

0.15 0.15 0.16 0.16 0.17

1.25 1.24 1.23 1.23 1.22

0.80 0.80 0.81 0.81 0.82

0.50 0.51 0.52 0.52 0.53

0.31 0.31 0.32 0.33 0.34

0.19 0.19 0.20 0.20 0.21

0.11 0.11 0.12 0.12 0.12

0.80 0.82 0.83 0.84 0.85 0.86 0.86 0.87 0.87 0.87

0.52 0.56 0.58 0.60 0.62 0.64 0.65 0.66 0.67 0.68

0.35 0.39 0.41 0.44 0.46 0.48 0.49 0.51 0.52 0.53

0.24 0.27 0.30 0.32 0.34 0.36 0.37 0.39 0.40 0.42

0.17 0.19 0.21 0.23 0.25 0.26 0.28 0.29 0.31 0.32

1.21 1.19 1.17 1.15 1.14 1.13 1.12 1.12 1.11 1.11

0.82 0.84 0.85 0.86 0.87 0.88 0.88 0.89 0.89 0.89

0.53 0.57 0.59 0.62 0.63 0.65 0.66 0.67 0.68 0.69

0.34 0.37 0.40 0.42 0.44 0.46 0.48 0.49 0.50 0.51

0.21 0.23 0.26 0.28 0.29 0.31 0.32 0.34 0.35 0.36

0.13 0.14 0.16 0.17 0.19 0.20 0.21 0.22 0.23 0.24

1.13

0.90

0.74

0.61

0.51

0.42

1.08

0.92

0.75

0.59

0.44

0.31

1 Yr

1.11

0.91

0.77

0.67

0.58

0.50

1.07

0.93

0.79

0.64

0.50

0.38

3 Yr

1.10

0.92

0.81

0.73

0.67

0.62

1.06

0.94

0.82

0.71

0.59

0.47

5 Yr

1.10

0.92

0.82

0.75

0.70

0.66

1.06

0.94

0.83

0.72

0.61

0.49

1.09

0.93

0.83

0.77

0.74

0.72

1.05

0.95

0.85

0.75

0.64

0.54

1

2

3

1

1.30 1.29 1.28 1.28 1.27

0.78 0.78 0.79 0.79 0.80

10

20 30 40 50 60 70 80 90 100

1.26 1.23 1.21 1.20 1.19 1.18 1.17 1.16 1.16 1.15

200

)

3 5 7 9

Final

-

-

Table A-5 - Design temperature strains’ (millionths) Temperature Zone (from Fig. A-l)

Normal Weight

Lightweight

Heated

Unheated

Heated

10

20 30

30 60 90

45 90 135

25 50 75

38 75 113

40 50 60

120 150 180

180 225 270

100 125 150

150 188 225

70 80 90 100

210 240 270 300

315 360 405 450

175

263 300 338 375

200 225 250

Unheated

1 Based on accepted coefficients of thermal expansion, reduced to account for thermal lag (see Ref.53). A-4

Table A-6 -Volume change strains for typical building elements (millionths) Prestressed Members (P/A = 600 psi) Lightweight Normal Weight Concrete

Heated 0 10 20 30 40 50 60 70 80 90 100

0 10 20 30 40 50 60 70 80 90 100

584 614 644 674 704 734 764 794 824 854 884

584 629 674 719 764 809 854 899 944 989 1034

533 563 593 623 653 683 713 743 773 803 833

533 578 623 668 713 758 803 848 a93 938 983

483 513 543 573 603 633 663 693 723 753 783

483 528 573 618 663 708 753 798 843 888 933

Concrete

Buildings

432 462 492 522 552 582 612 642 672 702 732

382 412 442 472 502 532 562 592 622 652 682

617 642 667 692 717 742 767 792 817 842 867

Unht

lted SI

432 477 522 567 612 657 702 747 792 837 882

382 427 472 517 562 607 652 697 742 787 832

564 589 614 639 664 689 714 739 764 789 814

512 537 562 587 612 637 662 687 712 737 762

459 484 509 534 559 584 609 634 659 684 709

407 432 467 482 507 532 557 582 607 632 657

564 602 639 677 714 752 789 827 864 902 939

512 549 587 624 662 699 737 774 812 849 887

459 497 534 572 609 647 684 722 759 797 834

407 444 482 519 557 594 632 669 707 744 782

lcture 617 654 692 729 767 804 a42 a79 917 954 992

Table A-7 - Volume change strains for typical building elements (millionths4 - .

Temp. Zone (fromFig.A-1)

Non-Prestressed Members Normal Weight Concrete Lightweight Concrete Avg. R. H. (from Fig. A-2) Avg. R. H. (from Fig. A-2) 401 501 601 701 80 401 501 601 701 80 Heated Buildings

0 10 20 30 40 50 60 70 80 90 100

269 299 329 359 389 419 449 479 509 539 569

242 272 302 332 362 392 422 452 482 512 542

215 245 275 305 335 365 395 425 455 485 515

188 218 248 278 308 338 368 398 428 458 488

0 10 20 30 40 50 60 70 80 90 100

269 314 359 404 449 494 539 584 629 674 719

242 287 332 377 422 467 512 557 602 647 692

215 260 305 350 395 440 485 530 575 620 665

188 233 278 323 368 413 458 503 548 593 638

161 191 221 251 281 311 341 371 401 431 461

Unheated 161 206 251 296 341 386 431 476 521 566 611

269 294 319 344 369 394 419 444 469 494 519

242 267 292 317 342 367 392 417 442 467 492

215 240 265 290 315 340 365 390 415 440 465

188 213 238 263 288 313 338 363 388 413 438

161 186 211 236 261 286 311 336 361 386 411

215 252 290 327 365 402 440 477 515 552 590

188 226 263 301 338 376 413 451 488 526 563

161 199 236 274 311 349 386 424 461 499 536

Structures 269 306 344 381 419 456 494 531 569 606 644

242 279 317 354 392 429 467 504 542 579 617

!

A-5

Table A-8 - Equivalent volume change strains for typical continuous -_ bbilding frames (millionths)

Temp. Zone (from Fig. 0 10 20 30 40 50 60 70 80 90 100

Prestressed Members (P/A = 600 psi) Normal Weight Concrete Lightweight Concrete Avg. R. H. (from Fig. A-2) Avg. R. H. (from Fig. A-2) A-l)

40

117 137 157 177 197 217 237 257 277 297 317

107 127 147 167 187 207 227 247 267 287 307

50

60 70 80 Heated Buildings

97 117 137 157 177 197 217 237 257 277 297

86 106 126 146 166 186 206 226 246 266 286

76 96 116 136 156 176 196 216 236 256 276

117 147 177 207 237 267 297 327 357 387 417

107 137 167 197 227 257 287 317 347 377 407

97 127 157 187 217 247 277 307 337 367 397

123 140 157 173 190 207 223 240 257 273 290

50

60

70

80

113 130 146 163 180 196 213 230 246 263 280

102 119 136 152 169 186 202 219 236 252 269

92 109 125 142 159 175 192 209 225 242 259

81 98 115 131 148 165 181 198 215 231 248

86 116 146 176 206 236 266 296 326 356

113 138 163 188 213 238 263 288 313 338

102 127 152 177 202 227 252 277 302 327

92 117 142 167 192 217 242 267 292 317

81 106 131 156 181 206 231 256 281 306

386

363

352

342

331

Unheated 0 10 20 30 40 50 60 70 80 90 100

40

Structures

Table A-9 -Equivalent volume change strains fol‘1 :ypical continuous building frames (millionths)

Temp. Zone -

(from Fig A - l )

Non-Prestressed Normal Weight Concrete Avg. R. H. (from Fig. A-2) 40

50

1

60

1

70

/

Members Lightweight Concrete Avg. R. H. (from Fig. A-2) 80

40

/

50

1

60

1

70

/

80

Heated Buildin! 0 10 20 30 40 50 60 70

a0

90

100 0 10 20 30 40 50 60 70

80

90 100

A-6

54 74 94 114 134 154 174 194 214 234 254

48 68 88 108 128 148 168 188 208 228 248

43 63 83 103 123 143 163 la3 203 223 243

38 58 78 98 118 138 158 178 198 218 238

32 52 72 92 112 132 152 172 192 212 232

54 70 a7 104 120 137 154 170 187 204 220

48 65 82 98 115 132 148 165 182 198 215

43 60 76 93 110 126 143 160 176 193 210

38 54 71 88 104 121 138 154 171 188 204

32 49 66 82 99 116 132 149 166 182 199

54 a4 114 144 174 204 234 264 294 324 354

48 78 108 138 168 198 228 258 288 318 348

43 73 103 133 163 193 223 253 283 313 343

3868 98 128 158 188 218 248 278 308 338

32 62 92 122 152 182 212 242 272 302 332

54 79 104 129 154 179 204 229 254 279 304

48 73 98 123 148 173 198 223 248 273 298

43 68 93 118 143 168 193 218 243 268 293

38 63 88 113 138 163 188 213 238 263 288

32 57 82 107 132 157 la2 207 232 257 282

Table A-10 - Reinforcing bar data

#9 #lO #ll

3.400 4.303 5.313

#14 #18

7.65 13.60

1.128 1.270 1.410

1 .oo 1.27 1.56

3.544 3.990 4.430

1.693 2.257

2.25 4.00

5.32 7.09

STANDARD HOOKS

1

STIRRUP AND TIE-HOOKS

Hook

46,or 4 2-1/2" Min.

L

IL

Beam

C, Beam

90"

Bar Size #3 #4 #5 #6 #7 #8/ # 9 1

180 d e gree D

A or G

90 deg J

90 deg

135"

135 degree

AorG

D

A or G

A or G

2-114 3 3-314

5 6 7

3 4 5

6 8 10

2-112 3 3-3t4

8 10 ll 15

6 7 ( 8 1 ll-314

12 14 16 19

4 4-112 6 12 14 16

4 4-ll2 5-1R

4-ll2 S-114 6 g-1/2

l-112 2 2-112 4-112 5-114 6

7-314 9 10-114

4-112 5-114 6

/

H

Note: All dimensions (D,A or G,J and H) are in inches

A-7

Table A-l 1 - Required embedment length for standard end hooks on Grade 60 bar9 Multiply table value by: z dh = 1200 db/ K; min. 8d, or 6 in.

0.7 for side cover r 2.5 in. and end cover (90 hook only) 12 in. 0.8 for tles or stlrrups spaced 2 3d, 1.3 for llghtweight concrete A LY!ZQL for excess reinforcement A s prov’d

where: d, = diameter of bar, in.

1 for Grade 40 bars, embedment lengths are two-thirds of the table values, but not less than the minimum Id,, For limitations, see ACI 318.83(6),

Sect. 12.5

Y

2-1/2” Min.

”h

XP

Standard 90” Hook

Standard 180” Hook

Embedment length, Id,, (in.) Bar Size #3 #4 #5 #6 #7 #8 #9

#lO #ll

A-8

Normal wefght concrete, f’e (psi) 3000

4000

5000

6000

7000

8000

Min. 1 dh

8 ll 14 17

7 10 12 14

7 9 ll 13

19

17

15

6 8 10 12 14 16

6 7 9 ll 13 15

6 7 9 10 12 14 15 17

6 6 6 6 7 8 9 10

19

12

22 25 28 31

19 22 24 27

17

19

22 24

18

20 22

16

18 20

Table A-l 2 - Required development and lap lengths for Grade 60 bar9 Multiply table values by: Tension:

1.4 1.33 1.18 0.8

1,= 2400 A,/Jf;c; min. 24d, or 12 in. Compression development length: t,= 1200 A,,/q; mln. 18d, or 8 In.

for top reinforcement for “all-llghwelght” concrete for “sand-lightwelght” concrete for bar spacing 6” or more (3” from member face)

As

req’d

Ao

prov’d

for excess relnforcement

Compresslon spllce length: compression t d; min. 30d, or 12 In. where: Ab = area of Individual bar, sq. in. d, = dlameter of bar, In.

For llmitations, see ACI 31&83(6), -

lBar Size #3 #4 #5 #6 #7 #8 #9 #lO #ll

l-

fc = 3000 psi 1renslon

12 12 15 19 26 35 44 56 68

12 12 15 18 23 30 38 48 59

Com-r pres-

Tenslon

F

1.3 ld

1.7 I,,

presslon Id

12 16 20 23 30 39 49 63 77

15 20 26 31 39 51 65 82 101

8 9 12 14 17 19 21 24 27

12 16 20 23 27 32 40 51 63

1.7 ld 15 20 26 31 36 42 53 67 82

1.3 Id

1.7 Zd

12 12 15 18 21 27 34 43 53

12 16 20 23 27 35 44 56 69

15 20 26 31 36 46 58 73 90

renslo

1.3 ld 12 12 15 18 21 24 29 36 45

12 16 20 23 27 31 37 47 58

1.7 ld 15 20 26 31 36 41 49 62 76

8 9 11 14 16 18 20 23 26

12 12 15 18 21 24 27 34 42

T

Mln. pres- fZomp slon !8pllce ld 8 9 ll 14 16 18 20 23 25 .

fc = 8000 psi Compresslon

presslon l-

Id 8 9 ll 14 16 18 20 23 26

ld

T Com-

‘enslof

T-Com-

Tenslon

f, = 7000 psi

sion 1.3 Id

fe P 5000 psi

l- Com- t

Tenslon

ll 14 16 19 22 25 28 31

fe = 6000 psi

Bar 1 ldSlze !

Chapter 12. Development and lap lengths (In.) fe = 4000 psi

Compresslon 6 8

1.3 Zd 11.75

1 for Grade 40 barwequired lengths are two-thirds of the table values, but not less than the required minimum lengths.

1.3 Zd

1.7 Id

ld

12 16 20 23 27 31 35 44 54

15 20 26 31 36 41 48 56 71

8 9 ll 14 16 18 20 23 26

12 15 19 23 26 30 34 38 42

T

Min, Zomp Splfce 12 15 19 23 26 30 34 38 42

A-9

Table A-13 - Allowable working stress and design strength of weldsl Electrode

Allowable Working Stress (ksi)

Design Strength* (ksi)

E60

18

30

E80

24

40

E90

27

45

El00

30

50

1 Based on AISC Spec. for Buildings(32). For bridges, use 90% of values. 2 Use factored loads and @ = 1 .O with these values.

Table A-14 - Strength of fillet welds for building construction’ E60 Working Stress (k/in)

Fillet Weld Size

I

I l

1/8

I

1.59

Electrodes Design Strength’ (Min) I

2.65

E70 Electrodes Working Design Stress (Min) Strength* (Min) I

1.86

I

3.09

3116

2.39

3.98

2.78

4.64

II4

3.18

5.30

3.71

6.19

5116

3.98

6.63

4.64

7.73

3J6 7ll6

I I

5.57

l

9.28

I

6.50

I

10.38

ll2

6.36

10.61

7.42

12.37

9116

7.16

11.93

8.35

13.92

518

7.95

13.26

9.28

15.47

1 Use 90% of values for bridges. Assumes 45’ fillet. 2 Use factored loads and $ = 1 .O with these values.

I

I

Table A-15- Size of fillet weld required to develop full strength of bar, welded one side Bar perpendicular lo plate, welded one side Plate f,

q

36 ksi Grade 40 Bar E70 Electrode

Bar Slze

E80

Electrode

E90

Electrode

Nominal Weld Mln. Plate Nominal Weld Mln. Plate Nominal Weld Mln. Plate Slze (In.) Thlckness (In.) Slze (In.) Thickness (In.) Slze (In.) Thlckness (In.)

#3

118

ll4

118

Il4

ll8

ll4

#4

3116

lf4

3116

ll4

3116

ll4

#5

ll4

5116

306

5116

3116

5116

#6

ll4

5116

ll4

5116

ll4

318

#7

SI16

318

5116

318

ll4

318

#8

318

7116

5116

7116

5116

7116

#9

7116

ll2

318

ll2

5116

ll2

#lO

7116

9116

318

9116

318

9116

#ll

ll2

518

7116

518

318

518

Grade 60 Bar #3 #4

3116 ll4

ll4 5116

3116 114

ll4 5116

3116 ll4

ll4 5116

#5

5116

318

5116

318

ll4

318

#6

318

7116

5116

ll2

5116

ll2

#7

7116

9116

318

9116

318

9116

318

#8

1/2

5i8

7116

518

#9

9116

11116

ll2

ll/16

7116

ll/16

#lO

SI8

314

9116

314

ll2

13116

#ll

ll/16

1306

518

13116

9116

718

’

518

A-ll

.

Table A-l 6 - Size of fillet weld required to develop full strength of bar, welded both sides Bar perpendicular to piate, weided both sides

/

Piate fy = 36 ksi

Grade 40 Bar E90 Electrode Min. Piate Nominal Weidl Min. Piate Min. Piate Nominal Weid Nominal Weid Thickness (In.) Size (In.) Thickness (ín.: Thickness (In.) Size (in.) Size (In.) E70 Electrode

Bar Size #3 #4 #5 #6 #7

l

#a #9 #lO #ll

va

lia lla 3116 3116 3116 ll4 ll4 ll4

E80 Electrode

306 ll4 5116 318 7116 ll2 ll2 9116 518

*

3116 114 5116 318 7116 ll2 9116 518 518

va ll8 ll8 lia 3116 3116 3116 ll4 114

Grade 60 Bar I

ll8 3116 3116 114 ll4 5116 5116 318 3i6

#3 #4 #5 #6 #7

#a #9 #lO #ll I

A-12

I

ll4 318 7116 ll2 518 11116 314 718 15116

ll4 318 7116 1R 518 11116 314 13116 15116 /

lia ll8 lia lia lia 3116 3116 3116 ll4 1

3116 ll4 5116 318 7116 ll2 9116 518 11116 J

va ll0 3116 3116 3116 ll4 ll4 5116 5116

ll4 3/6 7116 lf2 518 ll/16 314 716 15116

Table A-17 - Minimum length of weld to develop full strength of bar, weld parallel to bar’

Electrode

E70

Bar size

r

Min. plate thickness for weld length (In.) I

ll4

5116

318

#3 #4 #5

l-1/4 l-314 2-114

l-114 l-314 2-114

l-114 l-314 2-114

#6 #7 #8

2-314

2-112 3

2-112 3 3-112

2-ll2 3 3-112

3 3-112

4

4 4-114 5-l l4

4 4-114 4-314

j l

#9 #lO #ll

E80

#3 #4 #5

l-ll4 l-ll2 2

l-114 l-ll2 2

l-114 l-1/2

#6 #7 #8

2-314

2-114 3

2-114 2-314 3-114

/ 1

#3 #4 #5

1 l-112 2

1 l-112 l-314

1 l-ll2 l-314

#6 #7 #8

2-314

2-114 3

2 2-112 3-114

#9 #lO #ll

7116

ll2

9116

518

‘:

4 4-114 4-314

4 4-114 4-314

2

4

#9 #lO #ll

E90

I

-L-LL

2-ll4 2-314 3

2-314 3

3-112 4-114 5-114

31112 3-314 4-ll2

2 2-112 2-314 3-112 4-ll4 5-114

I

3-112 3-314 4-114

3-l 12 3-314 4;ll4

I 2-112 2-314 3 3-314 4-ll2

3 3-112 4

3 3-112 3-114

Min. I spllce length (In.)

Bar slze

l-114 l-ll2 2

#3 #4 #5

2-ll4 2-112 3

#6 #7 #8

3-114 3-314 4

#9 #lO

1 l-ll4 l-314

#3 #4 #5

2 2-114 2-112

#6 #7 #8

3 3-114 3-112

#9 #lO #ll

1 l-114 l-ll2

#3 #4 #5

l-3/4 2 2-114

#6 #7 #8

2-112 3 3-114

#9 #lO #ll

#ll

1 Table is based on reinforcing bar fv = 60 ksi. Plate shear yield -19.8 ksi A-13

I

Table A-18 - Design strength of connection with welded cross bar (kips)

Bars Same Size

Grade 40 Reinforcing bars; E70 weld electrodes

#3

#4

#5

#6

#7

#9

#lO

#ll

13.2 15.4 17.6

14.9 17.4 19.8

19.6 23.3

24.8

19.8 22.3 24.8

22.4 25.2 28.0

25.2 28.4 31.5

28.0 31.5 35.0

#8

#3 #4 #5

2.5 3.3 4.1

3.3 4.4 5.5

4.1 5.5 6.9

4.9 6.6 8.2

7.7 9.6

11.0

#6 #7

4.9

6.6 7.7

8.2 9.6 11.0

9.9 ll.5 13.2

11.5 13.5 15.4

14.9

17.4 19.6

#8 #9 #lO #ll

Grade 60 Reinforcing 1 Irs; E90 weld electrodes

#3

#4

#5

#6

#3 #4 #5

3.2 4.2 5.3

4.2 5.7 7.1

5.3 7.1 8.8

6.4 8.5 10.6

#6 #7 #8

6.4

8.5 9.9

10.6 12.4 14.1

12.7 14.8 17.0

#9 #lO #ll

A-14

19.1

I

#7

#8

#9

#lO

#ll

14.8 17.3 19.8

17.0 19.8 22.6

19.1 22.3 25.5

25.1 28.7

31.9

22.3

25.5

28.8

32.4

36.0

25.1

28.7 31.9

32.4 36.0

36.5 40.5

40.5 45.0

Table A-1 9 - Dimensions of headed studs

Shank Diameter d, (in.)

Head Diameter d, Un.1

Head Thickness t, Un.1

Stock Lengths (In.) (Nominal Dimensions)

114

ll2

3116

1,2-lR,4

3/8

3/4

9/32

3,4,6

ll2

1

5/16

2,3,4,5, 698

518

l-l/4

5116

2,4,6, 8

314

l-114

3f8

3,3-l&?, 4, 4-112, 5, 6,7, 8

718

l-318

318

3-112, 4, 5, 6, 7,8

Table A-20 - Development length for deformed bar anchorsls* Concrete Strength f’c

I

Normal Weight Concrete ( h = 1.0)

1

Sand-Lightweight Concrete ( li = 0.85)

Bar Diameter (In.) 114

318

112

518

3000

12

12

16

21

4000

12

12

14

5000

12

12

13

6000

12

12

7000

12

12

8000

12

12

Bar Dlameter (In.) 314 ~

Il4

318

112

518

314

25

12

15

19

24

29

18

21

12

13

17

21

25

16

19

12

12

15

19

23

12

15

17

12

12

14

17

21

12

13

16

12

12

13

16

19

12

13

15

12

12

12

15

18

1 f, = 60,000 psi; for values above 60,000 psi, multiply by (2 - 6otpoo ) 2 For top bars, multiply by 1.4

Y

A-15

.--*- __ -- -- __.__... --.-I -- .

TahlA A-21- Screw thread. balt head and nut

Diam. of Bolt

standards

Bolt head dimensions, rounded to nearest 1/16 Inch, are in accordance wlth ANSI 818.2.1-1972 (Square and Hex) Standard Dimensions for Bolt Heads Heavy Hex Square Hex Helght Width Width Height Width Width Height Width Width (Ll.)

ll2

,,n,

314

l-1/16

5116

3/4

718

318

718

SI8

15116

l-5116

7116

15116

l-1/16

7116

l-106

l-1/4

7116

314 718

l-118 l-5/16

l-9116 l-718

ll2 518

l-va l-5/16

l-5/16 l-112

1/2

l-114

l-7116

ll2

9116

l-711 6

l-11116

9116

1

l-1/2

2-118

ll/16

l-112

l-314

ll/16

i-518

l-718

11116

l-114

i-718

2-518

718

i

2-1116

718

2

2-5116

718

-718

1

318

1 r-N

Square

Nut Size (in.) 112 518

Nut dlmenslons, rounded to nearest 106 lnch, are In accordance with ANSI B18.2.2-1972 Dimensions for Nuts Square Hex Heavy Square Heavy Hex Wldth Width Height Width Wldth Height Wldth Width Helght Width Width Height N F C N F C N F C N F C (In.) (In.) (tn.) (In.) (In.) (In.) (In.) (In.) (In.) (In.) (In.) (In.) 13116 1

l-va l-7116

314

l-lia

718

l-5116

1 1l-1/4

314 718 1 l-114

A-16

7116 9116

314 15116

718 l-1116

7116 9116

l-9116

11116

l-lia

l-5116

l-718

13116

l-5/16

l-1/2

l-1/2

2-lla

718

l-112

l-718

2-518

l-1/8

l-718

.627 ,739 .a3a 1.075

.442 ,601 .7a5 1.227

.302 .419 551 .a90

.334 .462 .606 .969

718 l-1116

l-114 l-112

lf2 518

718 l-1/16

1 l-114

ll2 518

518

l-114

l-314

314

l-114

l-7116

314

314

l-7116

2-1116

718

l-7116 l-11116

718

l-314

718

i-cija

2-5116

1

2-3116

ll16

2

2-13116

l-114

10 9 8 7

i-518 2

112

518

314

fo 6 inches

l-1/4

l-112

l-314

Over 6 inches

l-112

l-3/4

2

Length of Bolt

i-718

1

Z-5116

718 2 2-114

l-114

1

2-l

l-114 14

2-112

Z-314 3

Table A-22 - Strength of bolts and threaded rods

r-

r

Bolt Nominal Iiametel Area (in.) (sq. In.)

rensile ;tress Area (sq. in.

l-

r

Threaded A-36 Rods l-

SI 9ei w

Ter lon Nominal Servlce itrength Load (kW3 (kW

Nomina Strengtl (kW4

Setvice Load (kW4

7.46

2.84 4.52

3.56 5.57

1.96 3.07

11.02

6.69

8.02

4.42

518

0.307

4.97

314

0.442

0.334

12.02

7.36

8.75

4.77

718

0.601

0.462

16.63

10.16

11.90

6.49

0.606

21.82

13.33

15.54

8.48

0.969

34.88

21.32

24.29

13.25

1

0.785

l-114

1.227

5.11 8.14

3.12

T-

Ten on She iàr L. Uomlnal jervlce INominal 4Sewice ;trength Load ! Strength Load (kW (kW) WW (kW4 4.69

3.88 6.08

0.196

ASTM A-307 Bolts

2.12 3.32

0.142 0.226

ll2

!I

i-

I

15.25

9.23

10.91

6.01

20.00

12.11

14.25

7.85

31.98

19.38

22.27 - 12.27

Table A-23 - Nominal strength of machine bolts in “ferrules” or “weld nuts” Bolt Dla. Un.1

Bolt Grade (ASTM)

Tenslle Strength PS (Ib)

A307 A307 A307 A307

4820 7680 11,360 20,600

ll2 518 314 1

Shear Ferrule Data Strength Threads/in. Bolt Length ‘J, (Ib) 3330 5220 7510 13,350

13 ll 10 8

1 l-116 l-118 l-114

Table A-24 - Strength of wireskods used in concrete inserts Wlre/Rod Nominal Díam. Un.) .218 .223 .240 .243 .262 .306 .306 .375 .440

Classlflcatlon

AISI or ASTM Number (Referente)

LowCarbon Medium High Carbon Low Carbon Medium High Carbon Low Carbn LowCarbon Medium High Carbon Medium Low Carbon Medium High Carbon

1008 1030 1008 1038 1008 1008 1038 1018 1038

Approx. Min. Ultimate Strength (Ib) 2,800 4,500 3,100 7,000 4,100 4,200 7,400 9,500 16,000

Approx. Mln. Yleld Strength (Ib) 6,400 3,800 2,500 6,000 3,200 3,300 6,500 7,300 13,500

Approx. Mln. Shear Strengtl (Ib) 1,850 3,000 2,050 4,650 2,750 2,800 4,950 6,350 10,650

Table A-25 - Range of expansion bolt strength&* (from manufacturers’ catalogs) Bolt Dlameter(ln.)

Tensile

Strength (Ib)

Shear Strength (Ib)

114

1,500 - 3,600

1,200 - 3,500

318

3,200

2,500

-

6,000

-

8,500

7300-15200

I

l-114

I

34,000

-40,000

I

40,000 - 63,000

1 Strengths vary wìth concrete strength. Concrete strengths range from 3500 to 5500 psi. 2 All values are at minimum recommended embedment.

I

Table A-26 - Plastic section moduli and shape factors Shape Factor

Plastlc Section Modulus, Z1, in3

Section

1.

bh2 4

1.5

Ab!-

x-x axis: 1.12 (approx.)

bt (h -t) + f (h - 2Q2

2. y-y axis: 1.55 (approx.)

& + (h - 2t)w2 2 4

t(ave.) 3.

bt (h -t) +

w(h - 2t)2 4

1.12 (approx.)

b74

4.

h3 -iii-

5.

1.70

$[1-(1-h)3]

16 cc

t th2 for t << h

7

6.

F[l- (l.$y

(l-h)‘]

1.27 for t « h

1 .12 (approx.) for thin walls

W

I-bd h 7.

A-18

2

Table A-27 - Prestressing steel properties and allowable deslgn loads Ultimate Strength (ksi)

Prestressing_ SMI 0.5 In. Strand

1

0.6 in. Strand 0.5 in. Strand

1

0.6 In. Strand

Ultímate Load (kW

Area (sq. in.)

Yield Load (kW

Prestress Load

0.8 Pu

0.7 Pu

(kW

(kW

250

j 0.144

1

36.0 /

30.6 1

28.81 /

25.2 1

250

1 0.216

1

54.0

1

45.9 1

43.0

1

37.6 1

270

I 0.153

(

41.3 1

35.1 1

33.0

1

28.9 1

270

1 0.217

46.9

/

41.0

/ 58.3

1 49.8

/

( 36.0

1 35.2

1

30.8 1 89.3 1

5/8 in. Diam. Bar

I

157

0.28

I

l in. Dlam. Bar

I

150

0.85

1 127.5

1 104.6

/ 102.0

/

l-1/4 In. Dlam. Bar

/

150

1.25

1 187.5

1 153.8

1 150.0

1 131.3

l-3/8 In. Dlam. Bar

1

1501

1.58

1 237.0

1 194.3

1 189.6

1 165.9

l-

44.0

1

Table A-28 - Design strength of concrete brackets, corbels, or haunches \ Design strength by Eqs. 4.8.4’or for following criteria:

4.8.5 AS

‘fY = 60,000 psi Nu= 0.2 V" b = width of bearlng, ìn. d = h - 1.25”(h In inches) $Vn 5 ~1000 h2bd (The design strength value listed

in the table above a blank entree corresponds to this limit. The blank entree in a given COlUmn will have the same value as the last llsted entree.)

Values of +Vn (klps)

75 85 96106

10

2-#5 2-##6 2-#7 2-##8 2-H

19 32 46 55 62 65 69 72 60 73 82 86 90

26 35 42 49 55 60 65 69 32 46 60 70 79 86 90 94

23 35 46 55 62 69 74 77 40 57 74 84 89 94 98 91108 114119 125140 142

2227 0 0 0 0 0 26 35 42 49 55 60 65 0 38 50 61 70 79 86 93 99 40 57 74 91 io ll9124 108125 140146 142159

4 6 8 10 12 14 16 18

12

A-20

2-#4 2-#5 2-##6 2-#7 2-#8 2-#9 3ä4 3.#5 3-##6 3-#7 3-#8 3-#9

142329 0 0 0 0 0 23 35 46 55 62 69 0 0 28 48 66 79 90 96100 105 69 89109 ll6122 128 110 130144 151 150 171 22 34 44 53 60 66 0 0 28 48 69 82 93 98103 107 89110 123130 136 130150 164 171

6 8

10 12 14 16 18 20

1722 26 35 38 50 48 68 69

0 0 0 0 0 0 42 49 55 0 0 0 61 70 79 86 93 99 83 96107 117127133 89110 130 144151 157 150171 181 25 33 40 47 52 0 0 0 39 52 63 73 82 90 97104 48 69 89105 118 129136141 110130 150164171 171 191

40 49 58 65 72 79 84 90

1822 28 34 40 49 54 67 57 74

0 0 0 0 0 0 40 45 50 55 0 0 58 65 72 79 84 90 78 89 98107 115122 91108125140 146152 142 159175

8 10 12 14 16 18 20 22 18 0 0 0 0 0 0 0 28 34 40 45 0 0 0 0 40 49 58 65 72 79 84 90 54 67 78 89 98 107115122 69 88103 116128 140150160 89110 130150 171 181 188 27 33 38 44 0 0 0 0 42 51 60 68 75 82 88 94 60 74 87 98108 118127135 69 89110 130148 161 171177 150 171 191 209 212

Table A-28 - Design strength of concrete brackets, corbels, or haunches (continued) lD (in.) h \ 4 2-#4 2+5 2-#6 2-#7 248 2#9

h

8

14

12

10 10 12 14 16 18 20 22 24

12 14 16 18 20 22 24 26

14 16 18 20 22 24 26 28

1822252830 29 34 39 43 47 42 49 56 62 68 45 55 65 75 85

19222427 30 34 38 42 49 54 55 65 74 75

192224 30 34 43 49 59 66 65 75

0 0 0 51 55 58 73 79 83 96106 109 116

0 42 60 82 85

0 0 0 45 48 52 55 65 70 74 79 88 95101 107 96106 116126

37 54 73 85

0 0 40 44 58 63 79 85 96106

0 0 0 47 49 52 67 71 75 91 97102 116126133 136

\ AS

10 12 14 16 18 20 22 24

12 14 16 18 20 22 24 26

14 16 18 20 22 24 26 28

2-#4 2-#5 2-##6 2-#7 2-##8 2-##9

182225 0 0 0 0 0 29 34 39 43 47 51 55 0 42 49 56 62 68 73 79 83 56 67 76 85 93100 107113 60 73 87100 114128139144 141 155

1922 30 34 42 49 58 66 73 87

19 0 0 0 0 0 0 0 30 34 37 40 44 0 0 0 43 49 54 56 63 67 71 75 59 66 73 79 85 91 97102 77 86 95 104112119126133 87100 114128141 151 160 168

h

0 38 54 74 97 100

0 0 0 0 0 42 45 48 0 0 60 65 70 74 79 82 66 95101107 106116124132140 114128141 155168

b

\ As

10 12 14 16 18 20 22 24

12 14 16 18 20 22 24 26

14 16 18 20 22 24 26 28

10

2-##4 245 2-##6 2-#7 2-##8 2-##9

18 0 0 0 0 0 0 0 29 34 39 43 47 0 0 0 42 49 56 62 68 73 79 83 56 67 76 85 93100 107113 74 87 99 110121 131 140148 91108 125142159175181

0 0 0 0 0 0 0 0 30 34 38 42 0 0 0 0 42 49 54 60 65 70 74 79 56 66 74 82 88 95101 107 76 87 97106 :16124132140 91108123135146157167177

0 30 43 59 77 97

10 12 14 16 18 20 22 24

12 14 16 18 20 22 24 26

14 16 18 20 22 24 26 28

0 0 0 0 0 0 0 0 29 34 39 0 0 0 0 0 42 49 56 62 68 73 79 0 56 67 76 65 93100 107113 74 87 96 110121 131 140 1 48 1 88 89110126140153165177 28 33 37 0 0 0 0 0 43 51 58 65 71 77 82 0 62 73 84 93102110118 1 25 85100114127139150160 1 70 69 110130150171 191 209216 212232

0 0 0 0 0 0 0 0 3034 0 0 0 0 0 0 42 49 54 60 65 70 0 0 58 66 74 82 88 95101 107 76 87 97106116 1 24132 140 96 110123135146 1 57167177 28 32 0 0 0 0 0 0 44 51 57 62 68 73 0 0 64 73 82 90 97 1 05111 118 87 99 111 122133 1 42152160 110130145160173186198209 150‘171 191212232252

0 0 0 0 0 0 0 0 30 0 0 0 0 0 0 0 43 49 54 58 63 0 0 0 59 66 73 79 65 91 97102 77 86 95 104112119126133 97 109120131 141 151 160168 29 0 0 0 0 0 0 0 45 51 56 61 65 0 0 0 65 73 80 87 94101 107112 88 99109119128137145153 1 115129143155167179189200 1 130150171 191 212226240253

b

12

2-#4 2ä6 2-#6 247 2-#8 2-##9 3-#4 3-#5 3-#6 3-#7 3-##8 3-#9

0 0 0 0 0 0 0 34 37 0 0 0 0 0 49 54 58 63 67 71 0 66 73 79 85 91 97102 86 95 104112119126133 109120131 141 151 160168

Table A-28 $ (in.)

Design strength of concrete brackets, corbels, or haunches (continued) . 4

244 2-#5 2-#6 2-##7 2-#8 14

16

18

20

A-22

344 2-##9 3ä5 3* 3ä7 9ä8 3-#9

2-#6 2-#7 2-##8 2-##9 3-#6 347 348 3-#9 4-#6 4ä7 4-#t8 4-##9

2ä6 2-#t7 2#8 2-#9 3-##6 347 3-#8 3-##9 4-##6 4-#7 4ä8 , 4-#9

2-#6 2-##7 2-#8 2-##9 3-#6 3-#7 3-#8 3-#9 4-#6 447 4-#8 4-#k9

6

8

4 6 8 10 12 14 16 18

6 8 10 12 14 16 18 20

8 10 12 14 16 18 20 22

142329 0 0 0 0 0 23 35 46 55 62 0 0 0 33 51 66 79 90 99106 110 57 80 104116123129135 128145153160 152176185 2i 34 44 53 60 0 0 0 33 53 69 82 93103 109113 57 80 104123131 137143 128152166174 176199

1722 0 0 0 0 0 0 26 35 42 49 0 0 0 0 38 50 61 70 79 86 93 0 51 68 83 96 107117127135 57 80104125140153160166 128152176185192 25 33 40 47 0 0 0 0 39 52 63 73 82 90 97 0 56 75 91 105118129140149 57 80104128152166174181 176199213 223

18 0 0 0 0 0 0 0 28 34 40 0 0 0 0 0 40 49 58 65 72 79 0 0 54 67 78 89 98 107115122 71 88103 116128140150160 80104128147163177190199 27 33 38 0 0 0 0 0 42 51 60 68 75 82 0 0 60 74 87 98 108118127135 80 101 118133148161 173184 104128152176199213222 223 247

4 6 8 10 12 14 16 18

6 8 10 12 14 16 18 20

8 10 12 14 16 18 20 22

33 51 66 79 90 99107 0 37 65 90 107122129136141 92 119144153161 168 146173186194 130137144151 146166175183 173 201 216 228 164173181 201 219 228

38 50 61 70 79 86 0 0 51 68 83 96 107117127135 65 89108125140153166174 92119146173186194202 75 91 105118129140149 92 119143161 175183190 146173 201 216225 228255 140157173181188 146173201 219228 228 255

40 49 58 65 72 0 0 0 54 67 78 89 98 107115122 71 88103116128140150160 90111 130147163177190202 60 74 87 98108118127135 82 101 118133148161 173184 92119146173193210225233 201 228 255 269 80 99 115131 144157169180 92119146173197214228236 201 228255278 282

4 6 8 10 12 14 16 18

6 8 10 12 14 16 18 20

8 10 12 14 16 18 20 22

33 51 66 79 90 99 0 0 42 69 90 107122135141 147 73 103134151 116168175 164185194203 99 118135143151 157 103134164174183191 195216 226 226256 162172181 189 164195219229 226256

38 50 61 70 79 0 0 0 51 68 83 96107117127135 67 89 108125 140153166177 73103134158177194203211 56 75 91 105118129140149 73 102124143161 176190199 103134164195216226235 226256272 100121140157173186196 103134i64195219229238 226256 281 287

40 49 58 65 0 0 0 0 54 67 78 89 98 107115 0 71 88103116128140150160 90 111 130147163177190202 60 74 87 98108118127135 82 101 118133148161 173184 103131154174193210225240 134164195226256272282 80 99 115131 144157169 180 103134157178197214230245 164195226256281291 287317

4 6 8 10 12 14 16 18

6 8 10 12 14 16 18 20

8 10 12 14 16 18 20 22

33 51 66 79 90 0 0 0 44 69 90 107122135146153 47 81115140157166174182 149181 192202211 76 99 118135149156163 81 115149171 181 190199 183213225235 217251 272 169179188196 183216228238 217251 281 285

38 50 61 70 0 0 0 0 51 68 83 96 107117127 0 67 89108125140153166177 81 112136158177194210220 56 75 91 105118129140 0 77 102124143 161 176 190203 81 115149183210225235245 217251 272283 75 100121140157173186199 81 115149183214228238248 217251 281 292 285319

40 49 58 0 0 0 0 0 54 67 78 89 98107 0 0 71 88 103116128140150160 90 111 130147163177190202 60 74 87 98108118 0 0 82 101 118133148 161 173184 107131 154 174 193210225240 115 149183217244265283294 80 99 115 131 144157169180 109134157178197214230245 115149183217251 280292303 285 319330

1

‘Table A-28 - Design strength of concrete brackets, corbels, or haunches (continued) 12 14 10 1, (W

14

16

2-#4 2-##5 2-#6 2-#7 2-#8 2* 3-##4 3-#5 3-##6 3-#7 3-#8 3+9

2* 247 2ä8 2ä7 3-#6 3-##7 348 3-#9 ti7 4ä8 4-#9

10 12 14 16 18 20 22 24

12 14 16 18 20 22 24 26

14 16 18 20 22 24 26 28

0 0 0 0 0 0 0 0 2934 0 0 0 0 0 0 42 49 56 62 68 0 0 0 56 67 76 85 9310~107113 74 87 99 110121 131 140148 93110128140153165177188 2833 0 0 0 0 0 0 43 51 58 65 71 0 0 0 62 73 84 93 102110118125 85100114127139150160170 104128149166181196210222 152176199223247265

0 0 0 0 0 0 0 0 30 0 0 0 0 0 0 0 42 49 54 60 0 0 0 0 58 66 74 82 88 95101 0 76 87 97 106116124132140 96110123135146157167177 28 0 0 0 0 0 0 0 44 51 57 62 0 0 0 0 64 73 82 90 97105111118 87 99 111 122133142152160 113130145160173186198209 128152176199219236253265

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 434954 0 0 0 0 0 59 66 73 79 85 91 0 0 77 86 95 104112119126133 97 109120131 141 151 160168 0 0 0 0 0 0 0 0 455156 0 0 0 0 0 65 73 80 87 94101 107112 88 99109119128137145153 115129143155167179189200 146164181197212226240253

10 12 14 16 18 20 22 24

12 14 16 18 20 22 24 26

14 16 18 20 22 24 26 28

42 49 56 62 0 0 0 0 56 67 76 85 93100107 0 74 87 99 110121 131 140148 93110126140153165177188 62 73 84 93102110118125 85100114127139150160170 110130149166181196210222 119146173201228248265279 83 98112124136147157167 113133152169185200214227 119146 173201 228255278288 282309

42 49 54 0 0 0 0 0 4349 0 0 0 0 0 0 58 66 74 82 88 95 0 0 59 66 73 79 85 0 0 0 76 87 97 106116124132140 77 86 95 104112119126133 96 110123135146157167177 97 109120131 141 151 160168 64 73 82 90 97105111 0 65 73 80 87 94101 0 0 87 99 111 122133142152160 88 99109119128137145153 113130145160173186198209 115129143155167179189200 143164184202219236251265 146164181197212226240253 85 97109120130140149157 86 97107117126134142150 116133148163177190202214 118132146159171182193204 146173194213231 248264279 154173190207223238253266 202228255282309337 173201 228255282302320337

10 12 14 16 18 20 22 24

18

2-#6 2-#7 2ä8 2-#9 3-#6 3ä7 3ä8 3-##9 3-##6 4-#7 4ä8 4-#9

42 49 56 0 0 0 0 0 5667768593100 0 0 74 87 99 110121 131 140148 93 110126140153165177188 62 73 84 93 102110118 0 85100114127139150160170 111130149166181196210222 134164188210229248265281 83. 98 112124136147157167 113133152169185200214227 134164195221 242261 279296 226256287317348 10 12 14 16 18 20 22 24

20

2* 2+7 248 2-#I9 3-##6 3-#7 348 3-#9 4-#6 4-#7 4ä8 4-#9

4249 0 0 0 0 0 0 56 67 76 85 93 0 0 0 74 87 99110121131140 0 93 110126140153165177188 62 73 84 93 102 0 0 0 85100114127139150160170 111 130149166181196210222 140165188210229248265281 83 98112124136147157167 113133152169165200214227 148174198221 242261 279296 149183217251285319350362

12 14 16 18 20 22 24 26

14 16 18 20 22 24 26 28

4 3 0 0 0 0 0 0 0 4249 0 0 0 0 0 0 59 66 73 79 0 0 0 0 58 66 74 82 88 0 0 0 76 87 97 106116124132140 77 86 95104102119126 0 97 109120131 141 151 160168 96110123135146157167177 6473829097105 0 0 65 73 80 87 94 0 0 0 87 99 111 122133142152160 88 99 109119128137145153 113130145160173186198209 115129143155167179189200 143164184202219236251265 146164181197212226240253 86 97107117126134142150 85 97109120130140149157 116133148163177190202214 118132146159171182193204 151 173194213231 248264279 154173190207223238253266 164195226256287314334353 194218241262282302320337 12 14 16 18 20 22 24 26

14 16 18 20 22 24 26 28

42 0 0 0 0 0 0 0 58 66 74 82 0 0 0 0 76 87 97106116124 0 0 96110123135143157167177 64 73 82 90 0 0 0 0 87 99 111 122133142152160 113130145160173186198209 143164184202219236251265 85 97109120130140149157 116133148163177190202214 151 173194213231248264279 183217245270292314334353

0 0 0 0 0 0 0 0 59 66 73 0 0 0 0 0 77 86 95104112 0 0 0 97 109120131 141 151 160188 65 73 60 0 0 0 0 o 88 99109119128137145 0 115129143155167179189200 146164181197212226240253 86 97 107117126 134142 0 118132146159171182193204 154173190207223238253266 194218241262282302320337

Table A-28 - Design strength of concrete brackets, corbels, or haunches (continued) 2, (in.)

4

6

8

-,--LS

b

h \ %

22

2-H 2-#7 2-#8 249 3-##6 3ä7 348 3-#t9 4-#6 4-#7 448 4-#9

b

\ 4

24

h 2-#6 247 2-#8 2-#9 3-#6 3-#7 348 3-#9 4-#7 4-#8

-.-.-.b

22

24

A-24

6 8 10 12 14 16 18 20

8 10 12 14 16 18 20 22

33 51 66 79 90 0 0 0 44 69 90 107122135146 0 51 89118140159172180188 126164188199210219 49 76 99 118135149161 168 51 89 126161 177188197206 164201 222233244 238269282 158175185195203 164201 224236247 238276 291 313

38 50 61 70 0 0 0 0 51 68 83 96 107117 0 0 67 89108125140153166177 84 112136158177194210224 56 75 91 105118129140 0 77102124143161176190203 89 126162187210230244253 164201 238269282 294 75 100121 140157173186199 89 126164191 214235247257 201 238 276 291 303 313350

40 49 58 0 0 0 0 0 54 67 78 89 98 0 0 0 71 88 103116128140150 0 90 111 130147163177190202 60 74 87 98108118 0 0 82101118133148161 173184 107131154174193210225240 126164195220244265285303 80 99 115131144157169180 lo9134157178197214230245 126164201 232257280 300315 238276313350364

4 6 8 10 12 14 16 18

6 8 10 12 14 16 18 20

8 10 12 14 16 18 20 22

38 50 61 0 0 0 0 0 51 68 83 96 107 0 0 0 67 89 108125 140153166 0 84 112136158177194210224 56 75 91 105118129 0 0 77 102124143161 176190203 97133162187210230248262 138179219260279292304 75 100121140157173186199 97 136165 191 214235254265 138179219260 288301 314 301 342362

4049 0 0 0 0 0 0 54 67 78 89 0 0 0 0 71 88 103116128140 0 0 90 111 130147163177190202 60748798108 0 0 0 82 101 118133148161 173184 107131154174193210225240 135166195220244265285303 80 99 115 131 144157169180 109 134157178197214230245 138175205232257280300320 179 219260301 342 362376

33 44 56

51 66 79 0 0 0 0 69 90 107122135 0 0 91118140159176186194 97138177194206216226 49 76 99118135149161 0 56 97 135 161 183194203212 138179216229241 252 219260279292 132158179191 201 209 138179219232244255 260288301 301 342

10 h \ % 2-#6 2ä7 248 2-#i9 3-##6 3ä7 3-#8 3-#i9 4-#7 4-##8

b

4 6 8 10 12 14 16 18

h % \ 2-#6 2-#7 2ä8 2-#7 3-M 347 3-#8 3-#9 4-#6 4-#7 4ä8 4-#9

12

14

10 12 14 16 18 20 22 24

12 14 16 18 20 22 24 26

14 16 18 20 22 24 26 28

4249 0 0 0 0 0 0 56 67 76 85 0 0 0 0 74 87 99 110121 131 0 0 93110126140153165177188 62738493102 0 0 0 85100114127139150160170 111 130149166181 196210222 140165188210229248265281 83 98112124136147157167 113133152169185200214227 148174198221 242261 279296 164201 238276306331 354375

42 0 0 0 0 0 0 0 58 66 74 0 0 0 0 0 76 87 97106116 0 0 0 96110123135146157167177 64 73 82 90 0 0 0 0 87 99 111 122133142152 0 113130145160173186198209 143164184202219236251 265 85 97 109120130140149 0 116133148163177190202214 151 173194213231 248264279 191 219 245 270292314334353

0 0 0 0 0 0 0 0 5966 0 0 0 0 0 0 77 86 95 104 0 0 0 0 97109120131141151 160 0 65 73 80 0 0 0 0 0 88 99 109119128137 0 0 115129143 155 167179189200 146164181 197212226 240253 86 97107117126134 0 0 118132146159171182193204 154173190 207223238 253266 194218241 262 282302320337

10 12 14 16 18 20 22 24

12 14 16 18 20 22 24 26

14 16 18 20 22 24 26 28

420 0 0 0 0 0 0 56 67 76 0 0 0 0 0 74 87 99110121 0 0 0 93110126140153165177188 62 73 84 93 0 0 0 0 85100114127139150160 0 111 130149166181 196210222 140165188210229248265281 83 98 112124136147157 0 113133152169185 200214227 148174198221 242261 279296 179219251 280306331 354375

0 0 0 0 0 0 0 0 5866 0 0 0 0 0 0 76 87 97106 0 0 0 0 96110123135146157167 0 64 73 82 0 0 0 0 0 87 99111 122133142 0 0 113130145160173186198209 143164184202219236251 265 85 97109120130140 0 0 116133148163177190202214 151 173194213231 248264279 191219245270292314334353

0 0 0 0 0 0 0 0 59 0 0 0 0 0 0 0 77 86 95 0 0 0 0 0 97 109120131 141 151 0 0 6573 0 0 0 0 0 0 88 99 109119128 0 0 0 115129143155167179189200 146164181197212226240253 86 97107117126 0 0 0 118132146159171 182193204 154173190207223238253266 194218241 262 282 302320337

Table A-29 - Design strength of structural steel haunches - concrete Values are for design strength of concrete by Eq. 4.9.1 for the following críteria: c = 5000 psi; for other concrete strengths multiply values by f’J5000 Adequacy of structural steel section should be checked. Additlonal design strength, +Vt can be obtained with reinforcing bars -- See Table A-30

-4 l,-3 l4 = 0.85 Values of +VC (klps) ihear span, a (in.)

tZmbedment,

-T-

Effective Width of Sectlon (In.) 6

7

8

9

10

ll

12

13

14

15

16

17

38 55 72 89 107 124 142 160 178

43 62 82 102 122 142 163 183 203

49 70 92 115 137 160 183 206 229

54 78 103 128 153 178 203 229 254

60 86 113 140 168 196 224 252 280

65

12 14 16 18 20 22

33 47 62 76 92 107 122 137 152

94 123 153 183 213 244 274 305

70 102 133 166 198 231 264 297 330

76 109 144 179 214 249 284 320 356

81 117 154 191 229 267 305 343 381

87 125 164 204 244 285 325 366 407

92 133 174 217 259 302 345 389 432

6 8 10 12 14 16 18 20 22

25 29 38 44 51 60 65 76 79 92 94 109 108 126 123 144 138 161

33 50 68 87 106 125 145 164 184

38 57 n 98 119 141 163 185 207

42 63 85 108 132 156 181 205 230

46 69 94 119 145 172 199 226 253

50 75 102 130 159 187 217 246 276

54 82 111 141 172 203 235 267 299

58 88 119 152 185 219 253 287 322

63 67 71 94 101 107 128 136 145 163 173 184 198 211 225 234 250 266 271 289 307 308 328 349 345 368 391

6

6 8 10 12 14 16 18 20 22

20 32 44 57 70 84 98 112 126

27 42 58 75 93 111 130 149 168

30 34 47 53 66 73 85 94 105 116 125 139 146 163 168 186 189 210

37 58 80 104 128 153 179 205 231

41 44 47 63 68 74 87 95 102 113 123 132 140 151 163 167 181 195 195 211 228 223 242 261 252 273 294

51 79 109 141 175 209 244 279 315

8

6 8 10 12 14 16 18 20 22

17 20 23 27 32 36 38 45 51 50 58 67 62 73 83 75 88 101 89 103 118 102 119 136 116 135 155

26 41 57 75 94 113 133 153 174

31 50 70 92 115 138 163 187 213

34 37 40 54 59 63 76 83 89 100 108 117 125 135 146 151 163 176 177 192 207 204 222 239 232 251 271

43 46 48 68 72 77 95 102 108 125 133 142 156 167 177 188 201 214 222 236 251 256 273 290 290 309 329

1, (in.) 6 8 10

-

24 37 51 66 82 97 114 130 147

29 45 64 83 104 126 148 170 193

54 84 117 151 186 223 260 298 336

58 89 124 160 198 237 276 317 357

A-25

Table A-30 - Design strength of structural steel haunches - reinforcement Values are for addifonaldesign strength obtained from refnforcement by Eq. 4.9.3 for following criteria: As = 2 bars welded to steel shape A’*=A. Relnforcement anchored In oniy one dlrectlon. When relnforcement, A, and A’., ls anchored both above and below steel shape, lt can be counted twlce (values may be doubled). For design strength of concrete, e see Table A-29

Ve , -4-I l,-3 LValues of Vr (kips)

Shear span, a (in.)

Embedment, Ie (in.)

#BI

Relnforcing bar slze fY = 60 ksl

#5

#/6

#7

#8

#9

#4

#5

#/6

#7

#8

##9

2

6 6 10 12 14 16 18 20 22

7 10 ll 12 13 14 14 14 15

ll 15 la 19 21 21 22 23 23

15 22 25 28 30 31 32 33 33

21 30 35 38 40 42 43 44 45

27 39 45 50 53 55 57 58 59

35 49 57 63 66 69 72 73 75

10 14 17 19 20 21 21 22 22

16 23 26 29 31 32 33 34 35

23 33 38 42 44 46 48 49 50

32 44 52 57 60 63 65 67 68

41 58 68 74 79 82 85 87 89

52 73 86 94 100 104 107 110 112

4

6 8 10 12 14 16 18 20 22

5 8 10 ll 12 12 13 13 14

8 12 15 17 18 19 20 21 21

12 18 21 24 26 28 29 30 31

16 24 29 33 36 38 39 41 42

21 31 38 43 47 49 51 53 55

27 40 48 54 59 62 65 67 69

8 12 14 16 17 la 19 20 20

12 18 22 25 27 29 30 31 32

18 27 32 36 39 42 43 45 46

24 36 44 49 53 57 59 61 63

31 47 57 64 70 74 77 80 82

40 60 73 82 88 93 98 101 104

6 8

4 7 8 9 10 ll 12 12 13

7 10 13 15 16 17 18 19 20

10 15 19 21 23 25 27 28 29

13 20 25 29 32 34 36 38 39

17 26. 33 38 42 45 47 49 51

21 33 42 48 53 57 60 62 64

6 10 12 14 16 17 la 18 19

10 16 19 22 24 26 28 29 30

14 22 28 32 35 38 40 41 43

19 30 38 44 48 51 54 56 58

25 40 50 57 63 67 71 74 76

32 50 63 72 79 85 89 93 96

4 6 7 9 9

8 13 16 19 21 23

ll 17 22 26 29 31

14 23 29 34 38 41

18 29 37 43 48 52

5 9 ll 13 14 15

a 13 17 20 22 24

12 19 25 29 32 35

16 26 34 39 43 47

21 34 44 51 57 61

27 43 55 65 72 78

26 27 24

3 35 36

46 47 43

58 5 60

18 16 17

28 25 27

40 37 39

50 52 5

68 65 71

90 83 87

10

12 14 16 18 20 22

6

a

/

A-26

Relnforclng bar slze f,, = 40 ksl

6 8 lo 12 14 16

10

6 9 ll 13 15 16

20 2 18

/ l 111 2

1i9 7la

rable A-31 - Shear strength of connection angles

4% =,

t

=

@

= 0.90

b

=

$

= yleld strength of angle steel = 36,000 psi

Q, fY b

(““)

width of angle (in.)

+Vn. . (Ib per lnch of wldth) Angle Thlckness t (in.)

e, = 3W

e, = 1”

e, = l-1/2”

SI16 318 7116

1055 1519 2067

791 1139 1550

527 759 1034

396 570 775

316 456 620

ll2 9116 518

2700 3417 4219

2025 2563 3164

1350 1709 2109

1013 1281 1582

810 1025 1266

e, I 2”

e, = 2.1/2”

Table A-32 - Axial strength of connection angles

t

=

@

= 0.90

b =

wldth of angle (In.)

f Y = yleld strength of angle steel = 36,000 psl

N”

+Nm. . (Ib per lnch of wldth) Angle Thlckness t (in.)

z, q 6” g = 4”

Zp!Y g

q

3”

z, = 7” g = 5”

5116

264

198

318 7116

380 517

285

228

388

310

1/2 9116 518

I

675 854 1055

/

506 641 791

I

405 513 633

Z, = 8” g = 6”

258

I

338 427 527

A-27

Table A-33 - Tensìle strength of welded headed studs and bolts (see Fig.- 4.11 .l) Maximum Design Tensile

Strength, $P,, Limited by Concrete Strength (klps) Sand-Llg

Normal Welght Concrete’ Edge Dist., d, (in.)

2

3

4

5

6

7

'8

Stud Length, 1 B (ín.)

Diameter, d, (in.)

Diameter, d, (In.) 114

310

ll2

518

314

710

114

3/8

ll2

518

314

718 ;.; . "9.5

2.5 4.0 5.0 6.0 7.0 8.0

4.5 6.8 8.3 9.8 ll.3 12.9

4.9 5.3 7.2 7.6 8.7 9.1 10.2 10.6 ll.7 12.1 13.2 13.6

5.7 7.9 9.5 11.0 12.5 14.0

5.7 5.9 7.9 8.1 9.5 9.6 11.0 ll.2 12.5 12.7 14.0 14.2

3.9 5.8 7.1 8.4 9.6 10.9

4.2 6.1 7.4 8.7 10.0 ll.3

4.5 6.4 7.7 9.0 10.3 ll.6

4.8 6.8 0.;

4.8 6.8 9.;

10:s ll.9

10:6 ll.9

10:s 12.1

2.5 4.0 5.0 6.0 7.0 8.0

5.7 10.2 12.5 14.8 17.0 19.3

6.1 6.6 10.8 ll.3 13.1 13.6 15.3 15.9 17.6 18.2 19.9 20.4

7.1 11.9 14.2 16.5 18.7 21.0

7.1 7.3 11.9 12.2 14.2 14.5 16.5 16.7 18.7 19.0 21.0 21.3

4.8 8.7 10.6 12.5 14.5 16.4

5.2 9.2 11.1 13.0 15.0 16.9

5.6 9.6 ll.6 13.5 15.4 17.4

6.0 10.1 12.1 14.0 15.9 17.8

6.0 10.1 12.1 14.0 15.9 17.8

6.2 10.4 12.3 14.2 16.2 18.1

2.5 4.0 5.0 6.0 7.0 8.0

'5.7 13.6 16.6 19.7 22,7 25.7

6.1 6.6 14.4 15.1 17.4 18.2 20.4 21.2 23.5 24.2 26.5 27.2

7.1 15.9 18.9 21.9 25.0 28.0

7.1 7.3 15.9 16.3 18.9 19.3 21.9 22.3 25.0 25.3 28.0 28.4

4.8 ll.6 14.1 16.7 19.3 21.9

5.2 12.2 14.8 17.4 19.9 22.5

5.6 12.9 15.4 18.0 20.6 23.2

6.0 13.5 16.1 18.7 21.2 23.8

6.0 13.5 16.1 18.7 21.2 23.8

6.2 13.8 16.4 19.0 21.5 24.1

2.5 4.0 5.0 6.0 7.0 8.0

5.7 13.6 20.8 24.6 28.4 32.2

6.1 6.6 14.4 15.1 21.8 22.7 25.5 26.5 29.3 30.3 33.1 34.0

7.1 15.9 23.6 27.4 31.2 35.0

7.1 7.3 15.9 16.3 23.6 24.1 27.4 27.9 31.2 31.7 35.0 35.5

4.8 ll.6 17.7 20.9 24.1 27.3

5.2 12.2 18.5 21.7 24.9 28.1

5.6 12.9 19.3 22.5 25.7 28.9

6.0 13.5 20.1 23.3 26.5 29.7

6.0 13.5 20.1 23.3 26.5 29.7

6.2 13.8 20.5 23.7 26.9 30.1

2.5 4.0 5.0 6.0 7.0 8.0

5.7 13.6 20.8 29.5 34.0 38.6

6.1 6.6 14.4 15.1 21.8 22.7 30.6 31.8 35.2 36.3 39.7 40.9

7.1 15.9 23.6 32.9 37.5 42.0

7.1 7.3 15.9 16.3 23.6 24.1 32.9 33.5 37.5 38.0 42.0 42.6

4.8 ll.6 17.7 25.1 28.9 32.8

5.2 12.2 18.5 26.0 29.9 33.8

5.6 12.9 19.3 27.0 30.9 34.7

6.0 13.5 20.1 28.0 31.8 35.7

6.0 13.5 20.1 28.0 31.8 35.7

6.2 13.8 20.5 28.5 32.3 36.2

2.5 4.0 5.0 6.0 7.0 8.0

5.7 13.6 20.8 29.5 39.7 45.0

6.1 6.6 14.4 15.1 21.8 22.7 30.6 31.8 41.0 42.4 46.3 47.7

7.1 15.9 23.6 32.9 43.7 49.0

7.1 7.3 15.9 16.3 23.6 24.1 32.9 33.5 43.7 "44.4 49.0 49.7

4.8 ll.6 17.7 25.1 33.8 38.3

5.2 12.2 18.5 26.0 34.9 39.4

5.6 12.9 19.3 27.0 36.0 40.5

6.0 13.5 20.1 28.0 37.1 41.6

6.0 13.5 20.1 28.0 37.1 41.6

6.2 13.8 20.5 28.5 37.7 42.2

2.5 4.0 5.0 6.0 7.0 8.0

5.7 13.6 20.8 29.5 39.7 51.4

6.1 6.6 14.4 15.1 21.8 22.7 30.6 31.8 41.0 42.4 53.0 54.5

7.1 15.9 23.6 32.9 43.7 56.0

7.1 7.3 15.9 16.3 23.6 24.1 32.9 33.5 43.7 44.4 56.0 56.7

4.8 11.6 17.7 25.1 33.8 43.7

5.2 12.2 18.5 26.0 34.9 45.0

5.6 12.9 19.3 27.0 36.0 46.3

6.0 13.5 20.1 28.0 37.1 47.6

6.0 13.5 20.1 28.0 37.1 47.6

6.2 13.8 20.5 28.5 37.7 48.2

ll4

318

112

510

314

718

2.7

6.0

10.6

16.6

23.9

32.5

Maximum Design Tensile Strength3,

PS of Studs, Limlted by Steel Strength (klps)

Dlameter(ln.) P*

1 f', = 5000 psi; for other strengths multiply by Jf’,

2 For stud groups, also check value from equations in Fig. 4.11.4 or Fig. A-3 3 See Table A-22 for bolt strengths A-28

htwelg ht Concrete’

Table A-34 - Stud groups: Minimum thickness of member for truncated pyramid failure h m,” = (2 + 2 1,)/2

where: z = lesser of the spacing x and y 2, = stud embedment length

g Y i-

Note: If h 2 hmln, truncated pyramld failure will occur (see Fig. 4.11.2. If h * hmln> fallure wlll penetrate through the member (see Flg. 4.11.3)

@

41

I:1 l--X4

Mlnlmum Thlckness, hmin (In.)

10

10 12

9 9

10

10

ll

ll

12 12

13 13

13 14

13 14

13 14

13 14

0 2 4 6 8 10 12

10

10

10

10

10

ll

ll

10 ll

10

11

10 ll

10

11 ll ll ll ll ll

ll

ll

ll

A-29

Fig. A-3 - Design pull-out strength of stud groups (including edge and member thickness effects) 36

27

21

k,

1 8 and 1 5 k’, 12 9 6 3 2 10

30 20 k, and k’,

40

50

The following nomenclature is required for use of Fig. A-3 (Example 4.11 .l illustrates its use): Design pull-out strength (see Fig. 4.11.4 - Case 61,

@PC = WC, - @PC* where: = 0.85 9 P = 4L$7 k,k, k,” = (x + d,, + d,,)* k* = (Y + d,, + d.J P = 4h \I;i’ kl,kl* kq = (x + 21e - 2h)** = (y + 2$ - 2h)‘* k’2 4 = stud embedment length h = member thickness * For d,, >Ze, d,, = le; i = 1,2,3,4 ** For h 2 h,,,, k’, = k’, = 0 (hmin is given in Table A-34) A-30

U

Table A-35 - Shear strength of welded headed studs and bolts

Maximum Design Shear Strength, @Vc, Edge

c (psi) 4000

Dist.,

F

Limited by Concrete Strength (kips) Sand-Lightweight Concrete ( h = 0.85)

Normal Weight Concrete ( h = 1 .O) Diameter, d, (in.)

Diameter, d, (in.)

f

de

l/4

318

l/2

518

314

718

II4

318

112

518

314

718

2 3 4 5 6 7 8 9

1.4 2.1 2.1 2.1 2.1 2.1 2.1 2.1

1.4 3.0 4.7 4.7 4.7 4.7 4.7 4.7

1.4 3.0 5.4 8.4 8.4 8.4 8.4 8.4

1.4 3.0 5.4 8.4 12.2 13.2 13.2 13.2

1.4 3.0 5.4 8.4 12.2 16.5 19.0 19.0

1.4 3.0 5.4 8.4 12.2 16.5 21.6 25.8

1.1 1.8 1.8 1.8 1.8 1.8 1.8 1.8

1.1 2.6 4.0 4.0 4.0 4.0 4.0 4.0

1.1 2.6 4.6 7.2 7.2 7.2 7.2 7.2

1.1 2.6 4.6 7.2 10.3 11.2 11.2 11.2

1.1 2.6 4.6 7.2 10.3 14.1 16.1 16.1

1.1 2.E 4.E 7.: 10.: 14.1 18.~ 22.t

1.5 2.4 2.4 2.4 2.4 2.4 2.4 2.4

1.5 3.4 5.3 5.3 5.3 5.3 5.3 5.3

1.5 3.4 6.0 9.4 9.4 9.4 9.4 9.4

1.5 3.4 6.0 9.4 13.6 14.7 14.7 14.7

1.5 3.4 6.0 9.4 13.6 18.5 21.2 21.2

1.5 2.0 6.0 9.4 13.6 18.5 24.2 28.9

1.3 2.0 2.0 2.0 2.0' 2.0 2.0 2.0

1.3 2.9 4.5 4.5 4.5 4.5 4.5 4.5

1.3 2.9 5.1 8.0 8.0 8.0 8.0 8.0

1.3 2.9 5.1 8.0 11.6 12.5 12.5 12.5

-1.3 2.9 5.1 8.0 11.6 15.7 18.0 18.0

. 1'. 2.! 5.' 8.f 1 1.f 15.' 20.! 24.1

1.7 2.6 2.6 2.6 2.6 2.6 2.6 2.6

1.7 3.7 5.8 5.8 5.8 5.8 5.8 5.8

1.7 3.7 6.6 10.3 10.3 10.3 10.3 10.3

1.7 3.7 6.6 10.3 14.9 16.2 16.2 16.2

1.7 3.7 6.6 10.3 14.9 20.3 23.3 23.3

1.7 3.7 6.6 10.3 14.9 20.3 26.5 31.7

1.4 2.2 2.2 2.2 2.2 2.2 2.2 2.2

1.4 3.2 4.9 4.9 4.9 4.9 4.9 4.9

1.4 3.2 5.6 8.8 8.8 8.8 8.8 8.8

1.4 3.2 5.6 8.8 12.7 13.7 13.7 13.7

1.4 3.2 5.6 8.8 12.7 17.2 19.8 19.8

1 3:; 5.1 8.1 12.' 17.: 22.! 26.!

or more

5000

2 3 4 5 6 7 8 9

or more

6000

2 3 4 5 6 7 8 9

or more

-

Maximum Design Shear Strength, $V,, , of Studs Limited by Steel Strength’ (kips); 41 = 1.0

-

Diameter ( in.) %

I

I/4

3/8

l/2

518

314

71

2.2

5.0

8.8

13.8

19.9

27

1 See Table A-22 for bolt strengths

A-31

b = width; d = depth

I

about Center of Gravity

‘P-

b(3d2 + b2) 6

%(bd:d)

s=

4.

---It-

4bd + d2 6

b2 ST= ~ 2b + d

5.

,, = (b +d)4 - 6b2d2 12 (b+d)

I, = s=bd+ $

-AL 2b + d

!I I: -Ibl--

P-b-l 7.

8b3 +6bd2 + d3 12

s=bd+y-d2

j$L cl

s=

2bd+d2 3

Ip

b3 =

+8d3 ,2

d4 -b + 2d

t--b-I 9.

I, = b3 + 3b2 + d3

r

6

L

JA-32

r

I, = 27c?

Table A-37 - Column base .date thickness reauirements . Thickness Required for Concrete Bearing (in.) f x0 = 4” (;;I) x, q 3” x0 = 5” 500 1000 1500 2000

518 314

1 l-1/8

314 1 l-3/8 l-1/2

1 l-318 i-98 l-718

2500 3000 3500 4000

5-l/4 l-318 l-1/2 l-5/8

l-518 l-718 2 2-118

2 2-l/4 2-l/2 2-98

-r b I External Anchor Bolts

Thickness Required

1 f Internal Anchor Bolts

for Bolt Loading (In.)

-

A-33

APPENDIX B REFERENCES

1. PCI Manual on Design of Connections for Precast Prestressed Concrete, First Edition, Prestressed Concrete Institute, Chicago, Illinois, 1973. 2. PCI Design Handbook - Precast and Prestressed Concrete, First Edition, Prestfessed Concrete Institute, Chicago, Illinois, 1971. 3. Marlin, L. D., and Korkosz, W. J., “Connections for Precast Prestressed Concrete Buildings Including Earthquake Resistance,” Technical Report No. 2, Prestressed Concrete Institute, Chicago, Illinois, 1982. 4. PCI Design Handbook - Precast and Prestressed Concrete, Third Edition, Presrressed Concrete Institute, Chicago, Illinois, 1985. 5. Clough, D. P., “Design of Connections for Precast Prestressed Concrete Buildings for the Effects of Earthquakes,” Technical Report No. 5, Prestressed Concrete Institute, Chicago, Illinois, 1986. 6. ACI Committee 318, “Building Code Requirements for Reinforced Concrete (ACI 318-83),” and “Commentary on Building Code Requirements for Reinforced Concrete (ACI 318R83),“AmericanConcrete Institute, Detroit, Michigan, 1983. 7. Stanton, J. F., Anderson, R. G., Dolan, C. W., and McCleary, D. E., “Moment Resistant Connections and Simple Connections,” PCI Specially Funded Research and Development Program - Research Project No. l/4, Prestressed Concrete Institute, Chicago, Illinois, 1986,436 PP. 8. Mattock, A. H., and Theryo, T. S., “Strength of Members with Dapped Ends,” PCI Specially Funded Research and Development ProgramResearch Project No. 6, Prestressed Concrete Institute, Chicago, Illinois, 1986, 214 pp. Summary paper published in PC/ Journal, V. 31, No. 5, September-October 1986, pp. 58-75.

9. Klein, G. J., “Design of Spandrel Beams,” PCI Specially Funded Research and Development Program - Research Project No. 5, Presrressed Concrete Institute, Chicago, Illinois, 1986, 104 pp. Summary paper published in PC/ Journal, V. 31, No. 5, September-October 1986, pp. 76124. 10. PCI Design for Fire Resistance of Precast Prestressed Concrete (MNL 124-82), Presrressed Concrete Institute, Chicago, Illinois, 1982. 11. PCI Manual for Quality Control for Plants, and Production of Precast and Prestressed Concrete Products (MNL 116-85), Prestressed Concrere Institute, Chicago, Illinois, 1985. for 12. PCI Committee on Tolerances,“Tolerances Precast and Prestressed Concrete,” PC/ Journal, V. 30, No. 1, January-February 1985, pp. 26-112. 13. The Design of Products to be Hot-Dip Galvanized after Fabrication (MA-35 Ml 184) American Hot-Dip Galvanizers Association, Washington, D. C., 1984 14. American Society for Testing and Materials (ASTM), Philadelphia, Pennsylvania. The following standards (with their serial designations and year of adoption or revision) of ASTM are cited in this Manual: A36-84a-Standard SpecificationsforStructural Steel l Al 08-81 -Standard Specifications for Steel Bars, Carbon, Cold-Finished, Standard Quality l Al 43-84-Recommended Practice for Safeguarding Against Embrittlement of HotDip Galvanized Structural Steel Products and Procedure for Detecting Embrittlement + A307-86 -Standard Specifications for Carbon Steel Bolts and Studs, 60,000 psi Tensile Strength l A32586a-StandardSpecificationsforHighStrength Bolts for Structural Steel Joints l A41 6-86 -Standard Specifications for Steel Strand, Uncoated Seven-Wire StressRelieved for Prestressed Concrete l

B-l

6 A490-85-Standard Specifications for HeatTreated Steel Structural Bolts, 150 ksi Tensile Strength 0 A49685 -Standard Specifications for Steel Wire, Deformed,forConcrete Reinforcement l A61586 Standard Specifications for Deformed and Plain Billet-Steel Bars for Concrete Reinforcement - Standard Specifications for Raill A616-86 Steel Deformed and Plain Bars for Concrete Reinforcement l A61 7-84 -Standard Specifications for AxleSteel Deformed and Plain Bars for Concrete Reinforcement l A706-86 - Standard Specifications for LowAlloy Steel Deformed Bars for Concrete Reinforcement l A722-86 - Standard Specifications for Uncoated High-Strength Steel Bar for Prestressing Concrete l C39-86-StandardTest Method for Cylindrical Concrete Specimens . C1019-84 - Standard Method of Sampling and Testing Grout 15. CSA Specification G164, “Galvanizing of Irregularly Shaped Articies,” Canadian Standards Association, Toronto, Canada. 16. Structural Welding Code; AWS D1.4-79 Reinforcing Steel, AWS Dl.l-86 - Steel, American Welding Society, Miami, Florida. 17. Uniform Building Code, lnternafional Conference of Building Officials, Whittier, California, 1988. 18. Paulay, T., “Deterministic Seismic Design Procedures for Reinforced Concrete Buildings,” Engineering Structures, V. 5, January 1983. 19. “Earthquake Hazards Reduction Issues for an Implementation Plan,” Office of Science and Technology Policy, Washington, D. C., 1978. 20. “Expansion Joints in Buildings,” Technical Report No. 65, National Research Council, National Academy of Sciences, 1974. 21. Speyer, I. J., for PCI Committee on Precast Concrete Bearing Wall Buildings, “Considerations for the Design of Precast Concrete Bearing Wall Buildings to Withstand Abnormal

B-2

Loads,” PC/ Journal, V. 21, No. 2, March-April 1976, pp. 18-51. 22. Mattock, A. H., “Shear Transfer in Concrete Having Reinforcement at an Angle to the Shear Plane,“ Shear in Reinforced Concrete, SP-42, American Concrete Institute, Detroit, Michigan, 1974, pp. 17-42. 23. Mattock, A. H., Li, W. K., and Wang, T. C., “Shear Transfer in Lightweight Reinforced Concrete,” PC/ Journal, V. 21, No. 1, JanuaryFebruary 1976, pp. 20-39. 24. Shaikh, A. F., “Proposed Revisions to ShearFriction Provisions,” PC/ Journal, V. 23, No. 2, March-April, 1978, pp. 12-21. 25. Walraven, J., Frenay, J., and Pruijssers, A., “Influence of Concrete Strength and Load History on the Shear Friction Capacity of Concrete Members,” PC/ Journal, V. 32, No. 1, JanuaryFebruary 1987, pp. 66-84. 26. Shaikh, A. F., “Photoelasticity Tests of Corbels and Dapped Ends,” University of WsconsinMilwaukee, Unpublished Report, 1979. 27. Schlaich, J., Schafer, K., and Jennewein, M., “Toward a Consistent Design of Structural Concrete,” PC/ Journal, V. 32, No. 3, May June 1987, pp. 74-l 50. 28. “Reinforcement Anchorages and Splices,” Concrete Reinforcing Steel Institute, Schaumburg, Illinois, 1980. 29. ACI Committee 439, “Mechanical Connections of Reinforcing Bars,” Concrete International, V. 5, No. 1, January 1983, pp. 24-35. J 30. Kriz, L. B., and Raths, C. H., “Connections in Precast Concrete Structures - Strength of Corbels,” PC/ Journal, V. 10, No. 1, February 1965, pp. 16-61. 31. “Screw Threads - ANSI B1.l - 1974”; “Bolt Head Dimensions and Minimum Length of Bolts - ANSI 818.2.1 - 1972,” American National Standards Insitute, New York, N. Y. 32. Manual of Steel Construction, Eighth Edition, American lnsritufe of Steel Construction, Chicago, Illinois, 1980.

33. Shaikh, A. F., and Yi, W., “In-Place Strength of Welded Headed Studs,” PC/Journal, V. 30, No. 2, March-April 1985, pp, 56-81. 34. Cannon, R. W., “Expansion Anchor Performance in Cracked Concrete,” AC/Journal, V. 78, No. 6, November-December 1981, pp. 471479. 35. Ehligehausen, “Loadbearing Tension,” Part nik, HEFT 1,

R., Fuchs, W., and Mayer, B., Behaviorof Anchor Fastenings in 2, Betonwerk + fertigteil-Tech1988, pp. 29-35.

44. “Reinforced Bearing Connections for Precast Concrete Members,” M. S. Thesis, Shah, V., (Faculty Advisor: Shaikh, A. F.), University of Wisconsin-Milwaukee, 1980. 45. Jacques, F. J., and Aswad, A., “Bearing Plate Design Parametric Study,” Unpublished Report, 1980, Communications to PC/ Committee on Connection Derails. 46. Mattock, A. H., “Behavior and Design of Dapped End Members,” Proceedings of the U. S. Japan Joint Seminar on Precast Concrete, Tokyo, Japan, October-November 1986.

36. Standard Specifications for Highway Bridges, Twelfth Edition, American Association of State Highway and Transportation Officials, Washington, D. C., 1977.

47. Mattock, A. H., “Design Proposals for Reinforced Concrete Corbels,” PC/ Journal, V. 21, No. 3, May-June 1976, pp. 18-42.

37. Iverson, J. K., and Pfeifer, D. W., “Criteria for Design of Bearing Pads,“Technical Report No. 4, Prestressed Concrete Institute, Chicago, Illinois, 1985, 118 pp.

48. Marcakis, K., and Mitchell, D., “Precast Concrete Connections with Embedded Steel Members,” PC/ Journal, V. 25, No. 4, JulyAugust 1980, pp. 88-116.

38. Aswad, A., and Tulin, L., “Behavior and Design of Selected Elastomeric Bearing Pads,” PC/ Journal, V. 32, No. 3, May-June 1987, pp. 1635.

49. “Moment Resistant Beam-Column Connection,” M. S. Thesis, Potter, M. T., (Faculty Advisor: Tadros, M. K.), University of Nebraska, 1984.

39. “Specifications for Non-Shrink Grout,” CRDC588-78A, U. S. Army Corps of Engineers, 1978.

50. “Cazaly, L., and Huggins, M., Canadian Prestressed Concrete Handbook, Canadian Prestressed Concrete Institute, Ottawa, Ontario, 1964.

40. ACI Committee503,“Useof Epoxy Compounds with Concrete,” AC/ Journal, Proceedings, V. 70, No. 9, September 1973, pp. 614-645. 41.

“Standard Specification for Epoxy-Resin-Base Bonding Systems for Concrete,” ANSI/ASTM C881-83, American Society for Testing and Materials, Philadelphia, Pennsylvania.

42. Aswad, A., “Rational Deformation Prediction of Prestressed Members,” Deflections of Concrete Structures - SP86, American Concrete Institute, Detroit, Michigan, 1985, pp. 263-282. 43. ACI Committee 435, “State-of-the-Art Report on Temperature-Induced Deflections of Reinforced Concrete Members,” Deflections of Concrete Structures - SP86, American Concrete Institute, Detroit, Michigan, 1985, pp. l14.

= 51. Loov, R., ‘A Precast Beam Connection Designed for Shear and Axial Load,” PC/ Journal, V. 13, No. 3, June 1968, pp. 12-27. f 52. Johal, L.S., and Hanson, N. W., “Design for Vertical Load on Horizontal Connections in Large Panel Structures,” PC/ Journal, V. 27, No. 1, January-February 1982, pp. 62-79. 53. PCI Committee on Design Handbook, “Volume Changes in Precast, Prestressed Concrete Structures,” PC/ Journal, V. 22, No. 5, September-October 1977, pp. 38-53. 54. Bernal, D., “Amplification Factors for Inelastic Dynamic P-A Effects in Earthquake Analysis,” Earthquake Engineering and Structural Dynamics, V. 15, 1987.

B-3

APPENDIX C LIST OF APPLICABLE CONVERSIONS BETWEEN US CUSTOMARY (USC) UNITS AND SI UNITS

USC to SI 1 in = 0.0254 m 1 ft = 0.3048 m

Length and Displacement

1 in* = 6.452 x 1C4 m* 1 ft* = 9.290 x lo-* m2

Area

1 in3=1.639x10-5m3 1 ft3 = 2.832 x lo-* m3

Section Modulus and Volume

1 m = 39.37 in

1 in4 =4.162x1V7m4 1 ft4 =8.631 xlQ3m4 1 1 1 1 1

lb = 4.448 N k=4.448kN lb/in = 1.751 x 1 O* N/m Ib/ft = 14.59 N/m wft = 14.59 kN/m

Force and Force per Unit Length

1 1 1 1 1

1 1 1 1

lb-in = 0.1130 N-m lb-ft = 1.356 N-m k-in = 0.1130 kN-m k-ft = 1.356 kN-m

Bending Moment

1 N-m = 8.850 lb-in 1 N-m = 0.737 lb-ft 1 kN-m = 8.850 k-in 1 kN-m = 0.737 k-ft

Stress and Modulus of Elasticity

1 kPa I= 0.145 psi 1 MPa = 0.145 ksi 1 Pa = 0.0209 psf

Temperature

T, = (T, -32)/l .8

Tt = 1.8 T, + 32

N = 0.225 lb kN = 0.225 k N/m = 5.711 x lo” lb/in N/m = 0.0685 Ib/ft kN/m = 0.0685 k/ft

c-1