Plate Girders: Ss En 1993‐1‐5: 2009

CE3166 Structural Steel Design and System

J Y R Liew & S D Pang

Plate Girders SS EN 1993‐1‐5: 2009 Eurocode 3 – Design of steel structures  Part 1‐5: Plated structural elements

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CE3166 Structural Steel Design and System

J Y R Liew & S D Pang

What are Plate Girders? Plate Girders are fabricated using plates welded together. They are usually used as flexural members to carry heavy loads over long spans.

Flange plate

Transverse stiffener

Web plate

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CE3166 Structural Steel Design and System

J Y R Liew & S D Pang

What are Plate Girders? flange thickness tf

web thickness tw web depth d

The flange plates are to resist the axial compressive and tensile forces arising from the applied bending moment while the web plate is to resist the applied shear force.

Overall depth h

They are usually deeper than the deepest rolled sections and their webs are thinner than rolled sections.

weld

weld

b

Cross–Section of Plate Girder

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CE3166 Structural Steel Design and System

J Y R Liew & S D Pang

When do we use Plate Girder? Plate girders are typically used as (1) long span floor girders in buildings (2) bridge girders (3) crane girders

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CE3166 Structural Steel Design and System

J Y R Liew & S D Pang

Scope of Coverage In this course, we will only consider laterally and torsionally restrained straight girder with equal flanges and transverse stiffeners.

Curved girder

Unequal flanges

Straight girder

Equal flanges

Laterally and Torsionally Restrained Girder

Girder with longitudinal and transverse stiffeners

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CE3166 Structural Steel Design and System

J Y R Liew & S D Pang

Elevation Views of Plate Girder Plate Girder with Rigid End Post Rigid End Post

Intermediate transverse stiffeners

Web

Flanges

tw h L

d

a

tf

Plan View

Plate Girder with Non‐Rigid End Post

Non-Rigid End Post

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CE3166 Structural Steel Design and System

J Y R Liew & S D Pang

Differences Between Plate Girder & Rolled Section Most plate girders have high d/tw ratio for the webs which subject them to  shear buckling and local buckling.

Shear Buckling of Web EN1993-1-5: Cl 5.1(2)

If d / t w  72 w /  for unstiffened web, or d / t w  31 w k /  for a stiffened web, webs are susceptible to Shear Buckling.   1.0

Rolled section with  most slender web

If S275 steel is used, 72w / = 66.6 If S355 steel is used, 72w / = 58.6 If S460 steel is used, 72w / = 51.5

k  5.34  4.00( d / a ) 2 when a / d  1 where k  4.00  5.34( d / a) 2 when a / d  1 End Post

Intermediate transverse stiffeners

Web

Flanges

tw h L

a

d tf 7

CE3166 Structural Steel Design and System

J Y R Liew & S D Pang

Shear Buckling of Web 

8

CE3166 Structural Steel Design and System

J Y R Liew & S D Pang

Differences Between Plate Girder & Rolled Section Local Buckling of Web EN1993-1-1: Table 5.2 (refer to Local Buckling and Section Classification Slide 12)

Plate girders are long flexural members (beams) which are primarily subjected to bending moment. This results in bending stresses (compressive and tensile stresses) in the web. If d / tw > 124, the webs will buckle due to the compressive stress. The web is Class 4 and part of the web is ineffective.

Class

Part subject to bending

For the majority of the plate girders, their d / tw is greater than 124.

1

c / t  72

2

c / t  83

3

c / t  124

Internal COMPRESSION Parts

Ineffective area

fy Compression –

Elastic neutral axis Tension fy

+

Web



235 fy

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CE3166 Structural Steel Design and System

J Y R Liew & S D Pang

Moment Capacity of Plate Girders Approach 1

Approach 2

The flanges are assumed to take bending moment while the web is assumed to take shear only.

Both the flanges and the web take bending moment. In addition the web will still take shear.

More conservative but simpler

More exact but more tedious

fy

If the web is a Class 4 element, the effective web has to be determined.

Ineffective area

fy Compression –

Elastic neutral axis Tension fy

+

fy 10

CE3166 Structural Steel Design and System

J Y R Liew & S D Pang

Initial Sizing for Plate Girders Span L

flange thickness tf

Overall depth : h  0.05L – 0.10L (simply supported girders) Overall depth : h  0.04L – 0.07L (continuous girders)

Web depth : d = h – 2tf

web thickness tw web depth d

Thickness of flange : tf ~ 0.045b – 0.083b

Overall depth h

Breadth of flange : b  0.25h – 0.33h

Web thickness : tw ~ 0.006d – 0.010d

These are just INDICATIVE VALUES ONLY! For Approach 1, the amount of steel used for the plate girder will be minimized when area of a flange bf tf = area of web d tw. (refer to Appendix I of Plate Girder)

weld

weld

b

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CE3166 Structural Steel Design and System

Design Flow Chart for Plate Girder

J Y R Liew & S D Pang

Determine design moment MEd Size the flange

NO

c f / t f  14

YES Calculate moment capacity M f , Rd  f yf A f ( d  t f )/ M 0

NO

M f , Rd  M Ed

YES

END

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CE3166 Structural Steel Design and System

J Y R Liew & S D Pang

Design Consideration for the Flange Classification of the flange The width to thickness ratio of the flange should at least satisfy the limits for Class 3. For the flange of an I-shaped plate girder, cf / tf  14

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CE3166 Structural Steel Design and System

J Y R Liew & S D Pang

Design Consideration for the Flange What can we do for the slender flanges of a box girder? Buckling of a plate with a  flexible longitudinal stiffener

Buckling of a plate with a  stiff longitudinal stiffener

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CE3166 Structural Steel Design and System

J Y R Liew & S D Pang

Design Consideration for the Flange Moment Capacity (Approach 1) A generally accepted method for designing plate girders subject to a moment MEd and a coincident shear VEd is to proportion the flanges to carry all the moment with the web taking all the shear. M f , Rd 

f yf A f (d  t f )

M0

 M Ed

 M 0  1.0

M Ed The size of the flange should then satisfy A f  bt f  f yf (d  t f )

fyf d + tf

b

tf fyf

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CE3166 Structural Steel Design and System

Design Flow Chart for Plate Girder

Determine design moment MEd

Determine design shear VEd

Size the flange

Size the web

NO

c f / t f  14

NO

d / tw  k

E ( Aw /A fc ) 0.5 f yf

YES Calculate moment capacity M f , Rd  f yf A f ( d  t f )/ M 0

NO

M f , Rd  M Ed

J Y R Liew & S D Pang

Check to be satisfied  in every web panel

YES

Calculate shear buckling resistance  (contribution from web) Vbw, Rd  (  w f yw dt w )/( 3 M 1 )

YES

Vbw, Rd  VEd

YES

NO Calculate shear buckling resistance  (contribution from flange) Vbf , Rd  (bt 2f f yf ) * [1  ( M Ed / M f , Rd ) 2 ]/( c M 1 )

Add more  stiffeners

Calculate shear buckling resistance Vb , Rd  Vbw, Rd  Vbf , Rd  ( f yw dt w )/( 3 M 1 ) NO

Vb , Rd  VEd

NO

YES

END

16

CE3166 Structural Steel Design and System

J Y R Liew & S D Pang

Design Consideration for the Web Maximum Allowable Slenderness for Web EN1993-1-5: Cl 8

To prevent the compression flange buckling in the plane of the web, the following criterion should be met: Aw A fc

Plastic rotation utilized: Plastic moment resistance utilized: Elastic moment resistance utilized:

k = 0.3 k = 0.4 k = 0.55 tw

Afc is the cross section area of the compression flange Aw is the cross section area of the web

d

d E k tw f yf

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CE3166 Structural Steel Design and System

J Y R Liew & S D Pang

Shear Buckling Resistance  EN1993-1-5: Cl 5.2

Vb , Rd  Vbw, Rd  Vbf , Rd 

 f yw dt w 3 M 1

Contribution from the web:

Vbw, Rd 

 w f yw dt w 3 M 1

 M 1  1.0

w is given by the table below: Rigid end post Non-rigid end post

w  0.83



0.83



 w  1.08

w  1.08





0.83

0.83

w

w

1.37 (0.7  w )

0.83

w

where

w 

w 

d 86.4t w w

d 37.4t w w k

If transverse stiffeners are present at supports only If transverse stiffeners are present at supports and intermediate positions

where k  5.34  4.00( d / a ) 2 when a / d  1

k  4.00  5.34( d / a) 2 when a / d  1

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CE3166 Structural Steel Design and System

J Y R Liew & S D Pang

Contribution from the flange:

Vbf , Rd

bt f yf   M Ed  1   M c M 1   f , Rd 2 f

   

2

   

a c

 1.6 bt 2f f yf where c  a  0.25  2 t d f yw w 

   

Tension field action in web panel

Plastic hinge

Yield zone

Post buckling of web panel The contribution from the flange is more significant when MEd /Mf,Rd is small.

Collapse of web panel

Verification EN1993-1-5: Cl 5.5

Vb , Rd  VEd This check must be satisfied in EVERY web panel. 19

CE3166 Structural Steel Design and System

J Y R Liew & S D Pang

What are the design values to be used in the checks?? P

P

P

a tw h L/4

L/4

L/4

L/4

d

tf

1.5P V(kN)

0.5P -0.5P -1.5P

M(kNm) 0.375PL

0.5PL

VEd  ??? Check Vb , Rd  VEd

Vb , Rd

M Ed  ???

 w f yw dt w bt f yf   M Ed     1 c M 1   M f , Rd 3 M 1  2 f

   

2

  f dt yw w   3 M 1 

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CE3166 Structural Steel Design and System

J Y R Liew & S D Pang

Example PG-1: Sizing of Plate Girder Design a plate girder to support the factored distributed and point loads shown in the figure below. Use S275 steel for your plate girder and ignore the sizing for the stiffeners. 92kN/m

760kN

9000

760kN

7000

9000

V(kN)

1082

1910

Maximum shear (at supports) = 12.5*92 + 760 = 1910kN

332

1910

1082

332

14028

Maximum moment (at mid–span) = 760*9 + 12.5*92*6.25 = 14028kNm

You must know  how to draw  SHEAR and  BENDING MOMENT diagrams!!!

M(kNm) 21

CE3166 Structural Steel Design and System

J Y R Liew & S D Pang

Initial Sizing Choose h = 0.08L = 2000mm tw

Choose b = 0.35h = 700mm

h

d

Choose tf = 0.055b = 38.5mm Select tf = 40mm  d = 1920mm Choose tw = 0.006d = 13.4mm Select tw = 13mm

tf 40

760kN

13

1920

92kN/m

760kN

700

Section A–A

40

Trial Section: 700x40mm flanges and 1920x13mm web

A

A 9000

7000

9000

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CE3166 Structural Steel Design and System

J Y R Liew & S D Pang

Flange Classification Flange thickness tf = 40 mm  fyf = 265 N/mm2

f = (235/265)0.5 = 0.942 cf /tf ≈ 0.5(700–13)/40 = 8.59 < 14 = 13.2 Flange is not Class 4  OK! Note: Size of weld has been neglected in determining cf .

Class

Part subject to Stress distribution compression (compression +ve)

1

c / t  9

2

c / t  10

3

c / t  14

Do we need to classify the web?

Moment Capacity M0



265 * 700 * 40 * (2000  40) * 10 6  14543kNm 1.0

M Ed  14028kNm  M f , RD  14543kNm

14028

M f , Rd 

f yf (bt f )( h  t f )

M(kNm)

The moment capacity check is satisfied. What would you do when the moment capacity check fails?

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CE3166 Structural Steel Design and System

J Y R Liew & S D Pang

Check for Flange Induced Buckling d 1920 E   148  0.4 tw f yf 13

Aw 210000 1920 * 13 *  0.4 *  300 A fc 265 700 * 40

This check is normally trivial  unless your web is very slender.

The maximum allowable slenderness of web check is satisfied.

Shear Buckling Resistance V pl , Rd 

 f yw dt w 3 M 1



1.0 * 275 * 1920 * 13 * 10  3  3963kN 3

Contribution from the web Vbw,Rd : w 

w 

1920 d   1.85 86.4 t w w 86.4 * 13 * 0.924

0.83

w

Vbw , Rd 

0.83   0.45 1.85

 w f yw dt w 3 M 1

0.45 * 275 * 1920 * 13  * 10  3  1779kN 3

Web thickness tw = 13 mm  fyw = 275 N/mm2 w = (235/275)0.5 = 0.924 Non-rigid end post w  0.83



0.83



 w  1.08

w  1.08

 0.83

w 0.83

w 24

CE3166 Structural Steel Design and System

J Y R Liew & S D Pang

Contribution from the flange Vbf,Rd : 2  1.6bt 2f f yf   1.6 * 700 * 40 * 265    25000 *  0.25    7150 c  a 0.25  2 2    13 * 1920 * 275  t w d f yw    2 2  bt f f yf   M Ed   700 * 40 2 * 265   14028  2  1    * 10  3  3kN     Vbf , Rd  1    14543   c M 1   M f , Rd   7150    

What can you do when the shear check fails???

V(kN)

332

332 1910

VEd  1910kN  Vb , Rd  1782kN The shear check FAILS.

1082

3 M 1

 3963kN 1082

Vb , Rd  Vbw , Rd  Vbf , Rd  1779  3  1782kN 

 f yw dt w

1910

Shear buckling resistance:

How about Lateral Torsional Buckling? How about deflection check?

25

CE3166 Structural Steel Design and System

J Y R Liew & S D Pang

What happens if we add more stiffeners and where do we add?? 760kN

92kN/m

760kN

If a = 9m, will it pass the shear check? 9000

7000

9000

Shear Buckling Resistance Contribution from the web Vbw,Rd : k  5.34  4.00( d / a ) 2  5.34  4.00 * (1920/3000 ) 2  6.98

w 

d 37.4 t w w

1920   1.62 k 37.4 * 13 * 0.924 * 6.98

0.83 w    0.51 w 1.62  w f yw dt w 0.51 * 275 * 1920 * 13  * 10 3  2034kN Vbw, Rd  3 M 1 3

Non-rigid end post w  0.83

0.83

VEd  1910kN  Vbw, Rd  2034kN



0.83



 w  1.08

w  1.08

 0.83

w 0.83

w

Will the deflection change when transverse stiffeners are added?

The shear check is satisfied.

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