Design Of Axially Loaded Column: Minggu Ke 4

MINGGU KE 4

DESIGN OF AXIALLY LOADED COLUMN

by

Department of Civil Engineering, University of Sumatera Utara

Ir. DANIEL R. TERUNA, MT; Ph.D, IP-U

CONTENT

Introduction Axial Load Capacity of Columns Failure of Tied and Spiral Columns Design Formula Examples Design of Axially Loaded Columns Formula Example Photograph of Column Detailing

 Introduction

shell core

concrete

Longitudinal bars ties

spiral concrete

Tied column

spiral column

FIGURE 1 Types of columns.

composite column

 Axial Load Capacity of Columns • It has been known for several decades that the stresses in the concrete and the reinforcing bars of a column supporting a longterm load cannot be calculated with any degree of accuracy. • Modulus of elasticity of the concrete is changing during loading

due to creep and shrinkage. Thus, the parts of the load carried by the concrete and the steel vary with the magnitude and duration of the loads. • At failure, the theoretical ultimate strength or nominal strength of a short axially loaded column is





Pn  0.85 f c' Ag  Ast  Ast f y

 Failure of Tied and Spiral Columns • Should a short, tied column be loaded until it fails, parts of the shell or covering concrete will spall off and, unless the ties are quite closely spaced.

• The longitudinal bars will buckle almost immediately, as their lateral support (the covering concrete) is gone. Such failures may often be quite sudden, and apparently they have occurred

rather frequently in structures subjected to earthquake loadings.

• When spiral columns are loaded to failure, the situation is quite different. The covering concrete or shell will spall off, but the core will continue to stand, and if the spiral is closely spaced, the core will be able to resist an appreciable amount of additional load beyond the load that causes spalling • The closely spaced loops of the spiral, together with the longitudinal bars, form a cage that very effectively confines

the concrete • As a result, the spalling off of the shell of a spiral column provides a warning that failure is going to occur if the load is further increased.

Secondary maximum load Cover spalls

Load

spiral breaks spiral column

Tied column

12.5mm

Displacement FIGURE 2 axially loaded columns.

25mm

Figure 3. column failure

• For this reason, the spiral is designed so that it is just a little stronger than the shell that is assumed to spall off.



shell strength  0.85 f c' Ag  Ac • where



Ac is the area of the core, which is considered to

have a diameter that extends from out to out of the spiral: • By considering the estimated hoop tension that is produced in spirals due to the lateral pressure from the core and by tests, it can be shown that spiral steel is at least twice as effective in increasing the ultimate column capacity as is

longitudinal steel

• Therefore, the strength of the spiral can be computed approximately by the following expression, in which

s

is the

percentage of spiral steel: the area of the core

spiral strength  2 s Ac f yt • Equating these expressions and solving for the required percentage of spiral steel, we obtain





0.85 f c' Ag  Ac  2 s Ac f yt

 Ag  f c'  s  0.425  1  Ac  f yt

 Ag  f c'  s  0.45  1  Ac  f yt (ACI Equation 10-5)

• Once the required percentage of spiral steel is determined, the spiral may be selected with the expression to follow, in which

s

is written in terms of the volume of the steel in one loop:

s 

Volume spiral in one loop

Volume of concrete core for a pitch s

as Dc  d b  4as Dc  d b  s   2 Dc / 4 s sDc2



s



db

In this expression, a s is the cross-sectional

area of the spiral bar, Dc is the diameter of the core out to out of the spiral, and d b is the diameter of the spiral bar

Dc h

 Code Requirements for Cast-in-Place Columns • Longitudinal bars

1% Ag  As  8% Ag To prevent sudden nonductile failure

To prevent honeycomb

• Usually the percentage of reinforcement should not exceed 4% when the bars are to be lap spliced. It is to be remembered that if the percentage of steel is very high, the bars may be bundled. • Ties For longitudinal bars

 32mm

For longitudinal bars > 32mm and bundled bars

 10mm  13mm

Not recommended

recommended

x

x

> 40mm

x

x

x

Note: ties shown dashed may be omitted if x <150mm

x

3 bars bundled

• 16 longitudinal bar diameters • 48 tie diameter

• Least dimension of column

Fig. 4 Typical tie arrangements

Required tie spacing

 Design Formula • For many years, the code specified that such columns had to be designed for certain minimum moments even though no calculated moments were present. h

• In today’s code, minimum eccentricities b

e

P

are not specified, but the same objective is accomplished by requiring that theoretical axial load capacities be multiplied by a

factor, which is equal to 0.85 for spiral P

columns and 0.80 for tied columns M  Pe









Pn  0.85 0.85 f c' Ag  Ast   Ast f y

Pn  0.80 0.85 f c' Ag  Ast   Ast f y

(ACI Equation 10-1)

(ACI Equation 10-2)

• It is to be clearly understood that the preceding expressions

are to be used only when the moment is quite small or when

there is no calculated moment. Note: e is less than 0.10h for tied columns or less than 0.05h for spiral columns.

 Examples Design of Axially Loaded Columns Formula

• Solusi



Pn  0.80 0.85 f c' Ag  Ast   Ast f y



Pn  0.80 x0.650.85x25Ag  0.02 Ag   0.02 Ag (400) 2600000  14.989 Ag  Ag  173460mm 2 Use 400mm x 400mm

( Ag  160000mm 2 )

• Selecting Longitudinal Bars

Pn  0.80 x0.650.85x25Ag  0.02 Ag   0.02 Ag (400) 2600000  0.80 x0.650.85x25160000  Ast   Ast (400) 2600000  0.80 x0.653400000  21.25 Ast  400 Ast  Use 12 D-22 mm

12 D-22

400mm

Ast  4224mm 2

Stirrup 10mm 400mm

( Ast  4560mm 2 )

1%  Apr  4560mm 2  8%

 Examples Column detailing