ZXL 2018 - CIV 2225 Columns - for printing PDF

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Summary

 CIV2225 Columns 1. Behaviour 2. Member Capacity (Columns) 3. Examples 1 1. Behaviour (Columns) For longer columns, failure is accompanied by a rapid increase in the lateral deflection. If the member is extremely slender, the load at which this increased deflection takes place is not sufficient to ...

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CIV2225 Columns

1. Behaviour 2. Member Capacity (Columns) 3. Examples

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1. Behaviour (Columns) For longer columns, failure is accompanied by a rapid increase in the lateral deflection. If the member is extremely slender, the load at which this increased deflection takes place is not sufficient to significantly yield the member. Thus the maximum load is not a function of the material strength but rather depends on the bending stiffness of the member (EI), and its length (L). The failure of a long column may occur at stress levels below that required to initiate local buckling of slender plate elements.

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Intermediate members are more complex to analyze but also are the most common in steel structures. They may fail by a combination of yielding, overall buckling and/or local buckling including interaction between buckling modes. The maximum strength of the column depends not only on the bending stiffness and length but also on the yield stress of the steel, the distribution of residual stress over the cross-section, the cross-section slenderness, and the magnitude of the initial imperfections in columns and component plates of the cross-section.

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2. Member Capacity

AS4100 The design member capacity can be calculated as Nc =  c Ns =  ckf An fy where capacity factor  = 0.90, kf is the form factor defined in Eq. (5), An is the net area of cross-section, fy is the yield stress and c is the member slenderness reduction factor.

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c depends on the modified member slenderness  n and section constant ab.

In which, L is the column length, ke is the effective length factor and r is the radius of gyration about the major (x) or minor (y) axis. A column may buckle about the major (x) axis or minor (y) axis. The critical capacity is governed by the case with the largest n value.

A column curve is normally plotted as c versus modified member slenderness n. 5

For members with idealised end restraints the effective length factor (ke) is specified in AS4100 – see Table 5.

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Not idealised end restraints – research is needed

Zhao, X.L., Lim, P., Joseph, P. and Pi, Y.L. (2000), Member capacity of columns with semi-rigid end conditions in Oktalok space frames. Structural Engineering and Mechanics - An International Journal, 10(1), 27-36

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Member Section Constant b are given in Table 6.3.3 of AS4100

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Uncoiling Levelling

Coil welding

Looping

Step 1: Uncoiling and Joining Coils

Steel strip

Electric resistance welding

Forming rollers

Squeeze rollers

Circular shape

Step 2: Forming

Weld trimmer

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Step 3: Welding

CHS

Squeeze rollers

SHS or RHS

Step 4: Sizing and Shaping Step 5: Cutting and Bundling Cutting machine Bundling machine

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The concept of multiple column curves has been adopted by most of the standards for column design. A column curve is normally plotted as non-dimensional axial capacity (i.e. a ratio of member capacity to section capacity, also called member slenderness reduction factor c in AS 4100) versus modified member slenderness n. Different column curves correspond to different crosssection types, and distributions and magnitudes of the residual stresses. The five column curves given in AS4100 are shown in Figure 6.

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The member slenderness reduction factor c can also be calculated from Eq. (16):

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The member slenderness reduction factor c can also be calculated from Tables given in AS4100

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3. Example A hot-rolled I section column is simply supported about both principal axes at each end, and has a central brace which prevents lateral deflections in the minor principal plane. The length of the column is 12m. Check the adequacy of the column for a design axial compressive load corresponding to a nominal dead load of 150 kN and a nominal live load of 250 kN.

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The dimensions and properties of the I-section are: Overall flange width b = 191 mm Overall depth d = 460 mm Flange thickness tf = 16mm Web thickness tw = 9.9 mm Corner radius r = 10.2 mm Radius of gyration rx = 188 mm Radius of gyration ry = 42.4 mm A = 10400 mm2 Yield stress of flange fyf = 300 MPa Yield stress of web fyw = 300 MPa

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Solution using AS4100

(1). Design axial load Design axial load N* = 1.2DL+1.5LL = 1.2150+1.5250 = 555 kN

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(2). Form factor

Flange

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Web

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be,web

  ey    (460  2  16) 45  407mm  (d  2t f )  47.3  e 

The effective area

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(3). Nominal section capacity

Ns = kf An fy = 0.98  10400  300 / 1000 = 3058 kN (4). Design section capacity Ns = 0.9  3058 = 2752 kN

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(5). Modified column slenderness Lex = kex Lx = 1.0  12 = 12 m Ley = key Ly = 1.0  6 = 6 m

Buckling about the minor (y) axis. n = ny = 154.2 27

(6). Design member capacity

b = 0 for hot-rolled I-section Reduction factor c  0.28

Nc =  c Ns = 0.28  2752 = 771 kN > N* = 555 kN The member is satisfactory.

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Additional example A hot-finished circular hollow section (CHS) member is to be used as an internal column in a multi-storey building. The column has a length of 4000 mm and is simply supported at both ends. Check the adequacy of the column for a design axial compressive load corresponding to a nominal dead load of 540 kN and a nominal live load of 900 kN. The dimensions and properties of the CHS are: Diameter d = 250 mm Thickness t = 10 mm Cross sectional area A = 7540 mm2 Second moment of area I = 54.38  106 mm4 Radius of gyration r = 84.93 mm L = 4000 mm fy = 350 MPa

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Solution using AS4100

(1) Design axial load Design axial load

N* = 1.2DL+1.5LL = 1.2540+1.5900 = 1998 kN

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(2). Form factor

Slenderness

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(3). Nominal section capacity

Ns = kf An fy = 1.0  7540  350 / 1000 = 2639 kN

(4). Design section capacity Ns = 0.9  2639 = 2375 kN

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(5). Modified column slenderness Le = ke L = 1.0  4000 = 4000 mm

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(6). Design member capacity b = -1 for hot-rolled CHS Reduction factor c  0.92 Nc =  c Ns = 0.92  2375 = 2185 kN > N* = 1998 kN

The CHS is satisfactory. 34

Summary

Columns

1. Behaviour 2. Member Capacity (Columns) 3. Examples

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Relevance to Project 1

Steel webs (shear) 35...