Question

A built up column with four angles is provided as shown. The column is 12 m long and supports an axial load of 500 kN. The ends of the column are held in position and restrained against rotation. Allowable slenderness ratio is 64. Angle section is 90 x 90 x 6 mm.



The properties of 90 x 90 x 6 mm angle section are as following:

$A=1047m{m}^2,r_{xx}=r_{yy}=27.7mm$
$C_{xx}=C_{yy}=24.2mm,I_{xx}=I_{yy}=80.1\times {10}^{4}m{m}^4$

Spacing of angle 'S' is _______.

Answer 1

Allowable slenderness ratio
$\frac{l}{r}=64$

$l=0.65\times 12\times {10}^3=7800mm$

$r=\frac{7800}{64}=121.875mm$

Moment inertia of section required
$I=A{r}^2$

$=4\times 1047\times {121.875}^2=6220.65\times {10}^{4}m{m}^4$

Moment of inertia required = Moment of inertia provided

$6220.65\times {10}^4=4\times 80.1\times {10}^4+4\times 1047\overline{y^2}$

$\overline{y^2}=118.69mm$

Spacing angles,
$S=2\times (118.69+24.2-90)$

= 105.78 = 106 mm