Question

A column consists of four ISA $150\times 150\times 12$ mm, riveted together as shown in figure. What is the slenderness ratio, if the effective length of column is 4.5 m?
Use : $I_{xx}=I_{yy}=735.4\times {10}^{4}m{m}^4;C_{xx}=C_{yy}=41.4mm;\pi =3459m{m}^2$

• A. 72.62
• B. 80.91
• C. 84.54
• D. 87.88

Answer 1

The correct option is A 72.62

When all the four angles are riveted together as shown they act as one unit.
$I_y-I_x=4[I_{xx}+a(C_{xx}{)}^2]$
$=4[735.4\times {10}^4+3459\times 41.4{)}^2]$
$=5313\times {10}^{4}m{m}^4$
Radius of Gyration, $r_{min}=\sqrt{\frac{I_{min}}{A}}$
$=\sqrt{\frac{5313\times {10}^4}{4\times 3459}}=61.97mm$
$\therefore$ Slenderness ratio, $\lambda =\frac{l_{eff}}{{\gamma }_{min}}=\frac{4500}{61.97}=72.62$