Question

A tension member 10 m long is subjected to an axial load of 200 kN. Section with channels facing each other are provided as shown in figure. An additional plate 300 x 6 mm is provided at top.


properties of ISMC 300

$A=4564m{m}^2,I_{xx}=6362.6\times {10}^{4}m{m}^4$

$T=13.6mm,I_{yy}=310.8\times {10}^{4}m{m}^4$

$t=7.6mm,g=50mm,{\gamma }_{xx}=118.1mm$

$C_{yy}=23.6mm,B=90mm$

The slenderness ratio of the member is ______.

• A. 92
• B. 108
• C. 74
• D. 82

Answer 1

The correct option is D 82

$I_{xx}=2\times 6362.6\times {10}^4+\frac{300\times 6^3}{12}+300\times 6\times {(132.22-\frac{6}{2})}^2+2\times 4564(156-132.22{)}^2$

$=16247.5\times {10}^{4}m{m}^4$

$A=300\times 6+2\times 4564=10928m{m}^2$

${\gamma }_{xx}=\sqrt{\frac{I_{xx}}{A}}=\sqrt{\frac{16247.5\times {10}^4}{10928}}=121.9mm$

$\lambda =\frac{L}{{\gamma }_{xx}}=\frac{10\times {10}^3}{121.9}=82$