Correct Answer - Option 2 : 346
Concept:
Slenderness ratio
\(S= \frac {L_e}{k}\),
where \(k= \sqrt {\frac {I_{min}}{A}}\)
where Le = Equivalent length of column, k = Radius of gyration, A = Cross-section area, Imin = Minimum Area Moment of Inertia
Calculation:
Given:
A = 10 × 20, Le = L = 1 m
For rectangular cross-section:
\(I= \frac {bd^3}{12}\)
∴ \(I_{min}= \frac {20\; \times\; 10^3}{12}=1666.67~ mm^4\)
\(k= \sqrt {\frac {1666.67}{20\; \times\; 10}}=2.88 ~mm\)
Hence
\(S= \frac {1000}{2.888}=346.26\)
