A column of rectangular cross-section of 10 mm × 20 mm and a length of 2 m. what is the slenderness ratio of the column?

Concept:

Slenderness ratio

\(S= \frac {L_e}{k}\),  \(k= \sqrt {\frac {I_{min}}{A}}\)

where L_e = equivalent length of column, k = radius of gyration, A = cross-section area, I_min =minimum area moment

Calculation:

Given:

A = 10 × 20, L_e = L = 2 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 \(S= \frac {2000}{2.888}=692.8\)