Question

Rankine’s formula is used for the analysis of steel compression member if the slenderness
ratio \(\left( \frac{l}{r} \right)\) is:-
1. \(120 < \frac{l}{r} < 200\)
2. \(200 < \frac{l}{r} < 250\)
3. \(100 < \frac{l}{r} < 150\)
4. None of above

Answer 1

Correct Answer - Option 4 : None of above

Concepts:

Rankin’s formula is an empirical formula used for the calculation of ultimate load both for short and long columns. Rankin's formula is also known as Rankin Gordon Formula. It gives the ultimate load that the column can bear before failure. 

Rankin’s formula is valid for both short and long columns. Hence, any value of slenderness ratio is suitable for it.

In this formula, both buckling and crushing failure is considered by Rankine while analyzing the compression members.

The failure load, P is given as:

\(P= \frac{\sigma_{c}A}{1 + a\gamma^2}\)

Where

σ_c  is the critical stress, A is the cross-sectional area, γ is slenderness ratio and a is constant.