Question

Consider the following statements for a compression member :
I. The elastic critical stress in compression increases with decrease in slenderness ratio.
II. The effective length depends on the boundary conditions at its ends.
III. The elastic critical stress in compression is independent of the slenderness ratio.
IV.The ration of the effective length to its radius of gyration is called as slenderness ratio.

The TRUE statements are

• A. II and III
• B. III and IV
• C. II, I and IV
• D. I, II and IV

Answer 1

The correct option is D I, II and IV

Elastic critical stress,
$s=\frac{{\pi }^{2}E}{{\lambda }^2}$
$\sigma \infty \frac{1}{{\lambda }^2}$
Where $\lambda =$slenderness ratio
$\lambda =\frac{\text{Effective length}}{\text{Radius of gyration}}$
Effective Length $\to$ Effective length is the length of the equivalent pinned-end member, or the distance between points of inflection in the deflection curve. It depends on the boundary condition at the end of member.