Compression Members MCQ with answer and solution

Concept

Rankine constant in column buckling theory

Formula

a = f_y / (π² × E)

Step-by-step solution

1. The Rankine constant a is defined as a = fy / (π² × E). 2. Since the modulus of elasticity E is in the denominator, the Rankine constant is inversely related to E. Answer: C

Explanation

The Rankine constant in column strength calculations is defined as the ratio of material yield stress to the product of π squared and the elastic modulus. Because modulus of elasticity appears in the denominator of this theoretical formula, the Rankine constant varies inversely with it. Therefore, option C correctly identifies modulus of elasticity as the inversely related property.

Why the other options are wrong

A) The radius of gyration affects the slenderness ratio directly rather than being inversely proportional to the Rankine constant. B) Effective length influences the critical buckling load but is not inversely proportional to the Rankine constant. D) Slenderness ratio is used alongside Rankine constant in column strength formulas rather than being inversely related.

Shortcut

Rankine constant a = fc / (π²E), which is inversely proportional to Modulus of Elasticity.

Common mistake

Assuming the Rankine constant is inversely related to slenderness ratio or effective length and selecting option B or D.