Compression Members MCQ with answer and solution

Concept

Slenderness ratio calculation for steel column

Formula

λ = K·L / r

Step-by-step solution

1. Actual column length L = 3 m = 3000 mm. 2. Effective length factor K = 0.65; effective length KL = 0.65 × 3000 = 1950 mm. 3. Radius of gyration r = 40 mm. 4. Slenderness ratio λ = KL / r = 1950 mm / 40 mm = 48.75. Answer: B

Explanation

The slenderness ratio of a compression member is defined as the effective length divided by the radius of gyration. With actual length 3000 mm, effective length factor 0.65, and radius of gyration 40 mm, the ratio is (0.65 × 3000) / 40 = 48.75.

Why the other options are wrong

A) 35 is an incorrect arithmetic calculation. C) 55 results from using an incorrect effective length factor. D) 65.75 is an incorrect ratio.

Shortcut

λ = (0.65 × 3000) / 40 = 1950 / 40 = 48.75.

Common mistake

Using actual length instead of effective length: 3000 / 40 = 75.