Compression Members MCQ with answer and solution

Concept

Radius of gyration grows when area is placed far from the centroidal axis, because I grows with distance squared.

Formula

r = √(I/A), I = Σ(A_i × y_i²)

Step-by-step solution

1. Radius of gyration r = √(I/A). 2. Moment of inertia I = Σ A_i y_i², where y_i is the distance of each area from the centroid. 3. For the same area A, I is largest when the material is far from the centroid (large y). 4. So r is maximum when the material is placed farthest from the centroid.

Explanation

Radius of gyration depends on how the area is spread, not only on how much area there is. If the material is kept far from the centroid, the moment of inertia becomes large for the same area, so r becomes large. This is why hollow tubes and built-up sections with spaced members are efficient as columns.

Why the other options are wrong

B: Material near the centroid gives small I, so r is small. C: Material at the centroid gives I nearly zero, so r is nearly zero. D: More area alone does not increase r. Doubling the area at the same distances doubles both I and A, so r stays the same.

Shortcut

Material far from the centroid gives large I and large r (example: hollow pipe column).

Common mistake

Thinking that more area means more r. Actually r depends on the spread of area, not the amount of area.