Shear Force and Bending Moment MCQ with answer and solution

Concept

Bending Moment in Cantilever Beams

Formula

M_max = P × L (at fixed support)

Step-by-step solution

1. Recall the bending moment formula for a cantilever beam with a point load P at its free end: M = P × x, where x is the distance from the free end. 2. Evaluate the bending moment at the free end (x = 0), which equals 0, and at the fixed support (x = L), where it reaches its maximum value M_max = P × L. 3. Identify Option (c) as incorrect because the bending moment is zero at the free end, not maximum, making Option (c) the correct choice for this question.

Explanation

In a cantilever beam, the bending moment at the free end is actually zero because there is no distance or support to create a turning effect at that point. The bending moment reaches its maximum value at the fixed support, where the distance from the point load is the largest.

Shortcut

To remember bending moment in a cantilever beam: - Free end = Free of moment (Zero BM at the free end) - Fixed end = Full moment (Maximum BM at the fixed support: M = P × L)

Common mistake

A common mistake is selecting option A, B, or D because students overlook the word "incorrect" in the question stem and pick a statement that is correct. Another frequent mistake is confusing the location of the maximum bending moment in a cantilever beam, assuming it occurs at the point of load application (free end) rather than at the fixed support where the moment arm is greatest.