Bending Stresses & Section Comparison – Problem 25 | Strength of Materials | Beam Analysis...

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Question : Three beams have the same length, the same allowable bending stress, and the same bending moment. The beam cross-sections are:

1. a square,

2. a rectangle with depth twice its width (d = 2b), and

3. a circle.
Find the ratios of the required widths/diameters of the circular and rectangular beams with respect to the square beam.

In this Strength of Materials problem, we compare square, rectangular (d = 2b), and circular beam sections under identical conditions: same span, same allowable bending stress, and same bending moment. Using section modulus (Z) and the bending equation , we derive the relative sizes needed for each cross-section to carry the same moment safely.
What you’ll learn:

How section modulus changes with shape (square vs. rectangle vs. circle)

How to set up size ratios when allowable stress and moment are fixed

Fast exam strategy for “which section is more efficient?” questions
Perfect for Mechanical/Civil/Structural students preparing for SoM/Strength of Materials exams and interviews.

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