Shear Stresses in Beams MCQ with answer and solution

Concept

Maximum shear stress in rectangular section

Formula

τ_max = 1.5 × τ_avg

Step-by-step solution

1. For a rectangular cross-section, the maximum shear stress occurs at the neutral axis. 2. The relation between maximum shear stress (τmax) and average shear stress (τav) is τmax = 1.5 × τav. 3. τmax = 1.5 × 50 MPa = 75 MPa. Answer: B

Explanation

For a beam with a rectangular cross-section subjected to shear, the shear stress distribution across the depth is parabolic. The maximum shear stress occurs at the neutral axis and is equal to 1.5 times the average shear stress. Multiplying the average shear stress of 50 MPa by 1.5 gives 75 MPa at the neutral axis.

Why the other options are wrong

A) 50 MPa is the average shear stress across the rectangular cross section. C) 90 MPa overestimates the peak shear stress ratio for rectangular sections. D) Option B correctly gives 75 MPa as 1.5 times the average shear stress.

Shortcut

Rectangular section shear stress at neutral axis: τ_max = 1.5 × τ_avg = 1.5 × 50 = 75 MPa.

Common mistake

Assuming maximum shear stress equals average shear stress rather than applying the 1.5 multiplier for rectangular sections.