Shear Stresses in Beams MCQ with answer and solution

Concept

Maximum Shear Stress in Rectangular Section

Formula

τ_max = 1.5 × (V / A) = 3V / (2 × b × d)

Step-by-step solution

1. Calculate cross-sectional area: A = b × d = 25 mm × 50 mm = 1250 mm² 2. Calculate average shear stress: τ\_avg = V / A = 5000 N / 1250 mm² = 4 MPa 3. Calculate maximum shear stress at neutral axis: τ\_max = 1.5 × τ\_avg = 1.5 × 4 MPa = 6 MPa

Explanation

For a rectangular beam, maximum shear stress occurs at the neutral axis and is equal to 1.5 times the average shear stress. First, calculate the average shear stress by dividing the shear force (5,000 N) by the cross-sectional area (25 mm × 50 mm = 1,250 mm²), which equals 4 MPa. Multiplying 4 MPa by 1.5 gives 6 MPa.

Shortcut

Use the formula τ_max = 1.5 × (V / A). Quickly calculate average stress (V / A) as 5,000 N / 1,250 mm² = 4 MPa, then multiply by 1.5 to get 6 MPa.

Common mistake

Students often mistake maximum shear stress for average shear stress by calculating V/A (5000 N / 1250 mm² = 4 MPa) or forget the 1.5 factor for rectangular sections, leading them to select incorrect options or misuse unit conversions.