For a rectangular cross-section in shear, what is the ratio of the maximum shear stress to the average (nominal) shear stress across the section?

Introduction / Context: Shear stress distribution over a rectangular section is parabolic, with zero at the free surfaces and maximum at the neutral axis. Designers must relate the peak shear to the average shear used in V / A calculations to ensure adequate safety when checking shear strength.

Given Data / Assumptions:

• Prismatic rectangular section subjected to transverse shear V.
• Average shear τ_avg = V / A.

Concept / Approach: The elastic shear formula gives τ = V * Q / (I * b). For a rectangle, τ varies parabolically and reaches τ_max = 1.5 * τ_avg at the centroidal axis. Thus the ratio τ_max / τ_avg equals 1.5, a standard result used widely for beams of rectangular section in both steel and timber design.

Step-by-Step Solution: Compute τ_avg = V / (b * h). Use elastic shear formula to find τ_max at neutral axis for a rectangle. Obtain τ_max = 3/2 * τ_avg ⇒ ratio = 1.5.

Verification / Alternative check: Textbook derivations integrate the parabolic distribution to recover the same average V / A, confirming internal consistency and the 1.5 ratio at the centroid.

Why Other Options Are Wrong:

• 2.0, 2.5, 3.0, 4.0: Overstate the peak; they would imply unrealistic stress amplification for rectangular sections.

Common Pitfalls:

• Assuming a uniform shear distribution; real elastic distribution is not uniform.
• Confusing with circular sections (ratio 4/3 ≈ 1.33).

Final Answer: 1.5.