Beam theory – shear stress at the neutral axis At the neutral axis of a beam subjected to transverse shear, the shear stress is:

Introduction / Context:Understanding the shear stress distribution across a beam depth is essential for web design, particularly in rectangular and I-sections. The neutral axis is the line of zero bending normal stress, but its role in shear distribution is different.

Given Data / Assumptions:

• Beam carrying a transverse shear force V.
• Cross-sections like rectangles and I-beams with non-zero web thickness at the neutral axis.
• Elastic, small-deflection conditions.

Concept / Approach:The shear stress at a level y is given by τ = V Q / (I b), where Q is the first moment of area about the neutral axis, I is the second moment of area, and b is the width at that level. For common sections, Q is maximum at the neutral axis; consequently, τ is also typically maximum there if b does not spike excessively.

Step-by-Step Reasoning:At extreme fibers, Q = 0, hence τ = 0.Moving toward the neutral axis, Q increases, reaching its maximum at the neutral axis.Since b is finite at the neutral axis for rectangular and I-sections (web thickness), τ attains a maximum there.

Verification / Alternative check:For a rectangle: τ_max = 1.5 * V / A and occurs at the neutral axis. For an I-beam, the maximum is in the web at the neutral axis region.

Why Other Options Are Wrong:Zero or minimum applies at extreme fibers, not at the neutral axis; infinity is non-physical; “equal to bending stress” mixes different stress components—bending normal stress is zero at the neutral axis, not equal to shear stress.

Common Pitfalls:Assuming “neutral axis” means all stresses are zero; only bending normal stress is zero there, not shear.

Final Answer:Maximum