Shear Stress Distribution in Beams — True/False When a rectangular beam is loaded longitudinally in bending and shear, the shear force develops on the top layer (extreme fiber). Choose the correct statement.

Introduction:This checks understanding of shear stress distribution across a rectangular beam depth under transverse loading.

Given Data / Assumptions:

• Rectangular cross-section; small-deflection, linear elastic bending.
• Beam experiences combined bending moment and shear force.

Concept / Approach:In rectangular beams, transverse shear stress varies parabolically over the depth: zero at both top and bottom extreme fibers and maximum at the neutral axis.

Step-by-Step Solution:Shear formula: τ = V * Q / (I * b)At the extreme fiber, the first moment of area Q = 0, so τ = 0 at the top and bottom surfaces.At the neutral axis, Q is maximum; hence τ is maximum at the mid-depth.

Verification / Alternative check:Standard shear diagrams and textbook distributions confirm a parabolic curve peaking at the neutral axis for rectangles.

Why Other Options Are Wrong:

• Agree / True near supports / under point loads / for non-prismatic beams: Shear magnitude may vary along the span, but at a given section the distribution across depth remains zero at the extreme fibers for a rectangular section.

Common Pitfalls:Confusing shear force (a resultant) with shear stress distribution, or assuming maximum at outer fibers (true for bending stress, not shear).

Final Answer:Disagree