The shear stress formula (τ = VQ/Ib), derived under the assumptions that shear stress is parallel to the shear force and uniformly distributed across the beam's width, applies rigorously only to prismatic beams whose cross-sectional edges are parallel to the axis of bending (e.g., rectangular sections), with accuracy dependent on the height-to-width ratio. For circular and I/T-shaped cross sections — where these assumptions break down (stresses are not parallel to the axis except along the neutral-axis diameter, or width varies abruptly between flange and web) — the formula is applied only at the neutral axis (circular sections, yielding maximum shear stress) or restricted to the web (I/T sections, where the flange's shear stress distribution is not amenable to this formula). This belongs to mechanics of materials / strength of materials, specifically the theory of transverse shear stress distribution in beams under bending, and relates to the theory of longitudinal (bending) strain through the concept of cross-sectional warping caused by non-uniform shear strain.
The shear stress formula (τ = VQ/Ib), derived under the assumptions that shear stress is parallel to the shear force and uniformly distributed across the beam's width, applies rigorously only to pris…