A transverse shear force $V$ produces shear stress across a beam cross-section. For many prismatic beams, the distribution can be calculated from

$$\tau=\frac{VQ}{It},$$

where $I$ is the area moment of inertia of the complete section, $t$ is the local width or thickness, and $Q$ is the first moment of area of the portion of the section above or below the point of interest.

Stress is not uniform

Unlike the simple average $V/A$, beam shear stress usually varies across the section.

For a rectangular section, the distribution is parabolic: zero at the top and bottom surfaces and maximum at the neutral axis.

I-sections

In an I-beam, the thin web carries most of the vertical shear because the shear-stress distribution is largest near the neutral axis, while the flanges are especially effective at resisting bending stress because much of their area lies far from that axis.

Bending and shear stresses therefore arise from different internal resultants and produce different distributions across the same beam section.