Beam Shear Stress — Zhuravsky Formula

For transverse bending, the shear stress at a point of the cross-section is determined by the Zhuravsky formula:

$$\tau=\frac{QS}{Ib}.$$

• $Q$ — shear force at the section;
• $S$ — first moment of the cut-off part of the area about the neutral axis;
• $I$ — second moment of area of the entire section about the neutral axis;
• $b$ — local section width at the level where $\tau$ is evaluated.

At a free upper or lower boundary of a solid section, $S$ tends to zero and therefore $\tau$ is zero. For a rectangular section, the maximum shear stress occurs at the neutral axis.