What is the formula for maximum shear in a rectangular cross section?

The formula for maximum shear stress in a rectangular cross section is based on the distribution of shear stress across the area of the section. In a rectangular cross section, the maximum shear stress occurs at the centroid of the section and can be determined using the equation ( \tau_{max} = \frac{3}{2} \frac{V}{A} ), where ( V ) is the vertical shear force and ( A ) is the area of the cross section.

This formula comes from the relationship between shear force, the geometric properties of the section, and how shear stress is distributed. The factor of ( \frac{3}{2} ) accounts for the way shear forces tend to concentrate towards the centroid in the case of a rectangle, and this higher value reflects the maximum condition under typical loading scenarios.

Other formulas do not capture the concentration of shear accurately or merely provide different contexts for shear stress under varying conditions. For instance, ( \frac{V}{A} ) represents the average shear stress across the entire area and does not reflect the maximum value at the centroid; similarly, ( 2V/A ) would overestimate the stress, and ( \frac{1}{2} \frac{V}{A