What is the specific equation for maximum shear stress of a rectangular cross-section?

The maximum shear stress for a rectangular cross-section is correctly represented by the equation T = (3/2)(V / A). This equation arises from the principles of mechanics of materials and deals specifically with how shear stress is distributed across a cross-section.

In the context of shear in a beam subjected to transverse loading, the shear force (V) applied to a section of the beam creates a distribution of shear stress across the section. For a rectangular cross-section, the shear stress varies linearly from zero at the top and bottom to a maximum value at the centroid of the section. The average shear stress is calculated as V/A, where A is the cross-sectional area.

However, due to the non-uniform distribution of shear stress within a rectangular section, the maximum shear stress typically exceeds the average shear stress. The factor of (3/2) accounts for this increase, providing a more accurate value for the maximum shear stress experienced at the centroid of the rectangular cross-section.

This relationship indicates that understanding the distribution of shear stress across different cross-sections is critical for engineering applications, especially in structural designs, as it helps ensure safety and structural integrity under load.