Shear Stress Distribution in Beams

The shear stress in any section at a distance ‘y’ from neutral axis is given by

Where

F = Shear force at the given section

A y  = moment of the area of the section above the level under consideration.

b = width of the beam at the level under consideration

I = M.I of the beam section about the N.A

Shear stress Distribution for Beam sections of various shapes:
Rectangular section: τavg

Average shear stress  = (F / bd)

τmax =  (3/2) τave 

For solid circular section:

For triangular section:

A beam of square section is placed horizontally with one diagonal placed horizontally:

For I - Section: