Shear Flow


Shear Flow
If the shearing stress fv is multiplied by the width b, we obtain a quantity q, known as the shear flow, which represents the longitudinal force per unit length transmitted across a section at a level y1 from the neutral axis.

$ q = f_v b = \dfrac{VQ}{I} $


Application of Flexural and Shearing Stresses to Rectangular Section
For rectangular section, $ \,\, I = \dfrac{bd^3}{12} \,\, $ and $ \,\, c = d/2. \,\, $

The bending stress at a level $ \,\,y\,\, $ from the neutral axis is

$ f_b = \dfrac{12My}{bd^3} $


and the maximum bending stress in the section is

$ (\,f_b\,)_{max} = \dfrac{6M}{bd^2} $


The maximum shearing stress in the section is

$ (\,f_v\,)_{max} = \dfrac{3V}{2bd} = \dfrac{3V}{2A} $