# Shear Flow

**Shear Flow**

If the shearing stress f_{v} 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 y_{1} 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

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

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