Shear Flow

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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
 

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

 

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