Design for Flexure and Shear

To determine the load capacity or the size of beam section, it must satisfy the allowable stresses in both flexure (bending) and shear. Shearing stress usually governs in the design of short beams that are heavily loaded, while flexure is usually the governing stress for long beams. In material comparison, timber is low in shear strength than that of steel.
 

For any cross-sectional shape, flexure and shear are given in the following formulas:

Flexure Formula

$f_b = \dfrac{Mc}{I}$

 

Horizontal Shear Stress

$f_v = \dfrac{VQ}{Ib}$

 

For rectangular beam, the following defines for flexure and shear:

Flexure formula for rectangular beam

$f_b = \dfrac{6M}{bd^2}$

 

Horizontal shear stress for rectangular beam

$f_v = \dfrac{3V}{2bd}$

 

Where
fb = flexure stress
fv = bending stress
M = maximum moment applied to the beam
V = maximum shear applied to the beam
I = moment of inertia about the neutral axis
Q = moment of area
b = breadth
d = depth
 

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