Bending Stress and Shearing Stress in Timber Beam
Bending Stress $f_b = \dfrac{M}{S} = \dfrac{Mc}{I}$ Horizontal Shear Stress 

For Rectangular Sections $f_b = \dfrac{6M}{bd^2}$ $f_v = \dfrac{3V}{2bd}$ 

For Circular Sections $f_b = \dfrac{4M}{\pi r^3} = \dfrac{32M}{\pi d^3}$ $f_v = \dfrac{4V}{3\pi r^2} = \dfrac{16V}{3\pi d^2}$ 
Where
f_{b} = actual bending or flexural stress
f_{v} = actual horizontal shear stress
M = maximum moment
V = maximum shear
c = distance from the neutral axis to the extreme fiber in bending
I = moment of inertial about the neutral axis
S = section modulus
Q = moment of area about the neutral axis
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