Bending and Shearing Stresses of Timbers

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

Horizontal Shear Stress
$f_v = \dfrac{VQ}{Ib}$

cross-section-beam-any-shape.jpg
For Rectangular Sections
$f_b = \dfrac{6M}{bd^2}$
 

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

cross-section-beam-rectangular.jpg
For Circular Sections
$f_b = \dfrac{4M}{\pi r^3} = \dfrac{32M}{\pi d^3}$
 

$f_v = \dfrac{4V}{3\pi r^2} = \dfrac{16V}{3\pi d^2}$

cross-section-beam-circle.jpg

Where
fb = bending or flexural stress
fv = 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
Q = moment of area about the neutral axis
 

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