Source: Mechanicalc

## Shear Stresses in Beams

The shear force, V, along the length of the beam can be determined from the shear diagram. The shear force at any location along the beam can then be used to calculate the shear stress over the beam’s cross section at that location. The average shear stress over the cross section is given by:

τ average =V.A τ average=V.A

The shear stress varies over the height of the cross section, as shown in the figure below:

Beam Illustration

Nomenclature:

R = Reaction force

V = Shear force

F = Loading force

M = Moment

l = beam length

a = Support to force dimension

b = Force to beam end dimension

x = location

E = Modulus of elasticity

I = Moment if Inertia

y = deflection

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