This page provides formula for beam shear, moment and deflection formula or a cantilever beam with Uniform loading.

Beam Illustration

Nomenclature:

R = Reaction force

V = Shear force

w = Distributed loading force

M = Moment

l = beam length

x = location

E = Modulus of elasticity

I = Moment if Inertia

y = deflection

Relationships:

————–

R1 = w * l

M1 = -(w * l^2)/2

V = w * (l – x)

M = -(w / 2) * (l – x)^2

y = (w * x^2) / (24 * E * I) * (4 * l * x – x^2 – 6 * l^2)

ymax = -(w * l^4) / (8 * E * I) at x = l

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