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

Beam Illustration

Nomenclature:

w = Uniform loading force

R = Reaction force

V = Shear force

M = Moment

l = beam length

x = location

E = Modulus of elasticity

I = Moment if Inertia

y = deflection

Relationships:

————–

R1 = 5 * w * l / 8

R2 = 3 * w * l / 8

V = 5 * w * l / 8 – w * x

M = w / 8 * (4 * x^2 + 5 * l * x – l^2)

M1 = – w * l^2 / 8

y = (w * x^2)/(48 * E * I) * (l – x) * (2 * x – 3 * l)

ymax = (w * l^4)/(185 * E * I)

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