This page provides formula for beam shear, moment and deflection formula for a simply supported beam with a moment load.

Beam Illustration

Nomenclature:

R = Reaction force

V = Shear force

M = Moment

l = beam length

x = location

a = Distance from right support to moment

b = Distance from left support to moment

E = Modulus of elasticity

I = Moment if Inertia

y = deflection

Relationships:

————–

R1 = -R2 = MB / l

V = MB / l

MAB = MB * x / l

MBC = MB / l * (x – l)

yAB = (MB*x) / (6*E*I*l) * (x^2 + 3*a^2 – 6*a*l + 2*l^2)

yBC = MB / (6*E*I*l) * (x^3 – 3*l*x^2 + x*(2*l^2 + 3*a^2) – 3*a^2*l)

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