T308-Simply Supported Beam with a Moment Load

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

Beam Illustration

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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