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

Beam Illustration

Nomenclature:

F = Loading force

R = Reaction force

V = Shear force

M = Moment

l = beam length

a = Distance from support to overhanging loading force

x = location

E = Modulus of elasticity

I = Moment if Inertia

y = deflection

Relationships:

————–

R1 = -F * a / l

R2 = F / l * (l + a)

VAB = -F * a / l

VBC = F

MAB = -F * a * x / l

MBC = F * (x – l – a)

yAB = (F * a * x)/(6 * E * I * l) * (l^2 – x^2)

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

yC = -(F * a^2)/(3 * E * I) * (l + a)

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