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

Beam Illustration

Nomenclature:

F = Loading force

R = Reaction force

V = Shear force

M = Moment

l = beam length

a = Distance from left support to loading force

b = Distance from loading force to right support

x = location

E = Modulus of elasticity

I = Moment if Inertia

y = deflection

Relationships:

————–

R1 = F * b / l

R2 = F * a / l

VAB = R1

VBC = -R2

MAB = F * b * x / l

MBC = F * a / l * (l – x)

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

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

ymax = -(F * l^3)/(48 * E * I) * (x^2 + a^2 – 2 * l * x)

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