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

Beam Illustration

Nomenclature:

w = Distributed 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 = R2 = w * l / 2

V = w * l / 2 – (w * x)

M = (w * x) / 2 * (l – x)

y = (w * x) / (24 * E * I) * (2 * l * x^2 – x^3 – l^3)

ymax = -(5 * w * l^4)/(384 * E * I)

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