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

Beam Illustration

Nomenclature:

F = 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 = F / 2

VAB = R1

VBC = -R2

MAB = F * x / 2

MBC = F / 2 * (l – x)

yAB = (F * x)/(48 * E * I) * (4 * x^2 – 3 * l^2)

ymax = -(F * l^3)/(48 * E * I)

Back Up Next