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

Beam Illustration

Nomenclature:

F = Loading force

R = Reaction force

V = Shear force

M = Moment

l = beam length

a = Distance from support to loading force

x = location

E = Modulus of elasticity

I = Moment if Inertia

y = deflection

Relationships:

————–

R1 = R2 = F

VAB = F

VBC = 0

VCD = -F

MAB = F * x

MBC = F * a

MCD = F * (l -x)

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

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

ymax = (F * a)/(24 * E * I) * (4 * a^2 – 3 * l^2)

Back Up Next