This page provides formula for beam shear, moment and deflection formula for a propped cantilever 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 = 11 * F / 16

R2 = 5 * F / 16

VAB = R1

VBC = -R2

M1 = -3 * F * l / 16

MAB = F / 16 * (11 * x – 3 * l)

MBC = 5 * F / 16 * (l – x)

yAB = (F * x^2)/(96 * E * I) * (11 * x – 9 * l)

yBC = (F * (l – x))/(96 * E * I) * (5 * x^2 + 2 * l^2 – 10 * l * x)

Back Up Next