T310

Simply Supported Beam with an Overhanging Load

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

Nomenclature:
F = Loading force
R = Reaction force
V = Shear force
M = Moment
l = beam length
a = Distance from support to overhanging loading force
x = location
E = Modulus of elasticity
I = Moment if Inertia
y = deflection

Relationships:
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R1 = -F * a / l
R2 = F / l * (l + a)
VAB = -F * a / l
VBC = F
MAB = -F * a * x / l
MBC = F * (x - l - a)
yAB = (F * a * x)/(6 * E * I * l) * (l^2 - x^2)
yBC = (F * (x - l))/(6 * E * I) * ((x - l)^2 - a * (3 * x -l))
yC = -(F * a^2)/(3 * E * I) * (l + a)