T306-Simply Supported Beam with an Intermediate Load

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

Beam Illustration

Beam Illustration

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

Relationships:
————–
R1 = F * b / l
R2 = F * a / l
VAB = R1
VBC = -R2
MAB = F * b * x / l
MBC = F * a / l * (l – x)
yAB = (F * b * x)/(6 * E * I * l) * (x^2 + b^2 – l^2)
yBC = (F * a * (l – x)) / (6 * E * I * l) * (x^2 + a^2 – 2 * l * x)
ymax = -(F * l^3)/(48 * E * I) * (x^2 + a^2 – 2 * l * x)

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