T309-Simply Supported Beam with Twin Loads

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

Beam Illustration

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)

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