T305-Simply Supported Beam with a Centered Load

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

Beam Illustration

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 = R2 = F / 2
VAB = R1
VBC = -R2
MAB = F * x / 2
MBC = F / 2 * (l – x)
yAB = (F * x)/(48 * E * I) * (4 * x^2 – 3 * l^2)
ymax = -(F * l^3)/(48 * E * I)

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