T307

Simply Supported Beam with Uniform Loading

This page provides formula for beam shear, moment and deflection formula for a simply supported beam with uniform loading.
Beam Illustration

Nomenclature:
w = Distributed 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:
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R1 = R2 = w * l / 2
V = w * l / 2 - (w * x)
M = (w * x) / 2 * (l - x)
y = (w * x) / (24 * E * I) * (2 * l * x^2 - x^3 - l^3)
ymax = -(5 * w * l^4)/(384 * E * I)