T313-Propped Cantilever Beam with Uniform Loading

This page provides formula for beam shear, moment and deflection formula for a propped cantilever beam with uniform loading.

Beam Illustration

Beam Illustration

Nomenclature:
w = Uniform 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 = 5 * w * l / 8
R2 = 3 * w * l / 8
V = 5 * w * l / 8 – w * x
M = w / 8 * (4 * x^2 + 5 * l * x – l^2)
M1 = – w * l^2 / 8
y = (w * x^2)/(48 * E * I) * (l – x) * (2 * x – 3 * l)
ymax = (w * l^4)/(185 * E * I)

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