T302-Cantilever Beam with Intermediate Load

This page provides formula for beam shear, moment and deflection formula for a cantilever beam with an Intermediate load.

Beam Illustration

Beam Illustration

Nomenclature:
R = Reaction force
V = Shear force
F = Loading force
M = Moment
l = beam length
a = Support to force dimension
b = Force to beam end dimension
x = location
E = Modulus of elasticity
I = Moment if Inertia
y = deflection

Relationships:
————–
R1 = V = F
M1 = -F * a
MAB = F * (x – a)
MBC = 0
yAB = (F * x^2)/(6 * E * I) * (x – 3 * a)
yBC = (F * a^2)/(6 * E * I) * (a – 3 * x)
ymax = (F * a^2)/(6 * E * I) * (a – 3 * l) at x = l

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