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

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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