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

Beam Illustration

Nomenclature:

F = Loading force

R = Reaction force

V = Shear force

M = Moment

l = beam length

a = Distance of load from left support

b = Distance of load from right support

x = location

E = Modulus of elasticity

I = Moment if Inertia

y = deflection

Relationships:

————–

R1 = F * b / (2 * l^3) * (3 * l^2 – b^2)

R2 = F * b / (2 * l^3) * (3 * l – a)

VAB = R1

VBC = -R2

M1 = F * b / (2 * l^2) * (b^2 – l^2)

MAB = F * b / (2 * l^3) * ((b^2 * l – l^3 + x * (3 * l^2 – b^2))

MBC = F * a^2 / (2 * l^3) * (3 * l^2 – 3 * l * x – a * l + a * x)

yAB = (F*b*x^2)/(12*E*I*l^3) * (3*l*(b^2 – l^2)) + x*(3*l^2 – b^2))

yBC = yAB – (F * (x – a)^3)/(6 * E * I)

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