T312-Propped Cantilever Beam with an Intermediate Load

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

Beam Illustration

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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