T311-Propped Cantilever Beam with a Centered Load

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

Beam Illustration

Beam Illustration

Nomenclature:
F = 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 = 11 * F / 16
R2 = 5 * F / 16
VAB = R1
VBC = -R2
M1 = -3 * F * l / 16
MAB = F / 16 * (11 * x – 3 * l)
MBC = 5 * F / 16 * (l – x)
yAB = (F * x^2)/(96 * E * I) * (11 * x – 9 * l)
yBC = (F * (l – x))/(96 * E * I) * (5 * x^2 + 2 * l^2 – 10 * l * x)

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