T315

Fixed Beam with an Intermediate Load

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

Nomenclature:
F = Loading force
R = Reaction force
V = Shear force
M = Moment
l = beam length
a = Distance from left end of beam
b = Distance from right end of beam
x = location
E = Modulus of elasticity
I = Moment if Inertia
y = deflection

Relationships:
--------------
R1 = (F * b^2) / l^3 * (3 * a + b)
R2 = (F * a^2) / l^3 * (3 * b + a)
M1 = (F * a * b^2) / l^2
M2 = -(F * a^2 * b) / l^2
VAB = R1
VBC = - R2
MAB = (F * b^2) / l^3 * (x * (3 * a + b) - l * a)
MBC = MAB - F * (x - a)
yAB = (F*b^2*x^2)/(6*E*I* l^3) * (x*(3*a + b) - 3*a*l)
yBC = (F*a^2*(l - x)^2) / (6*E*I*l^3) * ((l - x)*(3*b + a) - 3*b*l)