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

Beam Illustration

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)