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

Beam Illustration

Nomenclature:

F = Foading 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 = F / 2

R2 = F / 2

M1 = – F * l / 8

M2 = – F * l / 8

VAB = F / 2

VBC = – F / 2

MAB = F / 8 * (4 * x – l)

MBC = F / 8 * (3 * l – 4 * x)

yAB = (F * x^2)/(48 * E * I) * (4 * x – 3 * l)

ymax = (F * l^3) / (192 * E * I)

F = Foading 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 = F / 2 R2 = F / 2 M