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