T316-Fixed Beam with Uniform Loading

This page provides formula for beam shear, moment and deflection formula for a fixed beam with uniform loading.

Beam Illustration

Beam Illustration

Nomenclature:
w = Uniform 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 = (w * l) / 2
R2 = (w * l) / 2
M1 = -(w * l^2) / 12
M2 = -(w * l^2) / 12
V = w / 2 * (l – 2 * x)
M = w / 12 * (6 * l * x – 6 * x^2 – l^2)
y = -(w * x^2)/(24 * E * I) * (l – x)^2
ymax = -(w * l^4) / (384 * E * I)

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