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

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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