Beam Deflection and Stress Equations for a Beam supported One End, One End, Cantilevered at Defined Location and Distributed Load Between Supports

Beam Deflection and Stress Formula and Calculators

Area Moment of Inertia Equations & Calculators

Shear, Deflection and Stress Equations and Calculator for a Beam supported One End, Cantilevered at Defined Location and Distributed Load Between Supports

Structural Beam Deflection, Shear and Stress Equations and calculator for a Beam supported One End Cantilevered with Reversed Tapered Load.

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Beam Reaction and Shear Equation

Reaction and Shear Equation


Beam Bending Moments Equation

Bending Moments Equation

Beam Stress Maximum


Beam Deflection and End Slope Equation

Deflection and End Slope Equation


Where:

E = Modulus of Elasticity psi

(N/mm2)

I = Moment of Inertia in4 (mm4)
W = Beam Load, Total lbf (N)
w = Beam Unit Load lbs/in (N/mm)
y = Beam Deflection inches (mm)
a, b, c, d, x, L = Some distance as indicated inches (mm)
n = Beam Distance neutral axis inches (mm)
Vmax = Beam Shear Load lbf (N)
Mmax = Beam Moment lbs-in (N-mm)
θmax = Slope Angle degree (radian)
σmax = Stress max. psi (N/mm2)
  • Beam Deflections apply only to constant cross sections along entire length.

References:

  • Boeing Design Manual, Rev G. 1994 BDM

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