Beam Deflection Equations and Calculator including Stress and Reaction Loads for a Beam supported One End, Pin Opposite End and Two Tapered Distributed Load

Beam Deflection and Stress Formula and Calculators

Area Moment of Inertia Equations & Calculators

Beam Deflection, Shear and Stress Equations and Calculator for a Beam supported One End, Pin Opposite End and Two Tapered Distributed Load.

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 = 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 = Distance neutral axis inches (mm)
Vmax = Shear Load lbf (N)
Mmax = Beam Moment lbs-in (N-mm)
θmax = Slope Angle degree (radian)
σmax = Beam Stress max. psi (N/mm2)
  • Deflections apply only to constant cross sections along entire length.

References:

  • Boeing Design Manual, Rev G. 1994 BDM

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