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

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

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Reaction and Shear Equation

Bending Moments Equation

Stress Maximum

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 = Unit Load lbs/in (N/mm) y = 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 = Moment lbs-in (N-mm) θmax = Slope Angle degree (radian) σmax = Stress max. psi (N/mm2)
• Deflections apply only to constant cross sections along entire length.

References:

• Boeing Design Manual, Rev G. 1994 BDM