Structural Beam Deflection, Stress, Bending Equations and calculator for a Beam with bending moment applied

Beam Deflection, Stress, Strain Equations and Calculators

Structural Beam Deflection, Stress, Bending Equations and calculator for a Beam with bending moment applied

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Reaction and Shear Equation

Bending Moments Equation

Deflection and End Slope Equation

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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:

• Young, W. C., Budynas, R. G.(2002). Roark's Formulas for Stress and Strain . 7nd Edition, McGraw-Hill.