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.
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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/mm^{2}) 
I = 
Moment of Inertia 
in^{4} 
(mm^{4}) 
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) 
V_{max} = 
Shear Load 
lbf 
(N) 
M_{max} = 
Moment 
lbsin 
(Nmm) 
θ_{max} = 
Slope Angle 
degree 
(radian) 
σ_{max} = 
Stress max. 
psi 
(N/mm^{2}) 
 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, McGrawHill.
