Beam Deflection and Stress Formula and Calculators
Engineering Calculators
Area Moment of Inertia Equations & Calculators
Structural Beam Deflection, Stress, Bending Equations and calculator for Beam Supported on Both Ends Loaded at any Location.
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Beam Deflection, Stress
Beam Supported on Both Ends Calculator
Stress between load and "a" load point
Stress between load and "b" load point
Stress at load application
If the cross section is constant this is the maximum stress.
Deflection for location between load and "a" point
Deflection for location between load and "b" point
Maximum deflection at load
Let be the length of the shorter
segment and b of the longer one.
The maximum deflection

is in the longer segment, at 
Where:
E = 
Modulus of Elasticity 
psi 
(N/mm^{2)} 
I = 
Moment of Inertia 
in^{4} 
(mm^{4)} 
W = 
Load 
lbs 
(N) 
s = 
Stress at the crosssection being evaluated 
Lbs/in^{2} 
(N/mm^{2}) 
y = 
Deflection 
inches 
(mm) 
x = 
Some distance as indicated 
inches 
(mm) 
a = 
Some distance as indicated 
inches 
(mm) 
b = 
Some distance as indicated 
inches 
(mm) 
= 
Some distance as indicated 
inches 
(mm) 
Z = 
section modulus of the crosssection of the beam = I/z 
in^{3} 
(mm^{3)} 
z = 
distance from neutral axis to extreme fiber (edge) 
inches 
(mm) 
 Please note letter "" (lower case "L") is different than "I" (Moment of Inertia).
 Deflections apply only to constant cross sections along entire length.
References:
 Any Machinery's Handbook published since 1931 or,
 Machinery's Handbook, 21st Edition, Page 404 or,
 Machinery's Handbook, 23st Edition, Page 260 or,
 Machinery's Handbook, 27st Edition, Page 261
