Beam Deflection and Stress Formula and Calculators
Area Moment of Inertia Equations & Calculators
Structural Beam Deflection, Stress, Bending Equations and calculator for a Beam supported Both Ends Overhanging Supports Symmetrically, Uniform Load
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Section Modulus Z
Z = I/z
I = Moment of inertia Cross Section : Units in^{4} (m^{4})
z = Distance neutral axis to extreme fiber: Units in (m)
General Stress at any Given Point
Adjacent end stress:
Open:
Adjacent End Stress Beam Calculator
Between indicated supports
Open: Between Indicated Supports Beam Calculator
Stress at Critical Locations/Points
Stress at each support:
Open: Stress at Each Support Beam Calculator
Stress at Center of Beam.
Open: Stress at Center of Beam Calculator
Stress at support next to
end of length d:
If l is greater than 2c, the
stress is zero at points
On both sides of the center
If crosssection is constant
and if l = 2.828c, the stresses
at supports and center are
equal and opposite, and are:
Deflection at any Point
Between supports
Open: Deflection Between Supports Calculator
Between each support and adjacent end,
Open: Deflection Between each Support and Adjacent End Calculator
Deflection at Ends
Open: Deflection at Ends Calculator
Where:
E = 
Modulus of Elasticity 
psi 
(N/mm^{2}) 
I = 
Moment of Inertia 
in^{4} 
(mm^{4}) 
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) 
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) 
u = 
Some distance as indicated 
inches 
(mm) 
c = 
Distance as indicated 
inches 
(mm) 
L = 
Some distance as indicated 
inches 
(mm) 
= 
Some distance as indicated 
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 405 or,
 Machinery's Handbook, 23st Edition, Page 261 or,
 Machinery's Handbook, 27st Edition, Page 26
