Beam Deflection and Stress Formula and Calculators Area Moment of Inertia Equations & Calculators
Structural Beam Deflection, Stress, Bending Equations and calculator for a Beam Fixed at Both Ends with Uniform Loading.
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
Open: Stress at Given Point x Calculator
Stress at Critical Locations/Points
Maximum Stress (at fixed ends)
The greatest negative stress (at center)
Open: Maximum Stress and Negative Stress Calculator
Stress is zero at:
x = 0.7887l
and
x = 0.2113l
Deflection at any Point
Open: Deflection at any Point Calculator
Critical Deflections
Maximum Deflection (Center of Beam)
Open: Deflection Maximum Calculator
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) 
u = 
Some distance as indicated 
inches 
(mm) 
a, b = 
Some distance as indicated 
inches 
(mm) 
L = 
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
 Machinery's Handbook, 23st Edition
 Machinery's Handbook, 27st Edition
