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, Load at Center.
Moment and Loads at Supports
M = Wl/8
W_{1}=W/2
Open: Moment and Loads at Supports Calculator
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
Between each end and load
Open: Stress Between Each Support and Load Calculator
Stress at Critical Locations/Points
Stress at ends
Stress at Load
Open: Stress at each end and at Load Calculator
Note: These are the maximum
stresses and are equal and
opposite.
Stress is zero at x = (1⁄/4)l
Deflection at any Point
Maximum deflection, at load
Open: Stress at each End and at Load 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, c & d = 
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, Page 405 or,
 Machinery's Handbook, 23st Edition, Page 261 or,
 Machinery's Handbook, 27st Edition, Page 26
