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 One End, Supported at the Other, Load at any Point.
Lengths m & n
(Used in many equations)
m = (l + a)(l + b) +al
n = al(l + b) Open: Lengths m and n Calculator
Loads and Moment at Reaction points as Defined
Open: Loads at Reaction points as Defined Beam Calculator
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
Between point of fixture and load
Between support and load
Open: Stress Between point of fixture and load and Support Calculator
Stress at Critical Locations/Points
Open: Greatest Positive Stress at point of fixture and Negative Stress at Load Calculator
Deflection at any Point
Between point of fixture and load
Between support and load
Open: Deflection at point of fixture and load and Between Support at Load Calculator
Critical Deflections
Open: Deflection 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) 
m, n = 
Some calculated 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
