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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 in4 (m4)
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/mm2) |
| I = |
Moment of Inertia |
in4 |
(mm4) |
| W = |
Load |
lbs |
(N) |
| s = |
Stress at the cross-section being evaluated |
Lbs/in2 |
(N/mm2) |
| 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 cross-section of the beam = I/z |
in3 |
(mm3) |
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
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