Bending, Deflection and Stress Equations Calculator for Fixed at One End, Supported at the Other, Load at any Point
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.
Beam Lengths m & n
(Used in many equations)
m = (l + a)(l + b) +al
n = al(l + b)
Open: Lengths m and n Calculator
Beam Loads and Moment at Reaction points as Defined
Open: Loads at Reaction points as Defined Beam Calculator
Z = I/z
I = Moment of inertia Cross Section : Units in4 (m4)
z = Distance neutral axis to extreme fiber: Units in (m)
General Beam Stress at any Given Point
Beam Stress Between point of fixture and load
Beam Stress Between support and load
Open: Stress Between point of fixture and load and Support Calculator
Beam Stress at Critical Locations/Points
Open: Greatest Positive Stress at point of fixture and Negative Stress at Load Calculator
Beam Deflection at any Point
Beam Deflection Between point of fixture and load
Beam Deflection Between support and load
Open: Deflection at point of fixture and load and Between Support at Load Calculator
Beam 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 = | Beam Stress at the cross-section being evaluated | Lbs/in2 | (N/mm2) |
| y = | Beam 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) |
| l = | 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 "l" (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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