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.
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
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) |
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