Bending, Deflection and Stress Equations Calculator for Both Ends Overhanging Supports, Load at any Point Between
Beam Deflection and Stress Formula and Calculators
Area Moment of Inertia Equations & Calculators
Structural Beam Deflection, Stress, Bending Equations and calculator for a Beam with Both Ends Overhanging Supports, Load at any Point Between.
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
Stress at Load:
If cross-section is constant, this is the maximum stress.
Open: Stress at Load Beam Calculator
General Stress at any Given Point
Between supports:
For area length a,
Open: Stress Between Supports Length a Beam Calculator
For area of length b,
Open: Stress Between Supports Length b Beam Calculator
Beyond supports s = 0
Deflection at Critical Locations/Points
Deflection at any Point
Between supports for overhanging end of length c
Open: Deflection overhanging end of length c Beam Calculator
for overhanging end of length d
Open: Deflection overhanging end of length d Beam 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) |
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