|
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) |
 = |
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
|
