Bending, Deflection Calculator and Stress Equations for Fixed at Both Ends with Uniform Loading
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 Both Ends with Uniform Loading.
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
Stress at Critical Locations/Points
Maximum Stress (at fixed ends)
The greatest negative stress (at center)
Stress is zero at: x = 0.7887l and x = 0.2113l
Deflection at any Point
Critical Deflections
Maximum Deflection (Center of Beam)
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 = | 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
- Machinery's Handbook, 23st Edition
- Machinery's Handbook, 27st Edition