Bending, Deflection and Stress Equations Calculator for
Beam Supported on Both Ends Loaded at any Location

Structural Beam Deflection, Stress, Bending Equations and calculator for Beam Supported on Both Ends Loaded at any Location.

If the cross section is constant this is the maximum stress.

Deflection for location between load and "a" point

Deflection for location between load and "b" point

Let be the length of the shorter segment and b of the longer one.
The maximum deflection

 is in the longer segment, at

Where:

 E = Modulus of Elasticity lbs/in2 (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) a = Some distance as indicated inches (mm) b = 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 404 or,
• Machinery's Handbook, 23st Edition, Page 260 or,
• Machinery's Handbook, 27st Edition, Page 261