Bending, Deflection and Stress Equations Calculator for
Fixed at Both Ends, Load at any location

Beam Deflection and Stress Formula and Calculators

Structural Beam Deflection, Stress, Bending Equations and calculator for a Beam Fixed at Both Ends, Load at any location. Moment and Loads at Supports

M = Wab2 / l2
W1=(Wb2 / l3))(l + 2a)

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

For segment length a, For segment length b Stress at Critical Locations/Points

Stress at end nearest to segment of length a, Stress at end nearest to segment of length b, Maximum stress is at end nearest to shorter segment.
Stress is zero at and Greatest negative stress, at load Deflection at any Point

For length a, For length b Critical Deflections If b length is the longer segment and a is the shorter one.

The maximum deflection is in the longer segment: and 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) = 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
• Machinery's Handbook, 23st Edition
• Machinery's Handbook, 27st Edition  © Copyright 2000 - 2019, by Engineers Edge, LLC www.engineersedge.com Membership Register | Login   Home Engineering Book Store Engineering Forum Excel App. Downloads Online Books & Manuals Engineering News Engineering Videos Engineering Calculators Engineering Toolbox GD&T Training Geometric Dimensioning Tolerancing DFM DFA Training Training Online Engineering Advertising Center Copyright Notice 