Bending, Deflection and Stress Equations Calculator for
Fixed at Both Ends with Uniform Loading

Beam Deflection and Stress Formula and Calculators

Structural Beam Deflection, Stress, Bending Equations and calculator for a Beam Fixed at Both Ends with Uniform Loading.

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General Stress at any Given Point

Stress at Critical Locations/Points

Maximum Stress (at fixed ends)

Stress is zero at:
x = 0.7887l
x = 0.2113l

The greatest negative stress (at center)

Deflection at any Point

Critical Deflections

Maximum Deflection (Center of Beam)


E = Modulus of Elasticity psi


I = Moment of Inertia in4 (m4)
W =   Load lbs (N)
s =  Stress at the cross-section being evaluated Lbs/in2 (N/m2)
y = Deflection inches (m)
x = Some distance as indicated inches (m)
u = Some distance as indicated inches (m)
a, b = Some distance as indicated inches (m)
L = Some distance as indicated inches (m)
= Some distance as indicated inches (m)
Z = section modulus of the cross-section of the beam    
Z = I distance from neutral axis to extreme fiber (edge)    
  • Please note letter "" (lower case "L") is different than "I" (Moment of Inertia).
  • Deflections apply only to constant cross sections along entire length.


  • Any Machinery's Handbook published since 1931 or,
  • Machinery's Handbook, 21st Edition
  • Machinery's Handbook, 23st Edition
  • Machinery's Handbook, 27st Edition

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