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

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, Load at Center.

Moment and Loads at Supports

M = Wl/8

Open: Moment and Loads at Supports Calculator

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

Between each end and load

Open: Stress Between Each Support and Load Calculator

Stress at Critical Locations/Points

Stress at ends

Stress at Load

Open: Stress at each end and at Load Calculator

Note: These are the maximum stresses and are equal and opposite.

Stress is zero at x = (1⁄/4)l

Deflection at any Point

Maximum deflection, at load

Open: Stress at each End and at Load Calculator


E = Modulus of Elasticity psi


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.


  • 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

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