Bending, Deflection and Stress Equations Calculator for
Both Ends Overhanging Supports, Load at any Point Between

Beam Deflection and Stress Formula and Calculators

Area Moment of Inertia Equations & Calculators

Structural Beam Deflection, Stress, Bending Equations and calculator for a Beam with Both Ends Overhanging Supports, Load at any Point Between.


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

Stress at Load:

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

Open: Stress at Load Beam Calculator


General Stress at any Given Point

Between supports:

For area length a,

Open: Stress Between Supports Length a Beam Calculator


For area of length b,

Open: Stress Between Supports Length b Beam Calculator

Beyond supports s = 0


Deflection at Critical Locations/Points

Deflection at any Point

Between supports for overhanging end of length c

Open: Deflection overhanging end of length c Beam Calculator


for overhanging end of length d

Open: Deflection overhanging end of length d Beam Calculator


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, 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.

References:

  • 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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