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

Beam Deflection and Stress Formula and Calculators

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

Beam 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 Beam Stress

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

General Beam Stress at any Given Point

Between supports:

Beam Stress For area length a,

Beam Stress For area of length b,

Beyond supports s = 0

Beam Deflection at Critical Locations/Points

Beam Deflection at any Point

Beam Deflection Between supports for overhanging end of length c

Beam deflection for overhanging end of length d

Where:

 E = Modulus of Elasticity psi (N/mm2) I = Moment of Inertia in4 (mm4) W = Load lbs (N) s = Beam Stress at the cross-section being evaluated Lbs/in2 (N/mm2) y = Beam 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) l = 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 "l" (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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