### Bending, Deflection and Stress Equations Calculator for Fixed at One End, Supported at the Other, Load at any Point

Beam Deflection and Stress Formula and Calculators

Structural Beam Deflection, Stress, Bending Equations and calculator for a Beam Fixed at One End, Supported at the Other, Load at any Point.

Beam Lengths m & n
(Used in many equations)

m = (l + a)(l + b) +al
n = al(l + b)

Beam Loads and Moment at Reaction points as Defined

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 at any Given Point

Beam Stress Between point of fixture and load

Beam Stress Between support and load

Beam Stress at Critical Locations/Points

Beam Deflection at any Point

Beam Deflection Between point of fixture and load

Beam Deflection Between support and load

Beam Critical Deflections

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) m, n = Some calculated 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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