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

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 Center. 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)

Loads and Moment at Reaction points as Defined

General Stress at any Given Point

Stress between point of fixture and load  Stress at Critical Locations/Points

Maximum stress at point of fixture Stress is zero at x = (3⁄/1l)l
Greatest negative stress at center Deflection at any Point

Between point of fixture and load  Critical Deflections

Maximum deflection

v = 0.4474l

or  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) 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