### Beam Deflection and Beam 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. 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)

Beam Loads and Moment at Reaction points as Defined

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

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

Between point of fixture and load Beam Deflection Between support and load Critical Beam Deflections

Maximum Beam deflection

v = 0.4474l

or  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

Related