### Bending, Deflection Calculator and Stress Equations for Fixed at Both Ends with Uniform Loading

Beam Deflection and Stress Formula and Calculators

Structural Beam Deflection, Stress, Bending Equations and calculator for a Beam Fixed at Both Ends with Uniform Loading.

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 at any Given Point

Open: Stress at Given Point x Calculator

Stress at Critical Locations/Points

Maximum Stress (at fixed ends)

The greatest negative stress (at center)

Open: Maximum Stress and Negative Stress Calculator

Stress is zero at: x = 0.7887l and x = 0.2113l

Deflection at any Point

Open: Deflection at any Point Calculator

Critical Deflections

Maximum Deflection (Center of Beam)

Open: Deflection Maximum 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 = 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
• Machinery's Handbook, 23st Edition
• Machinery's Handbook, 27st Edition