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

**Beam Deflection and Stress Formula and Calculators**

Area Moment of Inertia Equations & 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 in^{4} (m^{4})

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**

**Critical Deflections**

Maximum Deflection (Center of Beam)

Open: Deflection Maximum CalculatorWhere:

E = | Modulus of Elasticity | psi | (N/mm |

I = | Moment of Inertia | in^{4} |
(mm^{4)} |

W = | Load | lbs | (N) |

s = | Stress at the cross-section being evaluated | Lbs/in^{2} |
(N/mm^{2}) |

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 | in^{3} |
(mm^{3)} |

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

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