### Beam Deflection Deflection and Stress Calculator Equations for Fixed at Both Ends, Load at Center

**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, Load at Center.

Beam Moment and Loads at Supports

M = Wl/8

W_{1}=W/2

Open: Moment and Loads at Supports Calculator

**Beam 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 Beam Stress at any Given Point

Beam Stress Between each end and load

Open: Stress Between Each Support and Load Calculator

**Beam Stress at Critical Locations/Points **

Beam Stress at ends

Beam Stress at Load

Open: Stress at each end and at Load Calculator

Note: These are the maximum Beam stresses and are equal and opposite.

Stress is zero at x = (1⁄/4)l

**Beam Deflection at any Point**

Maximum Beam deflection, at load

Open: Stress at each End and at Load Calculator

Where:

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

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

W = | Load | lbs | (N) |

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

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 | 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, Page 405 or,
- Machinery's Handbook, 23st Edition, Page 261 or,
- Machinery's Handbook, 27st Edition, Page 26

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