### Beam Deflection and Stress Equations Calculator for Beam Supported on Both Ends Loaded at any Location

**Beam Deflection and Stress Formula and Calculators**

Area Moment of Inertia Equations & Calculators

Structural Beam Deflection, Stress, Bending Equations and calculator for Beam Supported on Both Ends Loaded at any Location.

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**Beam Deflection, Stress Beam Supported on Both Ends Calculator**

Beam Stress between load and "a" load point

Beam Stress between load and "b" load point

Beam Stress at load application

If the cross section is constant this is the maximum stress.

Beam Deflection for location between load and "a" point

Beam Deflection for location between load and "b" point

Maximum Beam deflection at load

Let "a" be the length of the shorter segment and "b" of the longer one.

The maximum deflection

is in the longer segment, at |

Where:

E = | Modulus of Elasticity | lbs/in^{2} |
(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 = | Beam Deflection | inches | (mm) |

x = | Some distance as indicated | inches | (mm) |

a = | Some distance as indicated | inches | (mm) |

b = | 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 404 or,
- Machinery's Handbook, 23st Edition, Page 260 or,
- Machinery's Handbook, 27st Edition, Page 261

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