### Stress and Deflection Formula and Calculator Beam Both Ends Overhanging Supports Symmetrically, Uniform Load

**Beam Deflection and Stress Formula and Calculators**

Area Moment of Inertia Equations & Calculators

Structural Beam Deflection, Stress, Bending Equations and calculator for a Beam supported Both Ends Overhanging Supports Symmetrically, Uniform Load

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**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

Adjacent end stress:

Open: Adjacent End Stress Beam Calculator

Between indicated supports

Open: Between Indicated Supports Beam Calculator

**Stress at Critical Locations/Points **

Stress at each support:

Open: Stress at Each Support Beam Calculator

Stress at Center of Beam.

Open: Stress at Center of Beam Calculator

Stress at support next to end of length d:

If l is greater than 2c, the stress is zero at points

On both sides of the center

If cross-section is constant and if l = 2.828c, the stresses at supports and center are equal and opposite, and are:

**Deflection at any Point**

Between supports

Open: Deflection Between Supports Calculator

Between each support and adjacent end,

Open: Deflection Between each Support and Adjacent End Calculator

Deflection at Ends

Open: Deflection at Ends Calculator

Where:

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

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

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) |

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) |

c = | Distance as indicated | inches | (mm) |

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

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

- Please note letter "" (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