### Bending, Deflection and Stress Equations Calculator for Fixed at One End, Supported at the Other, 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 One End, Supported at the Other, Load at Center.

**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)

Loads and Moment at Reaction points as Defined

Open: Loads at Reaction points as Defined Beam Calculator

General Stress at any Given Point

Stress between point of fixture and load

Open: Stress Between Point of Fixture and Load Beam Calculator

Between support and load

Open: Stress Between Support and Load Beam Calculator

**Stress at Critical Locations/Points **

Maximum stress at point of fixture

Open: Stress Maximum at Point of Fixture Load Beam Calculator

Stress is zero at x = (3⁄/1l)*l
*
Greatest negative stress at
center

Open: Greatest negative stress at center Beam Calculator

**Deflection at any Point**

Between point of fixture and load

Open: Deflection between point of fixture and load Calculator

Between support and load

Open: Deflection between support and load Calculator

**Critical Deflections**

Maximum deflection

v = 0.4474*l *

or

Open: Maximum Deflection Calculator

Deflection at load

Open: Deflection at load Calculator

Where:

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, 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