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

**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 any Point.

Beam Lengths m & n

(Used in many equations)

m = (l + a)(l + b) +al

n = al(l + b)

Open: Lengths m and n Calculator

Beam Loads and Moment at Reaction points as Defined

Open: Loads at Reaction points as Defined Beam 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 point of fixture and load

Beam Stress Between support and load

Open: Stress Between point of fixture and load and Support Calculator

**Beam Stress at Critical Locations/Points **

Open: Greatest Positive Stress at point of fixture and Negative Stress at Load Calculator

**Beam Deflection at any Point**

Beam Deflection Between point of fixture and load

Beam Deflection Between support and load

Open: Deflection at point of fixture and load and Between Support at Load Calculator

**Beam Critical Deflections**

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 = | 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) |

m, n = | Some calculated 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

Related

- Combined Loading on Circular Beam or Shaft in Direct Tension and Deflection Equation and Calculator
- Combined Loading on Rectangular Beam or Shaft in Direct Compression and Deflection Equation and Calculator
- Combined Loading on Rectangular Beam or Shaft in Direct Tension and Deflection Equation and Calculator
- Combined Loading on Circular Shaft in Direct Compression and Torsion Equation and Calculator
- Combined Loading on Circular Shaft in Direct Tension and Torsion Equation and Calculator
- Maximum Shear Stress Theory Fatigue of a Shaft or Axle Formula and Calculator
- Shaft Torsional Deflection and Rigidity Formulas and Calculator
- Static Loading Shaft or Axle Analysis Formula and Calculator - Most shafts are subject to combined bending and torsion, either of which may be steady or variable. Maximum Shear Stress and Von Mises Stress
- Combined Loading on Offset Link, Circular Cross Section, in Direct Tension Equation and Calculator
- Beam Deflection Equations / Calculator Cantilevered Beam with One Load Applied at End