### Bending, Deflection and Stress Equations Calculator for Fixed at Both Ends, Load at any location Beam

**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 any location.

Moment and Loads at Supports

M = Wab^{2} / l^{2}

W_{1}=(Wb^{2} / l^{3)})(l + 2a)

Open: Moment and Loads at Supports Calculator

**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

For segment length a,

For segment length b

Open:Stress for Segment a and b Calculator

**Stress at Critical Locations/Points **

Stress at end nearest to segment of length a,

Stress at end nearest to segment of length b,

Open:Stress at end nearest a or b Calculator

Maximum stress is at end
nearest to shorter segment.

Stress is zero at

and

Greatest negative stress, at load

Open:Greatest negative stress at load Calculator

**Deflection at any Point**

For length a,

For length b

Open: Deflection at any point Length a or b Calculator

**Critical Deflections**

Deflection at load

Open: Deflection at Load Calculator

If b length is the longer
segment and a is the shorter one.

The maximum deflection is in
the longer segment:

and

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 = | 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
- Machinery's Handbook, 23st Edition
- Machinery's Handbook, 27st Edition