### Beam Deflection Equations and Calculator for a Beam supported One End, Pin Opposite End and One Tapered Distributed Load

**Beam Deflection and Stress Formula and Calculators**

Area Moment of Inertia Equations & Calculators

Beam Deflection, Shear and Stress Equations and Calculator for a Beam supported One End, Pin Opposite End and One Tapered Distributed Load.

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Beam Reaction and Shear Equation

Beam Bending Moments Equation

**Stress Maximum **

**Beam Deflection and End Slope Equation **

Where:

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

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

W = | Beam Load, Total | lbf | (N) |

w = | Unit Load | lbs/in | (N/mm) |

y = | Beam Deflection | inches | (mm) |

a, b, c, d, x, L = | Some distance as indicated | inches | (mm) |

e = | Centroid | inches | (mm) |

n = | Distance neutral axis | inches | (mm) |

V_{max} = |
Shear Load | lbf | (N) |

M_{max} = |
Moment | lbs-in | (N-mm) |

θ_{max} = |
Beam Slope Angle | degree | (radian) |

σ_{max} = |
Beam Stress max. | psi | (N/mm^{2}) |

- Beam Deflections apply only to constant cross sections along entire length.

References:

- Boeing Design Manual, Rev G. 1994 BDM

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