# Shaft Generator Calculation Formulas

Engineers Handbook:

These formulas are used to solve either a shaft (with one or more sections) or a beam (with one constant section) with multiple supports and loads.

The shaft/beam axis is aligned with the Z axis. If the impact of the material density is included in the calculation, the gravity vector is aligned with the Y axis.

*Shear forces:*

*Bending moments:*

*Deflection angle:*

where:

E | modulus of elasticity in tension | |

J | moment of inertia | |

G | modulus of rigidity | |

b | shear displacement ratio |

*Deflection:*

*Bending stress:*

*Shear stress:*

*Torsion stress:*

*Tension stress:*

*Reduced stress:*

where:

s_{B} |
bending stress | |

s_{T} |
tension stress | |

t | torsion stress | |

t_{S} |
shear stress | |

a | a = 3 for HMH | |

a = 4 for Tresca-Guest |

*Sample Calculation*

Modulus of elasticity E = 210 000 MPa

Modulus of rigidity G = 81 000 MPa

Shear displacement ratio b = 1.118

Mode of reduced stress: HMH

Do not include the material density.

*Support Forces:*

*Maximal shear stress:*

*Maximal torsion stress:*

*Maximal moment:*

*Maximal bending stress:*

*Maximal reduced stress:*

*Angle of twist:*

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