Modulus of rigidity is the ratio of shear stress to the corresponding shear strain within the proportional limit of a material. Modulus of rigidity is also known as shear modulus and rigidity modulus values of materials are determined by torsional tests. Modulus of rigidity formulas are G = τ/γ and G = E/(2(1+v)). Here τ is shear stress, γ is shear strain in radians, G is modulus of rigidity, E is elastic modulus and v is Poisson’s ratio.

Shear modulus of steel, aluminum, iron, copper, titanium, brass, bronze, etc. are given in the following table in GPA and psi.

Modulus of Rigidity (Shear Modulus) of Materials | ||

Material | GPa |
10^{6} psi |

Aluminum | 26 | 3.8 |

Aluminum alloys, various | 25.5 - 26.9 | 3.7 - 3.9 |

Aluminum, 6061-T6 | 26 | 3.8 |

Aluminum, 2024-T4 | 28 | 4 |

Aluminum, 7075-T6 | 26.9 | 3.9 |

Beryllium copper (C17200) | 50 | 7.2 |

Brass, 70-30 (C26000) | 41 | 6 |

Yellow Brass (C27000) | 39 | 5.6 |

Red Brass (C23000) | 44 | 6.4 |

Aluminum Bronze (C95500) | 42 | 6.1 |

Manganese Bronze (C86350) | 37 | 5.4 |

Oxygen Free Copper (C10100) | 44 | 6.4 |

Glass Ceramic (Mica) | 26 | 3.7 |

Inconel X750 | 79.3 | 11.5 |

Invar | 56 | 8.1 |

Iron | 82 | 11.9 |

Iron, cast | 36-57 | 5.2-8.2 |

Iron, ductile | 63-66 | 9.1-9.6 |

Iron, gray cast (Class 20) | 27-39 | 3.9-5.7 |

Iron, malleable | 64 | 9.3 |

Lead | 5.6 | 0.8 |

Magnesium | 17 | 2.4 |

Magnesium alloy | 17 | 2.5 |

Molybdenum | 120 | 17.4 |

Monel 400 | 65.3 | 9.5 9.5 |

Nickel silver 55-18 (C77000) | 47 | 6.8 |

Nickel | 76 | 11 |

Phosphor bronze (C51000) | 41 | 5.9 |

Steel, A36 | 79.3 | 11.5 |

304 Stainless steel | 77 | 11.2 |

Steel, cast | 78 | 11.3 |

Steel, cold-rolled | 79 | 11.5 |

Steel, all others
including
high-carbon, heat-treated |
76-82 | 11.0-11.9 |

Titanium Grade 2 (99.0 Ti) | 45 | 6.5 |

Titanium Grade 5 (Ti-6Al-4V) | 44 | 6.4 |

Tungsten | 160 | 23.2 |

Zinc | 43 | 6.2 |

**Modulus of elasticity (E):** The measure of rigidity or stiffness of a material; the ratio of stress to the corresponding strain below the proportional
limit. Also known as Young's modulus. The modulus of elasticity is the slope of the stress-strain
curve in the range of linear proportionality of stress to strain In the stress-strain curve.

Link | Usage |

Shear Modulus Calculator | Calculates modulus of rigidity of a material with modulus of elasticity and Poisson's ratio values. |

- Metals Handbook. Properties and Selection: Irons, Steels, and High- Performance Alloys. ASM International, 1990.
- Oberg, E. , Jones ,F.D. , Horton H.L. , Ryffel H.H., (2016) . Machinery's Handbook . 30th edition. Industrial Press Inc.

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