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 | 106 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 |