MODULUS OF RIGIDITY


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

Definitions:

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.

Supplements:

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

Reference:

  • 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.