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 
10^{6} psi 
Aluminum 
26 
3.8 
Aluminum alloys, various 
25.5  26.9 
3.7  3.9 
Aluminum, 6061T6 
26 
3.8 
Aluminum, 2024T4 
28 
4 
Aluminum, 7075T6 
26.9 
3.9 
Beryllium copper (C17200) 
50 
7.2 
Brass, 7030 (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 
3657 
5.28.2 
Iron, ductile 
6366 
9.19.6 
Iron, gray cast (Class 20) 
2739 
3.95.7 
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 5518 (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, coldrolled 
79 
11.5 
Steel, all others
including
highcarbon, heattreated 
7682 
11.011.9 
Titanium
Grade 2 (99.0 Ti) 
45 
6.5 
Titanium Grade 5 (Ti6Al4V) 
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 stressstrain
curve in the range of linear proportionality of stress to strain In the stressstrain 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.
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