# MODULUS OF RIGIDITY (SHEAR MODULUS)

Modulus of rigidity or shear modulus is the rate of change of unit shear stress with respect to unit shear strain for the condition of pure shear within the proportional limit. Modulus of rigidity formula is G = E/(2(1+v)), and modulus of rigidity is G, elastic modulus is E and Poisson's ratio is v in the formula. Modulus of rigidity value of a material is determined by a torsion test. Typical values of modulus of rigidity: Aluminum 6061-T6: 24 GPa, Structural Steel: 79.3 GPa.

Modulus of rigidity calculator has been developed to calculate modulus of rigidity of a material with modulus of elasticity and Poisson's ratio values. This calculator is valid for a linear, homogeneous, isotropic material. The formulas used for calculation are given in the "List of Equations" section.

### Calculator:

 PARAMETERS Parameter Value Unit Elastic modulus (E) GPa psi*10^6 Poisson's ratio (v) --- RESULTS Parameter Value Unit Modulus of rigidity (G) --- ---

Note: Use dot "." as decimal separator.

### Definitions:

Homogeneous Material: Material which has got same material properties at all of its points.

Hooke's Law: The relation in which the stress σ is directly proportional to the strain ε. (σ=E ε). Hooke’s law is also valid for shear stress and strain in the linear elastic range (τ=Gγ)

Isotropic Material: Material in which strength, elastic modulus and thermal conductivity properties are independent from the choice of coordinate system.

Modulus of elasticity (Young’s modulus): The rate of change of unit tensile or compressive stress with respect to unit tensile or compressive strain for the condition of uniaxial stress within the proportional limit. Typical values: Aluminum: 69 GPa, Steel: 200GPa.

Modulus of rigidity (modulus of elasticity in shear): The rate of change of unit shear stress with respect to unit shear strain for the condition of pure shear within the proportional limit. Typical values Aluminum 6061-T6: 24 GPa, Structural Steel: 79.3 GPa.

Poisson’s ratio: The ratio of lateral unit strain to longitudinal unit strain under the condition of uniform and uniaxial longitudinal stress within the proportional limit.

### List of Equations:

 Parameter Formula Modulus of rigidity (G) E/(2(1+v))

### Supplements:

 Link Usage Modulus of rigidity of materials Shows modulus of rigidity values of common materials.

### Reference:

• Beer.F.P. , Johnston.E.R. (1992). Mechanics of Materials , 2nd edition. McGraw-Hill