Modulus of Rigidity vs. Young's Modulus

Attribute	Modulus of Rigidity	Young's Modulus
Definition	Measure of the stiffness of a material when sheared	Measure of the stiffness of a material when stretched or compressed
Symbol	G	E
Units	Pascal (Pa)	Pascal (Pa)
Formula	G = Shear stress / Shear strain	E = Tensile stress / Tensile strain
Typical values	10^9 - 10^12 Pa	10^9 - 10^12 Pa

Definition

Modulus of Rigidity, also known as Shear Modulus, is a measure of a material's stiffness when subjected to shear stress. It describes the material's ability to deform under shear stress. Young's Modulus, on the other hand, is a measure of a material's stiffness when subjected to tensile or compressive stress. It describes the material's ability to deform under tension or compression.

Formula

The formula for calculating Modulus of Rigidity is G = τ / γ, where G is the Modulus of Rigidity, τ is the shear stress, and γ is the shear strain. Young's Modulus is calculated using the formula E = σ / ε, where E is Young's Modulus, σ is the tensile or compressive stress, and ε is the tensile or compressive strain.

Units

Modulus of Rigidity is typically measured in pascals (Pa) or gigapascals (GPa). Young's Modulus is also measured in pascals (Pa) or gigapascals (GPa). Both Modulus of Rigidity and Young's Modulus are scalar quantities, meaning they have magnitude but no direction.

Material Behavior

Modulus of Rigidity is important for materials that are subjected to shear stress, such as in torsion or bending applications. It helps determine how much a material will deform when subjected to shear forces. Young's Modulus, on the other hand, is crucial for materials that are subjected to tensile or compressive stress, such as in stretching or squeezing applications. It helps determine how much a material will deform under tension or compression.

Relationship

Modulus of Rigidity and Young's Modulus are related to each other through the Poisson's ratio of a material. Poisson's ratio is a measure of the ratio of transverse strain to axial strain when a material is subjected to tensile or compressive stress. The relationship between Modulus of Rigidity, Young's Modulus, and Poisson's ratio is given by the equation G = E / (2(1 + v)), where G is the Modulus of Rigidity, E is Young's Modulus, and v is the Poisson's ratio.

Applications

Modulus of Rigidity is commonly used in engineering applications where materials are subjected to shear stress, such as in the design of beams, shafts, and springs. Young's Modulus is widely used in structural engineering, aerospace engineering, and material science for predicting the behavior of materials under tension or compression. Both Modulus of Rigidity and Young's Modulus play a crucial role in determining the mechanical properties of materials and designing structures that can withstand various types of stress.