Practice Questions

Poisson's ratio is a dimensionless quantity, while shear stress and torque have units of N / (m ^ 2) and N.m respectively

Elastic modulus in materials depends on the inter-atomic bonding force, which results in resistance to elastic deformation. This force arises from stretching of interatomic bonds and changes in separation between two adjacent atoms. The slope of the stress-strain curve determines the modulus of elasticity, which is directly proportional to the strength of the bonds. Therefore, high elastic modulus in materials arises from high strength of bonds.

Poisson's ratio is the ratio of lateral strain to longitudinal strain. It is represented by the equation v =- epsilon |ateral / Elongitudinal.

Young's modulus is the ratio of normal stress to normal strain and is denoted by E. Shear modulus, also known as the modulus of rigidity, is the ratio of shear stress to shear strain and is denoted by G. Bulk modulus is the ratio of normal stress to volumetric strain and is denoted by K.

E = 2G(1 + v) and E = 3K(1 - v) where v is Poisson's ratio.

Young's modulus is a material's property and is denoted by Y. It does not depend on the length of the radius of the wire and is constant for the material. Therefore, if the radius of the wire is changed by a load to its half, the Young's modulus will be unaffected.

Bulk modulus is a ratio of direct stress to volumetric strain in a body. It is always positive and depends on applied direct stress and volumetric stress. It is also a function of Poisson's ratio. The bulk modulus of incompressible material is infinite. Elastic constants are used to determine stress and strain relationships, and for homogeneous and isotropic material, there are 4 elastic constants including young's modulus, bulk modulus, Poisson's ratio, and modulus of rigidity. Poisson's ratio is the ratio of lateral strain to longitudinal strain.

not an independent constant of material and it is always positive

an independent constant of material and it can be positive or negative

Poisson's ratio is the ratio of transverse strain to longitudinal strain. For perfectly isotropic elastic material, it is 0.25. For steels, it is 0.3. Among the given options, none have a Poisson's ratio greater than unity.

The value of Poisson's ratio for a rigid material is not defined.

A material having identical elastic properties in all directions is called an isotropic material. Examples of isotropic materials include metals and glasses. Orthotropic materials have three different properties in three mutually perpendicular directions, while anisotropic materials have different properties in each direction.

Poisson's ratio is the ratio of transverse contraction strain to longitudinal extension strain in the direction of the stretching force. It depends on the type of material, with most materials having values ranging between 0.0 and 0.5. Rubber has a Poisson ratio of nearly 0.5, while cork's Poisson ratio is close to 0. A perfectly incompressible material deformed elastically at small strains would have a Poisson's ratio of exactly 0.5. Most steels and rigid polymers exhibit values of about 0.3 before yield, increasing to 0.5 for post-yield deformation occurring deformation occurring largely at constant volume.

Poisson's ratio is the ratio of transverse strain to longitudinal strain. Most materials have values between 0.0 and 0.5. A perfectly incompressible material has a Poisson's ratio of 0.5. Steels and rigid polymers exhibit values of about 0.3, increasing to 0.5 for post-yield deformation. Rubber has a Poisson ratio of nearly 0.5, while cork's Poisson ratio is close to 0, showing little lateral expansion when compressed. The given range of Poisson's ratio for engineering materials is 0.25 to 0.35.

Poisson's ratio for aluminum is 0.31-0.34. It is the ratio of transverse strain to longitudinal strain and ranges from 0.0 to 0.5 for most materials. A value of 0.5 indicates a perfectly incompressible material.

The modulus of rigidity has the same unit as stress, pressure, and modulus of elasticity. Elastic modulus (E) is the ratio of stress and strain, while rigidity modulus (G) is the ratio of shear stress and shear strain. Stress is the force applied to a certain cross-sectional area, and pressure is the force applied perpendicular to the surface of an object per unit area. The unit for all of these is N/m² or Pascal.

Stress, pressure and modulus of elasticity

Poisson's ratio is the ratio of transverse strain to longitudinal strain. Stainless steel: 0.30-0.31, Steel: 0.27-0.30, Cast iron:0.21-0.26, Cork: 0.0, Rubber: 0.5.

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