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E, G, K and μ represent the elastic modulus, shear modulus, bulk modulus and poisson’s ratio respectively of a linearly elastic, isotropic and homogeneous material. To express the stress-strain relations completely for this material, at least
- a)E, G and μ must be known
- b)E, K and μ must be known
- c)Any two of the four must be known
- d)All the four must be known
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
E, G, K and μ represent the elastic modulus, shear modulus, bulk modu...
E = 3k (1 − 2μ) E = 2G (1 + μ) There are two equations and four unknown, so to express the stress-strain relations completely, at least any two of the four must be known. Remaining two can be found out by the equations.
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Most Upvoted Answer
E, G, K and μ represent the elastic modulus, shear modulus, bulk modu...
The stress-strain relations for a linearly elastic, isotropic, and homogeneous material can be expressed in terms of the elastic modulus (E), shear modulus (G), bulk modulus (K), and Poisson's ratio (μ).
1. Elastic Modulus (E):
The elastic modulus, also known as Young's modulus, represents the stiffness of a material in the linear elastic range. It relates the stress (σ) to the strain (ε) in the axial direction. The stress-strain relation for axial loading is given by σ = Eε.
2. Shear Modulus (G):
The shear modulus represents the material's resistance to deformation when subjected to shear stress. It relates the shear stress (τ) to the shear strain (γ). The stress-strain relation for shear loading is given by τ = Gγ.
3. Bulk Modulus (K):
The bulk modulus represents the material's resistance to volume change under hydrostatic stress. It relates the hydrostatic stress (σ_h) to the volumetric strain (ε_v). The stress-strain relation for hydrostatic loading is given by σ_h = Kε_v.
4. Poisson's Ratio (μ):
Poisson's ratio describes the ratio of lateral strain (ε_l) to axial strain (ε) when the material is subjected to axial loading. It is a dimensionless quantity and is usually between -1 and 0.5. Poisson's ratio is related to the elastic modulus and shear modulus through the equation μ = (E - 2G) / (2G).
To express the stress-strain relations completely for the material, at least two of the four parameters (E, G, K, μ) must be known. This is because each stress-strain relation requires the knowledge of at least two material properties.
For example:
- If E and G are known, the stress-strain relations for both axial and shear loading can be determined.
- If E and K are known, the stress-strain relations for axial loading and hydrostatic loading can be determined.
- If E and μ are known, the stress-strain relations for axial loading and lateral strain can be determined.
Therefore, the correct answer is option C: Any two of the four parameters (E, G, K, μ) must be known to express the stress-strain relations completely for the material.
1. Elastic Modulus (E):
The elastic modulus, also known as Young's modulus, represents the stiffness of a material in the linear elastic range. It relates the stress (σ) to the strain (ε) in the axial direction. The stress-strain relation for axial loading is given by σ = Eε.
2. Shear Modulus (G):
The shear modulus represents the material's resistance to deformation when subjected to shear stress. It relates the shear stress (τ) to the shear strain (γ). The stress-strain relation for shear loading is given by τ = Gγ.
3. Bulk Modulus (K):
The bulk modulus represents the material's resistance to volume change under hydrostatic stress. It relates the hydrostatic stress (σ_h) to the volumetric strain (ε_v). The stress-strain relation for hydrostatic loading is given by σ_h = Kε_v.
4. Poisson's Ratio (μ):
Poisson's ratio describes the ratio of lateral strain (ε_l) to axial strain (ε) when the material is subjected to axial loading. It is a dimensionless quantity and is usually between -1 and 0.5. Poisson's ratio is related to the elastic modulus and shear modulus through the equation μ = (E - 2G) / (2G).
To express the stress-strain relations completely for the material, at least two of the four parameters (E, G, K, μ) must be known. This is because each stress-strain relation requires the knowledge of at least two material properties.
For example:
- If E and G are known, the stress-strain relations for both axial and shear loading can be determined.
- If E and K are known, the stress-strain relations for axial loading and hydrostatic loading can be determined.
- If E and μ are known, the stress-strain relations for axial loading and lateral strain can be determined.
Therefore, the correct answer is option C: Any two of the four parameters (E, G, K, μ) must be known to express the stress-strain relations completely for the material.
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E, G, K and μ represent the elastic modulus, shear modulus, bulk modulus and poisson’s ratio respectively of a linearly elastic, isotropic and homogeneous material. To express the stress-strain relations completely for this material, at leasta) E, G and μ must be knownb) E, K and μ must be knownc) Any two of the four must be knownd) All the four must be knownCorrect answer is option 'C'. Can you explain this answer?
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E, G, K and μ represent the elastic modulus, shear modulus, bulk modulus and poisson’s ratio respectively of a linearly elastic, isotropic and homogeneous material. To express the stress-strain relations completely for this material, at leasta) E, G and μ must be knownb) E, K and μ must be knownc) Any two of the four must be knownd) All the four must be knownCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about E, G, K and μ represent the elastic modulus, shear modulus, bulk modulus and poisson’s ratio respectively of a linearly elastic, isotropic and homogeneous material. To express the stress-strain relations completely for this material, at leasta) E, G and μ must be knownb) E, K and μ must be knownc) Any two of the four must be knownd) All the four must be knownCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for E, G, K and μ represent the elastic modulus, shear modulus, bulk modulus and poisson’s ratio respectively of a linearly elastic, isotropic and homogeneous material. To express the stress-strain relations completely for this material, at leasta) E, G and μ must be knownb) E, K and μ must be knownc) Any two of the four must be knownd) All the four must be knownCorrect answer is option 'C'. Can you explain this answer?.
E, G, K and μ represent the elastic modulus, shear modulus, bulk modulus and poisson’s ratio respectively of a linearly elastic, isotropic and homogeneous material. To express the stress-strain relations completely for this material, at leasta) E, G and μ must be knownb) E, K and μ must be knownc) Any two of the four must be knownd) All the four must be knownCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about E, G, K and μ represent the elastic modulus, shear modulus, bulk modulus and poisson’s ratio respectively of a linearly elastic, isotropic and homogeneous material. To express the stress-strain relations completely for this material, at leasta) E, G and μ must be knownb) E, K and μ must be knownc) Any two of the four must be knownd) All the four must be knownCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for E, G, K and μ represent the elastic modulus, shear modulus, bulk modulus and poisson’s ratio respectively of a linearly elastic, isotropic and homogeneous material. To express the stress-strain relations completely for this material, at leasta) E, G and μ must be knownb) E, K and μ must be knownc) Any two of the four must be knownd) All the four must be knownCorrect answer is option 'C'. Can you explain this answer?.
Solutions for E, G, K and μ represent the elastic modulus, shear modulus, bulk modulus and poisson’s ratio respectively of a linearly elastic, isotropic and homogeneous material. To express the stress-strain relations completely for this material, at leasta) E, G and μ must be knownb) E, K and μ must be knownc) Any two of the four must be knownd) All the four must be knownCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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