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A rod of length L and diameter D is subjected to a tensile load P. Which of the following is sufficientto calculate the resulting change in diameter ?
- a)Young's modulus
- b)Shear modulus
- c)Poisson's ratio
- d)Both Young's modulus and shear modulus
Correct answer is option 'D'. Can you explain this answer?
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A rod of length L and diameter D is subjected to a tensile load P. Whi...
For a homogeneous and isotropic material minimum number of ELASTIC CONSTANT required to calculate all other parameters is TWO. It may be (E,G) or (E,K) or (K,G) or (E, Poisson's ratio) etc.
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A rod of length L and diameter D is subjected to a tensile load P. Whi...
Understanding the Problem
When a rod is subjected to a tensile load, it experiences elongation along its length. However, due to the nature of materials, this elongation also causes a change in the diameter of the rod. To analyze this behavior, we need certain material properties.
Key Material Properties
- Young's Modulus: This measures a material's ability to withstand changes in length when under lengthwise tension or compression. It helps in calculating the axial strain.
- Shear Modulus: This describes how a material deforms under shear stress. While it primarily relates to shear deformation, it provides insight into the material's overall response to various loads.
- Poisson's Ratio: This is the ratio of the transverse strain to the axial strain. It is crucial for understanding how the diameter of the rod changes as it is stretched.
Combination of Properties
To accurately determine the change in diameter under tensile loading:
- Young's Modulus is essential for calculating the initial elongation (strain) of the rod due to the tensile load.
- Poisson's Ratio is necessary to determine how much the diameter decreases as the rod elongates.
- While Shear Modulus is not directly needed for axial tension analysis, it can help in understanding material behavior under various loading conditions.
Conclusion
Thus, the correct answer is option 'D' because both Young's modulus and Poisson's ratio (which is often derived in conjunction with shear modulus) are essential for calculating the resulting change in diameter accurately when a tensile load is applied.
When a rod is subjected to a tensile load, it experiences elongation along its length. However, due to the nature of materials, this elongation also causes a change in the diameter of the rod. To analyze this behavior, we need certain material properties.
Key Material Properties
- Young's Modulus: This measures a material's ability to withstand changes in length when under lengthwise tension or compression. It helps in calculating the axial strain.
- Shear Modulus: This describes how a material deforms under shear stress. While it primarily relates to shear deformation, it provides insight into the material's overall response to various loads.
- Poisson's Ratio: This is the ratio of the transverse strain to the axial strain. It is crucial for understanding how the diameter of the rod changes as it is stretched.
Combination of Properties
To accurately determine the change in diameter under tensile loading:
- Young's Modulus is essential for calculating the initial elongation (strain) of the rod due to the tensile load.
- Poisson's Ratio is necessary to determine how much the diameter decreases as the rod elongates.
- While Shear Modulus is not directly needed for axial tension analysis, it can help in understanding material behavior under various loading conditions.
Conclusion
Thus, the correct answer is option 'D' because both Young's modulus and Poisson's ratio (which is often derived in conjunction with shear modulus) are essential for calculating the resulting change in diameter accurately when a tensile load is applied.
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A rod of length L and diameter D is subjected to a tensile load P. Which of the following is sufficientto calculate the resulting change in diameter ?a)Youngs modulusb)Shear modulusc)Poissons ratiod)Both Youngs modulus and shear modulusCorrect answer is option 'D'. Can you explain this answer?
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