Civil Engineering (CE) Exam > Civil Engineering (CE) Questions > If Poissons ratio for a material is 0.3, the ...
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If Poisson's ratio for a material is 0.3, the ratio of shear modulus of elasticity to Young's modulus of elasticity will be,
- a)0.38
- b)2.6
- c)8.6
- d)0.12
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If Poissons ratio for a material is 0.3, the ratio of shear modulus of...
Explanation:
Given data:
Poisson's ratio (ν) = 0.3
Definition of Poisson's ratio:
Poisson's ratio is the ratio of lateral strain to longitudinal strain when a material is stretched or compressed.
Relation between Poisson's ratio, shear modulus (G), and Young's modulus (E):
For an isotropic material, the relation between Poisson's ratio, shear modulus, and Young's modulus is given by the following equation:
ν = E / (2G) - 1
Substitute the given Poisson's ratio into the equation:
0.3 = E / (2G) - 1
0.3 + 1 = E / (2G)
1.3 = E / (2G)
E / G = 1.3
Ratio of shear modulus to Young's modulus:
The ratio of shear modulus of elasticity (G) to Young's modulus of elasticity (E) is calculated as:
G / E = 1 / (E / G) = 1 / 1.3 = 0.769
Convert the ratio to percentage:
G / E = 0.769 = 76.9%
Therefore, the ratio of shear modulus of elasticity to Young's modulus of elasticity is 0.769 or 76.9%.
In the given options, option 'A' is the closest to the calculated value:
a) 0.38
Therefore, the correct answer is option 'A'.
Given data:
Poisson's ratio (ν) = 0.3
Definition of Poisson's ratio:
Poisson's ratio is the ratio of lateral strain to longitudinal strain when a material is stretched or compressed.
Relation between Poisson's ratio, shear modulus (G), and Young's modulus (E):
For an isotropic material, the relation between Poisson's ratio, shear modulus, and Young's modulus is given by the following equation:
ν = E / (2G) - 1
Substitute the given Poisson's ratio into the equation:
0.3 = E / (2G) - 1
0.3 + 1 = E / (2G)
1.3 = E / (2G)
E / G = 1.3
Ratio of shear modulus to Young's modulus:
The ratio of shear modulus of elasticity (G) to Young's modulus of elasticity (E) is calculated as:
G / E = 1 / (E / G) = 1 / 1.3 = 0.769
Convert the ratio to percentage:
G / E = 0.769 = 76.9%
Therefore, the ratio of shear modulus of elasticity to Young's modulus of elasticity is 0.769 or 76.9%.
In the given options, option 'A' is the closest to the calculated value:
a) 0.38
Therefore, the correct answer is option 'A'.
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Community Answer
If Poissons ratio for a material is 0.3, the ratio of shear modulus of...
E=2C (1+ μ)
μ = 0.3
E/C = 2
1.3= 2.6
C/E = 1/2.6 = 0.384
μ = 0.3
E/C = 2
1.3= 2.6C/E = 1/2.6 = 0.384
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If Poissons ratio for a material is 0.3, the ratio of shear modulus of elasticity to Youngs modulus of elasticity will be,a)0.38b)2.6c)8.6d)0.12Correct answer is option 'A'. Can you explain this answer?
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