For a given elastic material, the Elastic Modulus E is 210 GPa an
| For a given elastic material, the Elastic Modulus E is 210 GPa and its Poisson’s Ratio is 0.27. What is the approximate value of its Modulus of Rigidity?
A. 105 GPa
B. 83 GPa
C. 159 GPa
D. 165 GPa
Please scroll down to see the correct answer and solution guide.
Right Answer is: B
SOLUTION
Concept:
Relation between E, K and μ is given by:
E = 2C (1 + μ)
E = 3K (1 - 2μ)
\({\rm{E}} = \frac{{9{\rm{K}}}}{{3{\rm{K}} + {\rm{C}}}}\)
Where,
E = Young's Modulus of Rigidity = Stress / strain
C = Shear Modulus or Modulus of rigidity = Shear stress / Shear strain
μ = Poisson’s ratio = - lateral strain / longitudinal strain
K = Bulk Modulus of elasticity = Volumetric stress / Volumetric strain
Solution:
210 = 2 × C (1+0.27)
∴ C = 83 GPa