Which of the following is the correct relation between E, G, and ν?
A
E = G(1 + ν) B
E = 2G(1 + ν) C
E = 3G(1 - 2ν) D
E = G(1 - ν)
Analysis & Theory
E = 2G(1 + ν) is the standard relation between Young's modulus, shear modulus, and Poisson’s ratio.
Which formula relates Young’s Modulus and Bulk Modulus through Poisson’s ratio?
A
E = 3K(1 - 2ν) B
E = 3K(1 + 2ν) C
E = 2K(1 + ν) D
E = 2K(1 - ν)
Analysis & Theory
The correct formula is E = 3K(1 - 2ν).
What does the relation E = 2G(1 + ν) help calculate?
A
Bulk Modulus B
Poisson's Ratio C
Young's Modulus from Shear Modulus and Poisson's Ratio D
Stress from strain
Analysis & Theory
It gives Young's modulus when G and ν are known.
If Poisson’s ratio (ν) = 0.25 and G = 80 GPa, what is Young’s modulus (E)?
A
100 GPa B
120 GPa C
160 GPa D
200 GPa
Analysis & Theory
E = 2 × 80 × (1 + 0.25) = 2 × 80 × 1.25 = 200 GPa
If a material has very high Bulk Modulus, it means:
A
It can resist compression well B
It has high Poisson's ratio C
It undergoes large volumetric strain D
It is very brittle
Analysis & Theory
High bulk modulus means the material resists volume change under pressure.