Which of the following equations give the relation between material properties like modulus of elasticity (E), modulus of rigidity (G), and Poisson’s ratio (u)?

If E, N, K and $$\frac{1}{{\text{m}}}$$ are modulus of elasticity, modulus of rigidity. Bulk modulus and Poisson ratio of the material, the following relationship holds good

A

$${\text{E}} = 3{\text{K}}\left( {1 - \frac{2}{{\text{m}}}} \right)$$

B

$${\text{E}} = 2{\text{N}}\left( {1 + \frac{1}{{\text{m}}}} \right)$$

C

$$\frac{3}{2}{\text{K}}\left( {1 - \frac{2}{{\text{m}}}} \right) = {\text{N}}\left( {1 + \frac{1}{{\text{m}}}} \right)$$

D

All the above

Which of the following relationships is correct for relating the three elastic constants of an isotropic elastic material (where, E = Young's modulus, G = Modulus of rigidity or shear modulus v = Poisson's ratio)?

A

E = 2G (1 + v)

B

E = G (1 + v)

C

$${\text{E}} = \frac{{{\text{G}}\left( {1 + {\text{v}}} \right)}}{2}$$

D

E = 2G (1 + 2v)

A cc slab of thickness 20 cm is constructed over a base of granular material with a modulus of reaction 10 kg/cm3. The maximum temperature differential between the top and bottom of the slab is found to be 19°C during summer day and night. The spacing between transverse joints is 8 m and the spacing between longitudinal joints is 4 m. The design wheel load is 5100 kg, radius of contact area is 15 cm, Poisson’s ratio is 0.15, modulus of elasticity is 3×105 kg/cm2, the thermal coefficient is 10 ×10-6 /°C and the coefficient of friction is 1.5. Using the above information, find the worst combination of stresses at the edge of the pavement.

A

51.59 kg/cm2

B

59.51 kg/cm2

C

59.15 kg/cm2

D

51.95 kg/cm2

If the modulus of elasticity is 130 GPa and Poisson’s ratio is 0.3 of steel then what will be the approximate value of modulus of rigidity of steel in MPa?

A

110000

B

50

C

50000

D

110

The Young's modulus of a material is 125 GPa and Poisson’s ratio is 0.25. The modulus of rigidity of me material is

A

30 GPa

B

50 GPa

C

80 GPa

D

100 GPa

If E, G and K denote Young’s modulus of elasticity, Modulus of rigidity and Bulk modulus, respectively, for an elastic material then which one of the following can be possibly true?

A

G = 2K

B

G = E

C

K = E

D

G = K = E

The modulus of rigidity and the modulus of elasticity of a material are 80 GPa and 200 GPa. What will be the Poissons ratio of the material?

A

0.25

B

0.30

C

0.40

D

0.50

Youngs modulus of elasticity and Poissons ratio of a material are 1.25 x 102 MPa and 0.34 respectively. The modulus of rigidity of the material is __________

A

0.9469 MPa

B

0.8375 MPa

C

0.4664 MPa

D

0.4025 MPa

In an experiment, the bulk modulus of elasticity of a material is twice its modulus of rigidity. The Poissons ratio of the material is ___________

A

1/7

B

2/7

C

3/7

D

4/7

If the modulus of elasticity for a given material is twice its modulus of rigidity, then bulk modulus is equal to

A

2C

B

3C

C

$$\frac{{2{\text{C}}}}{3}$$

D

$$\frac{{3{\text{C}}}}{2}$$

Which of the following equations give the relation between material properties like modulus of elasticity (E), modulus of rigidity (G), and Poisson’s ratio (u)?

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