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QUESTION: 1

The number of elastic constants for a orthotropic material are

Solution:

QUESTION: 2

Poisson’s ratio is defined as the ratio of

Solution:

Poisson’s ratio is the ratio of lateral strain to the longitudinal strain.

QUESTION: 3

Which one of the following materials has Poisson’s ratio more than 1?

Solution:

Poisson’s ratio can not be greater than 0.5.

QUESTION: 4

The maximum values of Poisson’s ratio for an elastic material is

Solution:

Poisson’s ratio lies between 0 to 0.5.

μ = 0.5 for pure elastic rubber

μ = 0.1 to 0.2 for concrete

μ = 0.25 to 0.33 for steel

QUESTION: 5

The relationship between modulus of elasticity (E) and modulus of rigidity (G) is

Solution:

QUESTION: 6

What is the relationship between elastic constants E, G and K?

Solution:

E = 2G(1 + μ) ......(i)

E = 3K(1 - 2μ) ......(ii)

Solving (i) and (ii)

⇒

QUESTION: 7

In terms of bulk modulus (K) and modulus of rigidity (G), the Poisson’s ratio can be expressed as

Solution:

E = 3K(1 - 2μ) ......(i)

E = 2G(1 + μ) .......(ii)

From (i) and (ii)

3K(1 - 2μ) = 2G(1 + μ)

3K - 6μK = 2G + 2μG

3K - 2G = 6μK + 2μG

3K - 2G = 2μ(G + 3K)

QUESTION: 8

What is the relationship between the linear elastic properties Young’s modulus (E), rigidity modulus (G) and bulk modulus (K)?

Solution:

E = 2G(1 + μ) .......(i)

E = 3K(1 - 2μ) ........(ii)

Solving (i) and (ii), we get

⇒

∴

QUESTION: 9

A cylindrical bar of 20 mm diameter and 1 m length is subjected to a tensile test. Its longitudinal strain is 4 times that of its lateral strain. If the modulus of elasticity is 2 x 10^{5} N/mm^{2}, then its modulus of rigidity will be

Solution:

But,

= 0.8 x 10^{5} N/mm^{2}

QUESTION: 10

E, G, K and μ represent the elastic modulus, shear modulus, bulk modulus and -Poisson's ratio respectively of a linearly elastic, isotropic and homogeneous material. To express the stress strain relations completely for this material, at least

Solution:

E = 2G(1 + μ) ...(i)

E = 3K (1 - 2μ) ...(ii)

In this cae there are four unknown quantities and only two equation are available. Hence any two of the four unknown quantities must be known for complete stress relationship.

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