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Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Civil Engineering (CE) MCQ


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20 Questions MCQ Test Topicwise Question Bank for Civil Engineering - Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3

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Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 1

The unit of elastic modulus is the same as those of 

Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 2

For a linearly elastic, isotropic and homogeneous material, the number of elastic constants required to relate stress and strain is

Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 3

If the cross-section of a member is subjected to a uniform shear stress of intensity ‘q’, then the strain energy stored per unit volume is equal to (G = modulus of rigidity)

Detailed Solution for Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 3

Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 4

In the case of an engineering material under unidirectional stress in the x-axis, the Poisson’s ratio is equal to (symbols have their usual meanings)

Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 5

A 100 mm long and 50 mm diameter steel rod fits snugly between two rigid walls 100 mm apart at room temperature. Young's modulus of elasticity and coefficient of linear expansion of steel are 2 x 105 N/mm2 and 12 x 10-6/°C respectively. The stress developed in the rod due to a 100°C rise in temperature will be 

Detailed Solution for Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 5

l = 100 mm, d = 50 mm,
E = 2 x 105 N/mm2, α = 12 x 10-6/°C 
δl = αlΔT, ε = δl/l, σ = E = Eα
= 2 x 105 x 12 x 10-6 x 100 = 240 N/mm2

Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 6

During tensile testing of a specimen using a Universal Testing Machine, the parameters actually measured include

Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 7

If the value of Poisson’s ratio is zero, then it means that

Detailed Solution for Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 7

Explanation:

  • Poisson's ratio: It is defined as the ratio of transverse strain to longitudinal strain in the direction of the stretching force.
  • When a material is stretched in one direction, it tends to get compressed in the direction perpendicular to the direction of the force. 
  • Thus, a longitudinal strain causes a transverse strain and vice versa.
  • Poisson's ratio is positive for tensile deformation and negative for compressive deformation.
  • Poisson's ratio is
  • Where ϵt is the transverse strain and ϵl is the longitudinal strain.
  • Poisson's ratio zero means that the longitudinal strain is zero and due to that transverse strain is also zero, which happens when the material is rigid.
Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 8

The stretch in a steel rod of circular section, having a length ℓ subjected to a tensile load P and tapering uniformly from a diameter d1, at one end to a 'diameter d2 at the other end, is given by

Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 9

If Poisson’s ratio for a material is 0.5, then the elastic modulus for the material is

Detailed Solution for Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 9

E = 2G(1 + μ) or E/G = 2 x 1.5 =3

Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 10

The Poisson’s ratio of a material which has Young’s modulus of 120 GPa, and shear modulus of 50 GPa, is 

Detailed Solution for Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 10

G = E/2(1+μ)
or, 1 + μ = 120/(2 x 50) = 1.2
∴ μ = 0.2

Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 11

A rod of material E = 200 x 103 MPa and α = 10-3 mm/mm/°C is fixed at both the ends. It is uniformly heated such that the increase in temperature is 30°C. The stress developed in the rod is

Detailed Solution for Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 11

σ = E ∝ T = -200 x 103 x 10-3 x 30
= -6000N/mm2

Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 12

The deformation of a bar under its own weight as compared to that when subjected to a direct axial load equal to its own weight will be

Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 13

The number of independent elastic constants required to express the stress-strain relationship for linearly elastic isotropic materia! is 

Detailed Solution for Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 13

There are two independent elastic constants E and G for an isotropic linear elastic material.

Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 14

A tapering bar (diameters of end sections being d1 and d2) and a bar of uniform cross-section ‘d' have the same length and are subjected to the same axial pull. Both the bars will have the same extension if ‘ d ’ is equal to

Detailed Solution for Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 14

δteper = 4Pl(πd1/d2E)
δuniform = 4Pl/(pd2 E)
∴ d = 

Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 15

The number of elastic constants for a completely anisotropic elastic material which follows Hooke’s law is

Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 16

For a given material, the modulus of rigidity is 100 GPa and Poisson’s ratio is 0.25. The value of modulus of elasticity in GPa is 

Detailed Solution for Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 16

E = 2G (1 + μ) = 2 x 100(1 + 0.25) 
= 250 GPa

Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 17

A cube having each side of length ‘a’ is constrained in all directions and is heated uniformly so that the temperature is raised to T°C. If α is the thermal coefficient of expansion of the cube material and E is the modulus of elasticity, the stress developed in the cube is

Detailed Solution for Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 17

For hydrostatic state stress = 0
σx = σy = σz = 0

σ = EαT/1-2μ

Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 18

Toughness for mild steel under uniaxial tensile loading is given by the shaded portion of the stress-strain diagram as shown in

Detailed Solution for Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 18

Toughness is the total area under the stress- strain curve upto fracture.

Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 19

Which one of the following is correct in respect of Poisson’s ratio (v) limits for an isotropic elastic solid?

Detailed Solution for Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 19

Isotropic Material: If the response of the material is independent of the orientation of the load axis of the sample, then we say that the material is isotropic. A material is said to be isotropic when it exhibits the same elastic properties in any direction at a given point.

The relationship between various elastic constants is:

Relating the above equations, we can get the maximum and minimum values of the Poisson's ratio of an isotropic elastic solid.

In equation (1), the value of shear modulus G approaches infinity when the value of v is -1. 

In equation (2), the value of bulk modulus of elasticity K approaches infinity when the value of v is 0.5.

Thus we can say that the range where Poisson's ratio vary for isotropic elastic solid is -1 ≤ v ≤ 1/2

Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 20

A bar of copper and steel form a composite system. They are heated to a temperature of 40°C. What type of stress is induced in the copper bar?

Detailed Solution for Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 3 - Question 20

Coefficient of expansion of copper is more than that of steei. Hence, copper will develop compressive stress.

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