Strength of Materials Questions and Answers – Strain Constants – 1

This set of Strength of Materials Multiple Choice Questions & Answers (MCQs) focuses on “Strain Constants – 1”.

1. What will be the elastic modulus of a material if the Poisson’s ratio for that material is 0.5?
a) Equal to its shear modulus
b) Three times its shear modulus
c) Four times its shear modulus
d) Not determinable

Explanation:
Explanation: Elastic modulus = E
Shear modulus = G
E = 2G ( 1 + μ )
Given, μ= 0.5, E = 2×1.5xG
E = 3G.

2. A rigid beam ABCD is hinged at D and supported by two springs at A and B as shown in the given figure. The beam carries a vertical load P and C. the stiffness of spring at A is 2K and that of B is K.

What will be the ratio of forces of spring at A and that of spring at B?
a) 4
b) 3
c) 2
d) 1

Explanation: The rigid beam will rotate about point D, due to the load at C.

From similar triangle,
δa/2a = δb/3b
Force in spring A/Force in spring B = Pa/Pb
= 2k/k x 3/2 = 3.

3. A solid metal bat of uniform diameter D and length L is hung vertically from a ceiling. If the density of the material of the bar is 1 and the modulus of elasticity is E, then the total elongation of the bar due to its own weight will be ____________
a) L/2E
b) L2/2E
c) E/2L
d) E/2L2

Explanation: The elongation of bar due to its own weight is δ= WL/2AE
Now W = ρAL
There fore δ= L2 / 2E.

4. A bar of diameter 30mm is subjected to a tensile load such that the measured extension on a gauge length of 200mm is 0.09mm and the change in diameter is 0.0045mm. Calculate the Poissons ratio?
a) 1/3
b) 1/4
c) 1/5
d) 1/6

Explanation: Longitudinal strain = 0.09/200
Lateral strain = – 0.0045/30
Poissons ratio = – lateral strain/ longitudinal strain
= 0.0045/30 x 200/0.09
= 1/3.

5. What will be the ratio of Youngs modulus to the modulus of rigidity of a material having Poissons ratio 0.25?
a) 3.75
b) 3.00
c) 1.5
d) 2.5

Explanation: Modulus of rigidity, G = E/2(1 + μ)
Therefore, E/G = 2x(1+0.25) = 2.5.

6. An experiment was done and it was found that the bulk modulus of a material is equal to its shear modulus. Then what will be its Poissons ratio?
a) 0.125
b) 0.150
c) 0.200
d) 0.375

Explanation: We know that, μ = (3K – 2G) / (6K + 2G)
Here K = G
Therefore, μ = 3-2 / 6+2 = 0.125.

7. A bar of 40mm dia and 40cm length is subjected to an axial load of 100 kN. It elongates by 0.005mm. Calculate the Poissons ratio of the material of bar?
a) 0.25
b) 0.28
c) 0.30
d) 0.33

Explanation: Longitudinal strain = 0.150/400 = 0.000375
Lateral strain = – 0.005/40 = -0.000125
Poissons ratio = – lateral strain/longitudinal strain
= 0.33.

8. What will be the approximate value of shear modulus of a material if the modulus of elasticity is 189.8 GN/m2 and its Poissons ratio is 0.30?
a) 73 GN/m2
b) 80 GN/m2
c) 93.3 GN/m2
d) 103.9 GN/m2

Explanation: The relationship between E, G, and μ is given by
is given by
E = 2G (1 + μ)
G = 189.8 / 2(1 + 0.30)
G = 73 GN/m2.

9. What will be the modulus of rigidity if the value of modulus of elasticity is 200 and Poissons ratio is 0.25?
a) 70
b) 80
c) 125
d) 250

Explanation: The relationship between E, G and μ is E = 2G (1 + μ)
G = 200 / 2(1 + 0.25)
G = 80.
Sanfoundry Global Education & Learning Series – Strength of Materials.