1. A cylindrical elastic body subjected to pure torsion about its axis develops
(a) tensile stress in a direction 45^{0} to the axis
(b) no tensile or compressive stress
(c) maximum shear stress along the axis of the shaft
(d) maximum shear stress at 45^{0} to the axis
(1 Mark, 1989)

Ans: a
Explanation:
2. An elastic body is subjected to a tensile stress X in a particular direction and a compressive stress Y in its perpendicular direction. X and Y are unequal in magnitude. On the plane of maximum shear stress in the body there will be
(a) no normal stress
(b) also the maximum normal stress
(c) the minimum normal stress
(d) both normal stress and shear stress
(1 Mark, 1989)

Ans: d
Explanation:
3. The three dimensional state of stress at a point is given by
[σ] = \quad \begin{bmatrix} 30 & 10\quad 10 \\ 10 & \quad 0\quad \quad 20\quad \\ 10 & 20\quad \quad 0 \end{bmatrix}MN/m^{2}
The shear stress on the xface in ydirection at the same point is then equal to
(a) zero MN/m^{2}
(b) 10 MN/m^{2}
(c) 10 MN/m^{2}
(d) 20 MN/m^{2}
(2 Mark, 1990)

Ans: c
Explanation:
4. At a point in a stressed body the state of stress on two planes 45^{0} apart is as shown below. Determine the principal stresses in MPa.
(a) 8.242, 0.658
(b) 9.242, 0.758
(c) 9.242, 0.658
(d) 8.242, 0.758
(2 Mark, 1993)

Ans: b
Explanation:
5. Determine the temperature rise necessary to induce buckling in a 1 m long circular rod of diameter 40 mm shown in the figure below. Assume the rod to be pinned at its ends and the coefficient of thermal expansion as 20\times { 10 }^{ 6 }/^{0}C. Assume uniform heating of the bar
(2 Mark, 1993)

Ans: 49.35 ^{0}C
Explanation:
6. A free bar of length l m is uniformly heated from 0°C to a temperature t°C. α is the coefficient of linear expansion and E is the modulus of elasticity. The stress in the bar is:
(a) αtE
(b) αtE/2
(c) Zero
(d) None of the above
(1 Mark, 1995)

Ans: c
Explanation:
7. If the two principal strains at a point are 1000 × 10^{6} and –600 × 10^{6}, then the maximum shear strain is
(a) 800 × 10^{−6}
(b) 500 × 10^{−6}
(c) 1600 × 10^{−6}
(d) 200 × 10^{−6}
(1 Mark, 1996)

Ans: c
Explanation:
8. A thin cylinder of 100 mm internal diameter and 5 mm thickness is subjected to an internal pressure of 10 MPa and a torque of 2000 Nm. Calculate the magnitudes of the principal stresses.
(2 Mark, 1996)

Ans: 1098, 40.2 MPa
Explanation:
9. A shaft subjected to torsion experiences a pure shear stress τ on the surface. The maximum principal stress on the surface, which is at 45° to the axis, will have a value
(a) τ cos 45°
(b) 2τ cos 45°
(c) τ cos^{2} 45°
(d) 2τ sin 45° cos 45°
(2 Mark, 2003)

Ans: d
Explanation:
Data for Q.10 – 11 are given below.
The state of stress at a point ‘P’ in a two dimensional loading is such that the Mohr’s circle is a point located at 175 MPa on the positive normal stress axis.
10. Determine the maximum and minimum principal stresses respectively from the Mohr’s circle are
(a) + 175 MPa, 175 MPa
(b) + 175 MPa, +175 MPa
(c) 0, 175 MPa
(d) 0, 0
(2 Mark, 2003)

Ans: b
Explanation:
11. Determine the directions maximum and minimum principal stresses at the point ‘P’ from the Mohr’s circle
(a) 0, 90°
(b) 90°, 0
(c) 45°, 135°
(d) all directions
(2 Mark, 2003)

Ans:d
Explanation:
12. Two identical circular rods of same diameter and same length are subjected to same magnitude of axial tensile force. One of the rods is made out of mild steel having the modulus of elasticity of 206 Gpa. The other rod is made out of cast iron having he modulus of elasticity of 100 Gpa. Assume both the materials to be homogeneous and isotropic and the axial force causes the same amount of uniform stress in both the rods. The stresses developed are within the proportional limit of the respective materials. Which of the following observations is correct?
(a) Both rods elongate by the same amount.
(b) Mild steel rod elongates more than the cast iron rod.
(c) Cast iron rod elongates more than the mild steel rod.
(d) As the stresses are equal strains are also equal in both the rods.
(1 Mark, 2003)

Ans: c
Explanation:
14. The figure below shows a steel rod of 25 mm^{2} cross sectional area. It is loaded at four points, K, L, M and N. Assume E_{steel} = 200GPa. The total change in length of the rod due to loading is
(a) 1μm
(b) 10 μm
(c) 16 μm
(d) 20 μm
(2 Mark, 2004)

Ans: b
Explanation:
15. In terms of Poisson’s ratio (μ) the ratio of Young’s Modulus (E) to Shear Modulus (G) of elastic materials is
(a) 2(1 + μ)
(b) 2(1 – μ)
(c) (1 + μ)
(d) (1 – μ)
(1 Mark, 2004)

Ans: a
Explanation:
16. The figure shows the state of stress at a certain point in a stressed body. The magnitudes of normal stresses in the x and y direction are 100 MPa and 20 MPa respectively. The radius of Mohr’s stress circle representing this state of stress is
(a) 120 MPa
(b) 80 MPa
(c) 60 MPa
(d) 40 MPa
(1 Mark, 2004)

Ans: c
Explanation:
17. A uniform, slender cylindrical rod is made of a homogeneous and isotropic material. The rod rests on a frictionless surface. The rod is heated uniformly. If the radial and longitudinal thermal stresses are represented by σ_{r} and σ_{z} respectively, then
(a) σ_{r} = 0, σ_{z} = 0
(b) σ_{r} \neq 0, σ_{z} = 0
(c) σ_{r} = 0, σ_{z} \neq 0
(d) σ_{r} \neq 0, σ_{z} \neq 0
(1 Mark, 2005)

Ans: a
Explanation:
18. The Mohr’s circle of plane stress for a point in a body is shown. The design is to be done on the basis of the maximum shear stress theory for yielding. Then, yielding will just begin if the designer chooses a ductile material whose yield strength is
(a) 45 MPa
(b) 50 MPa
(c) 90 MPa
(d) 100 MPa
(2 Mark, 2005)

Ans: d
Explanation:
19. A steel bar of 40 mm × 40 mm square crosssection is subjected to an axial compressive load of 200 kN. If the length of the bar is 2m and E = 200 GPa, the elongation of the bar will be:
(a) 1.25 mm
(b) 2.70 mm
(c) 4.05 mm
(d) 5.40 mm
(2 Mark, 2006)

Ans: a
Explanation:
20. A bar having a crosssectional area of 700 mm^{2} is subjected to axial loads at the positions indicated. The value of stress in the segment QR is:
(b) 50 MPa
(c) 70 MPa
(d) 120 MPa
(2 Mark, 2006)

Ans: a
Explanation:
21. According to VonMises’ distortion energy theory, the distortion energy under three dimensional stress state is represented by
(a) \frac { 1 }{ 2E } \left[ { \sigma }_{ 1 }^{ 2 }+{ \sigma }_{ 2 }^{ 2 }+{ \sigma }_{ 3 }^{ 2 }2\mu \left( { \sigma }_{ 1 }{ \sigma }_{ 2 }+{ { \sigma }_{ 3 }\sigma }_{ 2 }{ +\sigma }_{ 1 }{ \sigma }_{ 3 } \right) \right]
(b) \frac { 12\mu }{ 6E } \left[ { \sigma }_{ 1 }^{ 2 }+{ \sigma }_{ 2 }^{ 2 }+{ \sigma }_{ 3 }^{ 2 }+2\left( { \sigma }_{ 1 }{ \sigma }_{ 2 }+{ { \sigma }_{ 3 }\sigma }_{ 2 }{ +\sigma }_{ 1 }{ \sigma }_{ 3 } \right) \right]
(c) \frac { 1+\mu }{ 3E } \left[ { \sigma }_{ 1 }^{ 2 }+{ \sigma }_{ 2 }^{ 2 }+{ \sigma }_{ 3 }^{ 2 }\left( { \sigma }_{ 1 }{ \sigma }_{ 2 }+{ { \sigma }_{ 3 }\sigma }_{ 2 }{ +\sigma }_{ 1 }{ \sigma }_{ 3 } \right) \right]
(d) \frac { 1 }{ 3E } \left[ { \sigma }_{ 1 }^{ 2 }+{ \sigma }_{ 2 }^{ 2 }+{ \sigma }_{ 3 }^{ 2 }\mu \left( { \sigma }_{ 1 }{ \sigma }_{ 2 }+{ { \sigma }_{ 3 }\sigma }_{ 2 }{ +\sigma }_{ 1 }{ \sigma }_{ 3 } \right) \right]
(2 Mark, 2006)

Ans: c
Explanation:
22. A 200\times 100\times 50 mm steel block is subjected to a hydrostatic pressure of 15 MPa. The Young’s modulus and Poisson’s ratio of the material are 200 GPa and 0.3 respectively. The change in the volume of the block in { mm }^{ 3 } is
(a) 85
(b) 90
(c) 100
(d) 110
(2 Mark, 2007)

Ans: b
Explanation:
23. A steel rod of length L and diameter D, fixed at both ends, is uniformly heated to a temperature rise of The Young’s modulus is E and the coefficient of linear expansion is ‘α’. The thermal stress in the rod is
(a) 0
(b) \alpha \Delta T
(c) E\alpha \Delta T
(d) E\alpha \Delta TL
(1 Mark, 2007)

Ans: c
Explanation:
24. A stepped steel shaft shown below is subjected to 10 Nm torque. If the modulus of rigidity is 80 GPa, the strain energy in the shaft in Nmm is
(a) 4.12
(b) 3.46
(c) 1.73
(d) 0.86
(2 Mark, 2007)

Ans: c
Explanation:
25. A two dimensional fluid element rotates like a rigid body. At a point within the element, the pressure is 1 unit. Radius of the Mohr’s circle, characterizing the state of stress at the point, is
(a) 0.5 unit
(b) 0 unit
(c) 1 unit
(d) 2 unit
(2 Mark, 2008)

Ans: b
Explanation:
26. A rod of Length L and diameter D is subjected to a tensile load P. Which of the following is sufficient to calculate the resulting change in diameter?
(a) Young’s modulus
(b) Shear modulus
(c) Poisson’s ratio
(d) Both Young’s modulus and shear modulus
(1 Mark, 2008)

Ans: d
Explanation:
Statement for Linked Answer Questions 27 and 28.
A cylindrical container of radius R = 1 m, wall thickness 1 mm is filled with water up to a depth of 2 m and suspended along its upper rim. The density of water is 1000kg/m^{3} and acceleration due to gravity is 10 m/s^{2}. The selfweight of the cylinder is negligible. The formula for hoop stress in a thin – walled cylinder can be used at all points along the height of the cylindrical container.
27. The axial and circumferential stress (σ_{a}, σ_{c}) experienced by the cylinder wall at middepth (1 m as shown) are
(a) (10, 10) MPa
(b) (5, 10) MPa
(c) (10, 5) MPa
(d) (5, 5) MPa
(2 Mark, 2008)

Ans: b
Explanation:
28. If the Young’s modulus and Poisson’s ratio of the container material are 100GPa and 0.3, respectively, the axial strain in the cylinder wall at middepth is
(a) 2 × 10^{5}
(b) 6 × 10^{5}
(c) 7 × 10^{5}
(d) 1.2 × 10^{4}
(2 Mark, 2008)

Ans: a
Explanation:
29. If the principal stresses in a plane stress problem, are σ_{1} = 100MPa, σ_{2} = 40MPa, the magnitude of the maximum shear stress (in MPa) will be
(a) 60
(b) 50
(c) 30
(d) 20
(1 Mark, 2009)

Ans: c
Explanation:
30. A solid circular shaft of diameter d is subjected to a combined bending moment M and torque, T. The material property to be used for designing the shaft using the relation
(a) ultimate tensile strength (S_{u})
(b) tensile yield strength (S_{y})
(c) torsional yield strength (S_{sy})
(d) endurance strength (S_{e})
(1 Mark, 2009)

Ans: c
Explanation:
31. The state of planestress at a point is given by σ_{x} = −200 MPa, σ_{y} = 100 MPa and τ_{xy} = 100 MPa. The maximum shear stress in MPa is
(a) 111.8
(b) 150.1
(c) 180.3
(d) 223.6
(1 Mark, 2010)

Ans: c
Explanation:
32. Match the following criteria of material failure, under biaxial stresses σ_{1} and σ_{2} and yield stress σ_{y}, with their corresponding graphic representations
(b) PN, QM, RL
(c) PM, QN, RL
(d) PN, QL, RM
(1 Mark, 2011)

Ans: c
33. A thin cylinder of inner radius 500 mm and thickness 10 mm is subjected to an internal pressure of 5 MPa. The average circumferential (hoop) stress in MPa is
(a) 100
(b) 250
(c) 500
(d) 1000
(1 Mark, 2011)

Ans: b
Explanation:
34. A thin walled spherical shell is subjected to an internal pressure. If the radius of the shell is increased by 1% and the thickness is reduced by 1%, with the internal pressure remaining the same, the percentage change in the circumferential (hoop) stress is
(a) 0
(b) 1
(c) 1.08
(d) 2.02
(1 Mark, 2012)

Ans: d
35. The homogeneous state of stress for a metal part undergoing plastic deformation is
T = \begin{pmatrix} 10 & \quad 5\quad \quad 0 \\ 5 & 20\quad \quad 0 \\ 0 & \quad 0\quad 10 \end{pmatrix}
Where the stress component values are in MPa. Using von Mises yield criterion, the value of estimated shear yield stress, in MPa is
(a) 9.50
(b) 16.07
(c) 28.52
(d) 49.41
(2 Mark, 2012)

Ans: b
Explanation:
36. The state of stress at a point under plane stress condition is σ_{xx} = 40 MPa, σ_{yy} = 100 MPa and τ_{xy} = 40 MPa. The radius of the Mohr’s circle representing the given state of stress in MPa is
(a) 40
(b) 50
(c) 60
(d) 100
(2 Mark, 2012)

Ans: b
Explanation:
37. A solid steel cube constrained on all six faces is heated so that the temperature rises uniformly by ΔT. If the thermal coefficient of the material is α, Young’s modulus is E and the Poisson’s ratio is ν, the thermal stress developed in the cube due to heating is
(a) \frac { \alpha \left( \Delta T \right) E }{ 12\nu }
(b) \frac { 2\alpha \left( \Delta T \right) E }{ 12\nu }
(c) \frac { 3\alpha \left( \Delta T \right) E }{ 12\nu }
(d) \frac { \alpha \left( \Delta T \right) E }{ 3(12\nu ) }
(2 Mark, 2012)

Ans: a
Explanation:
38. A rod of length L having uniform crosssectional area A is subjected to a tensile force P as shown in the figure below. If the Young’s modulus of the material varies linearly from E_{1} to E_{2} along the length of the rod, the normal stress developed at the sectionSS is
(a) \frac { P }{ A }
(b) \frac { P\left( { E }_{ 1 }{ E }_{ 2 } \right) }{ A\left( { E }_{ 1 }+{ E }_{ 2 } \right) }
(c) \frac { P{ E }_{ 2 } }{ A{ E }_{ 1 } }
(d) \frac { P{ E }_{ 1 } }{ A{ E }_{ 2 } }
(1 Mark, 2013)

Ans: a
Explanation:
39. A long thin walled cylindrical shell, closed at both the ends, is subjected to an internal pressure. The ratio of the hoop stress (circumferential stress) to longitudinal stress developed in the shell is
(a) 0.5
(b) 1.0
(c) 2.0
(d) 4.0
(1 Mark, 2013)

Ans: c
Explanation:
40. Two threaded bolts A and B of same material and length are subjected to identical tensile load. If the elastic strain energy stored in bolt A is 4 times that of bolt B and the mean diameter of bolt A is 12 mm, the mean diameter of bolt B in mm is
(a) 16
(b) 24
(c) 36
(d) 48
(1 Mark, 2013)

Ans: b
Explanation:
41. A circular rod of length ‘L’ and area of crosssection ‘A’ has a modulus of elasticity ‘E’ and coefficient of thermal expansion ‘α’. One end of the rod is fixed and other end is free. If the temperature of the rod is increased by ΔT, then
(a) stress developed in the rod is E α ΔT and strain developed in the rod is α ΔT
(b) both stress and strain developed in the rod are zero
(c) stress developed in the rod is zero and strain developed in the rod is α ΔT
(d) stress developed in the rod is E α ΔT and strain developed in the rod is zero.
(1 Mark, 2014[1])

Ans: c
Explanation:
42. The state of stress at a point is given by σ_{x} = 6 MPa, σ_{y} = 4 MPa and τ_{xy} = 8 MPa. The maximum tensile stress (in MPa) at the point is ______.
(1 Mark, 2014[1])

Ans: 8.4
Explanation:
43. A 200 mm long, stress free rod at room temperature is held between two immovable rigid walls. The temperature of the rod is uniformly raised by 250°C. If the Young’s modulus and coefficient of thermal expansion are 200 GPa and 1×10^{−5} /°C, respectively, the magnitude of the longitudinal stress (in MPa) developed in the rod is ____.
(2 Mark, 2014[1])

Ans: 500
Explanation:
44. A metallic rod of 500 mm length and 50 mm diameter, when subjected to a tensile force of 100 kN at the ends, experiences an increase in its length by 0.5 mm and a reduction in its diameter by 0.015 mm. The Poisson’s ratio of the rod material is ____.
(1 Mark, 2014[1])

Ans: 0.3
Explanation:
45. A steel cube, with all faces free to deform, has Young’s modulus, E, Poisson’s ratio, ν, and coefficient of thermal expansion, α. The pressure (hydrostatic stress) developed within the cube, when it is subjected to a uniform increase in temperature, ΔT, is given by
(a) 0
(b) \frac { \alpha \left( \Delta T \right) E }{ 12\nu }
(c) – \frac { \alpha \left( \Delta T \right) E }{ 12\nu }
(d) \frac { \alpha \left( \Delta T \right) E }{ 3(12\nu ) }
(1 Mark, 2014[2])

Ans: a
Explanation:
46. A thin plate of uniform thickness is subject to pressure as shown in the figure below
Under the assumption of plane stress, which one of the following is correct?
(a) Normal stress is zero in the zdirection
(b) Normal stress is tensile in the zdirection
(c) Normal stress is compressive in the zdirection
(d) Normal stress varies in the zdirection
(1 Mark, 2014[2])

Ans: a
Explanation:
46. Consider the two states of stress as shown in configurations I and II in the figure below. From the standpoint of distortion energy (vonMises) criterion, which one of the following statements is true?
(a) I yields after II
(b) II yields after I
(c) Both yield simultaneously
(d) Nothing can be said about their relative yielding
(2 Mark, 2014[2])

Ans: c
47. The stressstrain curve for mild steel is shown in the figure given below. Choose the correct option referring to both figure and table.
(a) P1, Q2, R3, S4, T5, U6
(b) P3, Q1, R4, S2, T6, U5
(c) P3, Q4, R1, S5, T2, U6
(d) P4, Q1, R5, S2, T3, U6
(1 Mark, 2014[3])

Ans: c
48. If the Poisson’s ratio of an elastic material is 0.4, the ratio of modulus of rigidity to Young’s modulus is ___.
(1 Mark, 2014[4])

Ans: 0.357
Explanation:
49. The number of independent elastic constants required to define the stressstrain relationship for an isotropic elastic solid is ____.
(1 Mark, 2014[4])

Ans: 2
Explanation:
50. A thin gas cylinder with an internal radius of 100 mm is subject to an internal pressure of 10 MPa. The maximum permissible working stress is restricted to 100 MPa. The minimum cylinder wall thickness (in mm) for safe design must be _____.
(2 Mark, 2014[4])

Ans: 10
Explanation:
51. Which one of the following types of stressstrain relationship best describes the behaviour of brittle materials, such as ceramics and thermosetting plastics, (σ = stress and ε = strain)?

Ans: d
Explanation:
52. A rod is subjected to a uniaxial load within linear elastic limit. When the change in the stress is 200 MPa, the change in the strain is 0.001. If the Poisson’s ratio of the rod is 0.3, the modulus of rigidity (in GPa) is ____.
(1 Mark, 2015[2])

Ans: 77
Explanation:
53. In a plane stress condition, the components of stress at a point are σ_{x }= 20 MPa, σ_{y }= 80 MPa and τ_{xy} = 40 MPa. The maximum shear stress (in MPa) at the point is
(a) 20
(b) 25
(c) 50
(d) 100
(2 Mark, 2015[2])

Ans: c
Explanation:
54. A gas is stored in a cylindrical tank of inner radius 7 m and wall thickness 50 mm. The gauge pressure of the gas is 2 MPa. The maximum shear stress (in MPa) in the wall is
(a) 35
(b) 70
(c) 140
(d) 280
(1 Mark, 2015[2])

Ans: c
Explanation:
55. The principal stresses at a point inside a solid object are σ_{1} = 100 MPa, σ_{2} = 100 MPa and σ_{3} = 0 MPa. The yield strength of the material is 200 MPa. The factor of safety calculated using Tresca (maximum shear stress) theory is n_{T} and the factor of safety calculated using Von Mises (maximum distortional energy) theory is n_{V}. Which one of the following relations is TRUE?
(a) n_{T} = \left( \frac { \sqrt { 3 } }{ 2 } \right) n_{V}
(b) n_{T} = \left( \sqrt { 3 } \right) n_{V}
(c) n_{T} = n_{V}
(d) n_{V} = \left( \sqrt { 3 } \right)n_{T}
(2 Mark, 2016[1])

Ans: c
Explanation:
56. A hypothetical engineering stressstrain curve shown in the figure has three straight lines PQ, QR, RS with coordinates P(0,0), Q(0.2,100), R(0.6,140) and S(0.8,130). ‘Q’ is the yield point, ‘R’ is the UTS point and ‘S’ the fracture point.
The toughness of the material (in MJ/m^{3}) is _____.
(2 Mark, 2016[1])

Ans: 0.85
Explanation:
58. A circular metallic rod of length 250 mm is placed between two rigid immovable walls as shown in the figure. The rod is in perfect contact with the wall on the left side and there is a gap of 0.2 mm between the rod and the wall on the right side. If the temperature of the rod is increased by 200^{0}C, the axial stress developed in the rod is __________ MPa.
Young’s modulus of the material of the rod is 200 GPa and the coefficient of thermal expansion is 10^{−5} per ^{o}C.

Ans: 240
Explanation:
59. A shaft with a circular crosssection is subjected to pure twisting moment. The ratio of the maximum shear stress to the largest principal stress is
(a) 2.0
(b) 1.0
(c) 0.5
(d) 0
(1 Mark, 2016[2])

Ans: b
Explanation:
60. A thin cylindrical pressure vessel with closedends is subjected to internal pressure. The ratio of circumferential (hoop) stress to the longitudinal stress is
(a) 0.25
(b) 0.50
(c) 1.0
(d) 2.0
(1 Mark, 2016[2])

Ans: d
Explanation:
61. A square plate of dimension L × L is subjected to a uniform pressure load p = 250 MPa on its edges as shown in the figure. Assume plane stress conditions. The Young’s modulus E = 200 GPa.
The deformed shape is a square of dimension L − 2\delta . If L = 2 m and \delta = 0.001 m, the Poisson’s ratio of the plate material is ____.
(2 Mark, 2016[3])

Ans: 0.2
Explanation:
62. The state of stress at a point on an element is shown in figure (a). The same state of stress is shown in another coordinate system in figure (b).
The components (τ_{xx}, τ_{yy}, τ_{xy}) are given by
(a) \left( \frac { p }{ \sqrt { 2 } } ,\quad \frac { p }{ \sqrt { 2 } } ,\quad 0 \right)
(b) \left( 0,\quad 0,\quad p \right)
(c) \left( p,\quad p,\quad \frac { p }{ \sqrt { 2 } } \right)
(d) \left( 0,\quad 0,\quad \frac { p }{ \sqrt { 2 } } \right)
(1 Mark, 2016[3])

Ans:b
Explanation:
63. A point mass of 100 kg is dropped onto a massless elastic bar (crosssectional area = 100 mm^{2}, length = 1 m, Young’s modulus = 100 GPa) from a height H of 10 mm as shown (Figure is not to scale). If g = 10 m/s^{2}, the maximum compression of the elastic bar is _____mm.
(2 Mark, 2017[1])

Ans: 1.517
Explanation:
64. The Poisson’s ratio for a perfectly incompressible linear elastic material is ___.
(a) 1
(b) 0.5
(c) 0
(d) Infinity
(1 Mark, 2017[1])

Ans: b
Explanation:
65. In the engineering stressstrain curve for mild steel, the ultimate tensile strength (UTS) refers to
(a) Yield stress
(b) Proportional limit
(c) Maximum stress
(d) Fracture stress
(1 Mark, 2017[1])

Ans: c
Explanation:
66. In a metal forming operation when the material has just started yielding, the principal stresses are σ_{1 }= +180 MPa, σ_{2 }= 100 MPa and σ_{3 }= 0. Following von Mises criterion, the yield stress is ____ MPa.
(1 Mark, 2017[1])

Ans: 245.7
Explanation:
67. A rectangular region in a solid is in a state of plane strain. The (x, y) coordinates of the corners of the undeformed rectangle are given by P(0, 0), Q(4, 0), R(4, 3), S(0, 3). The rectangle is subjected to uniform strain ε_{xx} = 0.001, ε_{yy} = 0.002, γ_{xy} = 0.003. The deformed length of the elongated diagonal, upto three decimal places, is _____ units.
(2 Mark, 2017[1])

Ans: 5.014
Explanation:
68. A steel bar is held by two fixed supports as shown in the figure and is subjected to an increase of temperature ΔT = 100^{0}C. If the coefficient of thermal expansion and Young’s modulus of elasticity of steel are 11\times10^{6} /^{0}C and 200 GPa, respectively, the magnitude of thermal stress (in MPa) induced in the bar is _____.
(1 Mark, 2017[2])

Ans: 220
Explanation:
69. The principal stresses at a point in a critical section of a machine component are σ_{1 }= 60 MPa, σ_{2 }= 5 MPa and σ_{3 }= 40 MPa. For the material of the component, the tensile yield strength is σ_{y }= 200 MPa. According to the maximum shear stress theory, the factorof safety is
(a) 1.67
(b) 2.00
(c) 3.60
(d) 4.00
(2 Mark, 2017[2])

Ans: b
Explanation:
70. The state of stress at a point is σ_{x }= σ_{y }= σ_{z }= τ_{xz }= τ_{zx }= τ_{yz }= τ_{zy }= 0 and τ_{xy }= τ_{yx} = 50 MPa. The maximum normal stress (in MPa) at that point is _______.
(1 Mark, 2017[2])

Ans: 50
Explanation:
71. A cantilever beam of length L and flexural modulus EI is subjected to a point load P at the free end. The elastic strain energy stored in the beam due to bending (neglecting transverse shear) is
(a) \frac { { P }^{ 2 }{ L }^{ 3 } }{ 6EI }
(b) \frac { { P }^{ 2 }{ L }^{ 3 } }{ 3EI }
(c) \frac { { P }{ L }^{ 3 } }{ 3EI }
(d) \frac { { P }{ L }^{ 3 } }{ 6EI }
(1 Mark, 2017[2])

Ans: a
Explanation:
72. If σ_{1} and σ_{3} are the algebraically largest and smallest principal stresses respectively, the value of the maximum shear stress is
(a) \frac { { \sigma }_{ 1 }+{ \sigma }_{ 3 } }{ 2 }
(b) \frac { { \sigma }_{ 1 }{ \sigma }_{ 3 } }{ 2 }
(c) \sqrt { \frac { { \sigma }_{ 1 }+{ \sigma }_{ 2 } }{ 2 } }
(d) \sqrt { \frac { { \sigma }_{ 1 }{ \sigma }_{ 2 } }{ 2 } }
(1 Mark, 2018[1])

Ans: b
Explanation:
73. The state of stress at a point, for a body in plane stress, is shown in the figure below. If the minimum principal stress is 10 kPa, then the normal stress (in kPa) is
(b) 18.88
(c) 37.78
(d) 75.50
(2 Mark, 2018[1])

Ans: c
Explanation:
74. A carpenter glues a pair of cylindrical wooden logs by bonding their end faces at an angle of θ = 30^{0} as shown in the figure.
The glue used at the interface fails if
Criterion 1: the maximum normal stress exceeds 2.5 MPa.
Criterion 2: the maximum shear stress exceeds 1.5 MPa.
Assume that the interface fails before the logs fail. When a uniform tensile stress of 4 MPa is applied, the interface
(a) Fails only because of criterion 1
(b) Fails only because of criterion 2
(c) Fails because of both criteria 1 and 2
(d) Does not fail
(2 Mark, 2018[1])

Ans: c
Explanation:
75. A simply supported beam of width 100 mm, height 200 mm and length 4 m is carrying a uniformly distributed load of intensity 10 kN/m. The maximum bending stress (in MPa) in the beam is __________ (correct to one decimal place).
(2 Mark, 2018[1])

Ans: 30
Explanation:
76. A bimetallic cylindrical bar of cross sectional area 1 m^{2} is made by bonding Steel (Young’s modulus = 210 GPa) and Aluminium (Young’s modulus = 70 GPa) as shown in the figure. To maintain tensile axial strain of magnitude 10^{6} in Steel bar and compressive axial strain of magnitude 10^{6 }in Aluminum bar, the magnitude of the required force P (in kN) along the indicated direction is
(a) 70
(b) 140
(c) 210
(d) 280
(2 Mark, 2018[2])

Ans: d
77. A thinwalled cylindrical can with rigid end caps has a mean radius R = 100 mm and a wall thickness of t = 5 mm. The can is pressurized and an additional tensile stress of 50 MPa is imposed along the axial direction as shown in the figure. Assume that the state of stress in the wall is uniform along its length. If the magnitudes of axial and circumferential components of stress in the can are equal, the pressure (in MPa) inside the can is ___________ (correct to two decimal places).
(2 Mark, 2018[2])

Ans: 5
Explanation:
78. Consider two concentric circular cylinders of different materials M and N in contact with each other at r = b, as shown below. The interface at r = b is frictionless. The composite cylinder system is subjected to internal pressure P. Let (u_{r}^{M}, u_{θ}^{M}) and (σ_{rr}^{M}, σ_{θθ}^{M}) denote the radial and tangential displacement and stress components, respectively, in material M. Similarly (u_{r}^{N}, u_{θ}^{N}) and (σ_{rr}^{N}, σ_{θθ}^{N})denote the radial and tangential displacement and stress components, respectively, in material N. The boundary condition that need to be satisfied at the frictionless interface between the two cylinders are:
(a) u_{r}^{M} = u_{r}^{N} and σ_{rr}^{M} = σ_{rr}^{N }only.
(b) u_{r}^{M} = u_{r}^{N} and σ_{rr}^{M} = σ_{rr}^{N} and u_{θ}^{M} = u_{θ}^{N} and σ_{θθ}^{M} = σ_{θθ}^{N}
(c) u_{θ}^{M} = u_{θ}^{N} and σ_{θθ}^{M} = σ_{θθ}^{N}
(d) σ_{rr}^{M} = σ_{rr}^{N} and σ_{θθ}^{M} = σ_{θθ}^{N} only
(2 Mark, 2019[2])

Ans: a
Explanation: