1. A tapered cantilever beam of constant thickness is loaded as shown in the sketch below. The bending stress will be
(a) maximum near the fixed end
(b) maximum at x = \frac { 1 }{ 2 } L
(c) maximum at x = \frac { 2 }{ 3 } L
(d) Uniform throughout the length
(2 Mark, 1988)

Ans: d
Explanation:
2. For a simply supported beam on two end supports the bending moment is maximum
(a) usually on the supports
(b) always at mid span
(c) where there is no shear force
(d) where the deflection is maximum
(1 Mark, 1989)

Ans: c
3. A block of steel is loaded by a tangential force on its top surface while the bottom surface is held rigidly. The deformation of the block is due to
(a) shear only
(b) bending only
(c) shear and bending
(d) torsion
(1 Mark, 1992)

Ans: c
4. A circular rod of diameter d and length 3d is subjected to a compressive force F acting at the top point as shown below. Calculate the stress at the bottom most support point A.
(a) \frac { 12F }{ \pi { d }^{ 2 } }
(b) \frac { 16F }{ \pi { d }^{ 2 } }
(c) \frac { 4F }{ \pi { d }^{ 2 } }
(d) \frac { 12F }{ \pi { d }^{ 2 } }
(2 Mark, 1993)

Ans: a
5. The compound shaft shown is builtin at the two ends. It is subjected to a twisting moment T at the middle. What is the ratio of the reaction torques T_{1} and T_{2} at the ends?
(a) \frac { 1 }{ 16 }
(b) \frac { 1 }{ 8 }
(c) \frac { 1 }{ 4 }
(d) \frac { 1 }{ 2 }
(2 Mark, 1993)

Ans: a
6. Two shafts A and B are made of the same material. The diameter of shaft B is twice that of shaft A. The ratio of power which can be transmitted by shaft A to that of shaft B is:
(a) \frac { 1 }{ 2 }
(b) \frac { 1 }{ 4 }
(c) \frac { 1 }{ 8 }
(d) \frac { 1 }{ 16 }
(2 Mark, 1993)

Ans: c
6. The outside diameter of a hollow shaft is twice its inside diameter. The ratio of its torque carrying capacity to that of a solid shaft of the same material and the same outside diameter is
(a) 15/16
(b) 3/4
(c) 1/2
(d) 1/16
(1 Mark, 1993)

Ans: a
Explanation:
7. A solid shaft can resist a bending moment of 3.0 kNm and a twisting moment of 4.0 kNm together, then the maximum torque that can be applied is:
(a) 7.0 kNm
(b) 3.5 kNm
(c) 4.5 kNm
(d) 5.0 kNm
(1 Mark, 1996)

Ans: d
Explanation:
8. The second moment of a circular area about the diameter is given by (D is the diameter)
(a) \frac { \pi { D }^{ 4 } }{ 4 }
(b) \frac { \pi { D }^{ 4 } }{ 16 }
(c) \frac { \pi { D }^{ 4 } }{ 32 }
(d) \frac { \pi { D }^{ 4 } }{ 64 }
(1 Mark, 2003)

Ans: d
9. Maximum shear stress developed on the surface of a solid circular shaft under pure torsion is 240 MPa. If the shaft diameter is doubled then the maximum shear stress developed corresponding to the same torque will be
(a) 120 MPa
(b) 60 MPa
(c) 30 MPa
(d) 15 MPa
(1 Mark, 2003)

Ans: c
10. A concentrated load P acts on a simply supported beam of span L at a distance L/3 from the left support. The bending moment at the point of application of the load is given by
(a) \frac { PL }{ 3 }
(b) \frac { 2PL }{ 3 }
(c) \frac { PL }{ 9 }
(d) \frac { 2PL }{ 9 }
(1 Mark, 2003)

Ans: d
11. Two beams, one having square cross section and another circular crosssection, are subjected to the same amount of bending moment. If the cross sectional area as well as the material of both the beams are the same then
(a) maximum bending stress developed in both the beams is the same
(b) the circular beam experiences more bending stress that the square one
(c) the square beam experiences more bending stress than the circular one
(d) as the material is same both the beams will experience same deformation
(1 Mark, 2003)

Ans: b
12. A simply supported laterally loaded beam was found to deflect more than a specified value. Which of the following measures will reduce the deflection?
(a) Increase the area moment of inertia
(b) Increase the span of the beam
(c) Select a different material having lesser modulus of elasticity
(d) Magnitude of the load to be increased
(2 Mark, 2003)

Ans: a
13. A torque of 10 Nm is transmitted through a stepped shaft as shown in figure. The torsional stiffnesses of individual sections of lengths MN, NO and OP are 20 Nm/rad, 30 Nm/rad and 60 Nm respectively. The angular deflection between the ends M and P of the shaft is
(a) 0.5 rad
(b) 1.0 rad
(c) 5.0 rad
(d) 10.0 rad
(1 Mark, 2004)

Ans: b
14. A solid circular shaft of 60 mm diameter transmits a torque of 1600 N.m. The value of maximum shear stress develop is
(a) 37.72 MPa
(b) 47.72 MPa
(c) 57.72 MPa
(d) 67.72 MPa
(2 Mark, 2004)

Ans: a
Data for Q.1516 are given below.
A steel beam of breadth 120 mm and height 750 mm is loaded as shown in the figure. Assume E_{steel} = 200 GPa.
15. The beam is subjected to a maximum bending moment of
(a) 3375 kNm
(b) 4750 kNm
(c) 6750 kNm
(d) 8750 kNm
(2 Mark, 2004)

Ans: a
16. The value of maximum deflection of the beam is
(a) 93.75 mm
(b) 83.75 mm
(c) 73.75 mm
(d) 63.75 mm
(2 Mark, 2004)

Ans: a
17. Two identical cantilever beams are supported as shown, with their free ends in contact through a rigid roller. After the load P is applied, the free ends will have
(a) equal deflections but not equal slopes
(b) equal slopes but not equal deflections
(c) equal slopes as well as equal deflections
(d) neither equal slopes nor equal deflections
(1 Mark, 2005)

Ans: a
19. A cantilever beam carries the antisymmetric load shown, where w_{o} is the peak intensity of the distributed load. Qualitatively, the correct bending moment diagram for this beam is
(2 Mark, 2005)

Ans: c
20. A cantilever beam has the square cross section of 10 mm × 10 mm. It carries a transverse load of 10 N. considering only the bottom fibres of the beam, the correct representation of the longitudinal variation of the bending stress is
(2 Mark, 2005)

Ans: a
21. The two shafts AB and BC, of equal length and diameters d and 2d, are made of the same material. They are joined at B through a shaft coupling, while the ends A and C are builtin (cantilevered). A twisting moment T is applied to the coupling. If T_{A} and T_{C} represent the twisting moments at the ends A and C, respectively, then
(a) T_{C} = T_{A}
(b) T_{C} = 8T_{A}
(c) T_{C} = 16T_{A}
(d) T_{A} = 16T_{C}
(2 Mark, 2005)

Ans: c
Statement for Linked Answer Questions 22 & 23:
A simply supported beam of span length 6 m and 75 mm diameter carries a uniformly distributed load of 1.5 kN/m.
22. What is the maximum value of bending moment?
(a) 9 kNm
(b) 6.75 kNm
(c) 81 kNm
(d) 125 kNm
(2 Mark, 2006)

Ans: b
23. What is the maximum value of bending stress?
(a) 162.98 MPa
(b) 325.95 MPa
(c) 625.95 MPa
(d) 651.90 MPa
(2 Mark, 2006)

Ans: a
24. For a circular shaft of diameter d subjected to torque T, the maximum value of the shear stress is:
(a) \frac { 64T }{ \pi { d }^{ 3 }}
(b) \frac { 32T }{ \pi { d }^{ 3 } }
(c) \frac { 16T }{ \pi { d }^{ 3 } }
(d) \frac { 8T }{ \pi { d }^{ 3 } }
(1 Mark, 2006)

Ans: c
25. In a simplysupported beam loaded as shown below, the maximum bending moment in Nm is
(b) 30
(c) 35
(d) 60
(1 Mark, 2007)

Ans: b
26. A uniformly loaded propped cantilever beam and its free body diagram are shown below. The reactions are
(a) R_{1} = \frac { 5qL }{ 8 } , R_{2} = \frac { 3qL }{ 8 } , M = \frac { q{ L }^{ 2 } }{ 8 }
(b) R_{1} = \frac { 3qL }{ 8 } , R_{2} = \frac { 5qL }{ 8 } , M = \frac { q{ L }^{ 2 } }{ 8 }
(c) R_{1} = \frac { 5qL }{ 8 } , R_{2} = \frac { 3qL }{ 8 } , M = 0
(d) R_{1} = \frac { 3qL }{ 8 }, R_{2} = \frac { 5qL }{ 8 } , M = 0
(2 Mark, 2007)

Ans: a
Statement for Linked Answer Questions 27 and 28:
A machine frame shown in the figure below is subjected to a horizontal force of 600 N parallel to Z direction.
27. The normal and shear stresses in MPa at point P are respectively
(a) 67.9 and 56.6
(b) 56.6 and 67.9
(c) 67.9 and 0.0
(d) 0.0 and 56.6
(2 Mark, 2007)

Ans: a
28. The maximum principal stress in MPa and the orientation of the corresponding principal plane in degrees are respectively
(a) 32.0 and 29.52
(b) 100.0 and 60.48
(c) 32.0 and 60.48
(d) 100.0 and 29.52
(2 Mark, 2007)

Ans: b
29. The transverse shear stress acting in a beam of rectangular crosssection, subjected to a transverse shear load, is
(a) variable with maximum at the bottom of the beam
(b) variable with maximum at the top of the beam
(c) uniform
(d) variable with maximum of the neutral axis
(1 Mark, 2008)

Ans: d
30. An axial residual compressive stress due to a manufacturing process is present on the outer surface of a rotating shaft subjected to bending. Under a given bending load, the fatigue life of the shaft in the presence of the residual compressive stress is
(a) decreased
(b) increased or decreased, depending on the external bending load
(c) neither decreased nor increased
(d) increased
(1 Mark, 2008)

Ans: d
31. For the component loaded with a force F as shown in the figure, the axial stress at the corner point P is
(a) \frac { F(3Lb) }{ 4{ b }^{ 3 } }
(b) \frac { F(3L+b) }{ 4{ b }^{ 3 } }
(c) \frac { F(3L4b) }{ 4{ b }^{ 3 } }
(d) \frac { F(3L2b) }{ 4{ b }^{ 3 } }
(2 Mark, 2008)

Ans: d
32. A solid circular shaft of diameter 100 mm is subjected to an axial stress of 50 Mpa. It is further subjected to a torque of 10 kNm. The maximum principal stress experienced on the shaft is closest to
(a) 41 MPa
(b) 82 MPa
(c) 164 MPa
(d) 204 MPa
(2 Mark, 2008)

Ans: b
33. The strain energy stored in the beam with flexural rigidity EI and loaded as shown in the figure is
(a) \frac { { P }^{ 2 }{ L }^{ 3 } }{ 3EI }
(b) \frac { { 2P }^{ 2 }{ L }^{ 3 } }{ 3EI }
(c) \frac { { 4P }^{ 2 }{ L }^{ 3 } }{ 3EI }
(d) \frac { { 2P }^{ 2 }{ L }^{ 3 } }{ 3EI }
(2 Mark, 2008)

Ans: c
34. A frame of two arms of equal length L is shown in the adjacent figure. The flexural rigidity of each arm of the frame is EI. The vertical deflection at the point of application of load P is
(a) \frac { P{ L }^{ 3 } }{ 3EI }
(b) \frac { 2P{ L }^{ 3 } }{ 3EI }
(c) \frac { P{ L }^{ 3 } }{ EI }
(d) \frac { 4P{ L }^{ 3 } }{ 3EI }
(2 Mark, 2009)

Ans: d
35. A solid shaft of diameter, d and length L is fixed at both the ends. A torque, T_{0} is applied at a distance, L/4 from the left end as shown in the figure given below.
The maximum shear stress in the shaft is
(a) \frac { 16{ T }_{ 0 } }{ \pi { d }^{ 3 } }
(b) \frac { 12{ T }_{ 0 } }{ \pi { d }^{ 3 } }
(c) \frac { 8{ T }_{ 0 } }{ \pi { d }^{ 3 } }
(d) \frac { 4{ T }_{ 0 } }{ \pi { d }^{ 3 } }
(2 Mark, 2009)

Ans: b
Statement for Linked Answer Questions: 36 & 37.
A massless beam has a loading pattern as shown in the figure. The beam is of rectangular crosssection with a width of 30 mm and height of 100 mm.
36. The maximum bending moment occurs at
(a) Location B
(b) 2675 mm to the right of A
(c) 2500 mm to the right of A
(d) 3225 mm to the right of A
(2 Mark, 2010)

Ans: c
37. The maximum magnitude of bending stress (in MPa) is given by
(a) 60.0
(b) 67.5
(c) 200.0
(d) 225.0
(2 Mark, 2010)

Ans: b
38. A simply supported beam PQ is loaded by a moment of 1 kNm at the midspan of the beam as shown in the figure. The reaction forces R_{P} and R_{Q} at supports P and Q respectively are
(a) 1 kN downward, 1 kN upward
(b) 0.5 kN upward, 0.5 kN downward
(c) 0.5 kN downward, 0.5 kN upward
(d) 1 kN upward, 1 kN upward
(1 Mark, 2011)

Ans: a
Explanation:
39. A torque T is applied at the free end of a stepped rod of circular crosssections as shown in the figure. The shear modulus of the material of the rod is G. The expression for d to produce an angular twist θ at the free end is
(a) { \left( \frac { 32TL }{ \pi \theta G } \right) }^{ \frac { 1 }{ 4 } }
(b) { \left( \frac { 18TL }{ \pi \theta G } \right) }^{ \frac { 1 }{ 4 } }
(c) { \left( \frac { 16TL }{ \pi \theta G } \right) }^{ \frac { 1 }{ 4 } }
(d) { \left( \frac { 2TL }{ \pi \theta G } \right) }^{ \frac { 1 }{ 4 } }
(2 Mark, 2011)

Ans: b
Explanation:
Statement for Linked Answer Questions: 40 & 41.
A triangular–shaped cantilever beam of uniform–thickness is shown in the figure. The Young’s modulus of the material of the beam is E. A concentrated load P is applied at the free end of the beam.
40. The area moment of inertia about the neutral axis of a crosssection at a distance x measured from the free end is
(a) \frac { bx{ t }^{ 3 } }{ 6l }
(b) \frac { bx{ t }^{ 3 } }{ 12l }
(c) \frac { bx{ t }^{ 3 } }{ 24l }
(d) \frac { x{ t }^{ 3 } }{ 12l }
(2 Mark, 2011)

Ans: b
Explanation:
41. The maximum deflection of the beam is
(a) \frac { 24P{ l }^{ 3 } }{ Eb{ t }^{ 3 } }
(b) \frac { 12P{ l }^{ 3 } }{ Eb{ t }^{ 3 } }
(c) \frac { 8P{ l }^{ 3 } }{ Eb{ t }^{ 3 } }
(d) \frac { 6P{ l }^{ 3 } }{ Eb{ t }^{ 3 } }
(2 Mark, 2011)

Ans: d
Explanation:
42. A cantilever beam of length L is subjected to a moment M at the free end. The moment of inertia of the beam cross section about the neutral axis is I and the Young’s modulus is E. The magnitude of the maximum deflection is
(a) \frac { M{ L }^{ 2 } }{ 2EI }
(b) \frac { M{ L }^{ 2 } }{ EI }
(c) \frac { 2M{ L }^{ 2 } }{ EI }
(d) \frac { 4M{ L }^{ 2 } }{ EI }
(1 Mark, 2012)

Ans: a
Explanation:
43. A simply supported beam of length L is subjected to a varying distributed load sin (3πx/L) Nm^{1}, where the distance x is measured from the left support. The magnitude of the vertical reaction force in N at the left support is
(a) zero
(b) L/3π
(c) L/π
(d) 2L/π
(2 Mark, 2013)

Ans: b
Explanation:
45. The flexural rigidity (EI) of a cantilever beam is assumed to be constant over the length of the beam shown in figure. If a load P and bending moment PL/2 are applied at the free end of the beam then the value of the slope at the free end is
(a) \frac { 1 }{ 2 } \frac { { PL }^{ 2 } }{ EI }
(b) \frac { { PL }^{ 2 } }{ EI }
(c) \frac { 3 }{ 2 } \frac { { PL }^{ 2 } }{ EI }
(d) \frac { 5 }{ 2 } \frac { { PL }^{ 2 } }{ EI }
(2 Mark, 2014[2])

Ans: b
Explanation:
46. A cantilever beam of length, L, with uniform crosssection and flexural rigidity, EI, is loaded uniformly by a vertical load, w per unit length. The maximum vertical deflection of the beam is given by
(a) \frac { { wL }^{ 4 } }{ 8EI }
(b) \frac { { wL }^{ 4 } }{ 16EI }
(c) \frac { { wL }^{ 4 } }{ 4EI }
(d) \frac { { wL }^{ 4 } }{ 24EI }
(2 Mark, 2014[2])

Ans: a
Explanation:
47. Consider a simply supported beam of length, 50h, with a rectangular crosssection of depth, h, and width, 2h. The beam carries a vertical point load, P, at its midpoint. The ratio of the maximum shear stress to the maximum bending stress in the beam is
(a) 0.02
(b) 0.10
(c) 0.05
(d) 0.01
(2 Mark, 2014[3])

Ans: d
Explanation:
49. Two solid circular shafts of radii R_{1} and R_{2} are subjected to same torque. The maximum shear stresses developed in the two shafts are τ_{1} and τ_{2}. If R_{1}/R_{2} = 2, then τ_{2}/ τ_{1} is ____.
(1 Mark, 2014[3])

Ans: 8
Explanation:
50. A frame is subjected to a load P as shown in the figure. The frame has a constant flexural rigidity EI. The effect of axial load is neglected. The deflection at point A due to the applied load P is
(a) \frac { 1 }{ 3 } \frac { { PL }^{ 3 } }{ EI }
(b) \frac { 2 }{ 3 } \frac { { PL }^{ 3 } }{ EI }
(c) \frac { { PL }^{ 4 } }{ EI }
(d) \frac { 4 }{ 3 } \frac { { PL }^{ 3 } }{ EI }
(2 Mark, 2014[4])

Ans: d
Explanation:
54. A cantilever beam with square crosssection of 6 mm side is subjected to a load of 2 kN normal to the top surface as shown in the figure. The Young’s modulus of elasticity of the material of the beam is 210 GPa. The magnitude of slope (in radian) at Q (20 mm from the fixed end) is ______.
(2 Mark, 2015[2])

Ans: 0.158
Explanation:
55. A hollow shaft (d_{o} = 2d_{i} where d_{o} and d_{i} are the outer and inner diameters respectively) needs to transmit 20 kW power at 3000 RPM. If the maximum permissible shear stress is 30 MPa, d_{o} is
(a) 11.29 mm
(b) 22.58 mm
(c) 33.87 mm
(d) 45.16 mm
(2 Mark, 2015[2])

Ans: b
Explanation:
56. A hollow shaft of 1 m length is designed to transmit a power of 30 kW at 700 rpm. The maximum permissible angle of twist in the shaft is 1°. The inner diameter of the shaft is 0.7 times the outer diameter. The modulus of rigidity is 80 GPa. The outside diameter (in mm) of the shaft is___.
(2 Mark, 2015[2])

Ans: 44.5213
Explanation:
59. A cantilever beam having square crosssection of side a is subjected to an end load. If a is increased by 19%, the tip deflection decreases approximately by
(a) 19%
(b) 29%
(c) 41%
(d) 50%
(1 Mark, 2016[1])

Ans: d
Explanation:
60. The cross sections of two hollow bars made of the same material are concentric circles as shown in the figure. It is given that r_{3} > r_{1 }and r_{4} > r_{2}, and that the areas of the crosssections are the same, J_{1} and J_{2} are the torsional rigidities of the bars on the left and right, respectively. The ratio J_{2}/J_{1} is
(a) > 1
(b) < 0.5
(c) =1
(d) between 0.5 and 1
(1 Mark, 2016[1])

Ans: a
Explanation:
61. A simplysupported beam of length 3L is subjected to the loading shown in the figure.
It is given that P = 1 N, L = 1 m and Young’s modulus E = 200 GPa. The crosssection is a square with dimension 10 mm × 10 mm. The bending stress (in Pa) at the point A located at the top surface of the beam at a distance of 1.5L from the left end is ________.
(Indicate compressive stress by a negative sign and tensile stress by a positive sign.)
(2 Mark, 2016[1])

Ans: 0
Explanation:
62. A rigid horizontal rod of length 2L is fixed to a circular cylinder of radius R as shown in the figure. Vertical forces of magnitude P are applied at the two ends as shown in the figure. The shear modulus for the cylinder is G and the Young’s modulus is E.
The vertical deflection at point A is
(a) P{ L }^{ 3 }/(\pi { R }^{ 4 }G)
(b) P{ L }^{ 3 }/(\pi { R }^{ 4 }E)
(c) 2P{ L }^{ 3 }/(\pi { R }^{ 4 }E)
(d) 4P{ L }^{ 3 }/(\pi { R }^{ 4 }G)
(2 Mark, 2016[2])

Ans: d
Explanation:
64. A machine element XY, fixed at end X, is subjected to an axial load P, transverse load F, and a twisting moment T at its free end Y. The most critical point from the strength point of view is
(a) a point on the circumference at location Y
(b) a point at the center at location Y
(c) a point on the circumference at location X
(d) a point at the center at location X
(1 Mark, 2016[2])

Ans: c
Explanation:
65. A simply supported beam of length 2L is subjected to a moment M at the midpoint x = 0 as shown in the figure. The deflection in the domain 0 ≤ x ≤ L is given by w = \frac { Mx }{ 12EIL } (L – x)(x + c)
Where, E is the Young’s modulus, I is the area moment of inertia and c is a constant (to be determined) .
The slope at the center x = 0 is
(a) ML/(2EI)
(b) ML/(3EI)
(c) ML/(6EI)
(d) ML/(12EI)
(2 Mark, 2016[2])

Ans: c
Explanation:
66. The crosssections of two solid bars made of the same material are shown in the figure. The square crosssection has flexural (bending) rigidity I_{1}, while the circular crosssection has flexural rigidity I_{2}. Both sections have the same crosssectional area. The ratio I_{1}/I_{2} is
(a) 1/\pi
(b) 2/\pi
(c) \pi /3
(d) \pi /6
(1 Mark, 2016[3])

Ans: c
Explanation:
67. Two circular shafts made of same material, one solid (S) and one hollow (H), have the same length and polar moment of inertia. Both are subjected to same torque. Here, θ_{S} is the twist and τ_{S} is the maximum shear stress in the solid shaft, whereas θ_{H} is the twist and τ_{H} is the maximum shear stress in the hollow shaft. Which one of the following is TRUE?
(a) θ_{S} = θ_{H }and τ_{S} = τ_{H}
(b) θ_{S} > θ_{H }and τ_{S} > τ_{H}
(c) θ_{S} < θ_{H }and τ_{S} < τ_{H}
(d) θ_{S} = θ_{H }and τ_{S} < τ_{H}
(2 Mark, 2016[3])

Ans: d
Explanation:
68. A beam of length L is carrying a uniformly distributed load w per unit length. The flexural rigidity of the beam is EI. The reaction at the simple support at the right end is
(a)\frac { wL }{ 2 }
(b) \frac { 3wL }{ 8 }
(c) \frac { wL }{ 4 }
(d) \frac { wL }{ 8 }
(2 Mark, 2016[3])

Ans: b
Explanation:
69. Consider a beam with circular crosssection of diameter d. The ratio of the second moment of area about the neutral axis to the section modulus of the area is _____.
(a) \frac { d }{ 2 }
(b) \frac { \pi d }{ 2 }
(c) d
(d) πd
(1 Mark, 2017[1])

Ans: a
Explanation:
70. A motor driving a solid circular steel shaft transmits 40 kW of power at 500 rpm. If the diameter of the shaft is 40 mm, the maximum shear stress in the shaft is _______ MPa.
(1 Mark, 2017[1])

Ans: 60.79
Explanation:
71. For a loaded cantilever beam of uniform crosssection, the bending moment (in Nmm) along the length is M(x) = 5x^{2} + 10x, where x is the distance (in mm) measured from the free end of the beam. The magnitude of shear force (in N) in the crosssection at x = 10 mm is _____.
(1 Mark, 2017[2])

Ans: 110
Explanation:
72. 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: