# Strength of Materials - Civil Engineering Questions and Answers

Strength of Materials - Civil Engineering Questions and Answers

1. Modulus of rigidity is defined as the ratio of
a) longitudinal stress to longitudinal strain
b) shear stress to shear strain
c) stress to strain
d) stress to volumetric strain
Ans: b

2. If the Young's modulus of elasticity of a material is twice its modulus of rigidity, then the Poisson's ratio of the material is
a) -1
b) -0.5
c) 0.5
d) zero
Ans: d

3. Limit of proportionality depends upon
a) area of cross-section
c) type of material
d) all of the above
Ans: c

4. For an isotropic, homogeneous and elastic material obeying Hooke's law, number of independent elastic constants is
a) 2
b) 3
c) 9
d) 1
Ans: a

5. In a thin cylindrical shell, the ratio of longitudinal stress to hoop stress is
a) 0.5
b) 1
c) 2
d) 4
Ans: c

6. If all the dimensions of a prismatic bar are doubled, then the maximum stress produced in it under its own weight will
a) decrease
b) remain unchanged
c) increase to two times
d) increase to four times
Ans: c

7. The relationship between Young's, modulus of elasticity E, bulk modulus K and Poisson's ratio u is given by
a) E = 2K(l-2u.)
b) E = 3K(l + u)
c) E = 3K(l-2u)
d) E = 2K(l + u)
Ans: c

8. Limiting values of Poisson's ratio are
a) - 1 and 0.5
b) -land-0.5
c) 1 and - 0.5
d) 0 and 0.5
Ans: a

9. The elongation of a conical bar under its own weight is equal to
a) that of a prismatic bar of same length
b) one half that of a prismatic bar of same length
c) one third that of a prismatic bar of same length
d) one fourth that of a prismatic bar of same length
Ans: c

10. If a material has identical properties in all directions, it is said to be
a) homogeneous
b) isotropic
c) elastic
d) orthotropic
Ans: b

11. Two bars of different materials are of the same size and are subjected to same tensile forces. If the bars have unit elongations in the ratio of 4 : 7, then the ratio of moduli of elasticity of the two materials is
a) 7:4
b) 4:7
c) 4:17
d) 16 :49
Ans: a

12. A prismatic bar of volume V is subjected to a tensile force in longitudinal direction.
If Poisson's ratio of the material is u and longitudinal strain is e, then the final volume of the bar becomes
a) (l + e)(l-u)2V
b) (l-e)2(l + ue)V
c) (l + e)(l-ne)2V
d) (l-ue)3V
Ans: c

13. If a composite bar of steel and copper is heated, then the copper bar will be under
a) tension
b) compression
c) shear
d) torsion
Ans: b

14. Effective length of a weld is equal to
a) overall length - weld size
b) overall length - throat thickness
c) overall length - 2 x weld size
d) overall length - 2 x throat thickness
Ans: c

15. Size of a right angled fillet weld is given by
a) 0.707 x throat thickness
b) 0.414 x throat thickness
c) 2.0 x throat thickness
d) throat thickness
Ans: b

16. The effective length of a fillet weld designed to transmit axial load shall not be less than
a) 2 x size of weld
b) 4 x size of weld
c) 6 x size of weld
d) 10 x size of weld
Ans: b

17. Size of fillet weld with unequal legs is equal to
a) smaller leg length
b) longer leg length
c) throat thickness
d) average of smaller and longer leg lengths
Ans: a

18. Weakest section in a fillet weld is
a) throat of the fillet
b) smaller side
c) side parallel to force
d) side perpendicular to force
Ans: a

19. Effective throat thickness of a fillet weld is
a) 0.707 x size of weld
b) 1.414 x size of weld
c) a function of the angle between fusion faces
d) equal to the side of the fillet
Ans: c

20. According to Unwin's formula, the dia¬meter of rivet in mm to suit the t mm thickness of plate is given by
a) 6t
b) 6Vt
c) 1.9-y/t
d) 1.5 t+ 4
Ans: b

21. A flat carrying a pull of 69C kN is con-nected to a gusset plate using rivets. If the pulls required to shear the rivet, to crush the rivet and to tear the plate per pitch length are 68.5 kN, 46 kN and 69 kN respectively, then the number of rivets required is
a) 10
b) 12
c) 15
d) 20
Ans: c

22. If the rivet value is 16.8 kN and force in the member is 16.3 kN, then the number of rivets required for the connection of the member to a gusset plate is
a) 1
b) 2
c) 3
d) 4
Ans: b

23. At a point in a strained body carrying two unequal unlike principal stresses pi and p2 (Pi > P2X the maximum shear stress is given by
a) p,/2
b) p2/2
c) (p,-p2)/2
d) (p, + p2)/2
Ans: d

24. If a point in a strained material is subjected to equal normal and tangential stresses, then the angle of obliquity is
a) 0°
b) 45°
c) tan"1 (1/2)
d) tan"1 (2)
Ans: b

25. If a prismatic member with area of cross-section A is subjected to a tensile load P, then the maximum shear stress and its inclination with the direction of load respectively are
a) P/A and 45°
b) P/2Aand45°
c) P/2A and 60°
d) P/A and 30°
Ans: b

26. The sum of normal stresses is
a) constant
b) variable
c) dependent on the planes
d) none of the above
Ans: a

27. The radius of Mohr's circle for two equal unlike principal stresses of magnitude p is
a) p
b) p/2
c) zero
d) none of the above
Ans: a

28. Shear stress on principal planes is
a) zero
b) maximum
c) minimum
d) none of the above
Ans: a

29. The state of pure shear stress is produced by
a) tension in one direction and equal compression in perpendicular direction
b) equal tension in two directions at right angles
c) equal compression in two directions at right angles
d) none of the above
Ans: a

30. According to Rankine's hypothesis, the criterion of failure of a brittle material is
a) maximum principal stress
b) maximum shear stress
c) maximum strain energy
d) maximum shear strain energy
Ans: a

31. Maximum bending moment in a beam occurs where
a) deflection is zero
b) shear force is maximum
c) shear force is minimum
d) shear force changes sign
Ans: d

32. Rate of change of bending moment is equal to
a) shear force
b) deflection
c) slope
Ans: d

33. The diagram showing the variation of axial load along the span is called
a) shear force diagram
b) bending moment diagram
c) thrust diagram
d) influence line diagram
Ans: a

34. The difference in ordinate of the shear curve between any two sections is equal to the area under
a) load curve between these two sections
b) shear curve between these two sections
c) bending moment curve between these two sections
d) load curve between these two sections plus concentrated loads applied between the sections
Ans: d

35. The variation of the bending moment in the portion of a beam carrying linearly varying load is
a) linear
b) parabolic
c) cubic
d) constant
Ans: c

36. The maximum bending moment due to a moving load on a fixed ended beam occurs
a) at a support
b) always at the midspan
c) under the load only
d) none of the above
Ans: a

37. A cantilever beam AB of length 1 carries a concentrated load W at its midspan C. If the free end B is supported on a rigid prop, then there is a point of contraflexure
a) between A and C
b) between C and B
c) one between A and C and other between C and B
d) nowhere in the beam
Ans: a

38. A prismatic beam fixed at both ends carries a uniformly distributed load. The ratio of bending moment at the supports to the bending moment at mid-span is
a) 0.5
b) 1.0
c) 1.5
d) 2.0
Ans: d

39. A beam of overall length 1 with equal overhangs on both sides carries a uniformly distributed load over the entire length. To have numerically equal bending moments at centre of the beam and at supports, the distance between the supports should be
a) 0.2771
b) 0.403 1
c) 0.5861
d) 0.7071
Ans: c

40. A prismatic beam of length 1 and fixed at both ends carries a uniformly distributed load. The distance of points of contraflexure from either end is
a) 0.2071
b) 0.2111
c) 0.2771
d) 0.251
Ans: b

41. A simply supported beam of length 1 carries a load varying uniformly from zero at left end to maximum at right end. The maximum bending moment occurs at a distance of
a) 1/V3 from left end
b) 1/3 from left end
c) 1/V3 from right end
d) 1/3 from right end
Ans: a

42. A portion of a beam between two sections is said to be in pure bending when there is
a) constant bending moment and zero shear force
b) constant shear force and zero bending moment
c) constant bending moment and constant shear force
d) none of the above
Ans: a

43. The ratio of width to depth of a strongest beam that can be cut out of a cylindrical log of wood is
a) 1/2
b) 1/V2
c) 1/3
d) 2/3
Ans: b

44. Of the several prismatic beams of equal lengths, the strongest in flexure is the one having maximum
a) moment of inertia
b) section modulus
c) tensile strength
d) area of cross-section
Ans: b

45. Of the two prismatic beams of same material, length and flexural strength, one is circular and other is square in cross-section. The ratio of weights of circular and square beams is
a) 1.118
b) 1.342
c) 1.000
d) 0.793
Ans: a

46. A flitched beam consists of a wooden joist 150 mm wide and 300 mm deep strengthened by steel plates 10 mm thick
and 300 mm deep one on either side of the joist. If modulus of elasticity of steel is 20 times that of wood, then the width of equivalent wooden section will be
a) 150 mm
b) 350 mm
c) 500 mm
d) 550 mm
Ans: d

47. A beam of rectangular cross-section is 100 mm wide and 200 mm deep. If the section is subjected to a shear force of 20 kN, then the maximum shear stress in the section is
a) 1 N/mm2
b) 1.125 N/mm2
c) 1.33 N/mm2
d) 1.5 N/mm2
Ans: d

48. A beam of square cross-section with side 100 mm is placed with one diagonal vertical. If the shear force acting on the section is 10 kN, the maximum shear stress is
a) 1 N/mm2
b) 1.125 N/mm2
c) 2 N/mm2
d) 2.25 N/mm2
Ans: b

49. A prismatic bar when subjected to pure bending assumes the shape of
a) catenary
b) cubic parabola
d) arc of a circle
Ans: d

50. A beam of triangular cross section is placed with its base horizontal. The maximum shear stress intensity in the
section will be
a) at the neutral axis
b) at the base
c) above the neutral axis
d) below the neutral axis
Ans: c

51. A beam of uniform strength has at every cross-section same
a) bending moment
b) bending stress
c) deflection
d) stiffness
Ans: b

52. For no torsion, the plane of bending should
a) be parallel to one of the principal axes
b) pass through shear centre of section
c) pass through neutral axis of the section
d) pass through centre of gravity of the section
Ans: b

53. Two beams, one of circular cross-section and other of square cross-section, have equal areas of cross-section. If subjected to bending
a) circular section is more economical
b) square section is more economical
c) both sections are equally strong
d) both sections are equally stiff
Ans: b

54. The portion, which should be removed from top and bottom of a circular cross section of diameter d in order to obtain maximum section modulus, is
a) 0.01 d
b) 0.1 d
c) 0.011 d
d) 0.11 d
Ans: c

55. A beam of overall length / rests on two simple supports with equal overhangs on both sides. Two equal loads act at the free ends. If the deflection at the centre of the beam is the same as at either end, then the length of either overhang is
a) 0 152 1
b) 0.207 1
c) 0.252 1
d) 0.277 1
Ans: a

56. A beam ABC rests on simple supports at A and B with BC as an overhang. D is centre of span AB. If in the first case a concentrated load P acts at C while in the second case load P acts at D, then the
a) deflection at D in the first case will be equal to the deflection at C in the second case
b) deflection at C in the first case is equal to the deflection at D in the second case
c) deflection at D in the first case will always be smaller than the deflection at C in the second case
d) deflection at D in the first case will always be greater than the deflection at C in the second case
Ans: a

57. If the deflection at the free end of a uniformly loaded cantilever beam is 15mm and the slope of the deflection
curve at the free end is 0.02 radian, then the length of the beam is
a) 0.8 m
b) lm
c) 1.2 m
d) 1.5m
Ans: b

58. If the deflection at the free end of a uniformly loaded cantilever beam of length 1 m is equal to 7.5 mm, then the slope at the free end is
d) none of the above
Ans: c

58. A cantilever beam carries a uniformly distributed load from fixed end to the centre of the beam in the first case and a uniformly distributed load of same inten¬sity from centre of the beam to the free end in the second case. The ratio of deflections in the two cases is
a) 1/2
b) 3/11
c) 5/24
d) 7/41
Ans: d

59. If the length of a simply supported beam carrying a concentrated load at the centre is doubled, the defection at the centre will become
a) two times
b) four times
c) eight times
d) sixteen times
Ans: c

60. A simply supported beam with rectangular cross-section is subjected to a central concentrated load. If the width and depth of the beam are doubled, then the deflection at the centre of the beam will be reduced to
a) 50%
b) 25%
c) 12.5%
d) 6.25%
Ans: d

61. A laminated spring is given an initial curvature because
a) it is more economical
b) it gives uniform strength
c) spring becomes flat when it is subjec-ted to design load
d) none of the above
Ans: c

62. A laminated spring is supported at
a) ends and loaded at centre
b) centre and loaded at ends
c) ends and loaded anywhere
d) centre and loaded anywhere
Ans: b

63. Laminated springs are subjected to
a) direct stress
b) bending stress
c) shear stress
d) none of the above
Ans: b

64. Deflection in a leaf spring is more if its
a) strength is more
b) strength is less
c) stiffness is less
d) stiffness is more
Ans: c

65. Buckling load for a given column depends upon
a) length of column only
b) least lateral dimension only
c) both length and least lateral dimension
d) none of the above
Ans: c

66. When both ends of a column are fixed, the crippling load is P. If one end of the column is made free, the value of crippling load will be changed to
a) P/16
b) P/4
c) P/2
d) 4P
Ans: a

67. Euler's formula for a mild steel long column hinged at both ends is not valid for slenderness ratio
a) greater than 80
b) less than 80
c) greater than 180
d) greater than 120
Ans: b

68. A long column has maximum crippling load when its
a) both ends are hinged
b) both ends are fixed
c) one end is fixed and other end is hinged
d) one end is fixed and other end is free
Ans: b

69. Effective length of a chimney of 20 m height is taken as
a) 10 m
b) 20m
c) 28.28m
d) 40m
Ans: d

70. Rankine's formula for column is valid when slenderness ratio
a) lies between 0 and 140
b) lies between 0 and 100
c) is less than 80
d) has any value
Ans: d

71. Slenderness ratio of a 5 m long column hinged at both ends and having a circular cross-section with diameter 160 mm is
a) 31.25
b) 62.5
c) 100
d) 125
Ans: d

72. The effect of arching a beam is
a) to reduce bending moment throughout
b) to increase bending moment throughout
c) to increase shear force
d) to decrease shear force
Ans: a

73. Internal forces at every cross-section in a arch are
a) nornal thrust and shear force
b) shear force and bending moment
c) normal thrust and bending moment
d) normal thrust, shear force and bending moment
Ans: d

74. According to Eddy's theorem, the vertical intercept between the linear arch and the centre line of actual arch at any point represents to some scale
a) bending moment
b) shear force
c) normal thrust
d) deflection
Ans: a

75. Due to rise in temperature in a three hinged arch, induced stress is
a) direct compressive
b) direct tensile
c) shear
d) none of the above
Ans: d

76. In a three hinged arch, the linear and the actual arch meet at
a) at least three points
b) at least two points
d) nowhere
Ans: a

77. If a three hinged parabolic arch carries a uniformly distributed load over the entire span, then any section of the arch is subjected to
a) normal thrust only
b) normal thrust and shear force
c) normal thrust and bending moment
d) normal thrust, shear force and bending moment
Ans: a

78. Three hinged arch is
a) statically indeterminate by one degree
b) statically indeterminate by two degrees
c) statically determinate
d) unstable structure
Ans: c

79. A linear arch has
a) normal thrust only
b) shear force only
c) bending moment only
d) normal thrust and shear force
Ans: a

80. A three hinged arch is carrying uniformly distributed load over the entire span. The arch is free from shear force and bending moment if its shape is
a) circular
b) parabolic
c) elliptical
d) none of the above
Ans: b

81. For a determinate pin-jointed plane frame, the relation between the number of joints j and members m is given by
a) m = 2j - 3
b) m = 3j-6
c) m > 2j - 3
d) m > 3j - 6
Ans: a

82. The basic perfect frame is a
a) triangle
b) rectangle
c) square
d) hexagon
Ans: a

83. Method of joints is applicable only when the number of unknown forces at the joint under consideration is not more than
a) one
b) two
c) three
d) four
Ans: b

84. A short column of external diameter of 250 mm and internal diameter of 150 mm carries an eccentric load of 1000 kN. The greatest eccentricity which the load can have without producing tension anywhere is
a) 20 mm
b) 31.25 mm
c) 37.5 mm
d) 42.5 mm
Ans: d

85. Proof resilience is the maximum energy stored at
a) limit of proportionality
b) elastic limit
c) plastic limit
d) none of the above
Ans: b

86. Strain energy stored in a member is given by
a) 0.5 x stress x volume
b) 0.5 x strain x volume
c) 0.5 x stress x strain x volume
d) 0.5 x stress x strain
Ans: c

87. A rectangular block of size 200 mm x 100 mm x 50 mm is subjected to a shear stress of 100 N/mm2. If modulus of rigidity of material is 1 x 105 N/mm2, strain energy stored will be
a) 10 N.m
b) 25 N.m
c) 50 N.m
d) 100N.m
Ans: c

88. A steel rod of cross sectional area equal to 1000 mm2 is 5 m long. If a pull of 100 kN is suddenly applied to it, then the maximum stress intensity will be
a) 50 N/mm2
b) 100 N/mm2
c) 200 N/mm2
d) 400 N/mm2
Ans: c

89. If the depth of a beam of rectangular section is reduced to half, strain energy stored in the beam becomes
a) 1/4 time
b) 1/8 time
c) 4 times
d) 8 times
Ans: d

90. The specimen in a Charpy impact test is supported as a
a) cantilever beam
b) simply supported beam
c) fixed beam
d) continuous beam
Ans: b

91. Impact test enables one to estimate the property of
a) hardness
b) toughness
c) strength
d) creep
Ans: b

92. The phenomenon of decreased resistance of a material to reversal of stress is called
a) creep
b) fatigue
c) resilience
d) plasticity
Ans:

93. The property of metal which allows it to deform continuously at slow rate without any further increase in stress is known as
a) fatigue
b) creep
c) plasticity
d) resilience
Ans: b

94. The stress below which a material has a high probability of not failing under reversal of stress is known as
a) tolerance limit
b) elastic limit
c) proportional limit
d) endurance limit
Ans: b

95. A three hinged parabolic arch rib is acted upon by a single load at the left quarter point. If the central rise is increased and the shape of arch altered to segmental without changing the other details, the horizontal thrust will
a) increase definitely
b) decrease definitely
c) be difficult to predict
d) increase or decrease depending upon the radius of the segmental arch
Ans: b

96. For ductile materials, the most appropriate failure theory is
a) maximum shear stress theory
b) maximum principal stress theory
c) maximum principal strain theory
d) shear strain energy theory
Ans: a

97. At a point in a steel member, the major principal stress is 2000 kg/cm2 and the minor principal stress is compressive. If the uni-axial tensile yield stress is 2500 kg/cm2, then the magnitude of the minor principal stress at which yielding will commence, according to the maximum shearing stress theory, is
a) 1000 kg/cm2
b) 2000 kg/cm2
c) 2500 kg/cm2
d) 500 kg/cm2
Ans: d

98. For the design of a cast iron member, the most appropriate theory of failure is
a) Mohr's theory
b) Rankine's theory
c) Maximum strain theory
d) Maximum shear energy theory
Ans: b