Strength of materials (Objective Questions)

CAREER LAUNCHER SERIES
MECHANICAL ENGINEERING
(OBJECTIVE QUESTIONS)
OVER 4500 MCQs
FOR SSC-JE/PSU/GATE/ESE EXAMS
Edition: October, 2024
By AP Experts
A team of scholars and retired faculty from IIR, Roorkee
Aarushi Publications
India
See catalogue of books at:
https://www.aarushipublications.in
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CONTENT
(Use bookmarks to navigate)
Chapter 1 Engineering Mechanics
Chapter 2 Strength of Materials
Chapter 3 Theory and Design of Machines
Chapter 4 Fluid Mechanics and Machinery
Chapter 5 Thermodynamics
Chapter 6 Internal Combustion Engines
Chapter 7 Production Engineering
Chapter 8 Refrigeration
Chapter 9 Engineering Materials
Chapter 10 Power Plant Engineering
Chapter 11 Workshop Technology
Chapter 12 Heat Transfer
Every chapter contains:
• Warm Up Questions
• Questions from SSC-JE/PSU exams
• Questions from ESE (formerly IES) exams
• Questions from GATE exams

STRENGTH OF MATERIALS
WARM UP QUESTIONS
1. A material having identical properties in all
directions, is called
(a) elastic
(b) homogeneous
(c) isotropic*
(d) all the above
2. The ratio of unit stress to unit strain is called
(a) modulus of elasticity
(b) Young’s modulus
(c) both(a) and(b) *
(d) neither(a) nor(b)
3. The region in the stress-strain curve extending
from origin to proportional limit is called
(a) plastic range
(b) elastic range*
(c) semi plastic range
(d) semi elastic range
4. In a stress strain curve there is a point at
which there is increase in strain with no increase
in stress. This point is called
(a) point of failure
(b) point of rupture
(c) yield point*
(d) none of these
5. The work done on a unit volume of material,
as simple tensile force is gradually increased
from zero to such a value that the proportional
limit of the material is reached, is called
(b) modulus of toughness
(c) modulus of resilience*
(d) none of these
6. The work done on a unit volume of material,
as simple tensile force is gradually increased
from zero to a value causing rupture, is called
(b) modulus of toughness*
(c) modulus of resilience
(d) none of these
7.The unit of modulus of resilience is
(a) N-m-2
(b) Nm-m-3
(c) N-m-3
*
(d) none of these
8. For most metals, Poisson’s ratio() lies in the
range
(a) 0.1 to 0.9
(b) 0.05 to 0.1
(c) 1 to 10
(d) 0.25 to 0.35*
9. If a material contains same elastic properties
in all directions at any point of the body then it
is called
(a) anisotropic
(b) orthotropic
(c) isotropic*
(d) none of these
10. A round steel bar of overall length 40 cm
consists of two equal portions of 20 cm each
having diameters of 10 cm and 8 cm
respectively, If the rod is subjected to a tensile
load of 10 tonnes, the elongation will be given
by(E = 2 x 106
kg/cm2
)
(a)
1 1 1
cm
10 25 16
 
+
 
  
*
(b)
2 1 1
cm
10 25 16
 
+
 
  
(c)
3 1 1
cm
10 25 16
 
+
 
  
(d)
4 1 1
cm
10 25 16
 
+
 
  
11. A mild steel bar is in two parts having equal
lengths. The area of cross section of Part I is
double that of Part II. If the bar carries an axial
load P, then the ratio of elongation in Part I to
that in Part II will be
(a) 2
(b) 4

2.2
CAREER LAUNCHER SERIES | STRENGTH OF MATERIALS
(c) 1/2*
(d) 1/4
12. A tapering bar which is uniformly tapered
from diameter d1 to d2 in length L, is subject to a
force P. The elongation will be
(a)
1 2
PL
Ed d

(b)
1 2
2PL
Ed d

(c)
1 2
4PL
Ed d

*
(d) none of these
13. A round bar of steel tapers uniformly from a
diameter of 2.5 cm to 3.5 cm in length of 50 cm.
If an axial force of 60,000 N is applied at each
end, the elongation of bar will be(take E = 205
kN/mm2
)
(a) 0.426 mm
(b) 0.213 mm*
(c) 0.106 mm
(d) none of these
14. A bar of length L and constant cross
section(A) is hanging vertically. What would be
total increase in length due to self-weight(W)?
(a) WL/AE
(b) 2WL/AE
(c) WL/2AE*
(d) none of these
(d)
WL PL
AE 2AE
+
15. A steel wire 6 mm in diameter is used for
hoisting purposes in building construction. If
150 m of the wire is hanging vertically, and a
load of 1 kN is being lifted at the lower end of
the wire, what would be total elongation of the
wire. The weight density of steel is 7.7 x 104
Nm-3
and E = 200 GNm-2
.
(a) 26.5 mm
(b) 4.33 mm
(c) 30.88 mm*
(d) none of these
16. There is bar of tapering section having
diameter d at one end and 0 at other end. The
elongation due to self weight will be
(a) 2
2WL
d E

*
(b) 2
4WL
d E

(c) 2
WL
d E

(d) none of these
17. A mild steel bar is in three parts, each 20 cm
long. The diameters of parts AB, BC and CD are
2 cm, 1 cm, and 3 cm respectively. the bar is
subjected to an axial pull of 4t as shown in the
given figure. If E = 2 x 106
kg/cm2
and the
elongations in the three parts of the bar are 1,
2, and 3 respectively, then the ratio of the
greatest to the least of these elongations will be
(a) 9*
(b) 4
(c) 3
(d) 2
18. A square bar 50 mm on a side and 1 m long
is subject to an axial tensile force of 250 kN. E =
200 GNm-2
and  = 0.3. The decrease in lateral
dimension will be
(a) 1.5 x 10-4
mm
(b) 7.5 x 10-3
mm*
(c) 5 x 10-4
mm
(d) none of these
19. A three dimensional rectangular block is
stressed in x direction by a stress x. The change
of volume per unit volume due to this loading is
(a) x
V
(1 2 )e
V

= −  *
(b) x
V
(1 )e
V

= −
(c) x
V
(1 3 )e
V

= − 
(d) none of these
where ex is strain in x direction.

2.3
20. A bar of uniform section is subjected to axial
tensile loads such that the normal strain in the
axial direction is 1.25 mm per m. If the
Poisson’s ratio of the material of the bar is 0.3,
the volumetric strain would be
(a) 2 x 10-4
(b) 3 x 10-4
(c) 4 x 10-4
(d) 5 x 10-4
*
21. A square bar of aluminium 50 mm on a side
and 250 mm long is loaded by axial tensile
forces at the ends. The strain in the direction of
the load is 0.001. Considering  = 0.33, the
volume of the bar when the load is acting will be
(a) 6.25 x 105
mm3
(b) 6.252125 x 105
mm3
*
(c) 6.247875 x 105
mm3
(d) none of these
22. If x y z
e e e e
= + + where e is total strain,
then
(a) x x
E E
e e
(1 )(1 2 ) 1

 = +
+ −  +
(b) y y
E E
e e
(1 )(1 2 ) 1

 = +
+ −  +
(c) z z
E E
e e
(1 )(1 2 ) 1

 = +
+ −  +
(d) all the above*
23. For an isotropic material, the number of
independent material constants are
(a) 1
(b) 2
(c) 3
(d) 4*
24. In an experiment it is found that the bulk
modulus of a material is equal to its shear
modulus. The Poisson’s ratio is
(a) 0.125*
(b) 0.250
(c) 0.375
(d) 0.500
25. A given material has Young’s modulus E,
modulus of rigidity G and Poisson’s ratio 0.25.
The ratio of Young’s modulus to modulus of
rigidity of the material is
(a) 3.75
(b) 3
(c) 2.5*
(d) 1.5
26. The bulk modulus of elasticity of a material
is twice its modulus of rigidity. The Poisson’s
ratio of the material is
(a) 1/7
(b) 2/7*
(c) 3/7
(d) 4/7
27. A cylindrical bar of 20 mm diameter and 1 m
length is subjected to a tensile test. Its
longitudinal strain is 4 times that of its lateral
strain. If the modulus of elasticity is 2 x 105
N/mm2
, then its modulus of rigidity is
(a) 8 x 106
N/mm2
(b) 8 x 105
N/mm2
(c) 0.8 x 104
N/mm2
(d) 0.8 x 105
N/mm2
*
28. What would be the height to which a vertical
concrete wall may be built given an ultimate
compressive strength of 16 MPa and a safety
factor of 4? The weight density of concrete is 20
kNm-3
.
(a) 50 m
(b) 100 m
(c) 150 m
(d) 200 m*
29. What would be elongation of a conical bar of
circular cross section if it is suspended
vertically? Given that length = L, diameter = D,
weight density = , and modulus of elasticity =
E.
(a)
3
L
6E

(b)
2
L
6E

*
(c)
2
L
E

(d) none of these

2.4
30. Consider a state of stress of an element in
which a stress x is exerted in one direction and
lateral contraction is completely restrained in
each of the other two directions. The effective
modulus of elasticity will be
(a)
E(1 )
(1 2 )(1 )
−
−  + 
*
(b)
E(1 )
(1 )
−
+ 
(c) E(1-)
(d) none of these
31. In the above problem, what will be effective
Poisson’s ratio?
(a) 1
(b) 0.75
(c) 0.25
(d) 0*
32. A bar of uniform cross section is subject to
uniaxial tension and develops a strain in the
direction of the force of 1/800. Assuming  =
1/3, the change of volume per unit volume will
be
(a) 1/1000
(b) 1/1200
(c) 1/2400*
(d) 1/4800
33. A straight aluminium bar of diameter 30 mm
is subject to an axial tensile force of 50 kN. If E
= 70 GNm-2
and  = 1/4 then change in diameter
will be
(a) 0
(b) -0.05
(c) 0.01
(d) -0.01
34. A bar 4 cm in diameter is subjected to an
axial load of 4 t. The extension of the bar over a
gauge length of 20 cm is 0.03 cm. The decreases
in diameter is 0.0018 cm. The Poisson’s ratio is
(a) 0.25
(b) 0.30*
(c) 0.33
(d) 0.35
35. A bar 30 mm in diameter was subjected to
tensile load of 54 kN and the measured
extension on 300 mm gauge length was 0.112
mm and change in diameter was 0.00366 mm.
Poisson’s ration will be
(a) 0.25
(b) 0.326*
(c) 0.356
(d) 0.28
36. In the above problem, bulk modulus K will
be
(a) 77.2 kN/mm2
(b) 204.6 kN/mm2
(c) 196 kN/mm2
*
(d) 175 kN/mm2
37. In the above problem, modulus of rigidity N
will be
(a) 77.2 kN/mm2
*
(b) 204.6 kN/mm2
(c) 196 kN/mm2
(d) 175 kN/mm2
38. A bar of diameter 30 mm is subjected to a
tensile load such that the measured extension on
a gauge length of 200 mm is 0.09 mm and the
change in diameter is 0.0045 mm. The Poisson’s
ratio will be
(a) 1/4
(b) 1/3*
(c) 1/4.5
(d) 1/2
39. A steel cube of volume 8000 cc is subjected
to all round stress of 1330 kg/sq. cm. The
volumetric change is
(a) 8 cc*
(b) 6 cc
(c) 0.8 cc
(d) 0.01 cc
40. A thin circular plate of radius r and thickness
t is subjected to radial stress  throughout its
circumference. The unit volume change of the
entire plate is
(a) (1 )
E

−
(b)
2
(1 )
E

−

2.5
(c) (1 2 )
E

−  *
(d)
2
(1 2 )
E

− 
41. A square plate of thickness “t” is subjected
to a tensile stress x in one direction and a
compressive stress y = -x in one direction. If E
is the modulus of elasticity and  is the Poisson’s
ratio, the change in the plate thickness t(in z
direction) is
(a) 0
(b) x(1 - ).2t/E
(c) x(1 - ).t/2E*
(d) x(1 - ).t/E
42. A solid bar is enclosed in hollow tube and is
subjected to a compressive force P. Then force
P1 in solid bar will be
(a)
2 2
1 1
P
A E
1
A E
+
*
(b)
2 2
1 1
P
A E
A E
(c) 2 2
1 1
A E
P 1
A E
 
+
 
 
(d) none of these
43. A steel tube is surrounding a solid
aluminium cylinder. A force P is applied at the
assembly. The aluminium cylinder is 75 mm in
diameter and outside diameter of the steel tube is
90 mm. Given Esteel = 200 GNm-2
and Ealuminium
=25 GNm-2
If P = 200 kN, the stress in steel tube
will be
(a) 10 MPa
(b) 60.75 MPa
(c) 80.25 MPa*
(d) 100 MPa
44. In the above problem, stress in aluminium
will be
(a) 10 MPa*
(b) 60.75 MPa
(c) 80.25 MPa
(d) 100 MPa
45. A bar of length L is fitted between two
supports and the temperature is increased t0
. If
support does not yield, the temperature stress in
the bar will be
(a) 0
(b) tE
(c) t
(d) tE*
46. In the above if support yields by an amount
“a”, then temperature stress will be
(a) 0
(b) tE
(c) tE - a
(d)
E
(L t a)
L
 − *
47. The length, coefficient of thermal expansion
and Young’s modulus of bar A are twice that of
bar B. If the temperature of both bars is
increased by the same amount while preventing
any expansion, then the ratio of stress developed
in bar A to that in bar B will be
(a) 2
(b) 4*
(c) 8
(d) 16
48. A steel bar, 300 mm long and 24 mm
diameter, is turned down to 18 mm diameter for
one third of its length. It is heated 300
C above
room temperature, clamped at both ends and
then allowed to cool to room temperature. If the
distance between the clamped is unchanged, the
maximum stress in the bar( = 12.5 x 10-6
per 0
C
and E = 200 GN/m2
) is
(a) 25 MN/m2
(b) 50 MN/m2
(c) 75 MN/m2
(d) 100 MN/m2
*
49. A railway track is laid so that there is no
stress in the rails at 100
C. If there is no
allowance for expansion then stress in the rails
at 600
C will be
(a) 53.3 N/mm2
(b) 110.7 N/mm2
(c) 115 N/mm2
(d) 120 N/mm2
*

2.6
50. In the above problem if there is an expansion
allowance of 10 mm per rail then stress in the
rails at 600
will be
(a) 53.3 N/mm2
*
(b) 110.7 N/mm2
(c) 115 N/mm2
(d) 120 N/mm2
51. In the above problem what will be expansion
allowance if stress induced is zero
(a) 1 mm
(b) 7 mm
(c) 11 mm
(d) 18 mm*
52. A steel bar of 2m length is fixed at both ends
at 200
C. The coefficient of thermal expansion is
11 x 106
/0
C and the modulus of elasticity is 2 x
106
kg/cm2
. If the temperature is changed to
180
C, then the bar will experience a stress of
(a) 22 kg/cm2
(tensile)
(b) 22 kg/cm2
(compressive)
(c) 44 kg/cm2
(compressive)
(d) 44 kg/cm2
(tensile) *
53. If a bar consists of two materials and is
subjected to temperature change then
(a) tensile stresses will be set up in two materials
(b) compressive stresses will be set up in two
materials
(c) tensile stress in one material and compressive
stress will be set up in another material*
(d) none of these
54. A compound bar consisting of material A
and B is tightly secured at the ends. The
coefficient of thermal expansion of A is more
than of B. When the temperature is increased the
stresses induced will be
(a) tensile in both the materials
(b) tensile in material A and compressive in
material B
(c) compressive in material A and tensile in
material B*
(d) compressive in both the materials
55. A bar is made of steel and copper and is
subjected to an increase in temperature. Then
stresses in steel portion will be
(a) tensile in nature*
(b) compressive in nature
(c) either of(a) and(b)
(d) 0
56. In the above problem
(a) tensile force in steel will be greater than that
of copper
(b) tensile force in steel will be less than that of
copper
(c) tensile force in steel will be equal to tensile
force in copper*
(d) none of these
57. In above problem, force P in the bar will be
(a) c s
s s c c
t( )
1 1
A E A E
 − 
+
*
(b) c s s s
t( )A E
 − 
(c) c s c c
t( )A E
 − 
(d) none of these
58. A steel tube of 50 mm outside diameter and
40 mm inside diameter surrounds a solid brass
cylinder 35 mm in diameter. Both are joined to a
rigid cover plate at each end. the assembly is
stress free at temperature of 300 K. If the
temperature is then raised to 380 K, the stress in
each steel will be (For brass, E = 90 GNm-2
,  =
20 x 10-6
K-1
; for steel, E = 200 GNm-2
,  = 12 x
10-6
K-1
)
(a) 49 MPa*
(b) -49 MPa
(c) 37.5 MPa
(d) -37.5 MPa
59. In the above problem, stress in brass will be
(a) 49 MPa
(b) -49 MPa
(c) 37.5 MPa
(d) -37.5 MPa*
60. For a solid or a hollow shaft subject to a
twisting moment T, the torsional shearing stress
 at a distance r from the centre will be
(a) Tr / J
 = *
(b)  = Tr
(c)  = TJ/r
(d) none of these
where J is second moment of area.

2.7
61. Second moment of area(J) of hollow
cylindrical shaft will be
(a) ( )
4 4
0 i
D D
64

−
(b) ( )
4 4
0 i
D D
32

− *
(c) ( )
4 4
0 i
D D
128

−
(d) none of these
where D0 is outer diameter and Di is inner
diameter.
62. A solid shaft of circular cross section is
subjected to a torque T which produces a
maximum shear stress fs in the shaft. The
diameter of the shaft should be
(a) s
.f
16T

(b) s
3
f
16T

(c)
s
16T
f

(d) 3
s
16T
f

*
63. A solid shaft has diameter 80 mm. It is
subjected to a torque of 4 KNm. The maximum
shear stress induced in the shaft would be
(a) 75/ N/mm2
(b) 250/ N/mm2
(c) 125/ N/mm2
*
(d) 150/ N/mm2
64. If in a bar after twisting moment T has been
applied, a line on surface is moved by an angle 
then shearing moment will be
(a) /
(b) *
(c) /
(d) none of these
65. Shear modulus G is given by
(a) G /
=   *
(b) G = /
(c) G = T/
(d) G = T/
66. A shaft of length L is subject to a constant
twisting moment T along its length L, then angle
 through which one end of the bar will twist
relative to other will be
(a) T/
(b) T/GJ
(c) GJ/TL
(d) TL/GJ*
67. A circular shaft subjected to torsion
undergoes a twist of 10
in a length of 120 cm. If
the maximum shear stress induced is limited to
1000 kg/cm2
and if modulus of rigidity G = 0.8 x
106
then the radius of the shaft should be
(a) /8
(b) /27
(c) 18/
(d) 27/*
Hint: /r = G/l
68. At fully plastic twisting moment
(a) only fibres at surface are stressed to yield
point in shear
(b) fibres at centre are stressed to yield point in
shear
(c) all fibres are stressed to yield point in shear*
(d) none of these
69. For a solid circular bar subject to torsion
(a) e
p
T
T
3
=
(b) Tp = Te
(c) e
4T
3
*
(d) Tp = 4Te
where Tp is fully plastic twisting moment and Te
is elastic twisting moment.
70. The relationship among twisting moment(T)
acting on a rotating shaft, power in watt(W), and
angular velocity in radian per second() will be
(a) T = W/
(b) W = T*
(c) W = T/
(d) none of these

2.8
71. A shaft turns at 150 rpm under a torque of
1500 N-m. Power transmitted is
(a) 15 kW
(b) 10 kW
(c) 7.5 kW*
(d) 5 kW
Hint: P = 2NT/60
72. Two steel shafts “A” and “B” are used for
transmitting power. The ratio of revolutions of
shafts i.e. NA/NB = 2. The ratio of torques on
shafts i.e. TA/TB = 1/2. The ratio of the horse
power transmitted by the shafts i.e. PA/PB are
(a) 1/2
(b) 1/4
(c) 1*
(d) 2
73. A twisting moment of 1 kNm is impressed
upon a 50 mm diameter shaft, then maximum
shear stress will be
(a) 25 MPa
(b) 32 MPa
(c) 37 MPa
(d) 41 MPa*
74. In above problem, what is the angle of twist
in a 1 m length of the shaft if G = 85 GNm-2
?
(a) 0.011 radian
(b) 0.019 rad*
(c) 0.1 radian
(d) 0.0001 radian
75. The ratio of the torsional moments of
resistance of a solid circular shaft of diameter D,
and a hollow circular shaft having external
diameter D and internal diameter d is given by
(a)
4
4 4
D
D d
−
*
(b)
4 4
4
D d
D
−
(c)
3 3
3
D d
D
−
(d)
3
3 3
D
D d
−
76. There are two shafts of equal length. One
shaft is solid having diameter d and another
shaft is hollow with inner diameter equal to 3/4
of outer diameter(D).If both shafts are required
to transmit a given torsional load then weight of
hollow shaft will be ___ % of solid shaft.
(a) 25.7%
(b) 50%
(c) 56.3%*
(d) 75%
77. Consider the following statements:
If a solid circular shaft and hollow circular shaft
have the same torsional strength, then the weight
of the hollow shaft will be less than that of the
solid shaft the external diameter of the hollow
shaft will be greater than that of the solid shaft
the stiffness of the hollow shaft will be equal to
that of the solid shaft
Of these statements
(a) all are correct
(b) 2 and 3 are correct
(c) 1 is correct
(d) 1 and 2 are correct*
78. A hollow steel shaft 3 m long must transmit
a torque of 25 kNm. The total angle of twist in
this length is not to exceed 2.50
and the
allowable shearing stress is 90 MPa. The inside
diameter of the shaft will be
(a) 100 mm
(b) 125 mm*
(c) 145 mm
(d) 165 mm
79. In the above problem, the outside diameter
of the shaft will be
(a) 145 mm*
(b) 165 mm
(c) 175 mm
(d) 200 mm
80. A hollow steel shaft of external diameter 100
mm and internal diameter 50 mm is to be
replaced by a solid alloy shaft. Assuming the
same value of polar modulus for both, the
diameter of the solid alloy shaft will be
(a) 10x3 9375 mm
(b) 10 9375 mm
(c)
9375
10x3
10
*

2.9
(d) 3 9375 mm
81. An axial core of 100 mm is bored throughout
the length of a 200 mm diameter solid circular
shaft. For the same maximum shear stress, the
percentage torque carrying capacity lost by this
operation is
(a) 6.25*
(b) 12.5
(c) 25
(d) 45
82. A composite shaft is fabricated from a 50
mm diameter solid aluminium alloy, G = 30
GNm-2
, surrounded by a hollow steel circular
shaft of outside diameter 65 mm and inside
diameter 50 mm, G = 85 GNm-2
. This composite
shaft is loaded by a twisting moment of 1.5
kNm, the shearing stress at the outer fibres of
the steel will be
(a) 18 MPa
(b) 24 MPa
(c) 30 MPa
(d) 36 MPa*
83. In the above problem, the shearing stress at
the outer fibres of aluminium will be
(a) 1 MPa
(b) 2.8 MPa
(c) 5.6 MPa
(d) 9.8 MPa*
84. There is a rectangular thin walled tube of
thickness t and length b. The breadth is h. The
angle of twist will be
(a) 2 2
T(2b 4h)
b h Gt
+
(b) 2 2
T(2b h)
4b h Gt
+
(c) 2 2
T(2b 4h)
4b h Gt
+
*
(d) none of these
85. A hollow shaft has outer diameter 125 mm
and inner diameter 75 mm. Shearing stress at the
inside fibres is 50 MPa. The shearing stress at
the outer fibre will be
(a) 74.7 MPa
(b) 55 MPa
(c) 81.7 MPa
(d) 83.3 MPa*
86. A propeller shaft in a ship is 350 mm in
diameter. the allowable working stress in shear
is 50 MPa and the allowable angle of twist is 1
degree in 15 diameters of length. If G = 85
GNm-2
, then the shaft can transmit a maximum
torque of
(a) 350 kNm
(b) 378 kNm
(c) 416 kNm*
(d) 545 kNm
87. In the above problem if a 175 mm axial hole
is bored through the length of shaft and if other
conditions remain same then torsional load
carrying capacity of the shaft will be reduced by
(a) 1%
(b) 3%
(c) 6%*
(d) 9%
88. In the above problem, by what percentage is
the weight of the shaft reduced?
(a) 25%*
(b) 50%
(c) 75%
(d) 53.6%
89. If the driving torque is applied at one end
and the resting torque at the other end then the
shafts are said to be joined in
(a) series*
(b) parallel
(c) a combination of series and parallel
(d) none of these
90. If two shafts are joined in series then
(a) resulting shaft is called
compound(composite) shaft
(b) both shafts carry the same torque(T)
(c) total angle of twist at the fixed or resisting
end() is the sum of separate angles of twist of
the two shafts
(d) all of the above*
91. The shafts are said to be joined in parallel if
(a) torque(T) is applied at the junction of the two
shafts

2.10
(b) resisting torques T1 and T2 are applied at
their ends
92. If two shafts are connected in parallel then
(a) resulting shaft is called composite(or
compound) shaft
(b) angle of twist in each shaft will be equal
(c) both(a) and(b)
93. A compound shaft is composed of a 500 mm
length of solid copper 100 mm in diameter,
joined to a 1 m length of solid steel 125 mm in
diameter. A torque of 15 kNm is applied to each
end of the shaft. The maximum shear stress in
copper will be(G for copper = 40 GNm-2
and G
for steel is 85 GNm-2
)
(a) 76 MPa*
(b) 39 MPa
(c) 47 MPa
(d) 88MPa
94. In the above problem, maximum shearing
stress in steel will be
(a) 76 MPa
(b) 39 MPa*
(c) 47 MPa
(d) 88 MPa
95. In the above problem, total angle of twist of
the entire shaft will be
(a) 0.016 rad
(b) 0.026 rad*
(c) 0.046 rad
(d) 0.5 rad
96. Two shafts having same length and material
are joined in series and subjected to a torque of
10 kNm. If the ratio of their diameters is 2:1,
then the ratio of their angles of twist is
(a) 16:1*
(b) 2:1
(c) 1:2
(d) 1:16
97. A solid shaft of 100 mm diameter in a small
hydraulic turbine is subjected to an axial
compressive load of 100 kN and a torque of 5
kNm. The maximum shearing stress induced in
the shaft is
(a) 203 N/mm2
(b) 208 N/mm2
(c) 2015 N/mm2
(d) 2017 N/mm2
*
98. A shaft is subjected to a bending moment M
and torque T. The equivalent bending moment
“Meq” on the shaft is given by
(a)
2 2
M M T
4
+ +
(b)
M M T
2
+ +
(c)
2 2
M M T
2
− +
(d)
2 2
M M T
2
+ +
*
99. Wherever the bending moment is maximum
the shear force is
(a) zero*
(b) also maximum
(c) minimum
(d) of any value
100. The point of contraflexure lies where
(a) shear force changes sign
(b) bending moment is zero or changes sign*
(c) shear force is zero
(d) bending moment is maximum
101. For a moving load on a simply supported
beam, the maximum bending moment occurs
(a) at the supports
(b) under the load
(c) at the midspan*
102. The bending moment diagram for a
cantilever subjected to bending moment at the
free end is
(a) triangle
(b) rectangle*
(c) parabola
(d) elliptical

2.11
103. The variation of shear force due to a
uniformly distributed load is by
(a) cubic law
(b) parabolic law
(c) linear law*
(d) uniform law
104. The variation of bending moment due a
point load is by
(a) cubic law
(b) parabolic law
(c) linear law*
(d) uniform law
105. The variation of bending moment due
uniformly distributed load is by (a) cubic law
(b) parabolic law*
(c) linear law
(d) uniform law
106. Maximum bending moment in a cantilever
carrying a point load at the free end occurs at
the
(a) free end
(b) mid-span
(c) fixed end*
107. At the point of application of a point load
on a beam there is
(a) maximum bending moment
(b) sudden change of shape of bending moment
diagram*
(c) maximum deflection
(d) point of contraflexure
108. Maximum bending moment in a cantilever
carrying a uniformly distributed load is
(a) wl2
/4
(b) wl2
/8
(c) wl3
/4
(d) wl2
/2*
109. Maximum bending moment in a simply
supported beam carrying a point load at mid-
span is
(a) Wl/2
(b) Wl/4*
(c) Wl/6
(d) Wl/8
supported beam carrying a point load W at a
distance a from one end of the span / is
(a)
( )
Wa l a
l
−
*
(b) Wa2
/l
(c)
2
( )
Wa l a
l
−
(d) 2
( )
Wa l a
l
−
supported beam carrying a uniformly
distributed load is
(a) wl2
/4
(b) wl2
/8*
(c) wl2
/12
(d) wl/4
112. Variation of shear force in a cantilever
carrying a load the intensity of which varies
uniformly from zero at the free end to w per
unit run at the fixed end is by
(a) cubic law
(b) parabolic law*
(c) linear law
(d) none of these
113. Variation of bending moment in a
cantilever carrying a load the intensity of which
varies uniformly from zero at the free end to w
per unit run at the fixed end is by
(a) cubic law*
(b) parabolic law
(c) linear law
(d) none of these
114. A simply supported beam carries a couple
at a point on its span, the shear force
(a) varies by cubic law
(b) varies by parabolic law
(c) varies linearly
(d) is uniform throughout*
115. In a thin shell the thickness of the shell is
(a) 1/10 to 1/15 of diameter of shell*
(b) 1/5 to 1/30 of diameter of shell
(c) 1/2 to 1/10 of diameter of shell
(d) none of these

2.12
116. Normal stresses are uniformly distributed in
(a) thin shell*
(b) thick shell
(c) both(a) and(b)
117. A thin cylindrical shell is having an internal
diameter d, wall thickness t and length l. This
shell is subjected to internal intensity of pressure
p. Hoop stress(circumferential stress) in this
shell will be
(a) pd/2t*
(b) pd/4t
(c) pd/8t
(d) pd/16t
118. In the above question, intensity of
longitudinal stress will be
(a) pd/2t
(b) pd/4t*
(c) pd/8t
(d) pd/16t
119. If  is the efficiency of the longitudinal
riveted joint then hoop stress will be
(a) pd/2t*
(b) pd/4t
(c) pd/2t
(d) none of these
120. If  is the efficiency of circumferential
riveted joint then longitudinal stress will be
(a) pd/4t*
(b) pd/2t
(c) pd/4t
(d) none of these
121. Two closed thin vessels, one cylindrical
and the other spherical with equal internal
diameter and wall thickness are subjected to
equal internal fluid pressure. The ratio of hoop
stresses in the cylindrical to that of spherical
vessels is
(a) 4
(b) 2*
(c) 1
(d) 0.5
122. A cast iron pipe of 1 m diameter is required
to withstand a 200 m head of water. If the
limiting tensile stress of the pipe material is 20
MPa, then the thickness of the pipe is
(a) 25 mm
(b) 50 mm*
(c) 75 mm
(d) 100 mm
123. A thin cylindrical shell of diameter(d),
length(l) and thickness(t) is subjected to an
internal pressure(p). The ratio of longitudinal
strain to hoop strain is
(a) pd/2t
(b)
pd 1
1
2t m
 
−
 
 
(c)
m 2
2m 1
−
−
*
(d)
2m 1
m 2
−
−
124. If a cylindrical shell of diameter d and
thickness t is stressed by stress p. The
volumetric strain(neglecting radial stress) will be
(a)
pd 5 2
2tE 2 m
 
−
 
 
(b) l c
e 2e
+
where el is longitudinal strain and ec is
circumferential strain and 1/m is Poisson’s ratio.
125. A thin cylindrical shell of internal diameter
D and thickness t is subjected to internal
pressure p. The change in diameter is given by
(a)
2
pD
(2 )
4tE
− *
(b)
2
pD
(1 2 )
4tE
− 
(c)
2
pd
(1 2 )
2tE
− 
(d)
2
pd
(2 )
2tE
−
126. A cold drawn seamless steel tubing subject
to internal pressure, has a diameter of 6 cm and

2.13
wall thickness of 0.2 cm. The ultimate strength
of steel is 3600 kg/cm2
. The bursting
pressure(kg/cm2
) is
(a) 120
(b) 240*
(c) 480
(d) 960
127. A boiler of 2 m diameter is made of 20 mm
thick mild steel plates. The efficiency of
longitudinal riveted joint is 75%. If the
maximum tensile stress in the plate section
through the rivets is not to exceed 100 N/mm2
then permissible steam pressure in the boiler will
be
(a) 1 N/mm2
(b) 1.5 N/mm2
*
(c) 3 N/mm2
(d) none of these
128. In the above problem, circumferential stress
in the solid plate section will be
(a) 37.5 N/mm2
(b) 75 N/mm2
*
(c) 150 N/mm2
(d) none of these
129. In the above question if efficiency of
circumferential joint is 65% then longitudinal
stress will be
(a) 115.2 N/mm2
(b) 75.6 N/mm2
(c) 57.6 N/mm2
*
(d) none of these
130. A copper tube of 50 mm internal diameter,
1 metre long and 1.25 mm thick has closed ends
and is filled with water under pressure.
Volumetric strain will be(Poisson’s ratio = 0.3)
(a) 30p/E
(b) 36p/V
(c) 21p/V
(d) 38p/V*
131. In a spherical shell of diameter d and
thickness t then hoop stress in all directions will
be
(a) pd/t
(b) pd/2t
(c) pd/4t*
(d) pd/t
132. In a spherical shell, volumetric
strain(neglecting radial stress) will be
(a) 3e
(b)
3pd 1
1
4tE m
 
−
 
 
133. In the above question if radial stress is
considered then volumetric strain will be
(a)
3pd 1 3p
1
4tE m mE
 
− +
 
 
*
(b)
3pd 1 p
1
4tE m mE
 
− +
 
 
(c)
3pd 1 5p
1
4tE m mE
 
− +
 
 
(d) none of these
134. A 20 m diameter spherical tank is to be
used to store gas. The shell plating is 10 mm
thick and the working stress of the material is
125 MPa. The maximum permissible gas
pressure will be
(a) 0.20 MPa
(b) 0.50 MPa
(c) 0.70 MPa
(d) none of these*
135. The undersea research vehicle Alvin has a
spherical pressure hull 1 m in radius and shell
thickness of 30 mm. The pressure hull is steel
having a yield point of 700 MPa. If sea water
has a weight density of 104
Nm-3
then the depth
of submergence that would set up yield point
stress in vehicle will be
(a) 1200 m
(b) 2400 m
(c) 3200 m
(d) 4200 m*
136. A seamless spherical shell of 1 m internal
diameter and 5 mm thick is filled with a fluid
under pressure until its volume increases by 200
cubic centimetres. If E = 2.05 x 105
N/mm2
and
1/m = 0.3 then pressure exerted by the fluid on
the wall is
(a) 0.25 N/mm2

2.14
(b) 0.50 N/mm2
(c) 0.75 N/mm2
*
(d) none of these
137. There is a thin cylinder and a thin spherical
shell having same internal pressure and
diameter/thickness ratio. Also given 1/m =
0.3.The ratio of maximum tensile stress between
cylinder and sphere is
(a) 1
(b) 2*
(c) 3
(d) 4
138. In the above question, the ratio of
proportional increase in volume between
cylinder and sphere is
(a) 1.71
(b) 1.81*
(c) 1.90
(d) 2.33
139. A vertical cylindrical gasoline storage tank
is 30 m in diameter and is filled to a depth of 15
m with gasoline whose relative density is 0.74.
If the yield point of the shell plating is 250 MPa
and a safety factor of 2.5 is adequate then wall
thickness at the bottom should be
(a) 14.7 mm
(b) 15 mm
(c) 16.7 mm*
(d) 18.8 mm
140. A thin walled steel circular cylinder closed
at both ends and subjected to a uniform internal
pressure of 0.5 MPa. The wall thickness is 1.5
mm, radius is 350 mm, and  = 1/m = 0.3. E =
200 GNm-2
. The increase of volume per unit
volume will be
(a) 10-2
(b) 10-3
*
(c) 10-4
(d) none of these
141. A column buckles at a crippling load of 500
units when effectively held at both ends and also
restrained against rotation at both ends. What
would be the crippling load when one end is
restrained only against rotation?
(a) 400 units
(b) 250 units
(c) 330 units*
(d) 500 units
Hint: According to IS code
2
cr 2
EI
P
(0.65L)

=
142. A short column of external diameter D and
internal diameter d, is subjected to a load W,
with an eccentricity e, causing zero stress at an
extreme fibre. Then the value of “e” must be
(a)
2 2
D d
8 D
+

(b)
2 2
D d
8D
+
*
(c)
2 2
D d
8D
−
(d)
3 2
2
D d
8D
+
143. A hollow circular column of internal
diameter d and external diameter 1.5d is
subjected to compressive load. The maximum
distance of the point of application of load from
centre for no tension is
(a) d/8
(b) 13d/48*
(c) d/4
(d) 13d/96
144. Which one of the following pairs is not
correctly matched?
(a) Pin-Pin –– 2
EI/l2
(b) Fixed-Fixed –– 42
EI/l2
(c) Fixed-Free –– 0.252
EI/l2
(d) Fixed-Pin –– 2.2
EI/l2
*
145. For a column having its ends hinged, the
slenderness ratio is 160. The l/d ratio of the
column is
(a) 80
(b) 57
(c) 40*
(d) 20
146. A column of length l is hinged at both the
ends and restrained from lateral displacement at

2.15
mid height. The critical load of the column is
given by
(a)
2
2
EI
l

(b)
2
2
2 EI
l

(c)
2
2
4 EI
l

*
(d)
2
2
EI
4l

147. Four vertical columns of the same material,
height and weight have the same end conditions.
The buckling load will be the largest for a
column having the cross section of a/an
(a) solid square
(b) thin hollow circle*
(c) solid circle
(d) I-section
148. If the crushing stress in the material of a
mild steel column is 3300 kg/cm2
, Euler formula
for crippling load is applicable for slenderness
ratio equal to/greater than
(a) 40
(b) 50
(c) 60
(d) 80*
149. The resultant cuts the base of a circular
column of diameter “d” with an eccentricity
equal to d/4. The ratio between the maximum
compressive stress and maximum tensile stress
is
(a) 3*
(b) 4
(c) 5
(d) infinity
Hint: Stresses =
P M P P.e
A Z A Z
 = 
150. A short hollow CI column section “A” is
150 cm2
and section modulus Z = 10 x 105
mm3
carries an axial load of 250 kN, and a load of 50
kN on the bracket, the load line being 500 mm
from the axis of column.
The maximum and minimum stress intensities
are
(a) 50 N/mm2
tensile and 10 N/mm2
compressive
(b) 45 N/mm2
compressive and 5 N/mm2
tensile*
(c) 55 N/mm2
compressive and 5 N/mm2
tensile
(d) 60 N/mm2
tensile and 10 N/mm2
compressive
151. A compressive member always tends to
buckle in the direction od
(a) axis of load
(b) minimum cross section
(c) least radius of gyration*
perpendicular to the axis of load
QUESTIONS FROM SSC/PSU
EXAMS
152. The formula for the extension in the tapered
rod of length L and tapered diameter of D1 and
D2, under the axial tensile load P is
(a)
1 2
4PL
ED D

*
(b)
1 2
4PL
D D

(c)
1 2
PL
ED D

(d)
1 2
2PL
ED D

(SSC JE 2018)
153. If a load of 40 kN is applied in a
compressive manner of a rod whose cross
section is 10 mm × 20 mm. Then what will be
the compressive stress (MPa) on the rod
(a) 0.2
(b) 2
(c) 20
(d) 200* (SSC JE 2018)
154. What will be the thermal stress developed
in a rod having a diameter of 4 cm and length of
2 m. It experiences heating from temperature
500
C to 2000
C. The coefficient of thermal
expansion is α = 10×10-6
/0
C and young's
modulus is 250 GPa?
(a) 300
(b) 325
(c) 350

2.16
(d) 375* (SSC JE 2018)
Hint: (σth ) = αΔt.E
155. Which of the following is a dimensionless
quantity?
(a) Shear stress
(b) Poisson's ratio*
(c) Torque
(d) None of these (SSC JE 2018)
156. What is the formula for elongation of a
conical bar (with length L and self-weight W)
due to its self-weight?
(a)
min
2
WL
A E
(b)
2
min
2
WL
A E
(c)
max
2
WL
A E
*
(d)
2
max
2
WL
A E
(SSC JE 2018)
Hint: Elongation of the conical bar due to its
self-weight W having specific weight γ:
2
max
6 2
L WL
E A E

 = =
Where
3
AL
W

=
157. What will be the value of Poisson's ratio, if
the elasticity and rigidity of the material is 200
GPa and 66.67 GPa?
(a) 0
(b) 0.25
(c) 0.5*
(d) 1 (SSC JE 2018)
Hint: E = 2G(1+ μ)
158. The Yung's modulus and thermal stress
developed in a steel rod of diameter 2 cm and
length 2 m is 200 GPa and 288 MPa
respectively, this experiences heating from
temperature 300
C to 1500
C and the rod has
been restricted in its original position.
Calculate the value of coefficient of thermal
expansion.
(a) 1.2 × 10–5
/0
C*
(b) 12 × 10–4
/0
C
(c) 12 × 10–5
/0
C
159. Choose the CORRECT material which
belongs to the category of highly elastic?
(a) Brass
(b) Steel*
(c) Glass
(d) Rubber (SSC JE 2018)
Hint: Steel is the most elastic material. If the
object is elastic, the body regains its original
shape when the pressure is removed. Steel
having the steepest linear stress-strain curve
among all. A stiffer material will have a higher
elastic modulus.
160. What is the effect on the Young's modulus
of a wire, if the radius of a wire subjected to a
load P is doubled?
(a) Dubled
(b) Halved
(c) Become one-fourth
(d) Remains unaffected* (SSC JE 2018)
Hint: Youngs modulus (E) is the property of the
material, it does not depend up on the
dimensions of the material.
161. A steel rod of original length 200 mm and
final length of 200.2 mm after application of an
axial tensile load of 20 kN what will be the
strain developed in the rod?
(a) 0.01
(b) 0.1
(c) 0.001*
(d) 0.0001 (SSC JE 2018)
Hint:
f i
i
l l
l

−
=
162. To which of the following is the proof
stress related?
(a) Elongation
(b) Necking
(c) Yielding*
(d) Fracture (SSC JE 2018)
163. A cross sectional bar of area 700 mm2
is
subjected to an axial load as shown in the
figure below. What is the value of stress (MPa)
in the section RS?

2.17
(a) 30
(b) 40*
(c) 50
(d) 60 (SSC JE 2018)
Hint: See figure of QR section.
Stress = F/A = 28 x 103
/700 x 10-6
164. Calculate the value of modulus of rigidity
(N/mm2
) if the Poisson's ratio is 0.25 and
modulus of elasticity for the material is 200
N/mm2
?
(a) 50
(b) 80*
(c) 100
(d) 150 (SSC JE 2018)
165. Which equation correctly relates the
modulus of elasticity in terms of G and K?
(a)
3
9
G K
KG
+
(b)
3
9
G K
KG
+
(c)
9
3
KG
G K
+
*
(d)
9
3
KG
G K
+
(SSC JE 2018)
Hint: E = 3K(1 – 2μ)
and E = 2G (1 + μ)
166. There is ____ for a brittle material.
(a) no elastic zone
(b) no plastic zone*
(c) large elastic zone
(d) large plastic zone (SSC JE 2018)
167. The ability of a body to absorb energy and
to deform plastically without fracturing is
known as ____
(a) creep
(b) elasticity
(c) plasticity
(d) toughness* (SSC JE 2018)
168. The property of a material states that it is
rigid. The value of Poisson's ratio for this
particle is ______
(a) 0
(b) 1
(c) 2
(d) None of these* (SSC JE 2018)
Hint: Poisson's ratio is the ratio of transverse
strain to longitudinal strain .
A zero Poisson’s ratio means that there is no
transverse deformation resulting from an axial
strain.
Since, μ = 0/0
For a rigid body, the value of Poisson’s ratio is
not defined.
169. Which term states the S.I. unit of stress?
(a) kN/mm
(b) N/mm2
*
(c) N/mm3
(d) m3
/sec (SSC JE 2018)
170. The value of Poisson's ratio depends on
(a) material of the test specimen*
(b) magnitude of the load
(c) cross section
171. The materials which exhibit the same
elastic properties in all directions are called
(a) Homogeneous
(b) Inelastic
(c) Isotropic*
(d) Isentropic (SSC JE 2017)
172. The property of a material which allows it
to be drawn into a smaller section is called:
(a) plasticity
(b) ductility*
(c) elasticity
(d) malleability (SSC JE 2017)
173. If a part is constrained to move and heated,
it will develop
(a) principal stress
(b) tensile stress
(c) compressive stress*
(d) shear stress (SSC JE 2017)

2.18
174. Poisson's ratio is defined as the ratio of
____.
(a) longitudinal stress and longitudinal strain
(b) longitudinal stress and lateral strain
(c) lateral strain and longitudinal strain*
(d) lateral stress and lateral strain
(SSC JE 2017, 2014)
175. The Charpy test is conducted to measure
____.
(a) Toughness*
(b) Creep strength
(c) Fatigue strength
(d) Elastic strength of a material
(SSC JE 2017)
176. The stress produced by a suddenly applied
load as compared to that produce by the same
load when applied gradually is ____ times.
(a) 1.5
(b) 2*
(c) 3
(d) 4 (SSC JE 2017)
177. A load of 20,000 kg applied to a brass
cylinder 40 cm long and 10 cm in diameter
caused the length to increase 0.8 cm and the
diameter to decrease 0.005 cm. Poisson's ratio of
brass is _____.
(a) 0.025*
(b) 0.925
(c) 0.25
(d) 2.5 (SSC JE 2017)
Hint:
/
/
d d
l l


178. True stress represents the ratio of ____
(a) Average load and average area
(b) Average load and maximum area
(c) Maximum load and maximum area
(d) Instantaneous load and instantaneous area*
(SSC JE, 2010, 2017)
179. Bulk modulus of material is the ratio of
(a) volumetric strain to direct stress
(b) change in volume to modulus of elasticity
(c) direct stress to volumetric strain*
(d) stress to strain (SSC JE-2007)
180. Modulus of rigidity is the ratio of
(a) Axial stress to shear strain
(b) Linear stress to longitudinal strain
(c) Shear stress to shear strain*
(d) Hydrostatic stress to volumetric strain
(SSC JE 2010)
181. The value of normal stress is ____ in the
plane of maximum shear stress.
(a) minimum
(b) maximum
(c) zero
(d) None of these* (SSC JE 2018)
182. The value of the principal stress at a point
in a plane stressed element is
σx = σy = 500 MPa
Calculate the value of normal stress acting
(MPa) at the angle of 45o
at X axis
(a) 250
(b) 500*
(c) 750
(d) 1000 (SSC JE 2018)
Hint: cos2
2 2
x y x y
n
   
 
+ −
= +
183. A body is subjected to principle stresses at
a point having values as 200 MPa and 100 MPa
respectively. What is the value of maximum
shear stress (in MPa)?
(a) 25
(b) 50*
(c) 75
(d) 100 (SSC JE 2018)
Hint: max min
max
2
 

−
 
=  
 
184. The magnitude of the normal stresses in the
x and y direction is 100 MPa and 20 MPa
respectively. Both the stresses are tensile in
nature. Determine the radius of the Mohr's circle
(mm).
(a) 20
(b) 40*
(c) 60
(d) 80 (SSC JE 2018)
Hint: Radius = max
2
x y
 

−
=

2.19
185. Calculate the maximum shear strain at the
point where principal strains are 100 x 10–6
and
–200 x 10–6
.
(a) 100 × 10–6
(b) 200 × 10–6
(c) 300 × 10–6
*
(d) 400 × 10–6
(SSC JE 2018)
Hint: max 1 2
2 2
  
−
=
186. Calculate the maximum value of the
principal stress for the stress state shown in the
figure.
(a) σ
(b) – σ
(c) 2σ*
(d) – 2σ (SSC JE 2018)
Hint:
2
2
max ( )
2 2
x y x y
n xy
   
 
+ −
   
= + +
   
   
187. Principal plane is one which carries _____.
(a) no shear stress*
(b) maximum shear stress
(c) no normal stress
(d) maximum resultant of stresses
(SSC JE 2017)
188. The bending moment for a certain portion
of the beam is constant. For that section, shear
force would be ____.
(a) Zero*
(b) Increasing
(c) Decreasing
(d) Constant (SSC JE 2017)
189. What is the location of the maximum
bending moment from the end B in the beam
shown below?
(a) l/2
(b) l/3
(c) l/4
(d) l/3* (SSC JE 2018)
190. A simply supported beam of span length l
carries a uniformly distributed load of 2.0 kN/m
and has a diameter of 75 mm. The maximum
value of bending stress produced is 8.5 kN-m.
What is the value of span length (m) of the
beam?
(a) 5.8*
(b) 34
(c) 7
(d) 2 (SSC JE 2018)
Hint: 2
max /8
BM wl
=
191. The maximum value of bending moment in
the simply supported beam with a concentrated
load P at its mid span is .....
(a) PL/4*
(b) PL/2
(c) PL
(d) PL/8 (SSC JE 2018)
192. Which of the following statement is
INCORRECT?
(a) The value of the shear force at any point in
the beam is equal to the slope of the bending
moment curve.
(b) The value of distributed load at any point in
the beam is equal to the slope of the bending
moment curve*
(c) The value of distributed load at any point in
the beam is equal to the slope of the shear
force curve
(d) All option are correct
193. The shear force acting at the midpoint of
the cantilever beam is 12 kN. What is the value
of uniformly distributed load w (kN/m) acting

2.20
over the entire length, if the span length of the
beam is 4 m?
(a) 2
(b) 4
(c) 6*
(d) 8 (SSC JE 2018)
Hint: ds/dx = -W
ds = -Wdx
/2 /2
0 0
l l
ds Wdx
= −
 
194. The point in a beam at which the BM is
maximum, the shear force at that point is
______.
(a) maximum
(b) minimum
(c) zero*
(d) infinite (SSC JE 2018)
195. Which type of support has single reaction
component?
(a) hinge support
(b) Roller support*
(c) Fixed support
196. Determine the shape of the elastic curve
between the supports B and C for the beam is
shown in the figure below.
(a) A straight line
(b) Elliptical
(c) Parabolic*
(d) Circular (SSC JE 2018)
197. A beam of diameter 75m has a span length
of 10 m is subjected to uniform distributed load
of w kN/m. The maximum value of bending
stress produced is 6.75 kN-m. What is the value
of distributed load, if the beam is simply
supported
(a) 1.5
(b) 0.54*
(c) 2
(d) 5.4 (SSC JE 2018)
198. Which of the following shows the correct
relation between shear force (Vx), bending
moment (Mx) and load (w)?
(a)
2
2
x
d V
w
dx
= −
(b) x
dV
w
dx
= −
(c) x
x
dM
V
dx
=
(d) both (b) and (c)* (SSC JE 2018)
199. The maximum value of the bending
moment for a cantilever beam with a uniformly
distributed load (w) over the entire length is
given as .........
(a) 2
max / 2
M wl
= *
(b) 2
max / 8
M wl
=
(c) 2
max / 4
M wl
=
(d) 2
max / 6
M wl
=
200. The point on the beam where the curvature
changes from sagging to hogging is a point of
____
(a) centre of gravity
(b) contraflexure*
(c) maximum stress
(d) maximum shear stress (SSC JE 2018)
201. In a cantilever beam with point load at its
free end, the maximum bending moment occur
at
(a) Centre of the beam
(b) Free end of the beam
(c) Fixed end of the beam*
(d) At the point of application of the load (SSC
JE 2014)
202. The rate of change of bending moment is
equal to
(a) shear force at that section*
(b) deflection at that section
(c) loading at that section
(d) slope at that section (SSC JE 2017)

2.21
203. The shear stress distribution over a
rectangular cross–section of a beam follows
____
(a) A straight line path
(b) A circular path
(c) A parabolic path*
(d) An elliptical path (SSC JE 2017)
204. If the shear force along a section of a beam
is zero, the bending moment at the section
is____:
(a) zero
(b) maximum*
(c) minimum
(d) average of maximum-minimum
(SSC JE 2017)
205. Point of contraflexure occur when:
(a) bending moment is constant
(b) bending moment is maximum or minimum
(c) loading is constant
(d) bending moment is zero*
(SSC JE 2018)
206. The point of contra – flexure occurs only
in
(a) Continuous beams
(b) Cantilever beams
(c) Overhanging beams*
(d) Simply supported beams
(SSC JE 2015, 2017)
Hint: Overhanging beam: If the end portion of a
beam is extended beyond the support, such beam
is known as overhanging beam. In case of
overhanging beams, the B.M. is positive
between the two supports, whereas the B.M. is
negative for the over-hanging portion. Hence at
some point, the B.M. is zero after changing its
sign from positive to negative or vice versa. That
point is known as the point of contraflexure or
point of inflexion.
207. If the maximum value of the bending
moment in the simply supported beam is 6.75
kNm and the diameter of the beam is 75 mm.
Calculate the maximum value of bending stress
(MPa)
(a) 150.5
(b) 160.7
(c) 162.9*
(d) 165.5 (SSC JE 2018)
Hint: b
M
I y

=
Where y = D/2
208. Which is the CORRECT option for the
polar moment of inertia of the solid shaft?
(a)
4
64
d
J

=
(b)
4
32
d
J

= *
(c)
2
16
d
J

=
(d)
4
16
d
J

= (SSC JE 2018)
209. The variation of stress in the simple
bending of beams is _______.
(a) parabolic
(b) elliptical
(c) hyperbolical
(d) linear* (SSC JE 2018)
210. What is the shape of the stress distribution
across a rectangular cross section beam?
(a) Parabolic*
(b) Rectangular
(c) Triangular
(d) Both Rectangular and parabolic shape
(SSC JE 2018)
211. Bending stress on the neutral axis of the
cross sectional beam is............
(a) Maximum
(b) Minimum
(c) Zero*
(d) Infinity (SSC JE 2018)
212. The moment of inertia of a hollow circular
section whose external diameter is 8 cm and
internal diameter is 6 cm about centroidal axis –
––– cm4
.
(a) 437.5
(b) 337.5
(c) 237.5
(d) 137.5* (SSC JE 2017)
Hint: 4 4
( )
64
I D d

= −

2.22
213. If 'L' is the span of a light suspension
bridge, whose, each cable carries total weight
(w) and the central dip is 'y', the horizontal pull
at each support is ____.
(a) wL/4y
(b) wL/8y*
(c) wL/2y
(d) wL/y (SSC JE 2017)
214. The polar section modulus of a solid
circular shaft of diameter 'd' about an axis
through its centre of gravity is
(a) 3
( / 8) / d

(b) 3
( /16) / d
 *
(c) 3
( / 32) / d

(d)
3
( / 64) / d
 (SSC JE 2010)
Hint:
4
/ 32
/ 2
p
p
I J d
Z
R R d

= = =
215. Which of the following statement is TRUE
for sudden loading?
(a) Stress induced in sudden loading is double
that of normal loading*
(b) Stress induced in sudden loading is same as
that of normal loading
(c) Stress induced in sudden loading is half that
of normal loading
216. A body weighing 1000 kg falls 8 cm and
strikes a 500 kg/cm spring. The deformation of
spring will be ____ cm.
(a) 8*
(b) 4
(c) 16
(d) 2 (SSC JE 2017)
Hint: 2
1
2
mgh Wh kx
= = ; h = 8 + x
217. A steel bar 20 mm in diameter simply
supported at its ends over a total span of 40
cm, carries a load at its center. If the maximum
stress included in the bar is limited to 480/π
N/mm2
then the bending strain energy stored in
the bar is ____.
(a) 411 N mm
(b) 511 N mm
(c) 611 N mm*
(d) 711 N mm (SSC JE 2017)
Hint:
M
y I

=
max / 4
M Pl
=
3
48
Pl
EI
 =
Bending strain energy = (1/2)P
218. The strain energy stored in a body due to
external loading, within the elastic limit, is
known as
(a) Malleability
(b) Ductility
(c) Toughness
(d) Resilience* (SSC JE 2007)
219. Proof resilience in a member is stored strain
energy
(a) per unit volume
(b) in whole volume*
(c) per unit area
(d) per unit length (SSC JE 2008)
220. The strain energy stored in a body due to
direct stress 'f' is
(a) f / 2E× vol
(b) f2
/ E× vol
(c) f2
/ 2E× vol*
(d) 2f / E× vol (SSC JE 2010)
221. The strain energy stored in a cantilever
beam loaded as shown, will be
(a)
2 3
3
P l
EI
(b)
2 3
2
P l
EI
(c)
2 3
6
P l
EI
*
(d)
2 3
4
P l
EI

2.23
Hint: 2
0
1
2
l
U M dx
EI
= 
where M = Px
222. The cross-section of a member is subjected
to a uniform shear stress τ. The strain energy
stored per unit volume is equal to (G = modulus
of rigidity)
(SSC JE 2013)
(a) 2
2 / G

(b) 2
/ G

(c) 2
/ 2G
 *
(d) 2
2 /
G 
223. Calculate the value of shear stress (MPa) in
the solid circular shaft of diameter 0.1 m which
is subjected to the torque of 10 kNm.
(a) 40.5
(b) 50.93*
(c) 60.5
(d) 70.5 (SSC JE 2018)
Hint:
T G
J l R
 
= =
224. Which of the following conditions is
INCORRECT for the shafts connected in series
to each other
(a) θ = θ1 + θ2
(b) T = T1 = T2
(c) T1 = T2
(d) T = T1 + T2 and θ1 = θ2 both*
(SSC JE 2018)
225. Calculate the total angle of twist for a
stepped shaft which is subjected to the torque
(T) as shown in the figure below.
(a) 4
Tl
Gd

(b) 4
60Tl
Gd

(c) 4
66
Tl
Gd
(d) 4
36Tl
Gd

* (SSC JE 2018)
226. Consider the following relation for the
torsional stiffness (KT).
1. /
T
K T 
=
2. /
T
K GJ L
=
3. /
T
K G L

=
(a) (1), (2) and (3)
(b) Only (1) and (3)
(c) Only (1) and (2)*
(d) Only (2) and (3) (SSC JE 2018)
227. The ratio of the polar moment of inertia to
the radius of the shaft is known as
(a) Shaft stiffness
(b) Flexural rigidity
(c) Torsional rigidity
(d) Torsional section modulus*
(SSC JE 2007)
228. 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) 1/2
(b) 1/4
(c) 1/8*
(d) 1/16 (SSC JE 2017)
Hint:
2
60
NT
P Watt

=
229. For the two shafts connected in parallel,
find which statement is true
(a) Torque in each shaft is the same
(b) Shear stress in each shaft is the same
(c) Angle of twist of each shaft is the same*
(d) Torsional stiffness of each shaft is the same
(SSC JE 2017)
230. The shear stress at the centre of a circular
shaft under torsion is
(a) maximum
(b) minimum
(c) zero*
(d) unpredictable (SSC JE 2014)

2.24
231. For any given power and permissible shear
stress, the rotational speed of shaft and its
diameter are correlated by the expression
(a) ND3
= Constant*
(b) ND2
= constant
(c) ND = constant
(d) ND = constant (SSC JE 2014)
Hint: P = ND3
232. A solid shaft transmits a torque T. The
allowable shear stress is τ . The diameter of the
shaft is
(a) 3
16T

*
(b) 3
32T

(c) 3
4T

(d) 3
64T

(SSC JE 2011)
Hint:
T G
J l R
 
= =
4
;
32 2
d d
J R

= =
233. If two shafts of the same length, one of
which is hollow, transmit equal torques and have
equal maximum stress, then they should have
equal maximum stress, then they should have
equal
(a) polar moment of inertia
(b) polar modulus of section*
(c) diameter
(d) angleof twist (SSC JE 2013)
234. Torsional rigidity of a solid circular shaft of
diameter 'd' is proportional to:
(a) d
(b) d4
(c) d2
*
(d) 1/d2
(SSC JE 2015, Uttrakhand JE 2008)
Hint: 4
/ 32
GJ d

=
235. Two shafts, one solid and the other hollow,
are made of the same materials and are having
same length and weight. The hollow shaft as
compared to solid shaft isoes
(a) Have same strength
(b) More strong*
(c) None of the options
(d) Less strong (SSC JE 2015)
236. The change in slope is given by the ratio of
area under –––––––– to the flexural rigidity
between two points along the beam.
(a) bending moment diagram*
(b) shear force diagram
(c) area moment diagram
Hint:
2
2
x
BM
d y
dx EI
=
237. A uniform simply supported beam of span
(l) carries a point load (W) at the centre. Then
downward deflection at the centre will be
(a) Wl2
/8EI
(b) Wl3
/3EI
(c) 5Wl3
/384EI
(d) Wl3
/48EI* (SSC JE 2013)
238. A cantilever beam is deflected due to load
P. If load is doubled, then deflection compared
to earlier case will be changed by a factor of:
(a) 2 times*
(b) ½ times
(c) 1/8 times
(d) 8 times (SSC JE 2009)
Hint: Deflection due toload P is given by
3
3
Ll
EI
 =
239. Which of the following column has the
formula for the Euler's bucking load as 2
EI/l2
(a) Column with one end fixed and other end
free
(b) Column with one end fixed and other end
hinged
(c) Column with both ends fixed
(d) Column with both ends hinged*
(SSC JE 2018)
Hint:

2.25
240. If the diameter of the column is reduced by
30%, then what will be the change in the Euler's
buckling load (in%)?
(a) 25
(b) 50
(c) 75*
(d) 100 (SSC JE 2018)
Hint: 4
P I d
 
241. A column of length 8 m with both ends
fixed may be considered as equivalent to a
column of length ..........with both ends hinged.
(a) 2
(b) 4*
(c) 6
(d) 8 (SSC JE 2018)
Hint: For both ends fixed, Le = l/2
242. When a steel column is said to be short, the
slenderness ratio is?
(a) Less than 30*
(b) Greater than 30
(c) Less than 120
(d) Greater than 120 (SSC JE 2018)
Hint: Short columns have a slenderness ratio of
less than 32. Such columns are always subjected
to direct compressive stress only. The medium
column slenderness ratio is between 32 to 120.
Long columns have a slenderness ratio of more
than 120.
243. What is the ratio of the Euler's Bucking
loads of column having (i) both end fixed and
(ii) one end fixed and other end free is?
(a) 4 : 1
(b) 16 : 1*
(c) 1 : 4
(d) 2 : 1 (SSC JE 2018)
244. The expression for the slenderness Ratio
ratio of the columns is given as_____
(a)
2
min
e
l
k
 
 
 
(b)
2
min
2 e
l
k
 
 
 
(c)
min
e
l
k
 
 
 
*
(d)
min
2 e
l
k
 
 
 
(SSC JE 2018)
245. The expression for the Rankine's crippling
load is given as______.
(a) 2
1
c
e
A
P
l
k
k

=
 
−  
 
(b) 2
1
c
e
A
P
l
k
k

=
 
+  
 
*
(c) 2
1 2
c
e
A
P
l
k
k

=
 
−  
 
(d) 2
1
c
e
A
P
l
k
k

=
 
+  
 
(SSC JE 2018)
246. Rankine theory is applicable to the_____
(a) Short strut/column
(b) Long column
(c) Both short and long column*
(d) None of these
(SSC JE 2018, 2008)
247. If one end of the hinged column is made
fixed and the other is free, then by how much the
critical load is compared to the original value?
(a) 0.25*
(b) 0.5
(c) 2
(d) 4 (SSC JE 2018)

2.26
Hint: 2
b
e
EI
P
L

=
248. For which type of column the buckling load
will be maximum?
(a) One end clamped and other free.
(b) Both ends clamped*
(c) Both ends hinged
(d) One end hinged other is free
(SSC JE 2018)
249. A long circular cylinder has a diameter D
and length L. The slenderness ratio of the
column is:
(a) 2L/D
(b) 4L/D*
(c) (L/D)
(d) L/D (SSC JE 2014)
Hint: SR = L/K
2
I AK
=
4 2 2
64 4
D D K
 
=
250. Rankine formula (for a column) takes into
account which of the following?
(a) The eccentricity of loading
(b) The effect of direct compressive stress*
(c) The effect of slenderness ratio
(d) The initial curvature of the column
(SSC JE 2012)
251. For a cantilever beam of length L carrying
a uniform distribution load W over the whole
length, what will be the value of the maximum
bending moment?
(a) WL/2
(b) WL2
/4
(c) WL2
/2
(d) –WL2
/2* (DMRC 2018)
252. The ratio of the polar moment of inertia of
the shaft section to the maximum radius is
called ______.
(a) moment of resistance
(b) modulus of rigidity of shaft
(c) polar modulus*
(d) sectional modulus (DMRC 2018)
253. The Poisson’s ratio of cast iron is ______.
(a) 0.27*
(b) 0.30
(c) 0.29
(d) 0.28 (DMRC 2018)
254. The load at which the column member just
buckles is called _____.
(a) breaking load
(b) point load
(c) crippling load*
(d) design load
255. Variation of bending moment due to
concentrated loads will be:
(a) circular
(b) parabolic
(c) cubical
(d) linear* (DMRC 2017)
256. Consider two rods A, B of the same
material and subjected to equal axial load. The
rod A is of uniform cross-section with diameter
d, and the rod B taper uniformly from diameter d
at one end to diameter d/2 at other end. The ratio
of elongation of rod A to elongation of rod B
will be:
(a) 1 : 1
(b) 1 : 2*
(c) 1 : 3
(d) 1 : 4 (DMRC 2016)
257. The point of contraflexture in a loaded
beam refers to the section where:
(a) Bending moment is maximum
(b) Shear force is maximum
(c) Shear force is zero
(d) Bending moment change sign*
(DMRC 2016)
258. If the principle stresses on a plane stress
problem are S1 = 100 MPa and S2 = 40 MPa,
then the magnitude of shear stress (MPa) will
be:
(a) 60
(b) 50
(c) 30*
(d) None of these (DMRC 2016)
259. A spherical vessel with an inside diameter
of 2 m is made of material having an allowable
stress in tension of 500 kg/cm2
. The thickness of

2.27
a shell to withstand a pressure of 25 kg/cm2
should be:
(a) 5 cm
(b) 10 cm
(c) 2.5 cm*
(d) 1.25 cm (DMRC 2016)
260. A member of length 200 mm and diameter
25 mm is subjected to a tensile load of 20 kN.
The final length of the member is found to be
220 mm. The percentage increase in the length
of the member is :
(a) 2%
(b) 1%
(c) 5%
(d) 10%* (SSC JE 2021)
Hint:
0
0 0
%
f
l l
l
increaseinlength
l l
−

= =
261. Impact load is an example of :
(a) uniform load
(b) static load
(c) dynamic load*
(d) fatigue load (SSC JE 2021)
262. If Poisson's ratio of an elastic material is
0.4, then what will be the ratio of modulus of
rigidity to Young's modulus?
(a) 0.36*
(b) 0.16
(c) 0.06
(d) 0.86 (SSC JE 2020)
Hint: E = 2G(1 + μ)
263. A cylindrical metal bar of 12 mm diameter
is loaded by an axial force of 20 kN results in
change in diameter by 0.003 mm. Poisson's
ratio is given by: (Assume modulus of rigidity =
80 GPa)
(a) 0.56
(b) 0.056
(c) 0.2923*
(d) 0.025 (SSC JE 2020)
Hint: Longitudinal strain
2
/ 20,000 / ( 6 )
2 (1 ) 2 80,000(1 )
long
F A x
A G x
 

 
= = =
+ +
(1)
Lateral strain
4
0.003
2.5 10
12
lat
d
x
d

 −
= = = (2)
From (1) and (2)
μ = 0.2923
264. If stress measuring device shows reading as
1 MPa. It is equivalent to:
(a) 1 N/mm2
*
(b) 10 N/mm2
(c) 1 MN/mm2
(d) 1 kN/mm2
(SSC JE 2020)
Hint: 1 MPa = 1 x 106
N/m2
265. Strain has dimension as:
(a) M1
L0
T0
(b) M0
L1
T0
(c) M0
L0
T0
*
(d) M0
L0
T1
(SSC JE 2020)
266. A graphical method of determining the
normal, tangential and resultant stresses on an
oblique plane is:
(a) Coulomb circle
(b) force circle
(c) stress circle
(d) Mohr circle* (SSC JE 2020)
267. Which of the following statements about a
principal plane is true?
(a) It has maximum shear stress
(b) No shear stress is present*
(c) Shear stress can have any value
(d) It has no normal stress (SSC JE 2020)
268. What will be the magnitude of the shear
stress on the principal plane?
(a) Zero*
(b) Minimum
(c) Negative
(d) Maximum (SSC JE 2020)
269. For a simply supported beam, the bending
moment at the support is _______ kNm.
(a) 1
(b) 0*
(c) <1
(d) >1 (SSC JE 2014, 2020)
Hint: mA = W x (L/2_ - (W/2) x L = 0 = mb

2.28
270. The reaction and bending moments at point
A of the cantilever beam are:
(a) RA = 0 kN and MA = –11 kNm
(b) RA = 30 kN and MA = –115 kNm*
(c) RA = 30 kN and MA = 0 kNm
(d) RA = 30 kN and MA = –125 kNm
(SSC JE 2020)
Hint: RA = 10 + 5 + 15 = 30 kN
MA = –[15 × 6 + 5 × 3 + 10 × 1] = –115 kN-m
(–ve sign denotes hogging nature of beam)
271. Water is flowing in a pipe of 200 cm
diameter under a pressure head of 10000 cm.
The thickness of the pipe wall is 0.75 cm. The
tensile stress in the pipe wall in MPa is:
(a) 13.05
(b) 100
(c) 130.5*
(d) 1305 (SSC JE 2020)
Hint: P = ρgh and σc = Pd/2t
272. Which of the following factor does NOT
affect the buckling load?
(a) Area of cross-section*
(b) Area moment of inertia
(c) Slenderness ratio
(d) Modulus of elasticity (SSC JE 2020)
Hint: Pbl = πEImin/Le
2
273. Define strain energy :
(a) It refers to external work done on a bar
(b) It refers to change in length of a bar
(c) It is the potential energy stored by an elastic
body when deformed*
(d) It is the energy released by a bar during
loading process (SSC JE 2021)
274. The deflection at the centre of a fixed beam
carrying a point load at the center is related to
the deflection of simply supported beam by a
factor of:
(a) 0.50
(b) 1
(c) 0.25*
(d) 0.75 (SSC JE 2020)
Hint:
3
3
/192
/ 48
f
s
Wl EI
Wl EI


=
275. Select the option that correctly matches the
items given in List I to those given in List II.
List I
A. Central deflection in a fixed beam subjected
to uniformly distributed load.
B. Central deflection in a simply supported
beam subject to uniformly distributed load.
C. Central deflection in a simply supported
beam subject to concentrated load at midspan.
D. Deflection at free end of a cantilever subject
to concentrated load at free end.
List II
1. WL3
/3EI
2. WL3
/48EI
3. 5WL3
/384EI
4. WL3
/384EI
(a) A-3, B-4, C-1, D-2
(b) A-3, B-4, C-2, D-1
(c) A-4, B-3, C-2, D-1*
(d) A-4, B-3, C-1, D-2 (SSC JE 2020)
276. The theory of failure applicable to brittle
material is
(a) Maximum principal stress theory*
(b) Maximum shear stress theory
(c) Maximum strain energy theory
(d) Maximum shear strain energy theory
(SSC JE 2017, 2020)
Hint:
1. Maximum principal stress theory:
For brittle material
2. Maximum shear stress theory (Guest's or
Tresca's theory): For ductile material
3. Maximum shear strain energy theory or
Maximum Distortion energy theory (Von-Mises-
Henky Theory): For ductile material
4. Total strain energy theory (Haigh's theory):
For ductile material
5. Maximum principal strain energy (St. Venant
theory): For ductile material
6. Mohr's theory For brittle material

2.29
QUESTIONS FROM ESE EXAMS
277. Consider the following statements for stress
and strain analysis:
1. The stress components on any inclined plane
can easily be found with the help of
a geometrical construction known as Mohr's
stress circle.
2. The ratio of longitudinal strain to lateral strain
is known as Poisson's ratio.
3. When a body is acted upon by three mutually
perpendicular forces, there is change
in the volume of the body which is referred to as
dilation of the material.
4. The ratio of original volume to increase in
volume is known as volumetric strain.
Which of the above statements are correct?
(a) 1 and 3 only*
(b) 2 and 4 only
(c) 3 and 4 only
(d) 1, 2, 3 and 4 (ESE 2021)
278. The stresses on two perpendicular planes
through a point in a body are 160 MPa and 100
MPa, both compressive, along with a shear
stress of 80 MPa. What is the normal stress on a
plane inclined at 30° to the plane of 160 MPa
stress?
(a) -45.72 MPa*
(b) -75.7 MPa
(c) – 59.1 MPa
(d) -86.3 MPa (ESE 2021)
279. Consider the following statements
regarding types of supports and beams:
1. When both supports of beams are roller
supports, the beam is known as simply
supported beam.
2. A beam with one end fixed and the other end
free is known as fixed beam.
3. A beam with both ends fixed is known as
cantilever beam.
4. A beam with one end fixed and the other
simply supported is known as propped
cantilever.
Which of the above statements is/are correct?
(a) 1 only
(b) 1 and 4 only*
(c) 1, 3 and 4 only
(d) 2, 3 and 4 only (ESE 2021)
regarding stress in beam:
1. If a member is subjected to equal and opposite
couples acting in the same
longitudinal planes, the member is said to be in
pure bending.
2. The internal stresses developed in the beam
are known as flexural stresses.
3. There is an intermediate surface known as
neutral surface, at which the stress is
zero.
4. An axis obtained by intersection of the neutral
surface and a cross-section is known
as neutral axis.
(a) 2 and 3 only
(b) 1 and 4 only
(c) 3 and 4 only
(d) 1, 2, 3 and 4* (ESE 2021)
281. Consider the following statements for the
symmetric beam under pure bending.
1. In the elastic range, the normal stress varies
linearly with the distance from the neutral
surface.
2. As long as the stresses remain in the elastic
range, the neutral axis passes through
the centroid of the section.
3. If stresses are in the plastic range, the neutral
axis passes through the centroid of
the section.
Which of the above statement is/are correct?
(a) 1 only
(b) 2 only
(c) 1 and 2 only*
(d) 2 and 3 only (ESE 2021)
282. A cast-iron pipe of 750 mm diameter is
used to carry water under a head of 60 m. What
is the approximate thickness of the pipe if
permissible stress is to be 20 MPa?
(Take specific weight of water as 9.81 kN/m3
)
(a) 22 mm
(b) 14 mm
(c) 11 mm*
(d) 7 mm (ESE 2022)
Hint: For thin cylinder,
6
20 10
2
PD
x
t


2.30
283. A 120 mm wide and 10 mm thick steel
plate is bent into a circular arc of 8 m radius.
What is the bending moment which will produce
the maximum stress? (Take Young's modulus as
200 GPa)
(a) 250 Nm*
(c) 200 Nm
(b) 212 Nm
(d) 172 Nm (ESE 2022)
Hint: max
,max
b
EY
R
 =
,max
b NA
M Z

=
284. A simply supported beam of 8 m length
carries three-point loads of 8 kN, 4 kN and 10
kN at 2 m, 5 m and 6 m respectively from the
left end. What are the left and right support
reactions respectively?
(a) 12 kN and 10 kN
(b) 9 kNand 11 kN
(c) 11 kN and 9 kN
(d) 10 kN and 12 kN*
285. Which one of the following is NOT used as
support for beams?
(a) Roller support
(b) Hinged support
(c) Fixed support
(d) Independent support* (ESE 2022)
286. The distance between the supports of a
simply supported beam is L. The beam has
two equal overhangs of length L/3 over each
support. The beam carries a point load
2W at the centre and a point load Wat each end.
Deflection at the centre is
(a) 1.8 mm
(b) 7.2 mm
(c) 0 mm*
(d) 3.6 mm
287. The maximum bending moment at the fixed
end in a cantilever of length L carrying a
uniformly distributed load W per unit length
across the whole span is
(a) WL2
/2*
(b) WL2
/4
(c) WL3
/4
(d) WL3
/8 (ESE 2022)
Hint: max ( ).
2
L
M WL
=
288. A spherical vessel has 1 m diameter. It is
subjected to internal pressure of 1.5 N/mm2. If
maximum stress is not to exceed 200 N/mm2
and joint efficiency is 80%, then the thickness of
the plate required is
(a) 3.20 mm
(b) 4.21 mm
(c) 5.22 mm
(d) 2.34 mm* (ESE 2022)
Hint: max
4
PD
t



289. A material has modulus of rigidity equal to
0.4 x 105
N/mm2 and bulk modulus equal to
0.75 x 105
N/mm2
. The Poisson's ratio is
(a) 0.2736
(b) 0.1927
(c) 0.3121
(d) 0.4376 (ESE 2022)
290. What is the section modulus (Z) for a
triangular section of base width b and height h?
(a) bh2
/12
(b) bh2
/24*
(c) bh3
/12
(d) bh3
/24 (ESE 2023)
Hint: See figure.
3 2
max
/ 36
/
2 / 3 24
bh bh
Z I y
h
= = =
291. What is the maximum bending moment for
the simply supported beam as shown in figure?
(a) PL4
/12
(b) PL2
/4

2.31
(c) PL2
/2
(d) PL/4* (ESE 2023)
Hint: See following BMD.
292. What is the maximum shear force for the
simply supported beam loaded by a couple
of moment T applied at point B as shown in
figure?
(a) T/L*
(b) Ta/4
(c) TL2
/2
(d) TL/4 (ESE 2023)
Hint: Rc x L + T = 0 ⟹ Rc = -T/L
RA = -RC = T/L
Now, SFD is given below.
293. A Surveyor's steel tape 30 m long has a
cross-section of 15 mm x 0.75 mm. With this,
line AB is measured as 150 m. If the force
applied during measurement is 120 N more
than the force applied at the time of calibration,
what is the elongation? (Take modulus
of elasticity for steel as 200 kN/mm2
).
(a) 4.400 mm
(b) 3.375 mm
(c) 2.125 mm
(d) 1.600 mm*
Hint: ∆ = PL/AE
294. Which one of the following is defined as
the ratio of shearing stress to shearing strain
within elastic limit?
(a) Shear modulus
(b) Poisson's ratio
(c) Modulus of rigidity*
(d) Young's modulus (ESE 2023)
295. The extension of a bar uniformly tapering
from a diameter of (d + a) to (d - a) in a length
L is calculated by treating it as a bar of uniform
cross-section of average diameter d. What is the
percentage error?
(a) 25a2
/d2
(b) 50a2
/d2
(c) 75a2
/d2
(d) 100a2
/d2
* (ESE 2023)
Hint:
2 2
1 2
4 4 4
( )( ) ( )
taper
PL PL PL
d d E d a d a E d a E
 
 = = =
 + − −
2
4
uniform
PL PL
AE d E

 = =
% error =
2 2 2
2 2
4 4
( )
100
( )
PL PL
d a E d E
x
d a E
 

−
−
−
296. What is the torque, if a shaft of 200 mm
diameter can transmit safely and the shear
stress is not to exceed 50 N/mm2
?
(a) 78.54 N-m
(b) 78.54 kN-m*
(c) 152.45 kN-m
(d) 152.45N-m (ESE 2023)
Hint: T = (πd3
/16)τmax
297. For the design of a thin cylindrical shell, if
fa is allowable tensile stress for the material of
the shell, thickness t of the cylindrical shell of a
diameter d and internal pressure p, then the
criterion for the thickness is
(a) t ≥ p/2fa
(b) t ≥ d/2fa
(c) t ≤ pd/2fa
(d) t ≥ pd/2fa (ESE 2023)
Hint: σmax = σh = pd/2t
If fa is allowable stress then
σmax ≤ fa
∴ pd/2t ≤ fa
298. Consider the following assumptions for
Lame's problem of stress distribution in the thick
shells:
1. The material of the shell is heterogeneous and
isotropic.
2. Plane sections of the cylinder, perpendicular
to the longitudinal axis, remain plane

2.32
under the pressure.
3. The material of the shell is homogeneous and
isotropic.
Which of the above statements is/are correct?
(a) 1 only
(b) 3 only
(c) 2 and 3 only*
(d) 1 and 2 only (ESE 2023)
regarding modes of failure:
1. A ductile material is one which has a
relatively large tensile strain before fracture
takes place.
2. A brittle material has a relatively small tensile
strain before fracture.
3. A static load is defined as a force, which is
gradually applied to a mechanical component
and which changes its magnitude or direction
with respect to time.
(a) 1 and 2 only*
(b) 1 and 3 only
(c) 2 and 3 only
(d) 1, 2 and 3 (ESE 2024)
regarding theories of elastic failure :
1. Experimental investigations suggest that
maximum principal stress theory gives good
predictions for brittle materials.
2. Maximum shear stress theory predicts that the
yield strength in shear is equal to the yield
strength in tension.
3. Maximum shear stress theory is also known as
Coulomb, Tresca and Guest theory.
(a) 1 and 2 only
(b) 1 and 3 only*
(c) 2 and 3 only
(d) 1, 2 and 3 (ESE 2024)
regarding distortion energy theory:
1. It is known as Huber-van Mises- Hencky
theory.
2. The yield strength in shear is 0.577 times the
yield strength in tension.
3. Experiments have shown that the distortion
energy theory is in better agreement for
predicting the failure of a brittle component than
any other theory of failure.
(a) 1 and 2 only*
(b) 1 and 3 only
(c) 2 and 3 only
(d) 1, 2 and 3 (ESE 2024)
302. A piece of material is subjected to same
two perpendicular tensile stresses of 100 MPa
each. What is the direct stress?
(a) 90 MPa
(b) 100 MPa*
(c) 96 MPa
(d) 86 MPa (ESE 2024)
Hint: See Mohr circle given below
303. The strain energy per unit volume required
to cause the material to rupture is called
(a) modulus of toughness*
(b) modulus of rigidity
(c) resilience
(d) proof resilience (ESE 2024)
304. Consider the following regarding buckling
concept:
1. Buckling can occur when the induced stresses
are compressive such as in a column.
2. Buckling analysis uses the Young's modulus
of the material and the moment of inertia of the
column cross-section, as well as its length.
3. The load that buckles the column is called the
crushing load.
(a) 1 and 2 only*
(b) 1 and 3 only
(c) 2 and 3 only
(d) 1, 2 and 3 (ESE 2024)
regarding theories of failures:
1. Maximum principal strain theory is known as
St. Venant's theory.
2. Maximum shear strain energy theory is
known as Mises and Hencky theory.

2.33
3. Maximum strain energy theory is known as
Guest and Tresca theory
(a) 1 and 2 only*
(b) 1 and 3 only
(c) 2 and 3 only
(d) 1, 2 and 3 (ESE 2024)
regarding beams :
1. Beams with one end fixed and the other end
simply supported are known as propped
cantilevers.
2. Beams supported at more than two sections
are known as fixed beams.
3. Beams with one end fixed and the other end
free are known as cantilevers.
(a) 1 and 2 only
(b) 1 and 3 only*
(c) 2 and 3 only
(d) 1, 2 and 3 (ESE 2024)
regarding effective length of a column:
1. The effective length is the distance between
the points of inflection in the deformed shape of
the column, which is referred to as the elastic
curve.
2. At the inflection point, the moment does not
change sign and the member is not expected to
resist any moment.
3. At the transition point, the curvature is
changed and it is called the contraflexure point.
(a) 1 and 2 only
(b) 1 and 3 only*
(c) 2 and 3 only
(d) 1, 2 and 3 (ESE 2024)
regarding power transmitted through a circular
shaft :
1. The stress and deformation induced in the
shaft can be calculated by relating power to
torque.
2. The power produced by a motor is rated in
terms of shaft horsepower at a specified
rotational speed.
3. Power is defined as the work done per unit
time.
(a) 1 and 2 only
(b) 1 and 3 only
(c) 2 and 3 only
(d) 1, 2 and 3* (ESE 2024)
309. Which one of the following is the ability of
a material to regain its original shape on removal
of the applied load?
(a) Proof resilience
(b) Resilience
(c) Modulus of resilience*
(d) Gradual resilience (ESE 2024)
QUESTIONS FROM GATE
EXAMS
310. The magnitude of reaction force at joint C
of the hinge-beam shown in the figure is
_______ kN (round off to 2 decimal places).
(a) 10 kN
(b) 20 kN*
(c) 30 kN
(d) 40 kN (GATE 2020)
Hint: , 0
B right
M
 =
311. The truss shown in the figure has four
members of length l and flexural rigidity EI, and
one member of length l2 and flexural rigidity
4EI. The truss is loaded by a pair of
forces of magnitude P, as shown in the figure.

2.34
The smallest value of P, at which any of the
truss members will buckle is
(a)
2
2
EI
l

(b)
2
2
2 EI
l

(c)
2
2
2
EI
l

(d)
2
2
2 EI
l

* (GATE 2020)
Hint: See figures.
2
2
(4 )
( 2 )
EI
P
l

=
312. Bars of square and circular cross-section
with 0.5 m length are made of a material with
shear strength of 20 MPa. The square bar cross-
section dimension is 4 cm x 4 cm and the
cylindrical bar cross-section diameter is 4 cm.
The specimens are loaded as shown in the
figure.
Which specimen(s) will fail due to the applied
load as per maximum shear stress theory?
(a) Torsional load specimen
(b) Bending load specimen
(c) None of the specimens
(d) Tensile and compressive load specimens*
(GATE 2020)
Hint:
3
2
2
80 10
50 /
40
x
N mm
 = =
2
max / 2 25 / 20
N mm MPa
 
= = 
3
2
max 3 3
16 16 64 10
16 /
(40)
T x x
N mm
d


 
= = =
which is less than 20 MPa
3
2
3
320 10
30 /
40 / 6
x
N mm
 = =
2
max / 2 15 / 20
N mm MPa
 
= = 

2.35
313. A right solid circular cone standing on its
base on a horizontal surface is of height H and
base radius R. The cone is made of a material
with specific weight wand elastic
modulus E. The vertical deflection at the mid-
height of the cone due to self-weight is
(a) wRH/8E
(b) wH2
/8E*
(c) wRH/6E
(d) wH2
/6E (GATE 2021)
Hint:
3
x
Wxdx
E
 =

/2 3
H
H
Wx
dx
E
 = 
314. A cantilever beam of length, L, and flexural
ridigity, El, is subjected to an end moment, M,
as shown in the figure. The deflection of the
beam at x = L/2 is
(a)
2
16
ML
EI
(b)
2
4
ML
EI
(c)
2
2
ML
EI
(d)
2
8
ML
EI
* (GATE 2021)
Hint: Deflection (y) is given by
2
1 2
( )
2
x
x
EI y M x C x C
= + +
In our case, y comes out to be
2
2
Mx
y
EI
=
315. A prismatic bar PQRST is subjected to
axial loads as shown in the figure. The segments
having maximum and minimum axial stresses,
respectively, are
(a) ST and PQ
(b) QR and PQ
(c) ST and RS*
(d) QR and RS (GATE 2021)
Hint: See figure
316. An overhanging beam PQR is subjected to
uniformly distributed load 20 kN/m as shown in
the figure.
All dimensions are in mm.
The maximum bending stress developed in the
beam is _______ MPa (round off to one decimal
place).
(a) 200 MPa
(b) 250 MPa*
(c) 300 MPa
(d) none of these (GATE 2021)
Hint: Reaction at P comes out to be 15 kN.
0.75
15 0.75 20 0.75 5.625
2
s
M x x x kNm
= − =
max 20 1 0.5 10
Q
M M x x kNm
= = =
6
max
,max 2
10 10 6
24 100
b
M x x
Z x
 = =

2.36
317. An L-shaped elastic member ABC with
slender arms AB and BC of uniform cross-
section is clamped at end A and connected to a
pin at end C. The pin remains in continuous
contact with and is constrained to move in a
smooth horizontal slot. The section modulus of
the member is same in both the arms. The end C
is subjected to a horizontal force P and all the
deflections are in the plane of the figure. Given
the length AB is 4a and length BC is a, the
magnitude and direction of the normal force on
the pin from the slot, respectively, are
(a) 3P/8 and downwards*
(b) 5P/8 and upwards
(c) P/4 and downwards
(d) 3P/4 and upwards
Hint:
1 2
C C
 = 
3 3
8 64
3
Pa Fa
EI EI
=
318. A structure, along with the loads applied on
it, is shown in the figure. Self-weight of all the
members is negligible and all the pin joints are
friction-less. AE is a single member that
contains pin C. Likewise, BE is a single member
that contains pin 0. Members GI and FH are
overlapping rigid members. The magnitude of
the force carried by member
CI is ____ kN (in integer). (GATE 2022)
(a) 18 kN*
(b) 20 kN
(c) 22 kN
(d) none of these
319. A beam is undergoing pure bending as
shown in the figure. The stress (σ)-strain (ε)
curve for the material is also given. The yield
stress of the material is cry. Which of the
option(s) given represent(s) the bending stress
distribution at cross-section AA after plastic
yielding?
(a)
(b)
(c)

2.37
*
(d)
* (GATE 2023)
Hint: If bending stress at every fibre is equal to
yield strength of the material, then entire
cross-section undergoes plastic bending. Then,
option (c) is correct.
If bending stress at inner fibres is less than yield
strength and bending stress at extreme fibres is
equal to yield strength, then, option (d) is
correct.
320. The principal stresses at a point P in a solid
are 70 MPa, -70 MPa and 0. The yield stress of
the material is 100 MPa. Which prediction(s)
about material failure at P is/are CORRECT?
(a) Maximum normal stress theory predicts that
the material fails*
(b) Maximum shear stress theory predicts that
the material fails
(c) Maximum normal stress theory predicts that
the material does not fail
(d) Maximum shear stress theory predicts that
the material does not fail* (GATE 2023)
Hint: τmax = 100 MPa
As per MPST, σ1 = 70 MPa < Syt = 100 MPa
Hence safe.
As per MSST, τmax = 70 MPa > Sye = Syt/2 = 50
MPa (Unsafe)
321. Which of the plot(s) shown is/are valid
Mohr's circle representations of a plane stress
state in a material? (The center of each circle is
indicated by O).
(a) M1*
(b) M2
(c) M3
(d) M4 (GATE 2023)
322. The figure shows a block of mass m = 20
kg attached to a pair of identical linear springs,
each having a spring constant k = 1000 N/m.
The block oscillates on a frictionless horizontal
surface. Assuming free vibrations, the time
taken by the block to complete ten oscillations is
____ seconds. (Rounded off to two decimal
places). Take π = 3.14. (GATE 2023)

2.38
keq = k + k = 2k = 2 x 1000 = 2000
m = 20 kg
Natural frequency ,
2000
10 /
20
eq
n
k
rad s
m
 = = =
Time period of oscillation, Tn = 2π/ωn
Time taken to complete 10 oscillations
= 10 x 2π/10
323. A beam of length L is loaded in the xy-
plane by a uniformly distributed load, and by
a concentrated tip load parallel to the z-axis, as
shown in the figure. The resulting bending
moment distributions about they and the z axes
are denoted by My and Mz, respectively.
Which one of the options given depicts
qualitatively CORRECT variations of My and
Mz along the length of the beam?
(a)
(b)
(c)
(d)
(GATE 2023)
Hint: Due to UDL, BM is negative and varies
parabolically in vertical plane i.e bending
moment is acting about Z-axis (Mz)
Due to Horizontal concentrated point load,
bending moment is positive and varies
linearly in horizontal plane i.e. bending moment
is acting about Y-axis(My ).
324. The figure shows a thin-walled open-top
cylindrical vessel of radius rand wall thickness
t. The vessel is held along the brim and contains
a constant-density liquid to height h from the
base. Neglect atmospheric pressure, the weight
of the vessel and bending stresses in the vessel
walls.
Which one of the plots depicts qualitatively
correct dependence of the magnitude of axial
wall stress (σ1) and circumferential wall stress
(σ2) on y?
(a)
*
(b)
(c)

2.39
(d)
(GATE 2023)
Hint: P = ρgh
σh = PD/2t = ρgh(D/2t)
∴ σh ∝ h
Longitudinal stress will be developed because of
the total amount of fluid and since this amount is
constant, the longitudinal stress will be constant.
325. Cylindrical bars P and Q have identical
lengths and radii, but are composed of different
linear elastic materials. The Young's modulus
and coefficient of thermal expansion of Q are
twice the corresponding values of P. Assume the
bars to be perfectly bonded at the interface, and
their weights to be negligible.
The bars are held between rigid supports as
shown in the figure and the temperature is raised
by ∆T Assume that the stress in each bar is
homogeneous and uniaxial. Denote the
magnitudes of stress in P and Q by σ1 and σ2,
respectively.
Which of the statement(s) given is/are
CORRECT?
(a) The interface between P and Q moves to the
left after heating*
(b) The interface between P and Q moves to the
right after heating.
(c) σ1 < σ2
(d) σ1 = σ2* (GATE 2023)
Hint: See figure.
As the areas of both the bars are same, therefore,
the stress developed in both the bars will remain
same.
RL
P l T
AE

 = −
(2 )
(2 )
RL
Q l T
A E

 = −
We can say that ∆Q > ∆P. Therefore, interface
will move towards left side.
326. A cylindrical bar has a length L = 5 m and
cross section area S = 10 m2
. The bar is made of
a linear elastic material with a density ρ = 2700
kg/m3
and Young's modulus E = 70 GPa. The
bar is suspended as shown in the figure and is in
a state of uniaxial tension due to its self-weight.
The elastic strain energy stored in the bar equals
___ J. (Rounded off to two decimal places).
Take the acceleration due to gravity as g = 9.8
m/s2
. (GATE 2023)
Answer: 2.09 N-m
Hint:
2 2 2
6 6
W L AL
U
AE E

= =
327. A cylindrical transmission shaft of length
1.5 m and diameter 100 mm is made of a linear
elastic material with a shear modulus of 80 GPa.
While operating at 500 rpm, the angle of twist
across its length is found to be 0.5 degrees. The
power transmitted by the shaft at this speed is
____ kW. (Rounded off to two decimal
places) Take 1t = 3.14. (GATE 2023)
Answer: 239.246 kW
Hint: Use following equations.

2.40
TL
GJ
 = and
2
60
NT
P

=
328. The figure shows a thin cylindrical pressure
vessel constructed by welding plates
together along a line that makes an angle a = 60°
with the horizontal. The closed vessel has a wall
thickness of 10 mm and diameter of 2 m. When
subjected to an internal pressure of 200 kPa, the
magnitude of the normal stress acting on the
weld is ___ MPa. (rounded off to 1 decimal
place). (GATE 2024)
Hint:
0.2 2000
10
4 4 10
x L
PD x
MPa
t x
 
= = = =
0.2 2000
20
2 2 10
y h
PD x
MPa
t x
 
= = = =
See figure.
Normal stress (σn)θ =
cos sin 2
2 2
x y x y
xy
   
  
+ −
   
+ +
   
   
0
2
,30
10 20 10 20
cos(2 30 )
2 2
n
x

+ −
   
= +
   
   
= 12.5 MPa
329. A solid massless cylindrical member of 50
mm diameter is rigidly attached at one end, and
is subjected to an axial force P = 100 kN and a
torque T = 600 Nm at the other end as shown.
Assume that the axis of the cylinder is normal to
the support. Considering distortion energy
theory with allowable yield stress as 300 MPa,
the factor of safety in the design is ___ (rounded
off to 1 decimal place) (GATE 2024)
Hint: Axial stress due to P,
( )
3
2
100 10
50.93
50 / 4
x a
P x
MPa
A x
 

= = = =
Shear stress due to T,
3
3 3
16 16 600 10
24.446
50
xy
T x x
MPa
D x

 
= = =
σy = 0
2 2
, 3
l per x xy
  
 +
2 2
300
50.93 3 24.446
yt
S
x
N N
=  +
Giving N ≤ 4.529
330. A horizontal beam of length 1200 mm is
pinned at the left end and is resting on a roller
at the other end as shown in the figure. A
linearly varying distribution load is applied on
the beam. The magnitude of maximum bending
moment acting on the beam is __ Nm. (round off
to 1 decimal place) (GATE 2024)
Reactions are RA= 20 N and RB = 40 N (Do it
yourself)

2.41
Now, SF at section 'x-x' at a distance of x
SFx = 0
1 100
20 ( ). 0
2 1.2
x
x
− =
x = 0.693 m (BM will be maximum at this point)
max
1 0.693 100 0.693 0.693
20 0.693 .
2 1.2 3
x x
M x x
= −
= 9.2 kNm

Strength of materials (Objective Questions)

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