Strength of Materials Sample Objective

1.1 SIMPLE STRESS & STRAIN

1. The number of independent elastic constants for a
linear elastic isotropic and homogeneous material is
[GATE-2010][CE]
a) 4
b) 3
c) 2
d) 1

2. In terms of Poisson’s ratio () the ratio of Young’s
Modulus (E) to Shear Modulus (G) of elastic materials is
[GATE-2004][ME]
a) 2(1 + )
b) 2(1 - )
c) (1 + )
d) (1 - )

3. A large uniform plate containing a rivet-hole is
subjected to uniform uniaxial tension of 95 MPa. The
maximum stress in the plate is
[GATE-1992][ME]

a) 100 MPa
b) 285 MPa
c) 190 MPa
d) Indeterminate

4. The maximum value of Poisson’s ratio for an elastic
material is
[GATE-1991][CE]
a) 0.25
b) 0.5
c) 0.75
d) 1.0

5. The elongation of the bar due to its own weight is.
(a) Wl / 2 AE
(b) Wl / AE
(c) Wl / b2E
(d) 2Wl / AE

6. A steel rod of 2 cm2 area and 1m in height is subjected
to a pull of 40,000 N. If Young’s Modulus is 2 x 105 N /
mm2, the elongation of the rod in mm will be.
(a) 10
(b) 100
(c) 1
(d) 0.1

7. If all the dimensions of a vertically suspended circular
bar are doubled, then the maximum stress produced in it
due to its own weight will .
(a) become half
(b) remain unaltered
(c) be doubled
(d) be tripled

8. The diameter of a tapering rod varies from ‘D’ to ‘D/2’
in length of ‘L’ m. If it is subjected to an axial tension of
‘P’ the change in length is.
(a) 4 PL /ED2
(b) 8 PL /ED2
(c) 2 PL /  ED2
(d) None of the above

9. If a member is subjected to tensile stress of ‘Px’,
compressive stress of ‘Py’ and tensile stress of ‘Pz’ along
the x, y and z directions respectively, then the resultant
strain ‘ex’ along the x -direction would (E is Young’s
modulus of elasticity ‘ ‘ is Poisson’s ratio)
(a) (1/E)(Px + Py -Pz)
(b) (1/E)(Px + Py + Pz)
(c) (1/E)(Px- Py + Pz)
(d) (1/E)(Px - Py - Pz).

10. A hole to be punched in a plate of 10 mm thick. The
allowable crushing stress of the punch is 4 times the
shearing / stress of the plate. The diameter of the smallest
hole that can be punched in the plate is ‘mm’ is
(a) 10 mm
(b) 20 mm
(c) 40mm
(d) none

11. For the compound the bar shown below, the ratio of
greatest to the least elongations of different components
is,

12. The axial movement of bottom surface of a compound
bar loaded as shown below is .

(a) 1.5 (PL / AE)
(b) 2.0 (PL / AE)
(c) 2.5 (PL / AE)
(d) 3.0 (PL / AE)
13. The total elongation of the structural element fixed, at
one end, free at the other end, and of varying cross-
section as shown in the figure when subjected to a force p
at free end is given by
(GATE-1991) (CE)

a) PL/AE
b) 3 PL/AE
c) 2.5 PL/AE
d) 2PL/AE

14. Below Fig. shows a rigid bar hinged at A and
supported in a horizontal position by tow vertical identical
steel wires. Neglect the weight of the beam. The tension
T1 and T2 induced in these wires by a vertical load P
applied as shown are
[GATE-1994][ME]

a) T1  T2  P
2

b) T1  Pb1 , T2  Pb1
(a2  b2) (a2  b2)

c) T1  Pb1 , T2  Pb1
(a2  b2) (a2  b2)

d) T1  Pb1 , T2  Pb1
(a2  b2) (a2  b2)

15. A 200 x 100 x 50 mm steel block is subjected to a
hydrostatic pressure of 15 MPa. The Young’s modulus
and Poisson’s ratio of the material are 200 GPa and 0.3
respectively. The change in the volume of the block in
mm3 is
[GATE-2003][ME]
a) 85
b) 90
c) 100
d) 110

16. For the compound bar shown below, the ratio of
stresses in the portions AB:BC:CD will be .

(a) 4 : 1 : 2
(b) 1 : 2 : 4
(c) 1 : 4 : 2
(d) 4 : 2 : 1

17. The ratio of loads shared by parts ‘AB’ and ‘BC’ of
the bar shown below is

(a) 1 : 1
(b) 2 : 1
(c) 3 : 1
(d) 1 : 2

18. ABC is rigid bar. It is hinged at ‘A’ and suspended at
‘B’ and ‘C’ by two wires ‘BD’ and ‘CE’ made of copper
and steel respectively. The bar carries a load of 1 t at ‘F’
midway between ‘B’ and ‘C’ Given Ac = 4 cm2 , As = 2
cm2 , Ec = 1 x 106 kg/cm2 , Es = 2 x 106 kg/cm2
The ratio of forces in copper and steel wires is.

(a) 0.5
(b) 4
(c) 0.25
(d) 2

19. An elastic body is subjected to a direct compressive
stress ‘ Px’ in longitudinal direction. If the lateral strains
in the other two directions are prevented by applying ‘Py’
and ‘Pz’ in those directions, then Py = Pz is equal to
( Poisson’s ratio)
(a) Px / ( - 1)
(b)  . Px
(c) Px /  (1-2)
(d)  . Px / (1-  )

20. A short cast iron column carries a load of 50 t. If the
original dia is 8 cm, E = 1 x 106 kg/sq.cm and Poisson’s
ratio 0.25, the increase in dia of column in ‘cm’ would be
(a) 0.00318
(b) 0.00256
(c) 0.002
(d) 0.00280.

21. Assume that Young’s modulus of steel is twice that of
brass. two bars of brass and a bar of steel of equal cross
section form a single tension member with the help of
rigid pins as shown in the fig. The shear in the pin will be

(a) 0.25 P
(b) 0.5 P
(c) 0.33 P
(d) 0.4
22. A rigid beam ABCD is hinged at D and supported by
two springs at A and B as shown in the fig. The beam
carries a vertical load P at C. The stiffness of spring at A
is 2 K and that of B is K. The ratio of forces of spring at
A and that of spring at B is

(a) 1 (b) 2 (c) 3 (d) 4

23. In the given fig,. the wires AB and CD made of the
same material are used to suspend a rigid block to which
the gradual load ‘W’ is applied in such a way that both the
wires get stretched by the same amount. If stresses in
wires AB and CD are 1 and 2 respectively . then the
ratio 1 / 2 will be.

(a) 3 / 2
(b) 2 / 3
(c) 2
(d) 1/ 2

Questions 24 and 25 are based on the following data
(linked questions)
A steel rod of cross sectional area 2000 mm2 and two
brass rods each of 1000mm2 together support a load 10
kN, Es= 2 x 105 MPa ; Eb = 1 x 105 MPa.

24. The ratio of load taken by each steel bar to that of
brass bar is .
(a) 3 / 2
(b) 2 / 3
(c) 2 / 1
(d) 8 / 1

25. The stresses developed due to 10 kN in steel and brass
in MPa respectively are .
(a) 1.25& 3.75
(b) 3 & 1.5
(c) 2.5 & 2.5
(d) 4 and 1

Questions 26 and 27 are based on the following data
(linked questions)

A mild steel rod of 20 mm diameter and 300 mm long is
centrally enclosed inside a copper tube of same length and
having external diameter 30 mm and internal diameter
25mm. The ends are brazed together. The composite bar
is subjected to an external tensile force of 40kN.
Es= 200 GPa ; Ecu =100 GPa.

26. The stresses developed in steel and copper
respectively in ‘MPa’ are
(a) 150 and 25
(b) 75 and 25
(c) 47 and 37
(d) 95 and 47.

27. The extension of composite bar in ‘mm’ is
(a) 0
(b) 0.62
(c) 0.142
(d) 0.38

Questions 28 and 29 are based on the following data
Two wires are connected to a rigid bar as shown in the
fig. If the load of ‘w’ is to be placed on the rigid bar so as
to the wire on the left is of steel and having a cross
sectional of 0.1 cm2 and young’s modulus of 2000,00
MPa. wire on the right is made of aluminum having a
cross of 0.2 cm2 and a young’s modulus of 66,667 MPa.
the bar horizontal ,

28. The distance ‘x’ from the left end. (steel wire end)

where this weight should be placed is :

(a) 5.6 cm (b) 8.57 cm

(c) 9.21 cm (d) 11.24 cm

29. The stresses developed, in MPa, respectively in steel
and aluminum are .
(a) 23.56 & 12.65
(b) 456.78 & 34.5
(c) 715 & 145
(d) 500 & 250

Questions 30 and 31 are based on the following data

In the above problem if the load is applied at the center of
the two wires .

30. The stresses developed, in MPa, respectively in steel
and aluminum are .

(a) 23.56 and 12.65
(b) 45.78 & 678.78
(c) 715 and 145
(d) 500 and 250.

31. The angular displacement of rigid bar due to the load
at the center of the two wires is .

(a) 0.65(c.w)
(b) 0.43(c.w)
(c) 0.65 (anti c.w)
(d) 0.43 (anti c.w).

32. A steel bolt having a nominal diameter of 20 mm and
a pitch of 2.4 mm is used to connect two plates of 10 mm
thickness each. An aluminum tube of inner diameter
22mm and outer diameter of 40 mm is separating the
plates as shown in fig. The nut is pulled snug (just tight)
and then given a one- third additional turn. Find the
resulting stresses in the bolt and the tube neglecting the
deformation of the plates. Young’s modulus of steel and
aluminum are 207 x 103 MPa and 67.5 x 103 MPa
respectively.
(G-2K)

_____

1.1 SIMPLE STRESSES & STRAIN (ANS.)
1-c, 2-a, 3-c, 4-b, 5-a, 6-c,7-c, 8-b, 9-a, 10-a, 11- 9:1, 12-,
13-c, 14-b, 15-b, 16-c, 17-d, 18-a, 19-d, 20-c, 21-a, 22-c,
23-c, 24-c, 25-c, 26-d, 27-c, 28-b, 29-c, 30-d, 31-b, 32-b
= 72.55 N/mm2 r = 263.36 N/mm2

1.2 THERMAL STRESS

1. A uniform, slender cylindrical rod is made of a
homogenous and isotropic material. The rod rests on a
frictionless surface. The rod is heated uniformly. It the
radial and longitudinal thermal stresses are represented by
r and z respectively, then
[GATE-2004][ME]
a) r = 0 ,z = 0
b) r  0 ,z = 0
c) r = 0 ,z  0
d) r  0 ,z  0

2. A steel rod of length L and diameter D, fixed at both
ends, is uniformly heated to a temperature rise of T. The
Young’s modulus is E and the coefficient of linear
expansion is ‘’. The thermal stress in the rod is
[GATE-2007][ME]
a) 0
b)  T
c) E T
d) E TL

3. A cantilever beam of tubular section consists of 2
materials copper as outer cylinder and steel as inner
cylinder. It is subjected to temperature rise of 200C and
copper>steel. The stress developed in the tubes will be
[GATE-1991][CE]
a) Compression is steel and tension in copper
b) Tension in steel and compression in copper
c) No stress in both
d) Tension in both the materials

4. A square plate (a x a) rigidly held at three edges is free

to move along the fourth edge. if temperature of the plate

is raised by temperature ‘t’, then the free expansion at the

fourth edge will be(coefficient of thermal expansion of

the material is , modulus of elasticity of the material is E

and its Poisson’s ratio is v)

(a) a  t v (b) a  t (1+ v)

(c) a  t + t v. (d) a  t (1 + v)

5. A thin steel tyre of diameter ‘d’ is to be shrunk on to

slightly large wheel of diameter ‘D’, if ‘E’ is the modulus

of elasticity of steel, the circumferential stress developed

:

(a) ((D-d)/ d) E comp. (b) ((D-d)/ d )E tensile

(c) ((D-d)/ D ) E comp. (d) ((D-d)/ D ) E tensile.

6. A steel bar is kept between two copper(parallel) bars

and rigidly connected at room temperature. lf the system

is fixed at the ends and cooled suddenly the stresses

produced in the bars will be .

(a) tensile in steel & compression in copper

(b) compression in both steel & copper

(c) tension in both steel & copper

(d) compression in steel & tension in copper

7. A metal bar of length 100 mm is inserted between two

rigid supports and its temperature in increased by 100C. If

the coefficient of thermal expansion is 12 x 10-6 per OC

and the Young’s modulus is 2 x 105 MPa, the stress in the

bar is (GATE 2007) (CE)

a) zero b) 12 MPa

c) 24 MPa d) 2400 MPa

8. Determine the temperature rise necessary to induce
bucking in a 1m long circular rod of diameter 40 mm
shown in the figure below. Assume the rod to be pinned at
its ends and the coefficient of thermal expansion as 20 x
10-6/0C. Assume uniform heating or the bar.
[GATE-1993][ME]

Questions 9 and 10 are based on the following
data.(Linked questions)
A composite bar made up of aluminum and steel is held
between two rigid supports is shown in fig. The are stress
free at 380C , Es = 200GPa; Ea = 70GPa; s = 11 x 10-6
/ 0C ; a = 24 x 10-6 / 0C.,Ls = La = 1m ; As= 100 mm2,
Aa = 200 mm2. The temperature is increased to 580C;

9. The support reactions in kN are.
(a) 2.34
(b) 5.76
(c) 6.98
(d) 8.96.

10. The stresses in steel and aluminum bars respectively
in MPa.
(a) 57.65 & 57.65
(b) 57.65 & 28.82
(c)28.82 & 14.41
(d) none

Questions 11 and 12 are based on the following data.
(Linked questions)

A gun metal rod of cross section area 200 mm2 is
screwed at ends, passes through a steel tube of cross
sectional area of 100 mm2. The nuts on the rod are
screwed tightly home on the ends of the tube. the
temperature is decreased by 200 FEs = 200 GPa ; Egm =
100GPa; s = 6 x 10-6 / 0F, gm = 10 x 10-6 / 0F, Ls,
Lgm= 1.25 m;

11. The temperature thrust due to composite action is , in
kN.
(a) 2
(b) 4
(c) 6
(d) 8

12. The temperature stresses in steel and gun metal
respectively in MPa are .
(a) 80 & 200
(b) 80 & 40
(c) 40 & 120
(d) 60 & 120

Questions 13 and 14 are based on the following) data.
A rigid block weighing 60kN is supported by three rods
symmetrical placed as shown in fig.The lower ends the
rods are assumed to have been at the same level before
the block is attached. The cross section of the rods and the
modulus of elasticity of the materials the rods are given as
Es = 210GPa; Eb = 98GPa.As = 5 x 10-4 m2;
Ab 10 x 10-4 m2, ls = 0.5 m; lb = 1 m;

13. The stress in steel rod is
(a) 48.65 MPa
(b) 52.35 MPa
(c) 60 MPa
(d) 40 MPa

14. If the coefficient of thermal expansion for steel and

bronze are 11 x 106/ 0C and 19 x 106 / 0C respectively,

the temperature rise in 0C necessary to cause all the

applied load to be supported by the steel rods is .

(a) 10 (b) 10.58

(c) 15 (d) 28.00

15. If the rod fitted snugly between the supports as shown
in the fig, is heated, the stress induced in it due to 200c
rise temperature will be. [98]

(a) 0.07945 MPa
(b) -0.07945 MPa
(c) -0.03972 MPa
(d) 0.03972 MPa
1.2 THERMAL STRESSES : 1-a, 2-a, 3-b, 4-b, 5-b, 6-d,
7-c, 8-sol, 9-b, 10-b, 11-d, 12-b, 13-a, 14-b, 15-b.

1.1 & 1.2 PRACTICE QUESTIONS

1. The principle of superposition is made use of in
structural computations when :
[GATE-1990][CE]

a) The geometry of the structure changes by a finite
amount during the application of the loads
b) The changes in the geometry of the structure during the
application of the loads is too small and the strains in the
structure are directly proportional to the corresponding
stresses
c) The strains in the structure are not directly proportional
to the corresponding stresses, even though the effect of
changes in geometry can be neglected.
d) None of the above conditions are met

2. The figure below shows a steel rod of 25mm2 cross
sectional area. It is loaded at four points. K, L, M and N.
Assume Esteel = 200 GPa. The total change in length of
the rod due to loading is
[GATE-2004][ME]

a) 1m
b) -10m
c) 16m
d) - 20m

3. A steel bar of 40 mm x 40 mm square -section is
subjected to an axial compressive load of 200 KN. If the
length of the bar is 2m and E = 200 GPa. The elongation
of the bar will be
[GATE-2006][ME]
a) 1.25 mm
b) 2.70 mm
c) 4.05 mm
d) 5.40 mm

4. A bar having a cross-sectional area of 700 mm2 is
subjected to axial loads at the positions indicated. The
value of stress in the segment BC is
[GATE-2006][ME]

a) 40 MPa
b) 50 MPa
c) 70 MPa
d) 120 MPa
5. The axial movement of top surface of stepped column
as shown in figure is
[GATE-1989][CE]

a) 2.5 PL/AE
b) 3 PL/AE
c) 1.5 PL/AE
d) 2 PL/AE

6. The stretch in a steel rod of circular section, having a
length ‘I’ subjected to a tensile load ‘P’ and tapering
uniformly from a diameter d1 at one end to a diameter d2
at the other end, is given. [95]
(a) P.l /4 Ed1.d2
(b) P.l /Ed1.d2
(c) P.l /4E (d1.d2)
(d) 4P.l /E.d1.d2

7. The total extension of the bar loaded as shown in the
fig is. A= area of cross - section, E = modulus of
elasticity.
[95]

(a) 10 x 30/AE
(b) 26 x 10/AE
(c) 9 x 30/AE
(d) 30 x 22/AE

8. If Poisson’s ratio a material is 0.5, then the elastic
modulus for the material is.
[95]

(a) three times its shear modulus.
(b) for times its shear modulus.
(c) equal to its shear modulus.
(d) In terminate.

9. A bar of uniform cross-section of one sq.cm is
subjected to a set of five forces as shown in the given fig.
exulting in its equilibrium. the maximum tensile stress (in
kgf/cm2) produced in the bar is. [97]

(a) 1
(b) 2
(c) 10
(d) 11

10. Match List I (Elastic properties of an isotropic elastic

material) with List II (Natural of strain produced) and

select the correct answer using the codes given below the

lists :

[97]

List- I List - II

A. Young’s modulus - 1. Shear strain.

B. Modulus of rigidity - 2. Normal strain.

C. Bulk modulus - 3. Transverse strain.

D. Poisson’s ratio - 4. Volumetric strain

Codes:

ABCD

(a) 1 2 3 4

(b) 2 1 3 4

(c) 2 1 4 3

(d) 1 2 4 3

11. A 10 cm long and 5 cm diameter steel rod fits snugly

between two rigid walls 10 cm a part at room

temperature. Young’s modulus of elasticity and

coefficient of linear expansion of steel are 2 x 106kg/cm2

& 12 x 10-6 / 0C. respectively. The stress developed in

the rod due to a 1000C rise in temperature wall be. [97]
(a) 6 x 10-10 kgf /cm2
(b) 6 x 10-9 kgf /cm2
(c) 2.4 x 103 kgf /cm2
(d) 2.4 x 104 kgf /cm2

12. For a composite bar consisting of a bar enclosed
inside a tube of another material and when compressed
under a load ‘W’ as a whole through rigid collars at the
end of the bar. The equation of compatibility is given by
(suffixes)
1 and 2 refer to bar and tube respectively)
[97]
(a) W1 + W2 = W
(b) W1 + W2 = Constant.
(c) W1  W2

A1E1 A2 E2

(d) W1  W2
A1E2 A2 E1

13. A tapering bar (diameter of end sections being, d1 and
d2) and a bar of uniform cross-section ‘d’ have the same
length and are subjected the same axial pull. Both the bars
will have the same extension if ‘d’ is equal to.
[98]
(a) d1  d2

2

(b) d1d2

(c) d1  d2
2

(d) d1  d2
2

14. The number of independent elastic constraints

required to express the stress-strain relationship for a

linearly elastic isotropic material is. [98]

(a) one (b) two

(c) three (d) four

15. The deformation of a bar under its own weight as
compared to that when subjected toa direct axial load
equal to its own weight will be. [98]
(a) the same
(b) one fourth
(c) half
(d) double

16. If permissible stress in plates of joint through a pin as
shown in the fig. is 200 MPa, then the width w will be.
[98]

(a) 15 mm
(b) 20 mm
(c) 18 mm
(d) 25 mm

17. The number of elastic constants for a completely
anisotropic elastic material is.
[99]
(a) 3
(b) 4
(c) 21
(d) 25

18. A rod of material with E = 200 x 103 MPa and  = 10
-3mm/mmoC is fixed at both the ends. It is uniformly
heated such that the increase in temperature is 300C, The
stress developed in the rod is.
[99]
(a) 6000 N/mm2 (tensile)
(b) 6000 N/mm2 (compressive)
(c) 2000 N/mm2 (tensile)
(d) 2000 N/mm2 (compressive)

19. The Poisson ratio of a material which has Young’s
modulus of 120 GPa and shear modulus of 50 GPa, is.
[99]
(a) 0.1
(b) 0.2
(c) 0.3
(d) 0.4

20. For a given material, the modulus of rigidity is 100
GPa and Poisson’s ratio is 0.25. The value of modulus of
elasticity in GPa is.
(a) 125
(b) 150
(c) 200
(d) 250

21. A rigid beam of negligible weight is supported in a
horizontal position by two rods of steel and aluminum,
2m and 1m long having values of cross-sectional area 1
cm2 and 2 cm2 and E of 200 GPa and 100 GPa
respectively. A load P is applied as shown in the fig.

If the rigid beam is horizontal then.
(a) the forces on both sides should be equal.
(b) the force on aluminum rod should be twice the force
on steel.
(c) the force on the steel rod should be twice the force on
aluminum.
(d) the force P must be applied at the centre of the beam.

22. A straight bar is fixed at edges A and B. Its elastic
modulus is E and cross-section is A. There is a load P
=120N acting at C. Determine the reactions at the ends.

(a) 60 N at A, 60 N at B
(b) 30 N at A, 90 N at B
(c) 40 N at A, 80 N at B
(d) 80 N at A, 40 N at B

23. Toughness for mild steel under uniaxial tensile
loading is given by the shaded portion of the stress-strain
diagram as shown in.
(a)

(b)

(c)

(d)

24. The modulus of elasticity for a material is 200 GN/m2
and Poisson’s ratio is 0.25. what is the modulus of
rigidity ?
(a) 80 GN/m2
(b) 125 GN/m2
(c) 250 GN/m2
(d) 320 GN/m2

25. A bar of length L tapers uniformly from diameter 1.1
D at one end of 0.9 D at the other end . The elongation
due to axial pull is computed using mean diameter D.
What is the approximate error in computed elongation ?
(a) 10 %
(b) 5 %
(c) 1 %
(d) 0.5 %

26. A bar of copper and steel form a composite system.
They are heated to a temperature of 400C . What type of
stress is in deuced in the copper bar ?
(a) Tensile
(b) Compressive
(c) Both tensile end compressive
(d) Shear

27. A cube with a side length of 1 cm is heated uniformly
10C above the room temperature and all the sides are free
to expand. what will be the increase in volume of the
cube? (Given coefficient of thermal expansion is  per
0C)
(a) 3 cm3
(b) 3 cm3
(c) cm3
(d) zero

28. If E,G and K denote Young’s modulus, Modulus of
rigidity and Bulk Modulus, respectively, for an elastic
material, then which one of the following can be possible
true ?
(a) G = 2K
(b) G = E
(c) K = E
(d) G = K = E.

29. A solid uniform metal bar of diameter D and length L
is hanging vertically from its upper end. The elongation of
the bar due to self weight is.
(a) Proportional to L and inversely proportional to D2
(b) Proportional to L2 and inversely proportional to D2.
(c) Proportional to L but independent of D.
(d) Proportional to L2 but independent of D.

30. Two tapering bars of the same material are subjected
to a tensile load P, The lengths of both the bars are the
same. The larger diameter of each of the bars is D. The
diameter of the bar A at its smaller end is D/2 and that of
the bar B is D/3. What is the ratio of elongation of the bar
A to that of the bar B?

(a) 3 : 2
(b) 2 : 3
(c) 4 : 9
(d) 1 : 3

31. E,G,K and m represent the elastic modulus, shear
modulus, bulk modulus and Poisson’s ratio respectively
of a linearly elastic, isotropic and homogenous material.
To express the stress strain relations completely for this
material, at least.

(a) E,G and m must be known.
(b) E,K and m must be known.
(c) any two of the four must be know
(d) All the four must be known.

32. A metal rod is rigidly fixed at its both ends. The
temperature of the rod is increased by 1000c. if the co-
efficient of linear expansion and elastic modulus of the
metal rod are 10 x 10-6/oc and 200 GPa respectively, then
what is the
stress produced in the rod?
(a) 100 MPa (tensile)
(b) 200 MPa (tensile)
(c) 200 MPa (compressive)
(d) 100 MPa (compressive)

33. What is the phenomenon of progressive extension of
the material i.e., strain increasing with the time at a
constant load, called?
(a) Plasticity
(b) Yielding
(c) Creeping
(d) Breaking.

34. Which one of the following statements is correct ? If a
material expands freely due to heating, it will develop
(a) thermal stress
(b) tensile stress
(c) compressive stress
(d) no stress.

35. Which one of the following expresses the total

elongation of a bar of length L with a constant cross-

section of A and modulus of Elasticity E hanging

vertically and subject to its own weight W ?
(a) WL

AE

(b) WL
2 AE

(c) 2WL
AE

(d) WL
4 AE

36. If he ratio G/E (G= Rigidity modulus, E = Young’s
modulus of elasticity) is 0.4, then what is the value of the
Poisson’s ratio ?
(a) 0.20
(b) 0.25
(c) 0.30
(d) 0.33

37. What are the materials which show direction
dependent properties, called?
(a) Homogeneous materials
(b) Viscoelastic materials
(c) Isotropic materials
(d) Anisotropic materials

38.What is the relationship between the linear elastic
properties Young’s modulus (E), rigidity modulus (G) and
bulk modulus (K)?
(a) 1  9  3

E KG

(b) 3  9  1
E KG

(c) 9  3  1
E KG

(d) 9  1  3
E KG

39. A 100 mm x 5 mm x 5 mm steel bar free to expand is
heated from 150C to 400C. What shall be developed ?
(a) Tensile stress
(b) Compressive stress
(c) Shear stress
(d) No stress.

40. What is the relationship between elastic constants E,G
and K ?
(a) E  KG

9K  G

(b) E  9KG
K G

(c) E  9KG
K  3G

(d) E  9KG
3K  G

41. A bar produces a lateral strain of magnitude - 60 x 10-
5 m/m, when subjected to tensile stress of magnitude 300
MPa along the axial direction. Find the elastic modulus of
the material, if the Poisson’s ratio is 0.3
(a) 100 GPa
(b) 150 GPa
(c) 200 GPa
(d) 400 GPa

42. A bar of 2m length is fixed at both ends. If E = 2 x
106 kg/cm2. Coefficient of expansion is 1.5 x 10-6 / 0C
and the temperature rise is 200C, the stress developed in
the material is .
(a) 60 kg/cm2 (tensile)
(b) 60 kg/cm2 (compressive)
(c) 60 kg/cm2 tensile of one face and 60 kg/cm2
compressive on opposite face.
(d) No stress is developed.

43. A straight wire 15m long is subjected to tensile stress
of 2000 kg /cm2 , E = 2 x 106 kg/cm2 .= 12.5 x 10-6 / 0C.
The temp. change to produce the same elongation as due
to 2000 kg/ cm2, tensile stress in the material is .
(a) 40
(b) 80
(c) 120
(d) 160

44. A straight wire 15m long is subjected to tensile stress

of 2000 kgf /cm2 , Elastic modulus is 1.5 x 106 kgf/cm.

Coefficient of linear expansion for the material is 16.66 x

10-6F. The temp. change (in 0F) to produce the same

elongation as due to 2000 kgf /cm2, tensile stress in the

material is .

(a) 40 (b) 80

(c) 120 (d) 160

45. For the cantilever beam as shown in fig. the cross-
sectional area of the steel, aluminum and, bronze part is
500 mm2,400 mm2,and 200 mm2. respectively. The
maximum P that will not exceed a stress in steel of 140
MPa, in aluminum of 90 MPa or in Bronze of 100 MPa is

(a) 25000N
(b) 36030 N
(c) 14000 N
(d) 10000 N

46. ABC is a rigid bar. It is hinged at A and suspended at
B and C by two wires, BD and CE made of copper
and steel respectively, as shown in the given fig. The bar
carries a load of kN at F, midway between B and C.
Given that. Ac = 4cm2, As = 2cm2, Ec = 1 x 105
N/mm2, Es= 2 x 105 N/mm2. Subscript c and s stands for
copper and steel. If the extensions in the steel and
copper wires are Asand Ac respectively, the ratio As / Ac
would be

(a) 1/4
(b) 4
(c) 2
(d) 1 / 2

47. A block of steel is loaded by a tangential force on its
top surface while the bottom surface is held rigidity. The
deformation of the block is due to.

(a) Shear only
(b) Bending only
(c) Shear and bending
(d) Torsion

48. A gradually applied load W is suspended by wire
ropes AB and CD as shown in the fig. The wires AB and
CD, made of the same material and of the same cross
section are connected to a rigid block from which the load
W is suspended in such a way that both the ropes stretch
by the same amount. if the stress in AB and CD are p1
and p2 respectively, then the ratio p1/p2 will be.

(a) 3 / 2
(b) 2 / 3
(c) 9 / 4
(d) 4 / 9

49. A mild steel bar is in three parts, each 20 cm long.
The diameters of part AB,CB and CD are 2cm and 3 cm
respectively. The bar is subjected to an axial pull of 4 t as
shown in the given fig. If E = 2 x 106 kg/cm2 and the
elongation in the three parts of the bar and A1,A2, and
A3.respectively, then the ratio of the greatest to the least
of these elongations will be .

(a) 9
(b) 4
(c) 3
(d) 2

50. Match the following using the codes given below.

Type of material General value of Poisson’s ratio

A. Concrete - 1. 0

B. Cork - 2. 0.15

C. Rubber - 3. 0.25

D. Isotropic Materials - 4. 0.33

5. 0.5

CODES :

ABCD

(a) 2 1 5 4

(b) 2 1 5 3

(c) 3 1 5 4

(d) 3 5 1 4

51. Match list I with list II and select the correct answer

using the codes given below the lists:

List I (Material) List II (Modulus of Elasticity N/mm2)

A. Steel - 1. 0.6 x 105

B. Cast iron - 2. 1 x 105

C. Aluminum - 3. 2 x 105

D. Timber - 4. 0.1 x 105

Codes :-

ABCD

(a ) 3 2 1 4

(b) 2 3 1 4

(c) 3 2 4 1

(d) 2 3 4 1

52. Consider the following statements:
A : An isotropic material is always homogeneous
B : An isotropic material is one in which all the
properties are the same in all the directions at every point
of these statements .
(a) both A and B are true
(b) both A and B are false
(c) A is true but B is false
(d) A is false but B is true.

PRACTICE QUESTIONS (ANS.)
1-b, 2-a, 3-a, 4-a, 5-b, 6-d, 7-b, 8-a, 9-d, 10-c, 11-c, 12-c,
13-b, 14-b, 15-c, 16-a, 17-c, 18-b, 19-b, 20-d, 21-b, 22-d,
23-d, 24-a, 25-c, 26-b, 27-a, 28-c, 29-d, 30-b, 31-c, 32-c,
33-c, 34-d, 35-b, 36-b, 37-d, 38-d, 39-d, 40-d, 41-b, 42-b,
43-b, 44-d, 45-d, 46-d, 47-a, 48-a, 49-a, 50-b, 51-a, 52-d.

TEST PAPER

STM : UNIT - I

TIME : 90 MINUTES ] [ M.M. : 50 MARKS

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Question 1 to 10 will carry 1 mark each

1. Given that for an element in a body of homogenous

isotropic material subjected to plane stresses x,  y and

z are normal strains in x, y and z directions respectively

and is the Poisson’s ratio . The magnitude of unit

volume charge of the element is given by

(a) x + y + z

(b) x - ( y +  z )

(c)  (  x +  y +  z)

(d) (1 / x) + (1 /  y)+ (1 /  z)

2. A solid metal bar of uniform diameter D and length ‘L’
is hung vertically from a ceiling. if the density of the
material of the bar is p and the modulus of elasticity is E,
then the total elongation of the bar due to its own weight
is .
(a) pL/ 2E
(b) pL2 / 2E
(c) pE/ 2L
(d) pE/ 2L2.