Download Visvesvaraya Technological University (VTU) BE ( Bachelor of Engineering) ME (Mechanical Engineering) 2017 Scheme 2020 January Previous Question Paper 3rd Sem 17ME34 Mechanics of Materials
,2 50 Whro
Sokg Ao kF4
801vm
!o? o
c).200.1
Guaer,
114
0 ? if TO
USN
Third Semester B.E. Degree Examination, Dec.2019/Jan.2020
Mechanics of Materials
Time: 3 hrs. Max. Marks: 100
Note: Answer any FIVE full questions, choosing ONE full question from each module.
Module1
1 a. Explain principle of superposition. (03 Marks)
b. Derive an expression for Young's Modulus (E) interms of bulk modulus (K) and Poisson's
ratio (n). (07 Marks)
c. A stepped bar is subjected to forces as shown in Fig.Q.1(c). Determine the stress induced in
different portions and Net deformation in the stepped bar. Take E = 2 x10
N
. (10 Marks)
mm

Fig.Q.1(c)
OR
2 a. Derive an expression for the total elongation of tapered bar varying diameter from d
1
to d,
subjected to axial load 'W. (10 Marks)
b. A steel bar is placed between two copper bar, each having same area and length as the steel
bar. These are rigidly connected together at a temperature of 25?C. When the temperature is
raised to 325?C. The length of the bar is increased by 1.5mm compute the original length
and find the stresses in each bar. Take Ested = 210GPa, E. = 100GPa, asteet = 12 x 10
6
/?C,
oc,? = 17.5 x 106/?C. (10 Marks)
Module2
3 a.
Derive the expression for normal stress and shear stress on a plane inclined at 'A' angle to
the vertical axis in a biaxial stress system with shear stress. (10 Marks)
b.
Determine the wall thickness necessary for a thick steel cylinder shell having 200mm inner
diameter to withstand an internal pressure of 40MPa. Permissible tensile stress in the
material is lOOMPa. Also sketch the variation of hoop stress and radial stress across the
thickness. (10 Marks)
OR
4 a. A plane element subjected to stress shown in Fig.Q.4(a). Determine principal stresses, Max
shear stress and their plane. Use Mohr's circle method. (10 Marks)
4
#0
10 Pt P a_
Fig.Q.4(a)
40 MPq
60 m Pa_
tore,.
40 riPA.
b. A cylindrical thin drum 800mm in diameter and 3m long has a shell thickness of 10mm, If
the drum is subjected to an internal pressure of 25 bar. Calculate the change in diameter,
change in length and change in volume. Take E = 200GPa, n = 0.25.
(10 Marks)
1 of 2
17ME34
FirstRanker.com  FirstRanker's Choice
200 enrol
,2 50 Whro
Sokg Ao kF4
801vm
!o? o
c).200.1
Guaer,
114
0 ? if TO
USN
Third Semester B.E. Degree Examination, Dec.2019/Jan.2020
Mechanics of Materials
Time: 3 hrs. Max. Marks: 100
Note: Answer any FIVE full questions, choosing ONE full question from each module.
Module1
1 a. Explain principle of superposition. (03 Marks)
b. Derive an expression for Young's Modulus (E) interms of bulk modulus (K) and Poisson's
ratio (n). (07 Marks)
c. A stepped bar is subjected to forces as shown in Fig.Q.1(c). Determine the stress induced in
different portions and Net deformation in the stepped bar. Take E = 2 x10
N
. (10 Marks)
mm

Fig.Q.1(c)
OR
2 a. Derive an expression for the total elongation of tapered bar varying diameter from d
1
to d,
subjected to axial load 'W. (10 Marks)
b. A steel bar is placed between two copper bar, each having same area and length as the steel
bar. These are rigidly connected together at a temperature of 25?C. When the temperature is
raised to 325?C. The length of the bar is increased by 1.5mm compute the original length
and find the stresses in each bar. Take Ested = 210GPa, E. = 100GPa, asteet = 12 x 10
6
/?C,
oc,? = 17.5 x 106/?C. (10 Marks)
Module2
3 a.
Derive the expression for normal stress and shear stress on a plane inclined at 'A' angle to
the vertical axis in a biaxial stress system with shear stress. (10 Marks)
b.
Determine the wall thickness necessary for a thick steel cylinder shell having 200mm inner
diameter to withstand an internal pressure of 40MPa. Permissible tensile stress in the
material is lOOMPa. Also sketch the variation of hoop stress and radial stress across the
thickness. (10 Marks)
OR
4 a. A plane element subjected to stress shown in Fig.Q.4(a). Determine principal stresses, Max
shear stress and their plane. Use Mohr's circle method. (10 Marks)
4
#0
10 Pt P a_
Fig.Q.4(a)
40 MPq
60 m Pa_
tore,.
40 riPA.
b. A cylindrical thin drum 800mm in diameter and 3m long has a shell thickness of 10mm, If
the drum is subjected to an internal pressure of 25 bar. Calculate the change in diameter,
change in length and change in volume. Take E = 200GPa, n = 0.25.
(10 Marks)
1 of 2
17ME34
Fig.Q.5(b)
Module3
5 a. Explain different types of beams and loads.
b. Draw SFD and BMD for the beam shown in Fig.Q.5(b).
CACA 6k/1/,
(05 Marks)
1oK P
OR
,
6
a.
Prove the relations M
E
= ? = ? with usual notations.
1 y R
b. A cantilever beam of square section 200mm x 200rnm, 2m long just fails in bending, when a
load of 20kN is placed at its free end. A beam of the same material having a rectangular
crosssection 150mm x 300mm. Simply supported over a span of 3m is to be used under
uniformly distributed load 'W' ?
N
. What can be maximum value of W? (10 Marks)
rn
Module4
7 a. List all the assumptions and derive the torsion formula in standard form
GO
J R L
(10 Marks)
b. A hollow shaft having diameter ratio of 0.4, transmits 562.5kW power at 100rpm.
Determine crosssectional dimensions of the shaft, if shear stress is not exceed 60MPa and
twist in length of 2.5m should not exceed 1.3?. Maximum torque transmitted is 25% higher
than average torque G = 90GPa. (10 Marks)
1600
ii) Euler's formula, Young's modulus = 1.2 x 10
5
N/mm
2
. (10 Marko
Module5
9 a. Explain Factor of safety. (04 Marks)
b. Explain maximum normal stress theory and maximum shear stress theory. (08 Marks)
c. A bar of 5m long and 50mm diameter hangs vertically and it has collar attached to it to the
lower end rigidly. Determine maximum stresses induced when
i) Weight of 3000N falls through a height of 100mm on the collar.
ii) Weight of 30kN falls through a height of 10mm on the collar. Take = 2 x 10
5
N/mm
2
.
(08 Marks)
OR
10 a. Derive the expression for strain energy due to shear stress and bending. (10 Marks)
b.
The stresses induced at a critical point in a machine component made of steel (a, = 380MPa)
are as follows: a
x
=100
N
2 '
a
v
= 40
Mac 1
T
xy
= 80
mm 
le
N N
ate factor of safety by
i) Rankine's theory ii) Guest's theory.
, ?
(10 Marks)
* * * * *
2 of 2
(15 Marks)
(10 Marks)
OR
8 a. Derive an expression for critical load in a column subjected to compressive load, when one
end is fixed and the other end free. (10 Marks)
b. A 1.5m long column has a circular crosssection of 50mm diameter. One end of the column
is fixed and other end is free. Take factor of safety as 3, calculate the safe load using
i) Rankine's formula, take yield stress = 560 N/mm
2
and a = 1
FirstRanker.com  FirstRanker's Choice
This post was last modified on 02 March 2020