Guaer,
114
0 ? if TO
USN
--- Content provided by FirstRanker.com ---
Third Semester B.E. Degree Examination, Dec.2019/Jan.2020Mechanics of Materials
Time: 3 hrs. Max. Marks: 100
Note: Answer any FIVE full questions, choosing ONE full question from each module.
Module-1
--- Content provided by FirstRanker.com ---
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-
--- Content provided by FirstRanker.com ---
N. (10 Marks)
mm
-
Fig.Q.1(c)
--- Content provided by FirstRanker.com ---
OR2 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)
--- Content provided by FirstRanker.com ---
b. A steel bar is placed between two copper bar, each having same area and length as the steelbar. 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
--- Content provided by FirstRanker.com ---
/?C,oc,? = 17.5 x 10-6/?C. (10 Marks)
Module-2
3 a.
Derive the expression for normal stress and shear stress on a plane inclined at 'A' angle to
--- Content provided by FirstRanker.com ---
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
--- Content provided by FirstRanker.com ---
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
--- Content provided by FirstRanker.com ---
#010 Pt P a_
Fig.Q.4(a)
40 MPq
60 m Pa_
--- Content provided by FirstRanker.com ---
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.
--- Content provided by FirstRanker.com ---
(10 Marks)1 of 2
17ME34
FirstRanker.com - FirstRanker's Choice
200 enrol
--- Content provided by FirstRanker.com ---
,2 50 WhroSokg Ao k-F4
801vm
!----o? o
c).200.1
--- Content provided by FirstRanker.com ---
Guaer,114
0 ? if TO
USN
Third Semester B.E. Degree Examination, Dec.2019/Jan.2020
--- Content provided by FirstRanker.com ---
Mechanics of MaterialsTime: 3 hrs. Max. Marks: 100
Note: Answer any FIVE full questions, choosing ONE full question from each module.
Module-1
1 a. Explain principle of superposition. (03 Marks)
--- Content provided by FirstRanker.com ---
b. Derive an expression for Young's Modulus (E) interms of bulk modulus (K) and Poisson'sratio (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
--- Content provided by FirstRanker.com ---
. (10 Marks)mm
-
Fig.Q.1(c)
OR
--- Content provided by FirstRanker.com ---
2 a. Derive an expression for the total elongation of tapered bar varying diameter from d1
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
--- Content provided by FirstRanker.com ---
bar. These are rigidly connected together at a temperature of 25?C. When the temperature israised 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,
--- Content provided by FirstRanker.com ---
oc,? = 17.5 x 10-6/?C. (10 Marks)Module-2
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)
--- Content provided by FirstRanker.com ---
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)
--- Content provided by FirstRanker.com ---
OR4 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
--- Content provided by FirstRanker.com ---
10 Pt P a_Fig.Q.4(a)
40 MPq
60 m Pa_
tore,.
--- Content provided by FirstRanker.com ---
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)
--- Content provided by FirstRanker.com ---
1 of 217ME34
Fig.Q.5(b)
Module-3
5 a. Explain different types of beams and loads.
--- Content provided by FirstRanker.com ---
b. Draw SFD and BMD for the beam shown in Fig.Q.5(b).CACA 6k/1/,
(05 Marks)
1oK P
OR
--- Content provided by FirstRanker.com ---
,6
a.
Prove the relations M
E
--- Content provided by FirstRanker.com ---
= ? = ? 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
cross-section 150mm x 300mm. Simply supported over a span of 3m is to be used under
--- Content provided by FirstRanker.com ---
uniformly distributed load 'W' ?N
. What can be maximum value of W? (10 Marks)
rn
Module-4
--- Content provided by FirstRanker.com ---
7 a. List all the assumptions and derive the torsion formula in standard formGO
J R L
(10 Marks)
--- Content provided by FirstRanker.com ---
b. A hollow shaft having diameter ratio of 0.4, transmits 562.5kW power at 100rpm.Determine cross-sectional 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
--- Content provided by FirstRanker.com ---
ii) Euler's formula, Young's modulus = 1.2 x 105
N/mm
2
. (10 Marko
--- Content provided by FirstRanker.com ---
Module-59 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
--- Content provided by FirstRanker.com ---
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
--- Content provided by FirstRanker.com ---
.(08 Marks)
OR
10 a. Derive the expression for strain energy due to shear stress and bending. (10 Marks)
b.
--- Content provided by FirstRanker.com ---
The stresses induced at a critical point in a machine component made of steel (a, = 380MPa)are as follows: a
x
=100
N
--- Content provided by FirstRanker.com ---
2 'a
v
= 40
Mac 1
--- Content provided by FirstRanker.com ---
Txy
= 80
mm -
le
--- Content provided by FirstRanker.com ---
N Nate factor of safety by
i) Rankine's theory ii) Guest's theory.
, ?
(10 Marks)
--- Content provided by FirstRanker.com ---
* * * * *2 of 2
(15 Marks)
(10 Marks)
OR
--- Content provided by FirstRanker.com ---
8 a. Derive an expression for critical load in a column subjected to compressive load, when oneend is fixed and the other end free. (10 Marks)
b. A 1.5m long column has a circular cross-section 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
--- Content provided by FirstRanker.com ---
2and a = 1
FirstRanker.com - FirstRanker's Choice