Download VTU BE 2020 Jan ME Question Paper 15 Scheme 3rd Sem 5MEMA34 Mechanics of Materials

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5ME/MA34
Third Semester B.E. Degree Examination, Dee.2019/Jan.2020
Mechanics of Materials
Time: 3 hrs. Max. Marks: 80
Note: Answer any FIVE full questions, choosing ONE full question from each module.

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Module-1
1 a. Derive an expression for the extension of a uniformly tapering rectangular bar when it is
subjected to an axial load P. (08 Marks)
b. Calculate the modulus of rigidity and bulk modulus of a cylindrical bar of diameter of 25mm
and length 1.6m, if the longitudinal strain in a bar during a tension test is four times the

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lateral strain. Find the change in volume, when the bar is subjected to a hydrostatic pressure
of 100N/mm
2
. Take E = 1 x 10
5

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N/mm
2
. (08 Marks)
OR
2 a. A mild steel rod of 20mm diameter and 300mm long is enclosed centrally inside a hollow

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copper tube of external diameter 30mni and internal diameter of 25mm. The ends of the tube
and rods are brazed together, and the composite bar is subjected to an axial pull of 40kN. If
E for steel and copper is 200GN/m
-
and 100 GN/m

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-
respectively. Find the stresses
developed in the rod and tube. Also find the extension of the rod. (08 Marks)
b. A steel bar is placed between two copper bars each having the same area and length as the
steel bar at 15"C. At this stage , they are rigidly connected together at both the ends. When

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the temperature is raised to 315
?
C. the length of the bars increase by 1.5mm. Determine the
original length and final stresses in the bars. Take E
s

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= 2.1 x 10
5
N/mm
2
;

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E, = 1 x 10
5
N/mm
2
; a, = 0.000012 per

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?
C ; a
c
= 0.0000175 per
?

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C. (08 Marks)
Module-2
3 a. Define Principal planes. Starting from the expression of normal and tangential stresses
acting on inclined plane in an element subjected to 2D ? stress state, derive the expressions
for the magnitude and location of principal stresses. (08 Marks)

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b. The direct stresses acting at a point in a strained material are as shown in fig. Q3(b). Find the
normal , tangential and the resultant stresses on a plane 30
?
to the plane of the major
principal stress. Find also the obliquity of the resultant stresses. (08 Marks)

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Fig.Q3(b)
i2 t
12-0
t,
OR

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4 a. A thick walled cylindrical pressure vessel has inner and outer radii of 200mm and 250mm
respectively. The material of the cylinder has an allowable stress of 75 MN/m
2
. Determine
the maximum internal pressure that can be applied and draw the sketch of radial pressure

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and circumferential stress distribution. (08 Marks)
b. Derive expressions for circumferential Loop stress and longitudinal stress in thin cylinder.
State the assumptions made in the derivation. (08 Marks)
Module-3
5 a. Obtain the expressions for shear force and bending moment at a section of a cantilever beam

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carrying gradually varying load from zero at the free end to W per unit length at the fixed
end. Draw the shear force and bending moment diagrams. (06 Marks)
1 oft
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USN
treated as malpractice.
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JA
5ME/MA34

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Third Semester B.E. Degree Examination, Dee.2019/Jan.2020
Mechanics of Materials
Time: 3 hrs. Max. Marks: 80
Note: Answer any FIVE full questions, choosing ONE full question from each module.
Module-1

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1 a. Derive an expression for the extension of a uniformly tapering rectangular bar when it is
subjected to an axial load P. (08 Marks)
b. Calculate the modulus of rigidity and bulk modulus of a cylindrical bar of diameter of 25mm
and length 1.6m, if the longitudinal strain in a bar during a tension test is four times the
lateral strain. Find the change in volume, when the bar is subjected to a hydrostatic pressure

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of 100N/mm
2
. Take E = 1 x 10
5
N/mm

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2
. (08 Marks)
OR
2 a. A mild steel rod of 20mm diameter and 300mm long is enclosed centrally inside a hollow
copper tube of external diameter 30mni and internal diameter of 25mm. The ends of the tube

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and rods are brazed together, and the composite bar is subjected to an axial pull of 40kN. If
E for steel and copper is 200GN/m
-
and 100 GN/m
-

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respectively. Find the stresses
developed in the rod and tube. Also find the extension of the rod. (08 Marks)
b. A steel bar is placed between two copper bars each having the same area and length as the
steel bar at 15"C. At this stage , they are rigidly connected together at both the ends. When
the temperature is raised to 315

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?
C. the length of the bars increase by 1.5mm. Determine the
original length and final stresses in the bars. Take E
s
= 2.1 x 10

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5
N/mm
2
;
E, = 1 x 10

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5
N/mm
2
; a, = 0.000012 per
?

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C ; a
c
= 0.0000175 per
?
C. (08 Marks)

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Module-2
3 a. Define Principal planes. Starting from the expression of normal and tangential stresses
acting on inclined plane in an element subjected to 2D ? stress state, derive the expressions
for the magnitude and location of principal stresses. (08 Marks)
b. The direct stresses acting at a point in a strained material are as shown in fig. Q3(b). Find the

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normal , tangential and the resultant stresses on a plane 30
?
to the plane of the major
principal stress. Find also the obliquity of the resultant stresses. (08 Marks)
Fig.Q3(b)

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i2 t
12-0
t,
OR
4 a. A thick walled cylindrical pressure vessel has inner and outer radii of 200mm and 250mm

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respectively. The material of the cylinder has an allowable stress of 75 MN/m
2
. Determine
the maximum internal pressure that can be applied and draw the sketch of radial pressure
and circumferential stress distribution. (08 Marks)

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b. Derive expressions for circumferential Loop stress and longitudinal stress in thin cylinder.
State the assumptions made in the derivation. (08 Marks)
Module-3
5 a. Obtain the expressions for shear force and bending moment at a section of a cantilever beam
carrying gradually varying load from zero at the free end to W per unit length at the fixed

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end. Draw the shear force and bending moment diagrams. (06 Marks)
1 oft
15MEIMA
b. Draw the shear force and bending moment diagrams for the overhanging beam shown in
fig.Q5(b). Clearly indicate point of contra flexure. (10 Marks)

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Fig.Q5(b)
26
,
kN
?01

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OR
6
a. Derive the relation
M

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_L ) ?
E
with usual notations and list the basic assumptions.
1 Y R
(10 Marks)

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b. A simply supported beam of span 5m has a cross section 150mm x 250mm. if the
permissible stress is ION/mm
2
, find the maximum concentrated load P applied at 2m from
one end, it can carry. (06 Marks)

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Module-4
7 a. Determine the diameter of a solid shaft which will transmit 300 KW at 250 rpm. The
maximum shear stress should not exceed 30N/mm
2
and twist should not be more than 1 in a

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shaft length of 2m. Take modulus of rigidity = 1 x 10'N/mm
2
. (08 Marks)
b. The allowable shear stress in brass is 80N/mm
2

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and in steel 100N/mm
2
. Find the maximur,.
torque that can be applied in the stepped shaft shown in fig. Q7(b). Find also the total
rotation of free end with respect to the fixed end if G

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brass =
40 kl\l/mm
-
and
Gsteei =

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80kN/mm
2
. (08 Marks)
Fig.Q7(h)
t3

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r.? -

Drau cir- Pb
5'44 chic
1. 2. pr.

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OR
8 a. Find an expression for crippling load for a column with one end fixed and other end free.
(08 Marks)
b. Determine the buckling load for a strut of T - section , the flange width being 100mm,
overall depth 80mm and both flange and stem I Omm thick as shown in fig. Q8(b). The strut

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is 3m long and is hinged at both ends. E = 200GN/m
2
. (08 Marks)

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Fig.Q8(b)


_2_

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Module-5
9 a. Using Castiglione's first theorem, find the deflection at the free end of a cantilever beam
carrying a concentrated load at the free end. Assume uniform flexural rigidity. (06 Marks)
b. Derive an expression for strain energy stored in a body due to torsion. (10 Marks)
OR

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10 a. Write short notes on :
i) Maximum Principal stress theory ii) Maximum shear stress theory. (10 Marks)
b. A bolt is subjected to an axial pull of l2kN together with a transverse shear force of 6kN. .
7
0 Determine the diameter of the bolt by using Maximum principal str . '

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' .
ake
,
Li0e-
,

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\
Elastic limit in tension = 300 N/mm
2
, Factor of safety = 3. /, --..--------: o \( 06 Marks)
/ ? r ,/

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* * 2 of 2 * *
6-../ -cist
a , / ,.-, 6,,
,
?- ,

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-5 '1
'''' ? f
.
47., . \ AD 1
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