USN
22e ANo25 [22AS44]
FOURTH SEMESTER B.Tech EXAMINATION,
JANUARY- 204
MECHANICS OF SOLIDS
Time: 3 Hours Maximum Marks: 100
Instructions: i. Missing data may be suitably assumed.
ANSWER ALL QUESTIONS
05x02=10
PART A
1. Explain the HOOK'S LAW. 1 02
2
b Obtain the total elongation of the bar shown in 2 1 02
fig.
2 2 02
C. Explain the types of beams with the help of neat sketches.
d. 2 3 02
Obtain the section modulus of a hollow rectangular section with a
symmetrically placed opening.
2 4 02
e. Explain the assumptions considered in the theory of pure torsion
PART - B 06x0530
Explain the types of stresses with the help of neat sketches 2 1 05
2. a.
OR
Solve for
b. The bar shown in Fig. is subjected to a tensile load of 60 kN. 3 1 05
the diameter dimensions of the middle portion of the bar if the stress is
limited to 120 N/mm². Also, solve for the length of the middle portion
Take E = 2 x 105
of the total elongation of the bar is 0.12 mm.
N/mm².
60 KN
60 KN 50 mm
50 mm
X
250 mm
discuss their values for different 2
3. a. Explain all elastic constants and also 1 05
materials.
OR
neat
Illustrate the thermal Stresses
and strains with the help of 3 1 05
b.
sketches.
Page 1 of 4
2 2 05
Explain the sign force and
bending
moment diagrams
conventions used to draw the shear
of the beams.
OR 05
b. 3 2
wSear force and bending moment diagram for the beam loaded
as shown in fig.
3 3 05
and
A SImply supported beam of span 6 mts carries an udl of 20 kN/m
5. a.
a concentrated load of 10 kN at 4 m from the left side of the beam.
Solve for the cross-section of the beam, and assume the depth of the
beam is twice the width of the beam. Permissible bending stress Z0
kN/mm?
OR
3 3 05
be wound around a
b. A copper wire of 2 mm diameter is required to
stress in the
drum. Solve for the minimum radius of the drum, if the
copper
wire is not to exceed 80 MPa. Take modulus of elasticity for the
as 100 Gpa.
rpm. Solve for the 3 4 05
6. a. A solid shaft has to transmit 90 kW power at 160
suitable diameter of the shaft. If the Max. Torque transmitted in each
revolution exceeds the mean by 25%. Take allowable shear stress as
70 N/mm².
OR
b.
Obtain the equations for the principal stress from principal strain 3 5 05
equations
7.
Jsing Euler's formula, solve for the critical stress of a series of struts 3 6 05
having slenderness ration of 40, 80, 120, 160, and 200 under the
following conditions:
(1) Both ends hinged,
Both ends fixed
(i)
Take E = 2.05 x 105 N/MM2
OR
b. A boiler of 2 m diameter is made of 20mm thick mild
steel plates. 3
Taking the efficiency of the longitudinal riveted joint as 6
05
75%, solve for
Page 2 of 4
the
permissible steanm pressure in
stress in the the boiler if the maximum tensile
plate section
100N/mm². Solve for the through the rivet is not to exceed
section at this circumferential stress in the solid plate-
pressure and also longitudinal
section through the rivets stress in the plate
of a circumferential
joint if the efficiency is
65%.
06x10=60
PART -C
10
8. a. 1
Obtain the expression for the volumetric strain of the given 3
elemeit
OR
10
b. 3 1
Obtain the expression for the Relation between E, G, and u
10
9. a. 3 1
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. Obtain the percentage of error
OR
3 1 10
b. A specimen of steel 20 mm diameter with a gauge length off 200 mm
is tested for destruction. It has an extension of 0.25 mm under a load
of 80 kN and the load at elastic limit is 102 kN. The maximum load is
130 kN.
The total extension at the fracture is 56 mm and the diameter at the
neck is 15 mm.Solve for the following
i. The stress at elastic limit.
ii. Young's modulus.
iii. Percentage elongation.
iv. Percentage reduction in area.
V.
Ultimate tensile stress.
the point loads as shown in 3 2
A cantilever beam of length 2 m carries
10
10. a.
diagrams for the cantilever beam.
Fig. Draw the shear force and B.M.
300 N 500 N 800 N
B
D
-0.8 m
0.5 m
OR
support at Bac
A beamn of span 8 mbas roller support at A and hinge 3 2
10
shown in Fig. Draw SF and BM diagrams when the beam is subiected
to udi, a concentrated load. and an externally applied moment.
10 kN/m 20 KN
240 kN-m
RA
4 m 2 m + 2 m
11, a. Obtain the maximum deflection and slop of cantilever beam length T 3 3 10
subjected to uniformly distributed load intensity 'w/m' length.
OR
b. 3 5 10
Direct stress of 80 N/mm² tensile and 50 N/mm? compressive are
applied to an elastic material at a certain point, on planes at right
angles to one another. The grater principal stress in the material is
limited to 100 N/mm² tensile. Solve for shearing stress may the
material be subjected to the given planes and what will be the
maximum shear stress at the point?
3 3 10
subjected to a point
12. Obtain the maximum deflection of fixed beam
and 'b' distance from
load 'P applied at 'a' distance from left support
right support. Apply energy method.
OR
1.25mm 3 6 10
internal diameter, I meter long and
b. A copper tube of 50mm
filled with water under pressure.
thick has closed ends and is
of
Neglecting any distortion of the
end plates, Choose the alteration
water is
volume of 3 cubic centimeters of
pressure when an additional
pumped into the tube.
N/mm?
copper = 1.03 x 105
Modulus of elasticity for
Poisson's ratio = 0.3
= 2.1 x 103 N/mm²
Bulk modulus for water
both ende
critical load of a column with 3 6 10
Obtain the equation for the
13.
hinged
OR
hollow cvlindrical
Choose the cross-section dimensions of a cast iron 3 6 10
column 5 meters long with ends firmly built-in if it carries an
axial load
f 300 kN. The ratio of internal to external diameter is 3 / 4. Use a
factor of safety of 8. Take f= S67 NImm² and Rankine's Constant a_
1 /1600
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