Download AKTU (Dr. A.P.J. Abdul Kalam Technical University (AKTU), formerly Uttar Pradesh Technical University (UPTU) B-Tech 3rd Semester (Third Semester) 2018-2019 Mechanics Of Solids Rme 303 Question Paper
Pap" Id? 140303 MINO? EEEEDZIIED
B.TECH.
(SEM. Ill) THEORY EXAMINATION 2018-19
MECHANICS OF SOLIDS
' Time: 3 Hours Total Marks: 70
Note: Attempt all Sections. If require any missing data; then choose suitably.
I.
2.
3)
b)
c}
d)
6)
SECTION A
Attempt all questions in brief. 2 x 7 = 14
Differentiate between the terms section modulus and ?exural rigidity.
What do you understand by autofrettage? Explain it in brief.
Analytically differentiate between bending of straight and curved beam.
Differentiate between strain energy and shear strain energy.
What is the difference in analysis of closed and open coiled springs.
De?ne shear center and its importance.
Explain slendemess ratio and its importance in case of column.
mmmp-osr.?
SECTION B
Attempt any three of the following:
A beam ABCDE [5 continuous over four suppq H and Can'ies the loads shown 1n figure given
below Determine the \ alues of the fixing mements at each support I 1?,
20 RN :0 k N
A lkN?n B ?? auNAn c
kmsmm?psma?tjeqmit?
Derive the differential equation of de?ection curve
A close coiled helical spring is ?xed at one end and subjected to axial twist at the
other. When the spring is in use the axialimque varies from 0 75 N-m to 3 N? ?m: the
working angular de?ection between these?torques being 350. The spring is 'to be made
from rod of circular section the mammum permissible stress being 150 MN/m [he
mean diameter of the coils is eight times the rod diameter Calculate the mean Loil
diameter, the number of turns and the wire diameter.
The load to be canied by adi? may be dropped 10 cm on to the ?oor. The cage itself
weighs 100 kg and is supported by 25 m of wire rope weighing 0.9 kg/m, consisting
of 49 wires each 1.6 mm diameters The maximum stress in the wire is limited to 90
N/mm2 and E for the rope is 70000 N/mml. Find the maximum load which can be
eanied.
A timber beam 6 cm wide and 8 cm deep is to be reinforced by bolting on two steel
Hitches: each 6 cm by 5 mm in section in the following cases:
i. ?itches attached symmetrically at top and bottom:
7x3=21;/ii
Ii. ?itches attached symmetrically at the sides
Take allowable timber stress as 8 Wm? What is the maximum stress in the steel in
each case?? Take Ema = 210 kN/mmh Etimbcr = 14 kN/mm2
SECTION C
3. Attempt any one part 01' the following: 7 x 1 = 7
(a) A steel tube of 24 mm external diameter and 18 mm internal diameter encloses
a copper rod 15 mm diameter to which it is rigidly attached at each end. If, at a
temperature of 10?C there is no longitudinal stress, calculate the stresses in the
tube and rod when the temperature is raised to 200?C.
Estccl = 210 kN/mlancoppc1_210 kN/mmz
Coefficients of linear expansion:
as1==1= 11 x 10'6 /"C mopp=r= 11 x 10?6 /?C
(b) A small block is 40 mm long, 30 mm high and 5 mm in thick. 11 is subjected to
uniformly distributed tensile forces having the resultant values in N shown in
?gure. Compute the stress components developed along the diagonal AC.
A
1280
D ~- '/ C
2400 x'? 2400
?7 > - __ /JV F'~_+
A f," I B
1280 1
4. Attempt any one part 01' the following: 7 x I = 7
1a) A solid circular shatt of length 3 m and diameter of 50mm rotates at 1200
rpm by a 400 HP electric motor at its middle It de?v?es two machines of 150
111? and 250 HP at left and right ends of the sha?- -fespective1y Determine the
max1mum shear stress and relative displacement- of the two ends of the shaft
Take CF 85 GPa ? -
(b) Determine the de?ection of the beam at midpoint for the beam loading
system shown in the ?gure given belew
Take: E = 200 GN/m2 and I 5331x106 m4.
10 N/m [?0 N ?10 N
4 ?????? 1?
?W 'W ,
?Fm ,? ,,,,,,,,,,,, + _ ........... 1 ........... ,
1 U rm 5 rrl 10 111
5. Attempt any one part of the following: 7 x l = 7
1a) A short column is of hollow circular section, the center of the inside hole being
6 mm eccentric to that of the outside. The outside diameter is 96 mm and the
/\
('3)
inside 48 mm The line of action of the load intersects the cross-section at a
point in line with the two centers What are the limiting position of the load for
there to be no tensile stress set up?
Derive the relation to ?nd de?ection induced in the open coiled helical spring
subjected to axial Torque.
Attempt any one part of the following: 7 x l = 7
(a)
(b)
The cylinder for a hydraulic press has an inside diameter of 300 mm.
Determine the wall thickness required if the cylinder is to withstand an internal
pressure of 60 MPa without exceeding a shearing stress of 90 MP3.
In an experiment on a thick cylinder of 100 mm external diameter and 50 mm
internal diameter the hoop and longitudinal strains as measwed by strain
gauges applied to the outer surface of the cylinder were 240 x 10? and 60 x 10?
respectively, for an internal pressure of 90 MN/?m2, the external pressure being
zero. .
Determine the actual hoop and longitudinal stresses present in the
cylinder if E = 208 GN/mz and v = 0.29. Compare the hoop stress value so
obtained with the theoretical value given by the Lame equations.
Attempt any one part of the following: _ . 7 x 1 = 7
(a)
(b)
A 75 mm x 75 mm x 12 mm angle is usedds a cantilever with the face AB . .-
horizontal as shown in ?gure. A veng??aluldad of 3 KN is applied at the tip cg; 1;?
the cantilever which is 1 m long. Qetgihine the stresses at A. B and C.
The bending moment acting on the. med beam with a rectangular cross-
sectlon is M = 8 KN?m. Calculate the?hehding stress at point B.
:5
40 mm??xgb? i .
This post was last modified on 29 January 2020