Download AKTU (Dr. A.P.J. Abdul Kalam Technical University (AKTU), formerly Uttar Pradesh Technical University (UPTU) B-Tech 3rd Semester (Third Semester) 2017-2018 RME303 Mechanics Of Solids Question Paper
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B.Tech.
(SEM III) THEORY EXAMINATION 2017-18
MECHANICS 0F SOLIDS
T ime: 3 Hours T 0tal Marks: 70
Note: 1. Attempt all Sections. If require any missing data; then choose suitably.
SECTION A
1. Attempt all questions in brief. 2 x 7 = 14
a. What are principal planes and principal stresses?
b. Define Resilience, proof resilience and modulus of resilience.
c. What are the different methods of finding slope and de?ection of cantilever
d. What Do you understand by the term Torsional Rigidity
e. What is Shear center?
f. What do you understand by the term ?Buckling? of columns
g. What is the difference between Thin and Thick cylinder
SECTION B
2. Attempt any three of the following: 7 x 3 = 21
a. A beam of uniform section, 10m long ,is simply supported at its ends. It
carries point loads of 150KN and 65KN at a distance 2.6m and 5.5m
respectively from the left end, Calculate
(i) The maximum de?ection (ii) De?ection under each load.
b. Determine the internal and external diameter of a hollow shaft whose internal
diameter is 0.6 times external diameter and transmits 120kw at 210rpm and the
allowable stress is limited to 75MPa.If a bending moment of 2800Nm is
applied to the shaft, find the speed at which the shaft must rotate to transmit the
same power for the same value of maximum shear stress.
0. A mild steel hallow column, having 100mm external diameter, 40 mm thick
and 4 m long. Determine crippling load using Rankin?s formula, When both end
fixed? Take <5c=320N/mm2 and Rankine constant a=1/7500.?
d. Derive an expression for maximum principal stress in a thick cylindrical shell
subj ected to internal pressure only.
e. For a tube having E=2><105 N/mm2 and ?=03 the hoop stress at the inner
surface is twice internal pressure. find the thickness of the wall if internal
radius is 60mm
SECTION C
3. Attempt any one part of the following: 7 x 1 = 7
(a) Derive Euler?s equation for long column having its both end built in.
(b) Derive expression of de?ection angular rotation and stresses in case of open
coil helical spring subjected to axial load. Calculate what X the axial extension
is underestimated if the inclination of the coil of the coil is neglected for a
spring in which (1:25 ?. Assume n and R remain same
4. Attempt any one part of the following: 7 x 1 = 7
(a)
(b)
What is shear centre? Channel section has ?anges b*t1 and web h*t2.
Determine position of its shear center.
A 60mmx40mmx6mm unequal angle is placed with longer leg vertical and
used as a beam. It is subjected to a bending moment of 12 KN?cm acting in the
vertical plane through the Centroid of the section. Determine the max bending
stress induced in the section.
5. Attempt any one part of the following: 7 x 1 = 7
(a)
(b)
At a point in a material under stress, the intensity of the resultant stress on a
certain plane is 50MPa (tensile) inclined at 300 t0 the normal of that plane. The
stress on a plane at right angle to this has a normal tensile component of
intensity of 30MPa find:
(i) The resultant stress on the second plane.
(ii) The principal planes and stresses.
(iii) The plane of maximum shear and its intensity.
Explain different theories of failure along with their graphical representation
6. Attempt any one part of the following: 7 x 1 = 7
(a)
(b)
A crane hook is of trapezoidal c/s having inner side 80mm, outer side 300mm
and depth 120mm. the radius of curvature of inner side is 80 mm. if a load of
100 kN is applied to the hook passing through the center of curvature,
determine the maximum tensile and compressive stresses at the critical cross
section
Determine the dimensions of hollow shaft with a diameter ratio of 3:4, which is
to transmit 60KN at 200rpm. The maximum Shear stress is limited to 70
MN/mm2 and angle oftwist is 3.8? in a length of 4m. G=80 GPa.
7. Attempt any one part of the following: 7 x 1 = 7
(a)
('3)
Write down the assumption in Lame?s theory and also derive its equation for
thick shell.
Find the Euler?s buckling load of a long column length L subjected
compressive load P when one end of column are fixed and other is hinged.
Take EI Constant.
This post was last modified on 29 January 2020