Hall Ticket No Question Paper Code: BCC213
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
M.Tech II Semester End Examinations (Regular) July, 2018
Regulation: IARE-R16
STRESS ANALYSIS AND VIBRATION
Time: 3 Hours (CAD/CAM) Max Marks: 70
Answer ONE Question from each Unit
All Questions Carry Equal Marks
All parts of the question must be answered in one place only
UNIT I
1. Derive compatibility equations of a two dimensional state of strain in rectangular coordinate
system.
A pipe considering as simply supported beam of circular cross-section 50 mm diameter and 10
mm thick is 1000 mm in length. It carries a continuous load of 1000 N throughout the beam.
Determine the stresses in the simply supported beam at mid-length.
2. Derive the Lame's equations for a thick cylindrical shell.
Determine the maximum and minimum hoop stress across the section of a pipe of 400mm internal
diameter and 100mm thick, when the pipe contains a fluid at a pressure of 8 N/mm2 . Also sketch
the radial pressure distribution and hoop stress distribution across the section .
UNIT II
3. Derive the expression which relates maximum shear stress and torsion for thin rectangular plate.

A shaft is of elliptical cross section having semi-major axis 50mm and semi minor axis 25mm. It
is subjected to a torque of 1000 N-m . Determine the maximum shear stress developed in the
shaft.
4. Derive the relationship between torque, and angle of twist per unit length for a thin wall
hollow section.
Compare the weights per unit length of shafts of circular and elliptic cross-sections when shafts
are subjected to the same torsional moment and angle of twist per unit length is same.
UNIT III
5. A mass, when suspended by a helical spring has a natural frequency 125 cycles /minute. Now
the spring is cut into two equal halves and the same mass is suspended both halves in parallel.
Determine the natural frequency of the new system.
For the system ,let K=10,000 M=0.633 kg,xo=0.1m, vo=10 m/s and the damping ratio
=0.05.Compute the ratio of the damped to the un damped natural frequency for damping ratios
of 10% and 20% of the critical damping.
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6. Derive an expression for the magnification factor for a spring mass- damper system subjected
to external excitation. Draw the curve between magnification factor and ratio of frequencies of
system and natural frequency.
A machine part of mass 5Kg vibrates in a viscous medium. A harmonic exiting force of 36N acts
on the part and causes resonant amplitude of 15mm with a period of 0.32 sec. Find the damping
coefficient if the frequency of the exciting force is changed to 4Hz. Determine the increase in the
amplitude of forced vibration upon removal of the damper.
UNIT IV
7. Determine the response of the overdamped, single-degree-of freedom spring mass system
any method.
A single degree of freedom system is subjected to impulsive excitation of 0.5 Ns. Obtain the
expression for the response of the system. Use mass of body 1.5 Kg; c 0.5 kg/s and stiffness
is 5 N/m
8. Explain time domain analysis for random response of single degree of freedom system.
Differentiate among deterministic and nondeterministic forcing functions.
UNIT V
9. Determine the natural frequencies of three-rotor (semi-Definite) system by using Newton's method
.
A stepped shaft at fixed end has 80mm diameter and length 200mm another shaft of diameter
50mm and length 500mm is placed between a rotor and shaft of 80mm. The moment of inertia
of disc is 100 N/s2. Determine the natural frequency for torsional vibration of the system
10. Derive the mode shape equation of the transverse vibrations of beams.
Derive the frequency equation of a uniform beam fixed at one end and free at the other end for
transverse vibrations.