Hall Ticket No Question Paper Code: BCC206
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
M.Tech I Semester End Examinations (Regular) January, 2018
Regulation: IARE-R16
ADVANCED MECHANICS OF SOLIDS
(CAD/CAM)
Time: 3 Hours 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. Determine the position of shear centre for unequal I section as shown in Figure 1
Figure 1
Explain the method for finding bending stress in unsymmetrical bending.
2. A channel section has flanges 12 cm X 2 cm and web 16 cm X 1cm. Determine the shear centre
of the channel.
Determine the position of shear centre for the C-section as shown in Figure 2.
Figure 2
Page 1 of 3
UNIT II
3. Derive an equation for the value of h2 for a trapezoidal section
Determine
i. Location of neutral axis
ii. Maximum and minimum stress.
iii. Ratio of maximum and minimum stress, when a curved beam of rectangular cross- section of
width 20 mm and of depth 40 mm is subjected to pure bending moment of +600 Nm. The
beam is curved in a plane parallel to depth. The mean radius of curvature is 50 mm.
4. Derive an equation for the value of h2 for a circular section.
A closed ring of mean radius of curvature 90 mm is subjected to a pull of 3 kN. The line of
action of the load passes through the centre of the ring. Calculate the maximum tensile and
compressive stresses in the material of the ring is circular in cross-section with diameter equal to
15 mm.
UNIT III
5. A rectangular steel shaft is transmitting power at 300 rpm lifting a load of 40 kN at a speed of
10 m/min. If the maximum permissible shear stress in the shaft is 45 MN/m2 and efficiency of
the crane gearing is 60 percent, Determine:
i. Size of the shaft
ii. Angle of the twist per metre length. Take C 78.4 MN/m2, breadth to depth ratio 1.5
A shaft of hollow square section is of uniform wall thickness of 4 mm and centre line of the wall
forms a square of 200 mm side. It is to be replaced by a solid circular shaft of the same material
and having the same torsional stiffness. If the stress concentration factor K at the inner corners
of the hollow square section is 1.7 and the twisting moment applied is 800 Nm. Find
i. Diameter of the solid shaft
ii. Maximum shear stresses in both the shafts.
6. A steel disc of uniform thickness having diameter 900 mm is rotating about its axis at 3000 rpm.
Determine the radial and circumferential stresses at the centre and outer radius. The density of
the material of the disc is 7800 kg/m3 and poisson's ratio is 0.30
A disc of uniform thickness having inner and outer diameters 100 mm and 400 mm respectively
is rotating at 5000 rpm about its axis. The density of the material of the disc is 7800 kg/m3 and
poisson's ratio is 0.28. Determine the stress variations along the radius of the disc.
UNIT IV
7. Explain briefly about the strain displacement relations for plates with a neat sketch.
A square plate is simply supported on all edges as shown in Figure 3 and is loaded by gravel such
that P P0Sinx
a Siny
a a b
i. Determine the maximum deflection and its location
ii. Determine the maximum values of the Moments Mxx Myy
iii. Determine the maximum values of the Kirchhoff shear forces Vx,Vy.
Page 2 of 3
Figure 3
8. A rail road uses steel rails 200 GPa) with a depth of 184 mm. The distance from the top of
the rail to its centroid is 99.1 mm, and the moment of inertia of the rails is 36.9 X 106mm4 .The
rail is supported by ties, ballast and a road bed that together are assumed to act as an elastic
foundation with spring constant K 14 N/mm2.Determine the maximum deflection ,maximum
bending moment and maximum flexural stress in the rail for a single wheel load of 170 kN.

A steel I -beam 200 GPa) has a depth of 102 mm, width of 68 mm, moment of inertia of
IX 2.53X 106mm4, and of length 4 m. It is attached to a rubber foundation for which K0
0.350 N/mm3. A concentrated load P=30.0 kN is applied at one end of the beam. Determine
the maximum deflection, maximum flexural stress in the beam and the location of each.
UNIT V
9. Explain the deflection of bodies in point contact with a neat sketch.
Explain the stresses for two bodies in line contact with loads normal and tangent to contact area.

10. Explain the determination of contact stresses with a neat sketch.
Two steel cylinders each 80 mm in diameter and 150 mm long mounted on parallel shafts and
loaded by a force F 80 KN. The two cylinders 200 GPa and
0.29) are rotated at
slightly different speeds so that the cylinder surfaces slide across each other. If the coefficient of
sliding friction is determine the maximum compressive principal stress the maximum
shear stress max and the maximum octahedral shear stress.