Hall Ticket No Question Paper Code: BCC206
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
M.Tech I Semester End Examinations (Regular) February, 2017
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. A cantilever beam of rectangular section is subjected to a load of 1000N which is inclined at an
angle of 30o to the vertical. Determine the stress produced due to bending at point D.
Figure 1
A beam of length 5 m and of uniform rectangular section is supported at its ends and carries uniformly
distributed load over the entire length, calculate the depth of the section if the maximum
permissible bending stress is 8 N/mm2 and central deflection is not to exceed 10 mm. Take the
value of E 1.2 x 104 N/mm2.
2. Determine the shear stress distribution in a channel section of a cantilever beam subjected to a
load as shown in figure 2. Also, locate the shear centre of the section.
Figure 2
Page 1 of 4
For a simply supported beam of length 5 which is carrying a point load of 5 kN at a distance
of 3 m from the left end. Determine
i. slope at the left support,
ii. deflection under the load
iii. maximum deflection Take E 2x 105 N/mm2 and I 1 x 108mm4
UNIT II
3. Determine the maximum tensile and maximum compressive stresses across the sec. AA of the
member loaded, as shown in figure 3 load 19620 N
Figure 3
Determine the stress at point D of a hook having a trapezoidal section with following dimensions:
b1= 4 cm, b2 1 cm, r1= 3 cm, r2 10 cm, h 7 cm, force P 29400 N.
Figure 4
4. The open link shown in Figure 5 below loaded by forces each of which is equal to 14700 N.
Find the maximum tensile and compressive stresses in the curved end at section AB.
Figure 5
Derive an equation for the value of p2 of a trapezoidal section.
Page 2 of 4
UNIT III
5. Derive an expression for torque transmitted by a thin tubular section
The two tubular sections shown in figure 6 have the same wall thickness t and same circumference.
Neglecting stress concentration, find the ratio of the shear stresses for 7M]
i. Equal twisting moments in the two cases
ii. Equal angles of twist in the two cases

Figure 6
6. For figure 7 given below a two cell tubular section whose wall thicknesses are as shown. If the
member is subjected to a torque determine the shear flows and the angle of twist of the member
per unit length.
Figure 7
A thin walled rectangular tube 30 60mm is subjected to torque of 10Nm.The thickness of all
wall is 2mm.Determine the angle of twist per metre.Take G=80GPa
UNIT IV
7. A solid flat circular plate of 800mm diameter and 15mm thickness is acted upon by a concentrated
load of 40KN at the centre of the plate. Determine the central deflection and maximum radial
stresses at the edge .E 207GPa, and v 0.292
A square door has a side of 1.8m and thickness 15mm. The plate is simply supported and
subjected to uniform pressure. Determine the yield pressure.E 200 GPa, and v 0.29
8. A plate made of mild steel 200 GPa, v 0.29, and Yield stress= 315 MPa) has a thickness
h 10 mm and cover a circular opening having a diameter of 200 mm. The plate is fixed at the edges
and is subjected to a uniform pressure p.
i. Determine the magnitude of the yield pressure Py and deflection wmax at the centre of the plate
when this pressure is applied.
ii. Determine a working pressure based on a factor of safety of SF 2.00 relative to Py
Page 3 of 4
UNIT V
9. A 20 mm long cast iron rod of 25 mm diameter is pressed on to a thick copper plate with a
force of 20N. Determine the width of the contact area, the maximum pressure at the centre of
the contact area. The elastic constants for the materials are Cast iron E 41.4 GPa, v 0.211,
Copper E 44.7 GPa, v 0.326
Derive an expression for contact pressure of ball bearing
10. Carbon steel balls, each 25 mm in diameter is pressed by a flat carbon plate force 18N at the
centre of the area of contact. For carbon steel E 207 GPa and v 0.292
i. Determine the values of the principal stresses
ii. Determine the maximum shear stress. At what distance from the contact surface do they occur.