Download JNTUA (JNTU Anantapur) M.Tech ( Master of Technology) 1st Semester 2017 Feb 9D15103 Advanced Mechanics of Solids Previous Question Paper
M.Tech I Semester Regular & Supplementary Examinations January/February 2017
ADVANCED MECHANICS OF SOLIDS
(Machine Design)
Time: 3 hours Max. Marks: 60
Answer any FIVE questions
All questions carry equal marks
*****
1 Determine the shear center location C for an aircraft semi-circular box beam whose cross section is shown in
figure blow.
2 The masonry column carries an eccentric load P = 12 kN as shown in the figure below:
(a) Locate the points on the cross section where the neutral axis crosses the y- and the z-axes.
(b) Determine the maximum tensile and compressive normal stresses.
3 The curved beam in figure is subjected to a load P = 120 kN. The dimensions of section BC are also shown in
figure below. Determine the circumferential stress at B and radial stress at the junction of the flange and web at
section BC.
4 (a) What is Prandtl elastic membrane analogy? Explain.
(b) A rod with rectangular cross section is used to transmit torque to a machine frame with a width of 40 mm. The
first 3 m length of the rod has a depth of 60 mm, and the remaining 1.5 m length has a depth of 30 mm. The rod
is made of steel for which G = 77.5 GPa. For T
1
= 750 N-m and T
2
= 400 N-m, determine the maximum shear
stress in the rod. Determine the angle of twist of the free end.
Contd. in page 2
Page 1 of 2
x
y
C
V
O
250 mm
5 mm
5 mm
e
y
z
y
z
p
?
120 mm
8mm
16 mm
80 mm
C
B
p p
240 mm
P=12 kN
+
148 mm
168 mm
72 mm 120 mm
24 mm
C
B
Web
Flange
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Code: 9D15103
M.Tech I Semester Regular & Supplementary Examinations January/February 2017
ADVANCED MECHANICS OF SOLIDS
(Machine Design)
Time: 3 hours Max. Marks: 60
Answer any FIVE questions
All questions carry equal marks
*****
1 Determine the shear center location C for an aircraft semi-circular box beam whose cross section is shown in
figure blow.
2 The masonry column carries an eccentric load P = 12 kN as shown in the figure below:
(a) Locate the points on the cross section where the neutral axis crosses the y- and the z-axes.
(b) Determine the maximum tensile and compressive normal stresses.
3 The curved beam in figure is subjected to a load P = 120 kN. The dimensions of section BC are also shown in
figure below. Determine the circumferential stress at B and radial stress at the junction of the flange and web at
section BC.
4 (a) What is Prandtl elastic membrane analogy? Explain.
(b) A rod with rectangular cross section is used to transmit torque to a machine frame with a width of 40 mm. The
first 3 m length of the rod has a depth of 60 mm, and the remaining 1.5 m length has a depth of 30 mm. The rod
is made of steel for which G = 77.5 GPa. For T
1
= 750 N-m and T
2
= 400 N-m, determine the maximum shear
stress in the rod. Determine the angle of twist of the free end.
Contd. in page 2
Page 1 of 2
x
y
C
V
O
250 mm
5 mm
5 mm
e
y
z
y
z
p
?
120 mm
8mm
16 mm
80 mm
C
B
p p
240 mm
P=12 kN
+
148 mm
168 mm
72 mm 120 mm
24 mm
C
B
Web
Flange
Code: 9D15103
5 Derive the stresses for two bodies in line contact : Loads normal and tangent to contact area.
6 (a) What is plane stress and plane strain? Explain with suitable example.
(b) For a solid in a state of plane stress, show that if there are body forces P
x
, P
y
per unit volume in the direction of
the axes x, y respectively, the compatibility equation can be expressed in the form:
7 (a) What do you mean by compatibility equations? What is the necessity of compatibility equations? Write the
compatibility equations in Cartesian co-ordinates.
(b) In planar problems, stress components are expressed in Cartesian co-ordinate system where as the location at
which stress is considered is defined in polar co-ordinates. Why such mixed approach adopted? Discuss.
8 (a) Derive the equations of equilibrium in polar co-ordinates for radial direction & tangential direction.
(b) The stress components at a point are . Determine
the principle stresses and principle directions.
*****
Page 2 of 2
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This post was last modified on 30 July 2020