Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) ) BE/BTech Aero (Aerospace-Engg) 2020 March 7th and 8th Sem ASPE 409 Theory Of Plates Shells Previous Question Paper
Roll No. Total No. of Pages : 03
Total No. of Questions : 09
B.Tech.(Aerospace Engg.) (EL-2012 Onwards) (Sem.?7,8)
THEORY OF PLATES SHELLS
Subject Code : ASPE-409
M.Code : 72572
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.
SECTION?A
1. Write briefly :
a) Write down the differential equation of rectangular plate for combined lateral and in-
plane loading.
b) Write down the differential equations for buckling of cylindrical shell under
combined internal pressure and uniform axial load.
c) Classification of various types of shell with neat sketches.
d) Curved and shallow shells with coordinate system.
e) Briefly describe the structural behavior of thin shell in the context of bending and
buckling strength.
f) Give the physical explanation of the assumption ?
z
= ?
3
= 0 adopted in the general
linear theory of thin shells. Compare the order of the direct stresses ?
1
and ?
2
and ?
3
.
g) Flexural rigidity of shell.
h) Derive the relations between bending moment and curvature for pure bending of
plates.
i) Classification of plates with context of transverse shear and normal effects.
j) Distinguish between Synclastic and Anticlastic surfaces with example.
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1 | M-72572 (S2)-951
Roll No. Total No. of Pages : 03
Total No. of Questions : 09
B.Tech.(Aerospace Engg.) (EL-2012 Onwards) (Sem.?7,8)
THEORY OF PLATES SHELLS
Subject Code : ASPE-409
M.Code : 72572
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.
SECTION?A
1. Write briefly :
a) Write down the differential equation of rectangular plate for combined lateral and in-
plane loading.
b) Write down the differential equations for buckling of cylindrical shell under
combined internal pressure and uniform axial load.
c) Classification of various types of shell with neat sketches.
d) Curved and shallow shells with coordinate system.
e) Briefly describe the structural behavior of thin shell in the context of bending and
buckling strength.
f) Give the physical explanation of the assumption ?
z
= ?
3
= 0 adopted in the general
linear theory of thin shells. Compare the order of the direct stresses ?
1
and ?
2
and ?
3
.
g) Flexural rigidity of shell.
h) Derive the relations between bending moment and curvature for pure bending of
plates.
i) Classification of plates with context of transverse shear and normal effects.
j) Distinguish between Synclastic and Anticlastic surfaces with example.
2 | M-72572 (S2)-951
SECTION?B
2. For a simply supported square isotropic plate of side 2.5 cm, under UDL and SSL of
10KN/mm
2
. Find the maximum deflection taking v = 0.3, E = 200 KN/mm
2
, thickness of
plate h= 80mm. Adopt the Navier solution, take only the first term of the series.
3. A simply supported square plate is under the action of a lateral load P at its center C and
a uniform in-plane tension N
x
. Derive the equation of the deflection surface, using energy
method and by retaining the first term of the series solution.
4. A thin-walled cylinder is used to support a reactor of weight W. Find the maximum value
of w that can be applied to the cylinder without causing it to buckle. Take L = 10ft,
R = 2 ft, E = 29000 ksi, h = 0.2 in, v = 0.25 and the factor of safety (FS) is 2.5.
5. A horizontal, circular cylinder with rigidity built-in cylinder ends of radius a, thickness t,
and length L carries its own weight p. Derive the following expressions for the membrane
stresses :
2 2
2
? cos ; sin ; cos
12
x x
pa px p x L
va
t t t a a
? ?
? ?
? ? ? ? ? ? ? ? ? ? ? ? ?
? ?
? ?
6. A rectangular plate has two opposite edges y = 0 and y = b simply supported, the third
edges x = 0 clamped, and fourth edge x = a free subjected to UDL of magnitude p
0
as
shown below :
Fig.1
An approximate expression for the deflection surface is
2
sin
x y
w c
a b
? ? ?
?
? ?
? ?
where c is a constant. Determine : a) whether this deflection satisfy the boundary
condition of the plate; b) the approximate maximum plate strain component at the center,
for square plate a = b and v = 1/3.
a
b
Free
x
y
p
0
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1 | M-72572 (S2)-951
Roll No. Total No. of Pages : 03
Total No. of Questions : 09
B.Tech.(Aerospace Engg.) (EL-2012 Onwards) (Sem.?7,8)
THEORY OF PLATES SHELLS
Subject Code : ASPE-409
M.Code : 72572
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.
SECTION?A
1. Write briefly :
a) Write down the differential equation of rectangular plate for combined lateral and in-
plane loading.
b) Write down the differential equations for buckling of cylindrical shell under
combined internal pressure and uniform axial load.
c) Classification of various types of shell with neat sketches.
d) Curved and shallow shells with coordinate system.
e) Briefly describe the structural behavior of thin shell in the context of bending and
buckling strength.
f) Give the physical explanation of the assumption ?
z
= ?
3
= 0 adopted in the general
linear theory of thin shells. Compare the order of the direct stresses ?
1
and ?
2
and ?
3
.
g) Flexural rigidity of shell.
h) Derive the relations between bending moment and curvature for pure bending of
plates.
i) Classification of plates with context of transverse shear and normal effects.
j) Distinguish between Synclastic and Anticlastic surfaces with example.
2 | M-72572 (S2)-951
SECTION?B
2. For a simply supported square isotropic plate of side 2.5 cm, under UDL and SSL of
10KN/mm
2
. Find the maximum deflection taking v = 0.3, E = 200 KN/mm
2
, thickness of
plate h= 80mm. Adopt the Navier solution, take only the first term of the series.
3. A simply supported square plate is under the action of a lateral load P at its center C and
a uniform in-plane tension N
x
. Derive the equation of the deflection surface, using energy
method and by retaining the first term of the series solution.
4. A thin-walled cylinder is used to support a reactor of weight W. Find the maximum value
of w that can be applied to the cylinder without causing it to buckle. Take L = 10ft,
R = 2 ft, E = 29000 ksi, h = 0.2 in, v = 0.25 and the factor of safety (FS) is 2.5.
5. A horizontal, circular cylinder with rigidity built-in cylinder ends of radius a, thickness t,
and length L carries its own weight p. Derive the following expressions for the membrane
stresses :
2 2
2
? cos ; sin ; cos
12
x x
pa px p x L
va
t t t a a
? ?
? ?
? ? ? ? ? ? ? ? ? ? ? ? ?
? ?
? ?
6. A rectangular plate has two opposite edges y = 0 and y = b simply supported, the third
edges x = 0 clamped, and fourth edge x = a free subjected to UDL of magnitude p
0
as
shown below :
Fig.1
An approximate expression for the deflection surface is
2
sin
x y
w c
a b
? ? ?
?
? ?
? ?
where c is a constant. Determine : a) whether this deflection satisfy the boundary
condition of the plate; b) the approximate maximum plate strain component at the center,
for square plate a = b and v = 1/3.
a
b
Free
x
y
p
0
3 | M-72572 (S2)-951
SECTION?C
7. Derive the differential equation for cylindrical bending of plate from fundamental.
8. Determine the critical value of the in-plane compressive forces q
x
acting on the plate
reinforced by two equally spaced stiffner, as shown below :
Fig.2
The plate is simply supported on all edges. Let A
i
and B
i
(B
i
= EI
i
) be the area of the
cross section and the bending stiffness of a stiffner, and c
i
be the spacing of the stiffeners.
Use energy approach.
9. Let a rectangular, simply supported plate of sides a and b be loaded by uniformly
distributed compressive q
x
and compressive q
y
forces. The q
x
forces are applied parallel
to the side a and q
y
forces act in the direction parallel to the side b. Find the nontrivial
solution of equation.
4 4 4 2 2
4 2 2 4 2 2
1
2 0
x y
w w w w w
q q
x x y y D x x
? ? ? ? ? ? ?
? ? ? ? ?
? ?
? ? ? ? ? ?
? ?
for this loading and calculate the critical value of the parameter ? if q
y
= ?q
x
and a = b.
Compare this result with the case when the above plate is equally compressed in two
directions q
y
= q
x
.
Fig.3
NOTE : Disclosure of identity by writing mobile number or making passing request on any
page of Answer sheet will lead to UMC case against the Student.
q
x
a
y
q
x
x
x
b q
x
q
y
q
y
q
x
Y
a
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This post was last modified on 21 March 2020