Download JNTUK M-Tech 2020 R19 Civil 1104 Analytical& Numerical Methods For Structural Engineering Model Question Paper

Download JNTUK (Jawaharlal Nehru Technological University Kakinada (JNTU kakinada)) M.Tech (ME is Master of Engineering) 2020 R19 Civil 1104 Analytical& Numerical Methods For Structural Engineering Model Previous Question Paper

[M19 ST 1104]

I M. Tech I Semester (R19) Regular Examinations
ANALYTICAL& NUMERICAL METHODS FOR STRUCTURAL ENGINEERING
(STRUCTURAL ENGINEERING)
MODEL QUESTION PAPER
TIME: 3 Hrs. Max. Marks: 75 M
Answer ONE Question from EACH UNIT
All questions carry equal marks
*****
CO KL M
UNIT - I
1. a). Using the Laplace transform method solve the Initial Bndary Value Problem
(IBVP) described as PDE
2
2
t
u
?
?
=
t
u
c ?
?
2
2
1
- t ? cos ; 0 x ? < ? , 0 t ? < ? . Also
given bndary conditions areu( t
u (x,0) = u(x, 0) = 0.
CO1 K3 12
b).
Write the Laplace transform of . }
1
{
t

CO1 K2 3
OR
2. a). A string is stretched as fixed between two points (0, 0) & ( l , 0). Motion is initiated
by displacing the string in the form of ) sin(
l
x
u
?
? ? and released from rest at time
0 ? t . Find the displacement of any point on the string at any time . t
CO1 K3 12
b). State the heat conduction problem in semi ? infinite rod. CO1 K2 3
UNIT - II
3. a). Using the Frier transform method solve the solution of 2D Laplace equation
0
2
2
2
2
?
?
?
?
?
?
y
u
x
u
, is valid in the half - plane , y > 0 , is subjected to the condition U
(x, 0) = 0 if x< 0, u (x, 0) = 1 if x > 0 and 0 ) , ( lim
2 2
?
? ? ?
y x u
y x
in the half plane.
CO2 K3 12
b). Write the change of scale property of Frier transforms CO2 K2 3
OR
4. a).
Find the curves on which the functional dx xy y ) 12 (
1
0
2
1
?
?
withy(0) = 0 and y(1) = 1
can be extremised.
CO2 K3 7
b).
Show that the curve which extremises the functional dx x y y I ] ) [(
2 2 2
4
0
? ? ? ? ?
?
?

under the conditions
CO2 K3 8
UNIT - III
5. a). Verify that u(x) = x e
x
is a solution of the Voltaerra Integral equation
?
? ? ?
x
dt t u t x x x u
0
) ( ) cos( 2 sin ) (
CO3 K2 8
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[M19 ST 1104]

I M. Tech I Semester (R19) Regular Examinations
ANALYTICAL& NUMERICAL METHODS FOR STRUCTURAL ENGINEERING
(STRUCTURAL ENGINEERING)
MODEL QUESTION PAPER
TIME: 3 Hrs. Max. Marks: 75 M
Answer ONE Question from EACH UNIT
All questions carry equal marks
*****
CO KL M
UNIT - I
1. a). Using the Laplace transform method solve the Initial Bndary Value Problem
(IBVP) described as PDE
2
2
t
u
?
?
=
t
u
c ?
?
2
2
1
- t ? cos ; 0 x ? < ? , 0 t ? < ? . Also
given bndary conditions areu( t
u (x,0) = u(x, 0) = 0.
CO1 K3 12
b).
Write the Laplace transform of . }
1
{
t

CO1 K2 3
OR
2. a). A string is stretched as fixed between two points (0, 0) & ( l , 0). Motion is initiated
by displacing the string in the form of ) sin(
l
x
u
?
? ? and released from rest at time
0 ? t . Find the displacement of any point on the string at any time . t
CO1 K3 12
b). State the heat conduction problem in semi ? infinite rod. CO1 K2 3
UNIT - II
3. a). Using the Frier transform method solve the solution of 2D Laplace equation
0
2
2
2
2
?
?
?
?
?
?
y
u
x
u
, is valid in the half - plane , y > 0 , is subjected to the condition U
(x, 0) = 0 if x< 0, u (x, 0) = 1 if x > 0 and 0 ) , ( lim
2 2
?
? ? ?
y x u
y x
in the half plane.
CO2 K3 12
b). Write the change of scale property of Frier transforms CO2 K2 3
OR
4. a).
Find the curves on which the functional dx xy y ) 12 (
1
0
2
1
?
?
withy(0) = 0 and y(1) = 1
can be extremised.
CO2 K3 7
b).
Show that the curve which extremises the functional dx x y y I ] ) [(
2 2 2
4
0
? ? ? ? ?
?
?

under the conditions
CO2 K3 8
UNIT - III
5. a). Verify that u(x) = x e
x
is a solution of the Voltaerra Integral equation
?
? ? ?
x
dt t u t x x x u
0
) ( ) cos( 2 sin ) (
CO3 K2 8
b).
Convert 1
2
2
? ? xy
dx
y d
, y(0) = 0, y(1) = 1 into an integral equation
CO3 K2 7
OR
6. a). Find the Eigen values and Eigen functions of the Integral Equation
?
?
?
1
0
) ( ) ( dt t u e x u
t x
?
CO3 K2 8
b). Solve the homogenes Fredholm Integral equation of second kind
?
? ?
?
?
2
0
) ( ) sin( ) ( dt t u t x x u
CO3 K2 7
UNIT - IV
7. a). From the following table, estimate the number of students who obtain marks
between 40 and 45.
Marks 30-40 40-50 50-60 60-70 70-80
No. of
Students
31 42 51 35 31

CO4 K2 7
b). Find by Teylor?s series method the value of y at x = 0.1 and x = 0.2 to five places
of decimals from 1
2
? ? y x
dx
dy
, y(0) =1
CO4 K2 8
OR
8. a). A beam of length l, supported at n points carries a uniform load w per unit
length. The bending moments M
1
, M
2
, M
3
, ?,M
n
at the supports satisfy the
Clapeyron?s equation: M
r+2
+ M
r+1
+ M
r
=
2
2
1
wl . If a beam weighing 30 kg is
supported at its ends and at two other supports dividing the beam into three equal
parts of 1 meter length, show that the bending moments at each of the two middle
supports is 1 kg meter.
CO4 K3 8
b).
The deflection of Beam is given by the equation ) ( 81
4
4
x y
dx
y d
? ? ? , where ?(x) is:
x 1/3 2/3 1
?(x) 81 162 243
And bndary condition y(0) = y
1
(0) = y
11
(1) = y
111
(1) = 0. Evaluate the deflection
at the pivotal points of the beam using three sub intervals.

CO4 K3 7
UNIT - V
9. a). Given Values
x 5 7 11 13 17
f(x) 150 398 1492 2366 5202
Evaluate f(9) using Lagrange Formula
CO5 K2 8
b). Use the Composite Trapezoidal Rule with m = n = 2 to evaluate the dble integral
? ?
?
2
1
0
2
1
0
dxdy e
y x

CO5 K3 7
OR
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[M19 ST 1104]

I M. Tech I Semester (R19) Regular Examinations
ANALYTICAL& NUMERICAL METHODS FOR STRUCTURAL ENGINEERING
(STRUCTURAL ENGINEERING)
MODEL QUESTION PAPER
TIME: 3 Hrs. Max. Marks: 75 M
Answer ONE Question from EACH UNIT
All questions carry equal marks
*****
CO KL M
UNIT - I
1. a). Using the Laplace transform method solve the Initial Bndary Value Problem
(IBVP) described as PDE
2
2
t
u
?
?
=
t
u
c ?
?
2
2
1
- t ? cos ; 0 x ? < ? , 0 t ? < ? . Also
given bndary conditions areu( t
u (x,0) = u(x, 0) = 0.
CO1 K3 12
b).
Write the Laplace transform of . }
1
{
t

CO1 K2 3
OR
2. a). A string is stretched as fixed between two points (0, 0) & ( l , 0). Motion is initiated
by displacing the string in the form of ) sin(
l
x
u
?
? ? and released from rest at time
0 ? t . Find the displacement of any point on the string at any time . t
CO1 K3 12
b). State the heat conduction problem in semi ? infinite rod. CO1 K2 3
UNIT - II
3. a). Using the Frier transform method solve the solution of 2D Laplace equation
0
2
2
2
2
?
?
?
?
?
?
y
u
x
u
, is valid in the half - plane , y > 0 , is subjected to the condition U
(x, 0) = 0 if x< 0, u (x, 0) = 1 if x > 0 and 0 ) , ( lim
2 2
?
? ? ?
y x u
y x
in the half plane.
CO2 K3 12
b). Write the change of scale property of Frier transforms CO2 K2 3
OR
4. a).
Find the curves on which the functional dx xy y ) 12 (
1
0
2
1
?
?
withy(0) = 0 and y(1) = 1
can be extremised.
CO2 K3 7
b).
Show that the curve which extremises the functional dx x y y I ] ) [(
2 2 2
4
0
? ? ? ? ?
?
?

under the conditions
CO2 K3 8
UNIT - III
5. a). Verify that u(x) = x e
x
is a solution of the Voltaerra Integral equation
?
? ? ?
x
dt t u t x x x u
0
) ( ) cos( 2 sin ) (
CO3 K2 8
b).
Convert 1
2
2
? ? xy
dx
y d
, y(0) = 0, y(1) = 1 into an integral equation
CO3 K2 7
OR
6. a). Find the Eigen values and Eigen functions of the Integral Equation
?
?
?
1
0
) ( ) ( dt t u e x u
t x
?
CO3 K2 8
b). Solve the homogenes Fredholm Integral equation of second kind
?
? ?
?
?
2
0
) ( ) sin( ) ( dt t u t x x u
CO3 K2 7
UNIT - IV
7. a). From the following table, estimate the number of students who obtain marks
between 40 and 45.
Marks 30-40 40-50 50-60 60-70 70-80
No. of
Students
31 42 51 35 31

CO4 K2 7
b). Find by Teylor?s series method the value of y at x = 0.1 and x = 0.2 to five places
of decimals from 1
2
? ? y x
dx
dy
, y(0) =1
CO4 K2 8
OR
8. a). A beam of length l, supported at n points carries a uniform load w per unit
length. The bending moments M
1
, M
2
, M
3
, ?,M
n
at the supports satisfy the
Clapeyron?s equation: M
r+2
+ M
r+1
+ M
r
=
2
2
1
wl . If a beam weighing 30 kg is
supported at its ends and at two other supports dividing the beam into three equal
parts of 1 meter length, show that the bending moments at each of the two middle
supports is 1 kg meter.
CO4 K3 8
b).
The deflection of Beam is given by the equation ) ( 81
4
4
x y
dx
y d
? ? ? , where ?(x) is:
x 1/3 2/3 1
?(x) 81 162 243
And bndary condition y(0) = y
1
(0) = y
11
(1) = y
111
(1) = 0. Evaluate the deflection
at the pivotal points of the beam using three sub intervals.

CO4 K3 7
UNIT - V
9. a). Given Values
x 5 7 11 13 17
f(x) 150 398 1492 2366 5202
Evaluate f(9) using Lagrange Formula
CO5 K2 8
b). Use the Composite Trapezoidal Rule with m = n = 2 to evaluate the dble integral
? ?
?
2
1
0
2
1
0
dxdy e
y x

CO5 K3 7
OR
10. a). integral ? ?
? ?
?
1
0
2
3 2
x
x
dydx y x
CO5 K3 7
b). Apply New Marks Method with suitable example CO5 K3 8

CO: Crse tcome
KL: Knowledge Level
M: Marks





















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