The document outlines the syllabus for the first semester M.Tech exam in computational structural mechanics, covering topics like static and kinematic indeterminacy, flexibility and stiffness methods, finite element analysis of beams, frames and trusses, and numerical techniques for solving systems of equations. It lists 10 questions, asking students to solve structural analysis problems using different analytical methods, perform structural modeling, and carry out structural design computations. Short notes may also be asked on topics related to matrix operations and structural analysis algorithms.

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2 0 1 6
Advanced lWatics
Tirne: 3 hrs.
lote: Ansu,er any FIVE full questiotts.
I a. Construct QR factorization for the matrix :
l-+ 2 2)
A=l r -3 3l
tt
L6 6 ol
b. Solve the system of equations :
x: f 2x+: I
-t Zxz 1- 2y -t 3w:2
in the least - square sense.
3 a. Derive Euler - Lagrange's formula in the ror* $-a[4]= oturq ,r "'" '""^' ay d* [ ry' )-
"
Z a. Apply the shifted QR algorithm to the matrix O = [] 1-1. ar*, out three iterations.
Ll 5-l
tro Marksi
(07 t'Iarks)
2t I
"iF'g'2
+2y(x +v)l dx = 0, given that y(l) - v(2) :0.
' ,07 ['Iarks)
n/
/2r
'(lrr',' + (z')2 * zvrla* .
0
b. Find the singular - value decomposition of the matrix A:
c. Solve the variation problem
b. Find the extremum of tunctionat : vJ[v(x, = jtn;c4x, given y(0) : 0 and v(1)
: 1 .
0
4 a. Find the tunction y(x) for which tkn'
0
y(0) : 0, y(r) : i.
b. Find the extremals of the
"[l):1,2(o)
- /n)
-2
) . =u''r)=
,l
II
-v2l a*is stationary. Given that f-r,'dx=1 anci
0
(10 Marks)
functional : I =
-1.
gii,en that y(0) : 0.
1 af2
(l0lHarks)

2. 14ELD11
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a. UsingtheLaplacetransformmethod.sotue { -+,0<x<1, t>0subjecttoboundary
Af Ax'
conditionr; (0, t):u(1,0:0 fort> 0 and initialconditionsu(x,0): sin 7rx,
fff*,oi = -sinmx for o < x < i.
6a.
b.
I
D.
Ea.
b. Using the Fourier sine transform find the ternperature u(x, t) in a semi infinite medium
0 < x < oo deterinined by the PDE : Kur* : ut, 0 ( X ( o, t > 0 subject to u(0, t) : uo for t > 0
and u(x, 0) : 0 for 0 < x ( 6, u and u, bothtend to zero as x -) co. (1S Marks)
Solve : V2 u : 0, -6 ( X ( 6, 0 < y< m under the conditions u(x, 0) : (x), *oo ( x ( co and
the limiting conditions u(x, y) -+ 0 as y -> oo ;u and $ Uotf, vanish as I xi -+ .o. ({2 Marks)
ov,
lf$istheharrnLonicfunctioninRand{9=OondRthenprovethat$isaconstantinR.
on
{{}E N{arks}
A farmer baX<es two types of cakes (chocolate and vanilla) to supplement his incoiae. Each
chocolate cake can be sold for Rs. 50/- and vanilla cake for Rs 25l-. Each chocoiate cake
reqriires 20 minutes of baking time and need 4 eggs. Each vanilla cake requires 40 minutes
of baking time and requires one egg, The farmer has 8 hours of bake time and 30 eggs with
him available. Formulate the LPP and solve for maximizing sales using Simplex method.
use two -- plaase rnerrhod to :
(u,8 Marks)
h4axirnize Z: -4xt -- 3xz * 9xt
Subject to 2xr + 4xz* 6x: > 15
q.
(10 Marks)
itr2 Marks)
(10 Marks)
(10 Marks)
I^
U.
6x1 + xz+ 6> L2
x1, X2 X3 ) 0.
Sclve the following non * linear programming using Lagrangean rnethod :
Maximize z : 4x1 - 0.A2xy2 I xz - 0.02x22
x1 * 2x2: 120
X1, X2 ) 0.
Using Kuhn - Tucker conditions :
2^2
l4axlmlze) L: Xt tKtXz- ZXt
Subject to 4x1 +2x2<24
5xr+10x2<30
X1, X2 ) 0.
*+*{<{<
IOT Z

3. OFT
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I4CSE11
(S8 &trarks)
(i)6 h{arks)
CE?.{TRAL
LTBRARY
First Semester M.Tech. Degree Ex ation, /.20151Jan.2015
Gomputational Struc anics
Tirne: 3 hrs. Max. Marks: tr00
Note: Answer any FIVE full questions"
I a. Determine the static and kinematic indeterminacy of the structures shown in Fig. Q1(ai),
Ql(az), Ql(a:). {06 Marks)
a)
o
o
d
o.
.l
d)
o
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T.r
-,I.: al
Y()
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at
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=ijrr'i
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=cdr+o
tr>
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z
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Frg. QI(a1) r'ig. Ql(az)
b. Coiapare flexibility method and stiffness rnethod.
c. Differentiate local from global coordinates system with example.
a. Compute the system flexibility matrix for the axially rigid continuous beam shown in Fig.
Q2 (a). Consider the moment at fixed end and the vertical reaction at mid-support as
redundants. (I{} hlanks)
f3 = C"mst*'n*
Fig. Q2 (a)
b. Develop the system flexibility matrix of the truss shown ira Fig. Q2 (b) iry choosing the forec
in member BD and horizontal reaction at support 'D' as redundant. Take AE constant for all
members. (1CI Marks)
Fig. Q2 (b)
Analyse the continuous beam if the support B sinks by 20 mrn. Adotrrt flexibility itethod b3z
developing ftirce transformation matrix. Draw BMD. Take EI : 8000 kl,kn2 for all tnembers.
(20 Marks)
:r,
Fie. Q1(ar)
Frg. Ql(a:)
ek* ]h,
I of2
Fis. Q3

4. Analyse the frarne shown
BMD and elastic curve.
in Fig. Q4 by flexibility method. Adopt
1. .
o K-
14CSE11
eiement approach. Draw
(2S Marks)
at1
-+I
I
Analyse the continuous beam shown in Fig. Q7
allmembers.
go k*
=L-i{""',^ ff5*+I*r+ fi
k=+r-eEft3
.x'
8a.
b.
Write short notes on:
i) Banded ntatrix ii) Band width
Fig. Q7
iii) Sky line storage
Solve the following linear simultaneous equation by Gauss elimination rnethod:
5x+2y t z=12; x+ 6y +22=19; 2x+y +4z:16
*rrrr**
2 of2
(88 Marks)
(12 Marks)
k,tlru6
-+ Fig. Q4
Analyse tnre continuous beam shown in Fig. Q5 by stiffness method using element approach.
i20 Marhs)
Fig. Qs
Analyse the &ame shown in Fig. Q6 by element approach of stiffness rnethod. (20 Marks)
Fig. Q5
by direct stiffness method. Ei constant f,or
{2S h{arks}
zrn
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5. USN
Self weight of roof
Live load on floor
Live load on roof
Area ofeach floor
Location of building
Damping
Height of each floor
: 1109.6rkN
:2.89 kN/#
= 1.20 kN/m2
= 144 rfi
: zofle III on hard soil
- <o,/
- J,/O
:3.2 m.
I4CSE22
(10 Marks)
(10 Marks)
(20 Marks)
(10 Marks)
(10 Marks)
a.
oo
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p.
a)
ts
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no
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d9
=r,
oo lr
.= ..!
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xoox()o=
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a
Second Semester M.Tech. Degree on, Dec.20l5lJan.20l6
Time: 3 hrs.
Earthquake Resistant Structures
Max. Marks: 100
Note: 7. Answer any FIWfull questions.
2. (Jse of IS - 1893 - 2002 is permitted.
a. Briefly explain the geological and tectonic features of India.
b. Write a note on seismic instruments.
a. Distinguish between structural behavior under gravity load and earthquake forces. (10 Marks)
b. What are the requirements of efficient earthquake resistant structural system? (10 Marks)
3 a. Explain strong motion characteristics. (10 Marks)
b. Qualitatively explain the inelastic displacement and aeceleration response spectra including
influence of ductility and damping. (10 Marks)
Calculate the base shear and storey forces for a four storeyed special moment resisting frame
residential building for the following data :
Self weight of each floor : 1439.2 kN
5 a. Discuss the effect of infill masoffy walls on frames. Explain any two methods of modeling
6 a. What are the different methods to make the masonry structure earthquake resistant?
(10 Marks)
b. Explain the behavior of masonry building during earthquakes including failure pattern.
(10 Marks)
Define ductility. Explain the general requirements to improve the ductility in RCC
structures. (10 Marks)
Explain ductile detailing provisions for columns in RCC structure. (10 Marks)
masonry infill.
b. Expl4ur soft storey and design requirements of soft storey.
Write short notes on following :
a. Linear and nonlinear procedures of seismic analysis
b. Performance based seismic engineering method
c. Seismic retrofitting of structures
d. Seismic response control concept.
*a**rr
(20 Marks)

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Second Semester M.Tech. Degree Ex i Dec.20l5lJan.20l6
Design Goncepts of Substructure
Time: 3 hrs. Max. Marks:100
Note: Answer any FIW full questions.
I a. What are the objectives of subsoil exploration? What are the steps involved in planning and
execution of subsurface exploration? (10 Marks)
b. What are the basic requirements of a foundation? (04 Marks)
c. What is meant by significant depth? What are guide liners to determine the same? (06 Marks)
2 a. Explain the concept of total and effective strength parameter and their uses. (08 Marks)
b. Discuss how inclined and eccentric loads are considered in the design of footings. (08 Marks)
c. What are the components of settlement? (04 Marks)
3 a. Explain how allowable bearing pressure for raft foundation in granular and cohesive soils
determined? 110 Marks)
b. What is coefficient of subgrade reaction? WhAt are the factors affecting the value of
coefflrcient of sub grade reaction? (10 Marks)
4 a. Explain the step involved is design of trapezoidal footing. (10 Marks)
b. Discuss rigid and flexible approach in the design of raft foundation. (10 Marks)
5 a. How do you estimate the pile load capacity using static analysis? Discuss in detail.
(10 Marks)
(06 Marks)
(04 Marks)
6 a. What is group efficiency of piles? How it is determined? Discuss any two methods?
(l0 tVlarks)
b. How settlqlnenJ of a group of piles determined in cohesionless and cohesive soils?
(10 Marks)
7 a. What are the forces acting on the well foundation? (08 Marks)
b. Explain the components of a well foundation with the help of a neat sketch. (04 Marks)
c. Write a note on sinking of wells and explain tilt and shifts. (08 Marks)
b. Write a note on laterally loaded piles.
c. What are the limitations of dynamic formulae?
8 a. What are.the types of foundation used for transmission line towers? Explain the
selecting a proper type of foundation.
b. How is the safety of a tower foundation checked against
i) uplift ii) overturning iii) Lateral thrust? Explain.
14CSB24
method of
(10 Marks)
(10 Marks)