1) The document discusses various questions related to the finite element method and analysis. It includes questions on determining stresses and displacements in a bar element, principle of minimum potential energy, derivation of shape functions, consistent nodal load vector, Gauss quadrature, advantages and disadvantages of finite element method, Hermite shape functions, and short notes on topics like C0, C1 and C2 functions. 2) The questions cover various fundamental concepts in finite element method like discretization, shape functions, potential energy approach, assembly of global stiffness matrix, consistent loading, numerical integration and analysis of trusses, beams and frames. 3) The document tests the candidate's understanding of basic finite element method concepts and their ability to

1. 14CSE23USN
Second Semester M.Tech. Degree Examination, June/July 2015
Finite Element Method and A-nalvsis
Time: 3 hrs. Max. Marks;100
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.i. T D. L)etermrne the stress and drsplacement at mrcl lengthuW the bar shown rn Frg.Q.t(b), uslng
E $ Rayleigh-Ritz method. Assume E = 70GPa,A= *Q0mm'. Assume second order polynomial.
E tP * M-/ . - (10 Marks)
t g t-fi.
?, ,* t*L
Note: 7. Answer any FIVE full questions. 1j
d 2. Assume any missing d.ata suitably. ry., -
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E I a. Explain briefly principle of minimum potential energy and determine nqdal displacements
a(n
fie ' sl<
E.9 tfl
; E members subjectq(tffixial loads. Explain any one step briefly. (08 Marks)
; E 3 a. Oeriqry#lt up. function for a two noded bar element using Lagrange's interpolation and
; E sk#kffidy the variation of shape functions for the following bar elements shown in
E H ffiQ.ltul. (r2 Marks)
e= {*f r+
A:" (-'** l#3 2- 3 H; a *l I E--= E- : --> -',
g t *A* Fie.e.3(a)(i) Fie.e.3(aXii)
5 E. flry- b. Evaluate the shape functions atP(3.75,4) within the element shown in Fig.Q.3(b). Also find
ffi"*
Jacobean for the element and area of the element. (08 Marks)
JN
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cd
o
Fie.Q.3(b)
1o'f )
; E A*'i,o -J< &o
E B' T"h _. T^
i a -{e Fie.Q.l(b)
9": *#**
5 I 2 a. What are kinematic and{Gffivariables? Give examples. (04 Marks)€ ; 2 a. What are kinematic an{{tntic variables? Give examples. (04 Marks)
E E b. Mention the.steps
iqbheg I r:l"Tg problems'in finite element method h .:lry:,"].]
E I c. Which of thq f06'fi,ing functions are in the state of stable/unstable/neutral equilibrium?q4
E I State why? i@= q2 ii) n = (2q- q') iii) n = qa. (08 Marks)
tro.
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2. 14CSE23
4 a. Obtain the consistent nodal load vector for the elements shown in Fig.Q.a(a) and Fig.Q.a@).
(12 Marks)
ti"S"l ,7.z
&rctl "*
L j,r-
-*** Iv==
Fig.Q.a(aXii)
b. Using one point and two point formula of Gauss quadrature evaluate: .W*'!r
* 1 I 6, ,& irr Marks)ll:eE+q'j,L (1+2) ) {.n '
5 a. Mention the advantages and disadvantages of finite element mettro4ryilft (08 Marks)
b. Obtain the expression for shape function in case of a CST,1gLk"rt. Adopt Cartesian
co-ordinates. Also sketch the shape function variation at each so$s{ (tz Marks)
C)*'hJ
6 a. Derive the Hermite shape function for a two noded b@dlement in natural coordinates.
Also plot the variations. m, - (10 Marks)
b. For the fixed beam shown in Fig.Q.6(b), determineWd displacement and slopes at node@
and reaction force of nodeO only. E =210 x lflQfm2. (10 Marks)
^tl(
E ,2tu*lolrvlt*L I uo k*
zokN-r{ ll /4.
c*
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l''
::: _!:... n+!ri
.:- r:!
.. l.rr
+i ---V Hrt )
Fie.Q.a(a)(i)
?aehr"
t3F
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t .4......
ilf",h ojg*'l'*
=,^
_J<.. 3r.
-u"
d?t
For the two ba6
ffis shown in Fig.Q.7, determine nodal displacements and reaction
forces/suppoq re-ftdffion using the concept of direction cosines and elimination techniques.
Adopt FEM.gproach. AssumeE=210 GPa, A = 600mm2 (Finite Element Method) for Lach
element. l,J'* (2LMarks)
Fie.Q.6(b)
,., t'"r,''
.8
...'".,
a.
b.
c.
d.
Write short note on:
Co, C' and C2 function
Node numbering to minimize band width
Serendipity and Lagrangian finite element
Patch test.
Fig.Q.7
*x{<**
(20 Marks)

3. Time: 3 hrs.
USN
5a.
b.
6a.
b.
Note: Answer any FIVE full questions.
14CSE21
Max. Marks:100
with small deflections and
(06 Marks)
laterally loaded rectangular
(14 Marks)
with straight
(20 Marks)
Second Semester M.Tech. Degree Examination, June/July 2015
Design of Plates a nd She lls
la.
b.
a)
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Enlist the assumption made in the
limitations of the theory.
Derive the equations of equilibrium
plates.
analysis of thin plates
for small deflections for a
2 a. Enlist the advantages of Navier solution. (04 Marks)
b. Find the Navier solution for a simply supported rectangular plate subjected to udl load, plate
size (axb). (16 Marks)
Find the Levy's solution for simply supported rectangular plate subjected to UDL of
intensity. 'q'. (20 Marks)
Determine the maximum deflection of a clamped
Assume that the plate is subjected to constant lateral
rectangular plate by the Ritz method.
load and ur. 3 = 1.5 (spara ratio).
b
(20 Marks)
Discuss the classification of shells. (05 Marks)
Derive the equations of equilibrium for cylindrical shell subjected to membrane force.
(15 Marks)
Enlist the assumption made in the beam theory of cylindrical shells and also advantage of
beam theory. (08 Marks)
Derive expression for membrane stress resultants for a spherical dome due to self weight.
(12 Marks)
Find the solution for membrane theory of rectangular hyperbolic parabolids
line generators as boundaries.
Write short notes on the following :
a. Classification of shells surfaces
b. Behavior of folded plates
c. Levy's approach for plate analysis
d. Edge beam theory - cylindrical shells.
*r<***
(20 Marks)

4. I4CSE22USN
Second Semester M.Tech. Degree Examination, June/July 2015
Earthquake Resistant Structures
la.
b.
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Time: 3 hrs.
3a.
b.
4a.
b.
5a.
Note: T.Answer any FIVE full questions.
2. (Jse of IS iags - iooz is permitted-
Explain "Reid's Elastic Rebound theory" for the origin of earthquakes.
Max. Marks:100
(05 Marks)
Explain the characteristics of different types of seismic waves and its quantification.
(15 Marks)
2 a. What is a response spectra? How is it constructed and compare it with a design spectra.
(06 Marks)
b. A ten storey OMRF building has plan dimensions as shown in Fig.Q2(b) below. The storey
height is 3.0 m. The dead load perunit area of the floor consisting of the floor slab, finishes
etc is 4 kN/m2 weight of partitions on the floor can be assumed to be 2 kN/m2. The intensity
of live load on each floor is 3kN/m2. The soil below the foundation is hard and the building
is located in Delhi. Determine the seismic forces and shear forces at different floor levels.
Refer Fig.Q2(b). Take column of size 0.3 m x 0.6 m and beam of size 0.3 x 0.6 m.
(14 Marks)
List out the various structural irregularities which affect the performance of RC building
during earthquakes. (10 Marks)
Explain the various earthquake resistant features that can be introduced in a masonry
building to improve its performance during an earthquake. (10 Marks)
Explain the various lateral load resisting structural system and discuss their performance
characteristics. (10 Marks)
What is base isolation in buildings? Illustrate the same with neat sketches. (10 Marks)
What are the general requirements for ductile concrete detailing so as to enhance earthquake
resistance as per IS13920 1993? (10 Marks)
b. Explain in detail with sketches, the ductile detailing provision for flexural members.

5. I4CSE22
a. Explain the conventional methods of retrofitting of existing structures listing the technical
and constructional considerations along with the limitations. (10 Marks)
b. With the help of neat sketches, explain the special confining reinforcement in a column at :
i) column beam junction
ii) footings
iii) column under discontinued walls.
a. What do you mean by "soft storey''? How does a frame with a soft storey behave under
earthquake and what are the precautions suggested if a soft storey cannot be avoided?
(10 Marks)
b. List out the limitations of "Equivalent Lateral Force" and response spectrum analysis
adopted for seismic analysis. How is time history analysis different from the above
mentioned methods? (10 Marks)
(10 Marks)
(20 Marks)
Write short notes on :
a. Elasto plastic behaviour of systems
b. Capacity design procedure
c. Shear walls
d. Retrofitting techniques.
***r<x
2 of2

6. USN
Time: 3 hrs.
'to
b.
3a.
b.
5a.
b.
6a.
b.
7a.
b.
8
14CSE24
(10 Marks)
(0'l Marks)
(10 Marks)
(10 Marks)
( l0 )Iarks)
(10 Marks)
(10 )larksl
( l0 Iarkst
of construction?
Second Semester M.Tech. Degree Examination, June/July 2015
Design Goncepts of Substructures
Max. Marks:100
Note: Answer any FIVE full questions.
What ale the steps involved in planning and execution of subsurface exploration? (Oo Marks)
)U
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c-lL :-
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a
tr
la.
b. What are the general requirements of foundations? Explain in.detail.
How you would compute the loads on foundations?
soils?
Explain the proportioning of combined rectangular trapezoidal footing.
What are the components of well foundation? Explain des
component.
What is settlement of fbundation? Name different types pf settlement. How they are
estimated? Explain any two of them. ,' (10 Marks)
Bring out clearly the difference between total and effective shear strength paran-reters and
their uses. ( l0 Marks)
How do you determine bearing pressure for raft foundation in lrarulu, soils and cohesive
4a
b
. Define coefficient of subgrade reaction. What are the factors effecting the values of
coefficient of subgrade reaction?
How do you determine the bearing capacity of footing on laye;pd soils?
f;lt
Explain how the load carrying capacity of a pile group is
What is group efficiency? Explain the methods of determine
What is a "Caisson"? How are Caissons classified based on t
(08 Marks)
of any one of the
(12 Marks)
,,lr{,
With a neat sketch, explain two types of tower foundations. I (10 Marks)
How the safety of a tower foundation is checked against, (i) upfift and (ii) overturning?
(10 Marks)
I
Write short notes on any FOUR of the following:
a. Standard penetration test
b. Dynamic cone penetration test
c. Pile group efficiency
d. Sinking of wells
e. Footing on slopes.
*>F**r<
(20 Marks)

7. &*4 Sr.,wt cv M:TttL
USN
Time: 3 hrs.
Note: L. Answer any FIVE full questions.
2. Use of IS-875 (Part-3)-IS-1893 shall be permitted
3. Assume missing data suitably
I a. Write an explanatory note on design criteria for tall structures.
b. Explain sequential loading with respect to tall structures.
c. Explain High pertormance concrete.
a. Explain the types and the behaviour of shear wall with examples.
b. Explain the types and the behaviour of braced frames with examples.
t4csBz52
(10 Marks)
(05 Marks)
(05 Marks)
(10 Marks)
(10 Marks)
(10 Marks)
(10 Marks)
(10 Marks)
(10 Marks)
Second Semester M.Tech. Degree Examination, June/July 2015
Design of Tall Structures
Max. Marks:100
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2 a. Write an explanatory note an Gravity loading an tall structures. Also explain live load
reduclide. (12 Marks)
b. A RC highrise building is built with each floor being completed in 'T' days (say are week)
with'2' levels of shores and no reshores. Assuming it takes'5' days to set up shores make a
diagrammatic representation of the operator to determine the loads to be carried by the slabs
and shores @ each of the levels of construction. Explain with a neat diagram and write the
conclusion. (08 Marks)
a. Explain the concepts of structural planning of earthquake resistant Buildings. (06 Marks)
b. A multistory frame building has the following data
i) 50m long. IOm wide and 60m height ii) Life of structure = 50 years
iii) Tenain category = III
v) Location = Bhubaneswar.
iv) Topography = Flat
Find the design wind pressure and also wind force @ 20m,40m and 60m height. (14 Marks)
5 a. Explain modeling for analysis with different approaches of modeling. (10 Marks)
b. Explain how approximate analysis is made for "approximate representation of bents" with
an example. (05 Marks)
c. Explain the "reduction techniques" for symmetric and anti symmetric structures. (05 Marks)
6 a. State the structural and non-structural
for high-rise buildings.
points which goveffi the selection of structural form
b. Explain the merits of any three types of lateral load resisting system.
7 a. Explain approximate method of overall buckling analysis of frames.
b. Explain p-Delta effects of gravity loading on toll structures
I Write shoft notes on:
a) Response spectrum method of analysis.
b) Creep, shrinkage effects on toll structures
c) Effect of foundation rotation on toll structures
d) Hight weight concrete. (20 Marks)

8. 4!r L* Cv
USN
Time: 3 hrs.
Note: Answer any FIVE full questions.
a. What is principle of contragradience? Explain briefly.
b. Determine static and kinematic indeterminancies for
(v)(iv) ,,'..'",,,..;;""
Fig.Q1(t
With usual notations, prove that [K]=lb]tlKl.tbl and [f] = [a]r[f]"[a].
Mention briefly the steps involve8 in flexibility method using element approach.
Di fferentiate fl exib i lity from stiffne s s methods.
l4CSErl
20ts
Marks:100 '
(05 Marks)
(05 Marks)
(10 Marks)
(08 Marks)
(06 Marks)
tm element shown in
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a.
b.
c.
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a
Obtain stiffiress matrix for a prismatic beam element Fig.2(c).
trFig.Q2(c) (06 Marks)
a. Develop the,"{lexibility matrix for the Fig.Q3(a) cantilever beam with coordinates shown in
Fig.Q3(a). (10 Marks)
Fig.Q3(a)
b. Develop flexibility matrix for the structure with coordinates shown in Fig.Q3(b). (10 Marks)
Analyze the continuous beam shown in Fig.Q4 by flexibility method. Also draw the bending
moment diagram.
Fig.Qa
1 nf1
Z* / 1rr
l1 Eilltvr
(20 Marks)

9. Analyze the
moment.
continuous beam shown in Fig.Q5 by
eotsnr 3ot<x
14CSE11
stiffiress method. Also draw bending
lo rilI*.C
y' alA ) zr.t r 2-r
Fig.Qs
Analyze the frame in Fig.6 by flexibility method. Also, draw the
subjected to a clockwise moment of 50 kN-m at B.
Analyze the truss shown
section for all members.
in Fig.Q7 by stiffrress
f6016$
T
,{l+
+{u4
Fig.Q7
Exfla$h"briefly steps involved in Cholesky method of decomposition.
AnfllitrGauss elimination method to solve the following equations:
x+4y-z=-5; x+y-62=-12; 3x-y-z=4
Mention the four important properties of a stiffrress matrix. Obtain the same
truss member.
{. ,1. * d< rF
(20'Ma'rk$
i.r' 1,
BMD. ,Thg,,'frame is
t1
(20 Marks)
method assuming uniform area of cross
8a.
b.
c.
(20 Marks)
(05 Marks)
(10 Marks)
for an axial
(05 Marks)
6ortl'trl
Fig.Q6
2 ofZ

10. 14CSE14USN
Time: 3 hrs.
2a.
b.
3a.
b.
4a.
b.
' gffi-**-;
First Semester M.Tech. Degree Examinrltfo-ri, June/July 2015
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Note: Answer any FIWfull questions.
I a. Define damping in dynamic system and briefly explain different type of damping. 1to Marks)
b. Derive the equation of motion for free vibration of rigid beam with lumped mass, m as
shown in Fig.Ql(b). If k : 80 N/m, m:25 kg and c: 12 N-s/m, compute the natural period
and damping ratio of the system. (10 Marks)
Fig.Qa@)
Compute the response due to harmonic
Given kr : 2.5 x 106 N/m ; kz : 5.0 x
Pr(t) : (50000 sin 20 t) N, Pz(t) : 0 (kr
Structural Dynamic
Max. Marks:1O0
loading for the shear building shown in Fig.Q5.
106 N/m, m1 :25 x 103 and mz : 15 x 103 kg,
and kz are stiffnesses of each colum, ,r;;ffi:il];
Fig Q1(-b)
Derive an expression for logarithmic decrement and explain how the damping ratio is
computed from the logarithmic decrement. (10 Marks)
A 100 kg machine is mounted on spring of stiffness k: 12 x 10s N/m with damp ing of 20o/o.
A2kg piston within machine has reciprocating motion with a stroke of 0.08 m and speed
3500 cpm. Assuming motion of the piston to be harmonic, determine the steady state
amplitude of the vibration of }4pehine and force transmitted to the foundation. (10 Marks)
Derive an expression fors[ldy state motion of a single degree of freedom system under
harmonic force. (10 Marks)
Derive Duhamel's integral for computing undamped vibration response due to general
dynamic loading. (10 Marks)
Explain the orthogonality property of modes and prove the same. (10 Marks)
Compyte the frequencies and modes for the shear building shown in Fig. Q4(b). Given
m1 =5i000 kg, m, : 10,000 kg floor stiffiress, kr : 70 kN/m, kz = 50 kN/m. (10 Marks)
-> ?$)
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3r1
I1
3r,
J.
Fig.Q5

11. 14C$814
Compute the fundamental natural frequency using Stodola's method or any iterative
procedure (approx method), for the following shear building (Refer Fig.Q6).The mass and
stiffnesses of each floor are indicated in Fig. Q6. Where, k:160x 106N/m;m:20x 103kg.
(20 Marks)
"i'. ;)),,"". ,,,
trg.Q6
What are the conditions for uncoupling the damping matrix? Explain the normal mode
approach for damping uncoupling. (10 Marks)
For the three storey shear building model shown in Fig.Q7(b), derive the Raleigh damping
matrix fCl that will have 5%o dampine in each of the three modes. Given below the free
vibration analysis results.
Given I fi11 : rllt :1113 :}'kg; k1 : 600 N/m, kz : 1200 n/m ; k: : 2400 Nim. (10 Marks)
it
la.
b.
Fie.Q7(b)
a- Derive equation of motion, namely,
[tr#)
.
[,,,#)
for free flexural vibration of beam.
b. Explain concept of lumpedmass and eonsistent mass for a dynamic system. [:ilffi:i
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2 of2
Fig.Q6

12. USN r4CSE13
Max. Marks:100
and e: €** e;+ er. (10Marks)
First Semester M.Tech Degree Examination, June/July 2015
Mechanics of Deformable Bodies
3a.
b.
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Time: 3 hrs.
a. Prove that
^
(1, +C)5+GV2u * x = 0, where 7, =/^ OX
Note: Answer any FIVE full questions.
pE
(1- 2p)(1 + p)
b. The possible state of stress is given by
or: c1 x2yz
3
oy: c2xyz
o,:2(x3+y3- 2yz)
t*r: -3xy2z
'cyz: c3rcf^r'- 5xza + 8(x2 + y')]
tr*: -3xyz2. Find the values of c1, c2 and e:.
a. Prove that
If the replace E by j! and pr by
t-p;
plane strain constituti ve relations.
b. The state of stress at a poin{ is given by o* : 100 KPa o, : 200 KPa o, : -100KPa
t*r: -200 KPa tr,: 100 KPa r,": -300 KPa. Determine i) Principal stresses
ii) Direction cosines of major principal plane.
Derive differential equation in terms ofpolar co-ordinates,
Show that
, -P ,(e-sinze)
0 = -:-r'l
-
| represents a sffess function. Determine the stresses o,r , o0 and t,e.
'2n 2 )
(10 Marks)
A straight beam of uniform cross - section of width unity and depth 2C is subjected to uniformly
distributed load w over its entire span as shown in figure. Verify the stress function.
l- s I I r J aJ a a I
. wrv vx Lv'x Cv' J^, , 3--, rt
0=.-l r..-r " +"r'--"r +1-C'yx' -al-C'xy+C'x'1. Obtain the expression for' 4c'[10 2 2 2 2 2 ]
(10 Marks)
-E - in plane stress constitutive relations, we obtain
l-Fr
(10 Marks)
(10 Marks)
(10 Marks)
stresses and evaluate the forces.
l',
I
t r^l r*fr1
l,ofL
(20 Marks)

13. 14CSE13
Evaluate the stress concentration factor due to the effect of a circular hole on the stress
distribution in a rectangular plate subjected to tensile stress in x - direction. (20 Marks)
Evaluate the expressions forthe stresses in the axisymmetric case of a hollow cylinden subjected
to uniform internal and external pressure and prove that
a. The maximum hoop stress is always numerically greater than the internal pressure.
b. The stresses o. and oe produce uniform extension or contraction. (20 Marks)
a. Prove that the contour lines for an elliptic warped cross - section are hyperboles having the
principal axis ofthe ellipse as asymptotes. (10 Marks)
b. The aluminum (G : z7JGPa) hollow thin walled torsion membef Shown in fig.Q7(b) is
subjected to a torque of T: 11kN-m. Determine the maximum shear stress and angle of
twist. Length of the member is 3m. (10 Marks)
Fig.Q7(b)
z oo fnrn -l'+.€1 trtm--1
Write a note on Tresca and Von - Mises theory.
T
tu
nq
L
8a.
b.
(06 Marks)
The load on a bolt consists of an,,axial pull of 8kN together with a direct shear of 3kN.
Estimate the diameter of the bolt abcording to various theories of failure. E : 200kN lmm2,
p: 0.3, Factor of safety: 3 and eiastic limit in simple tension:270N/mm2. (14 Marks)
2 of2