14CSE23 USN Second Semester M.Tech. Degree Examination, June/July 2015 Finite Element Method and A-nalvsis Time: 3 hrs. Max. Marks;100 ! E A I Elrpirn* 3 eod ,41-,"/;- t->- 6DN E8 - I oo- H= 'A-yy-4 .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., - "' .3 I 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 o o z 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. *- "*t "o r 1,3) 3 t\'b)
Transcript
14CSE23USN
Second Semester M.Tech. Degree Examination, June/July 2015Finite Element Method and A-nalvsis
Time: 3 hrs. Max. Marks;100
!E A I Elrpirn*3 eod ,41-,"/;- t->- 6DN
E8 - Ioo-H= 'A-yy-4
.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. 1jd 2. Assume any missing d.ata suitably. ry., -
"'
.3IE 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)
JNoozcd
o
Fie.Q.3(b)
1o'f )
; E A*'i,o -J< &oE 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.
*- "*t "o
r 1,3)
3 t\'b)
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 Cartesianco-ordinates. Also sketch the shape function variation at each so$s{ (tz Marks)
C)*'hJ6 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*
"@n l''
::: _!:... n+!ri.:- r:!
.. l.rr+i\ ---V Hrt\ )Fie.Q.a(a)(i)
?aehr"
t3F
y O IE*DENt .4......
ilf",h ojg*'l'* =,^
_J<.. 3r.\-u"
d?t\
For the two ba6 ffis shown in Fig.Q.7, determine nodal displacements and reactionforces/suppoq re-ftdffion using the concept of direction cosines and elimination techniques.Adopt FEM.gproach. AssumeE=210 GPa, A = 600mm2 (Finite Element Method) for Lachelement. l,J'* (2LMarks)
Fie.Q.6(b)
,., t'"r,''
.8
...'".,
a.
b.c.d.
Write short note on:Co, C' and C2 functionNode numbering to minimize band widthSerendipity and Lagrangian finite elementPatch test.
Fig.Q.7
*x{<**
(20 Marks)
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 2015Design of Plates a nd She lls
la.
b.
a)
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Z
LC1
Enlist the assumption made in thelimitations of the theory.Derive the equations of equilibriumplates.
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 ofintensity. '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 ofbeam 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 parabolidsline generators as boundaries.
Write short notes on the following :
a. Classification of shells surfacesb. Behavior of folded platesc. Levy's approach for plate analysisd. Edge beam theory - cylindrical shells.
*r<***
(20 Marks)
I4CSE22USN
Second Semester M.Tech. Degree Examination, June/July 2015Earthquake Resistant Structures
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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 storeyheight is 3.0 m. The dead load perunit area of the floor consisting of the floor slab, finishesetc is 4 kN/m2 weight of partitions on the floor can be assumed to be 2 kN/m2. The intensityof live load on each floor is 3kN/m2. The soil below the foundation is hard and the buildingis 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 buildingduring earthquakes. (10 Marks)Explain the various earthquake resistant features that can be introduced in a masonrybuilding to improve its performance during an earthquake. (10 Marks)
Explain the various lateral load resisting structural system and discuss their performancecharacteristics. (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 earthquakeresistance as per IS13920 1993? (10 Marks)
b. Explain in detail with sketches, the ductile detailing provision for flexural members.
I4CSE22
a. Explain the conventional methods of retrofitting of existing structures listing the technicaland 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 junctionii) footingsiii) column under discontinued walls.
a. What do you mean by "soft storey''? How does a frame with a soft storey behave underearthquake 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 abovementioned methods? (10 Marks)
(10 Marks)
(20 Marks)
Write short notes on :
a. Elasto plastic behaviour of systemsb. Capacity design procedurec. Shear wallsd. Retrofitting techniques.
***r<x
2 of2
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:100Note: Answer any FIVE full questions.
What ale the steps involved in planning and execution of subsurface exploration? (Oo Marks)
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cz
atr
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 descomponent.
What is settlement of fbundation? Name different types pf settlement. How they areestimated? Explain any two of them. ,' (10 Marks)Bring out clearly the difference between total and effective shear strength paran-reters andtheir 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 ofcoefficient of subgrade reaction?How do you determine the bearing capacity of footing on laye;pd soils?
f;ltExplain how the load carrying capacity of a pile group isWhat 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)
IWrite short notes on any FOUR of the following:
a. Standard penetration testb. Dynamic cone penetration testc. Pile group efficiencyd. Sinking of wellse. Footing on slopes.
*>F**r<
(20 Marks)
&*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 permitted3. 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 2015Design of Tall Structures
Max. Marks:100
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7r)-*llcco.= an
.>a2
!y
-c>P
x!
o!e
u=;iLO
c.-
=ao.- c6=EtY!
(r<-alo
z
q
2 a. Write an explanatory note an Gravity loading an tall structures. Also explain live loadreduclide. (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 slabsand shores @ each of the levels of construction. Explain with a neat diagram and write theconclusion. (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 yearsiii) Tenain category = IIIv) 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-structuralfor 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 structuresc) Effect of foundation rotation on toll structuresd) Hight weight concrete. (20 Marks)
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(tWith 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 inar:rro*G
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a.
b.c.
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*otr>
trsea"* "
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oa
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 inFig.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 bendingmoment diagram.
Fig.Qa1 nf1
Z* / 1rr
l1 Eilltvr
(20 Marks)
Analyze themoment.
continuous beam shown in Fig.Q5 by
eotsnr 3ot<x
14CSE11
stiffiress method. Also draw bending
lo rilI*.C
y' al\A ) 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 shownsection for all members.
in Fig.Q7 by stiffrress
f6016$
T,{l+
+{u4Fig.Q7
Exfla$h"briefly steps involved in Cholesky method of decomposition.
AnfllitrGauss elimination method to solve the following equations:x+4y-z=-5; x+y-62=-12; 3x-y-z=4Mention the four important properties of a stiffrress matrix. Obtain the sametruss member.
I a. Define damping in dynamic system and briefly explain different type of damping. 1to Marks)b. Derive the equation of motion for free vibration of rigid beam with lumped mass, m as
shown in Fig.Ql(b). If k : 80 N/m, m:25 kg and c: 12 N-s/m, compute the natural periodand damping ratio of the system. (10 Marks)
Fig.Qa@)
Compute the response due to harmonicGiven kr : 2.5 x 106 N/m ; kz : 5.0 xPr(t) : (50000 sin 20 t) N, Pz(t) : 0 (kr
Structural Dynamic
Max. Marks:1O0
loading for the shear building shown in Fig.Q5.106 N/m, m1 :25 x 103 and mz : 15 x 103 kg,
and kz are stiffnesses of each colum, ,r;;ffi:il];
Fig Q1(-b)
Derive an expression for logarithmic decrement and explain how the damping ratio iscomputed from the logarithmic decrement. (10 Marks)A 100 kg machine is mounted on spring of stiffness k: 12 x 10s N/m with damp ing of 20o/o.
A2kg piston within machine has reciprocating motion with a stroke of 0.08 m and speed3500 cpm. Assuming motion of the piston to be harmonic, determine the steady stateamplitude of the vibration of }4pehine and force transmitted to the foundation. (10 Marks)
Derive an expression fors[ldy state motion of a single degree of freedom system underharmonic force. (10 Marks)Derive Duhamel's integral for computing undamped vibration response due to generaldynamic loading. (10 Marks)
Explain the orthogonality property of modes and prove the same. (10 Marks)Compyte the frequencies and modes for the shear building shown in Fig. Q4(b). Givenm1 =5i000 kg, m, : 10,000 kg floor stiffiress, kr : 70 kN/m, kz = 50 kN/m. (10 Marks)
-> ?$)
*3r1
I1
3r,
J.Fig.Q5
14C$814
Compute the fundamental natural frequency using Stodola's method or any iterativeprocedure (approx method), for the following shear building (Refer Fig.Q6).The mass andstiffnesses 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 modeapproach for damping uncoupling. (10 Marks)For the three storey shear building model shown in Fig.Q7(b), derive the Raleigh dampingmatrix fCl that will have 5%o dampine in each of the three modes. Given below the freevibration analysis results.
b. Explain concept of lumpedmass and eonsistent mass for a dynamic system. [:ilffi:i
*X<{<rFt
2 of2
Fig.Q6
USN r4CSE13
Max. Marks:100
and e: €** e;+ er. (10Marks)
First Semester M.Tech Degree Examination, June/July 2015Mechanics of Deformable Bodies
3a.b.
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()
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troo
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z6!oc.
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 byor: c1 x2yz
3oy: c2xyzo,: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 byt-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 stressesii) 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 uniformlydistributed 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--, rt0=.-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 obtainl-Fr
(10 Marks)
(10 Marks)
(10 Marks)
stresses and evaluate the forces.
l',I
t r^l r*fr1
l,ofL
(20 Marks)
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) issubjected to a torque of T: 11kN-m. Determine the maximum shear stress and angle oftwist. 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.
Ttunq
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)
