,/l

I tni;tr)g1, SqiES'Tg&N'F;*FflR I

B.]r' Aercmauticai Engineeting

V Serntstet'

AE 331' ,ESRCRAS'T STRTJCT{']RE *g

Viaxim'"lm Ma-rks ; 100

Time : 3 Hours

PART'*A (i0 x2:2A Marks)

l.WhatistheslopeatfleeendofacantiieverbeamofiengthLand.rniformEiwhen it is subiected to a load P at the free end?

2.AcantiieverbeamofunifonrrElissubjectedtomomentMatthefreeend.Sketch

theloadof.thecorrespondingconjucatebearn?

3. Explain the use of Ciailrpeyron's three moillent theorem?

4. Explain rn'hat is meant by distribution factor? -..r-.iontert rn a oonc

5.AcantileverbeamoliengthL,anduniformElissubjectedtoaconcentratedload

tothefreeend.ExplainhowtheslopeatthefreeendisobtainedrrsingCastigliano' s theotem2

6. State and explain Maxwell's reciprocai theorem?

1. Explain what is meant by bealn of unifoim strength?

S.Thecrosssectionofacolumnisrectanguiarofwidth50mmanddepthl00mm.whatisthevaluetorsecondmornentofareathatmustbeusedforbucklingload

calculation?

g. Define the sienderness ratio f'lr a column of circular sectton'

10. Define beam column with suitable exarnf'le'

I t.

PART'*'ts (5 x 16: 80 Marks)

AbeamoflengthLanduniforrnElissimplySuppoitj]datitsendsandsuDjCCiCdro a load w at a di$;;;";-rro*

'"ft ;;."dbiullia"R"ttion at the mid point and

at rhe point of "ooil;;"; oi rn. ro*a-"rlc double integration method or area

*o*.n, method?

l2.a)AbeamissimplySlwole6atitsen<ls.}tisoflengthLandE,lis'unifornandsubjected ,o u-rfua D'at tire rnid point of the beam' u-"ng conjucate beam nrethcd

com'ure ".;'li;'

J;;;; *d maximum deflection'

:"1

:

:

?

Yr

I CIFi

i2..it,i A tinber beain lti crn .wide ancl 2C ctr rieep is'i* i::: ii:inib;:ced by siecl strips

each i6 cm wicie ancl i cm thick. I'ind the lrlonrer;i':i l*:'.istance \vi1en qii the steel

strips are attaciied at the top and bottorn so tha'r orierail all Cepth is 22 cui and iii)the steel strips are attached syrnmeilically at the side:: so that overali 'viclth is i8cm. Allowable stress in the timber is 6 mpa'

l3 a)i)Derive the expression for three moment equation' (4)

ii) A simply supported beam ABC is of length 6 m and supporled al A, B, ancl C' AB: 3.6 m.anC bC :2.4 m. A load of 2 kN is applied at i.8 rn from A arrd auothe-,:

load of 4 kN is applied ar 1.8 m from C. Assuming EI is constant compute

reaciions at the supporf poinrs. (12)

OR

l3.b) Obtain the reaction at the suppon points of the beam shown in fig.1. Using

moment distribution method.

Fig 1

l4.a)i) Derive the expression for strain energy stored in a beam due to bending- (4)

ii) A beam of length L an{ uniform EI is simply supported at its ends. It is subjected

uniformly distiibuted load of intensity q Nlm. Compute the maximum deflection

using Castigliano's theorem . 02)OR

14.b) A propped cantilever beam AB of length L and uniform EI is subjected uniformly

distributed load of intensity q Nim and a concentrated load W at its mid-point.

The beam is fixed at A and on roller suppori at B. Using Castigliano's theorem or

any other method compute the reaction forces at the support points A and B'

15.a)i) Derive the expression for Rankiiie 's fonnula (4)

ii) Compare the buckling ioads given by Rankine's and Buller's formulae for a

tabular column 2.25m long having outer diameter 37.5mm and inner diameter

32.5mm and both ends are pin ended joints. Assume yieid stress to be 315 mpa,

i

Rankine's constant i, -l aced E:200 Gpa'7.500

900 N2knJm

(12)

$xq,

15.b)i) Derive the expression for buckling loar1 for a uoi';lnn.'ryith one end fixed and the

other entj free. -- ' (6)

ii) Determine the ratio of buckling loads ol two cohimns :l :*:]1'i,t"il-i-3itilff;"iliffi',jio il eiter solio i"t.n both are made of same material, have-same

Tr - :-^-^* Al^^a+or ^f hnllnrxr

l;*-;:t'ilrr-*.,a; ur"u und end conditions. The inner diameter of hollowr6)(6)

column is half-its outer diameter'

:&

4.

:&

q

q

3

-i

33

:i

t&,r

&

lb

hv

tt

:r

*,

*t*

h

t1$.

3!;'J

4h&g

Y!

e\

\st\

.#

i

{%

&e

1.

2.

i+&C^':J$- QUESTIOI{ tr "'PER

B.E. Aeronauiical E'ngineering

V Semesie"

AE 33X A{RCR,AS'T STRTJCTU&'g' _T

I

4"/j

Maximum Marks : i00'fime : 3 Hours

11. A beam of length L and uniforrnto a ioad W at a ciistance 'a' fuom

P.AR.T-A (i0 x2:2A N4arks)

WhatisthesiopeatfreeendofacantileverbeamoflengthLanduniformEl

rvhen it is subjected to a load P at the free end?

A cantilever beam of uniform EI is subjected to moment M at the free end' Sketch

the ioad oithe con-esponding conjucate bearn?

3. Explain the use of Clampeyron's three moment theorem?

4. Explain what is meant by distribution factor?

5.Acanti}everbeamoflengthLanduniformE,Iissubjectedtoaconcentratedload

tothefreeend'ExplainhowtheslopeatthefreeendisobtainedusingCasti gliano' s theorem?

6. State and explain Maxwell's reciprocal theorem?

7. Explain whai is meant by beam of uniform strength?

g. The cross section of a column is rectangular of width 50 mm and depth 100 mm'

what is the value fbr second moment of area that must be used for buckling load

calculation?

g. Define the sienderness ratio lor a column of circular section'

10. Define beam column with suitable example'

PART - B (5 x 16 : "30

Marks) '

El is simply supported at its ends and subjected

left end. Obtain deflection at the mid point and

at the point ol aPPlication of the

moment method?

load using double integration method or area

|2.a}Abeamissimpiysupportedatitsends.itisoflengthLandElisr:niformandsubjected ,o

^ iiuo D'at the mid foint of the beam, Using conjucate beam method

compute slope at he supporl and maximum deflection'

i2.b)

.;F

A tinrber bea::i :5 clii ',riiCe a*d' 2* gi1; r.ie cl rs t'r be reirltbre ed by steei strips

ea-eh i6 en-r.;i'je anc -i cj]l i1:irk. Fir;d ii:e lr,ioillerri oiresi:tance -whel] (i) tlie steel

strips are attached at iraic top and botioni si: ihal cverali aii depth is 22 cn and (ii)

the steei strips aia aili:,:heil s-vmmetriczrllv ;.,' 'i sicies so thai overaii rvi'lth is 18

cm. Allorvabie stress in tile tiinber is 6 mpia' "

i 3.a)i) Derive the e xpressicn 1-'rr three nioment equaitoii' (4)

ii) A simply supporieC bei"m ABC is

:3.6 m and RC: 2.4 n' A laa<i

load of 4 kN is aPPiied at i 'Breactions at the suppor{ Points'

13.b) Obtain the reaction at the suppon points

moment distribution nr ethod'

2 knlrr'

of length 6 m and supporied at A, B, and {l' AR

of 2 kN is appiied ai i.8 m from A and another

rn tiom C. Assuming EI is constant cctnpute(12)

OR

of the beam shown in fig.1. Using

0.4 m 0.4 m

0.5 m

Fig 1

ia.a)i) Derive the expression for strain energy stored in a beam due to bending' (4)

at its ends" It is subjecied

the maximum deflecticn{12}

ii) A beam of length L and unifoim Ei is simply supporteci

uniformly clistiibuted load of intensity q N/ril' Compute

using Castigliano's thecrem'

@R

14.b) A proooeci cantilever beam AB of iength L and unilonn El is subjected unift;rmly

distributed load of intr:nsity q N/mand a concentrated load W at its mid-point'

The beam is fixed at A and on roller support at B. Using Castigliano's theorem or

anyothermethodcomputethereactio*fb'.-'atthesupportpointsAandB.

15.a)i) Derive the expression for Rankine's formuia (4)

ii) Compare the brrckling loads given b-v Rankine's and Bulier,s formulae for a

tabular coiumn 2.25m long having outer diameter 37'5mm and inner diameter

32.5mm and both en4s are pin .nJed jcints' Assume yield stress to be 315 mpa'

R.ankine's constant is +- aceci E:200 Gpa'7500

q00 N

{,12}

rr!

I

&:t

!i

&a

d[

1

t

'r

i.w'

sR.

15.b)i) Derive ihe expi'ession for buckling load for a colunin wrth cne

other end free.

Qq

:w

Se

lxa

-t4t\

end t-rxed and the(6)

ii) Determine the ratio of buckling ioads of trvo colutnns of circuiar cross-secticn

one ho110tv and the etuer soiid when both-are made of same maierial' have same

length, cross-section area and etld conditions. The inner diameter of hollow

column is half its outer diameter' (6)

' r'll,/,L"/

B "E./E.Te ch. DE GREE EXAMINATION, NOVEMBEfi/DE CEIVItsER 2006'

' F orrrtir Sernester

Aeronautical Engineering

F'-E 1254 - AIRCRAFT STRUCTURES - I

(Regulation 2004)

Time : Ttrree hours Maximum : i"00 marks

' Answer A-LL questians'

-PARTA-(10 x2=Z}marks)

..1. What are the pr-imary and. seconCary stressls in the analysis of a truss'

2. Give a relation between the nrrmber of members and joints in a truss and

explain its use.

ntei-nal dialqeter and 1 crn thick is surrounded

by a brass tube of same length La tni"13 -' T: tubes carrJr an axial load of

150kN.EstlrnaLetheioadcarriedbyeachE"=2L0GFa,Eu=].00GPa.

write down tlrree moment equation in the general for-m'

Define stiffness {'actor in rnoment fistribution method'

State F,eciProca! theorern'

Give expression for strain energy

(a) Torsion

(b) - Bending-

8. Diii'erentrate bebween long and short column'

9. Give Renkirre's ror-mula and its ad'vantages'

L0. A sc'lid c,:be of i:teei (E = 210 GFa) is sub'jecieC t'o e iension 150 &{Fa' find the

strain cTlergY cel' tl-ti. vciurtt''

---

K S&{}ry

b.

7.

;14w

*ue.

k*

{'w

\*

t

*

&

&

1q

q

:

P7\s,T B -- 15 x i6 = 80 rna::ks'r

i1.(a)Fin<j.threforcesinthernernbersoithetrussskrownint,hefig"ibyaJ}y+rremet'hcd'

llDoo$F^-.,-€ JUO tt

D

Fig' 1

Or

(b)Thetrussshowninfrg.2issupportedascantileveralthejointsAandH.Find the forces in the members'

i5o]-

loo r{

E

i,+-r-'r',,*.,-i{tJv.u rrrt rr!

Fig' 2

L2.(a)Findthesr-rpportmomentsanddrawben_dingmomentdiagramofthecon*'inuous bearn shown hif- Ag-g using three iacrnent equaiion'

?-coo:'\i'r,1

1,+ r,w+&+*:_{

.-aeds. effi r;:{=n"gff:L.il.}i::i l

y v t'lr x-E \;{ FYF I_'

.)."fl_+-i{, "nr", -'...""-._rr Lr| I

A*r *-_+{4*-!

Fig' 3flr

-! i*- r; i:'1.: -

Find Lire gr:ppor'"' rni)n1er'l r i::lu -i1 :

' -:-- ; ^.,,-'r r:i:!, r"

r;o6i.irt,;uu:r l-reirili slio-"vn ii;'-;'J"-1;;"; ;:;-';i "' '

1r.*I:,4::''l tiila|JT'l')'r{r' cf t'he-- r'l-'-':i

'' i i-.-i,-i i' ii,l-r'l-:'r-i uli :irrs rirvs"'

T E$S?

1"3. {a} ti) Find the defiectioa at the :a.d.-point cf a simpny supported bea:n oflength L, subjected to a **|*r*ly d.istributed load using udt load*^il,nr{ (8)

Find'the redupdani force in ti:e eember OC o{'the truss shown in{"5"4 (B)

(ii)

(b)

E'io d

Or

area of bars inFo:' the truss shown in the fig' 5 the cross section

cornpression are 30 crn2 aqd othut5 !2- "\'' Deterrnine the vertical

di*p1u."u*ent of.point c and horizontal displacement of point B' Given

E = 210 GFa.

Fig.5

A**':--

q- ESQ?

$i"'i

h,,l[I:r

hfl5.*wEElrrEB.hH'H5.#Ir"'

BlrHiH!ll\Pffi-qti':€:{3E!R-+

Ef.xrf,d#qi.;l*q,:^'rg

JFiil4w*€:itq..':

-sa*.ffi-(:

v,i1mffi-*ql

ditt{i$

"sc-$wr'

ilL:tldiqi

5!:..t.!

*il*iiw.i,

tt

-t!*ri'-,',

:

T

't.."

L.tr { t1) ii) Si;nte anti F3"cri e {-'::sl.gilani:'ii i'iiarltenr

(ii) Derive arr e"<pression ibr rhc ciiticalcross section.

'Or

F'indthebucklingStressofahinged-hingedColurnnofiengthl00cmagrdhaving T - cross sectian' The 'limensions of ttre fiange are 10 cra x 2 cm

r;:C the '"vcb 10 "r* '* 2 cn' Derive the fcrrnula uscd' ! = ?0 GPa'

A beam - column marle of sleei (E = 210 GPa) sirnply supportei at both

endsissubjected.toauniform}ydistributedload.ofs00N/mandarraxialjoariofi000N.Findiieei.ncmenia-La]rrySectionandhenceflndthernaximrrm stress" Give L - 4m, b = 2A mrn' d = 40 rnm'

\,i j

icad oi a ccl.'mn of variabl.e{tr\r.u,

(b)

15. {a)

Or

(b) ' Explain any four failure theories and their reiative merits and deo erits'

--. -^-.g:r:*-1*-bf

-l

Reg" I{o.:

4rI-itlt

KA, gSlS

ts " E.iB.?eeh. DEGREE EXAMINATICN, NOVEME EF/DECEMBER 200?.

Fourth Semester

Aeronautieal Engineering

AE 1254 - AIRCRAFT STRUCTURES ..-= I

(Regulation 2004)

Maximum: 100 marksTime : Three hours

Answer ALL questions.

PART A -- (10 x 2 = 20 marks)

Differentiate between staticaliy determinate and indeterminate trusses withexamples.

2.

3.

A

E

b.

7.

What is equivalent rigldity of a cornposite beam? Explain with an exarnple.

Explain unit load rnethod with an example.

Define carry-over factor in moment distribution rnethod-

State Castigiiano's bheorerns.

State Reciprocal theorern.

Calculate the strain energy stored in a cantilever of Length L, subjected to a tipload P.

1.

ffiF,'

&u

h-ry.

;p'*d&:-

l

iita ;ffi-

kF'F.

td'

k.gr.

btr-F

hFr..

*:f.

LY

g. Draw Euler's curve for a column a:ad explain citical slenrlerness ratio.

9- t$"t is Southwell's p,[ot?

]-S" A solid cube of st€el(G = 80 GPa) is subjected to a shear of 56 l\4Pa. Firrd thes&rain energy Per uei.t volulae"

d-E&&e---,,-*--

PAF"T E - (5 x i.€ = 80 marks)

I

11. (a) Find the forces in the rirembers of the truss shown in the Fig. Qn. 11{a)bv aav one method"

(n\r 5oW 5oNJv lt I r

5cN

\oog Y\00N

b xz::\5o€,^

Fig. 1. Qn. 11(a)

Or

(b) The truss shown in Fig. Qn. 11(b) is supported as cantilever at the jointsA and H. Find the forces in the members.

--n.II

3o

\oo rt

T3o e-.

_t

Fig.2. Qn. 11(b)

12. (a) Find the support moments and draw bending moment diagram of thecontinuous bearn shown in the Fig.. Fig. Qn. 12(a) and 12(b) using threernoment equation.

zDob N loc'o h{

r*Im++I

Fig. 3. Qn. 12(a) and 12(b)

m.onnent -diagram of theand 12(b) using sroment

r .trs

F**a 6 -+l-<-35I e,rnl I

rD40 -i

Find the support ryToraentsconbiri.uor.ls beau-rn sh.own fu.dish-i.bution method.

Or

a,nd draw benr{ingthe Fig. Qn. 1,2(a)

2

2ooo Nlw\

(b)

R g@n6

13. (a) A thin circr-dar ring of ra.Cius R anC bendi.ng rigidity EI is subjected futhree syrnmetic radial co:-nryressive loads lyrt g in the pla:re of the ringstructure. O}:tain the expression for the bending moment a*d piot itsdistribution.

Or

(b) Calculate the vertical de{iection of the point E and the }lorizonta-l

movernent of D in the pin-joined frame work shovrn in the Fig. Qn. 13(b).

All rnernbers of the frarne work are linearly elastic and have cross

Ittl*-4* -+.- 4sr-_='{

Fig. a. Qn. 13(b)

Find the critical load and stress for the(E = 210 GPa) shown in the Fig. Qn. 14(a),

pinned.

t.6EM.t&s.2 e^^ d^l^

rtoo ku ,

i*-+ ' -*{

14. (a) column made

assuming bothof Steel,ends are

1.5€*A &ri

l+-z(t-cm

lllau,-Y--rrcm cm

F'ig. 5. Qn. 14(a)

Or

(b) A beam-colusrn made of steel sirnpiy supported at both ends is subjected

to a concentrated load of 1000 N at a distsnce 1 m frorn thre rightsupport a:ad an axial load of 1000 N. Find the deflecbion at nrid-pointa-nd the maximum defiection. Given : L = 4 $t, b = 20 m:n, d = 40 r::rm.,

E = 2l-0 GPa, caLculate the load the columa can carry. Serive the forseulaused. b is the width of the cross section *nd d is the depth of the seetion.

R S81S

15. (a) Expiain the various theories of faiiure and their relative 4rerits andI demerits. I

Cr

A circular shaii of tensile yield strength 3b0 MFa is subjected to acombined state of ioafing defined by a bending mornent M = 15 kN-rnand Torque T = 10 kN-rn. Calculate the d.iameter d which the bar musthave in'order to achieve a factor of safety N = 2. Apply the followingtheories.

(i) Maximum shear stress theory.

(ii) Maximum distorsion energ'y theory.

(iii) Octahedral shear stress theory. '

:i.!

*a

*

(b)

K 3SL5

xs sss

B.g./B.Tech" DEGREE EXAMINATIONS, MAY/.]UNE 20 10"

F'OURTH SEMtrSTER,

AER,OI\TAUTI CAL ENGINEERING

AE 45 - AIRCRAFT STR,UCTURtrS _ X

(RtrGUIATIONS zOOs)

Time : Three hours Maximum : 100 marhs

. Answer ALL questions.

PARTA-(to* 2=2A marks)

1. Explain, with suitable example, the difference between aframe and a truss.

2. What is the condition for a plane truss to be stable or notwith respect to the number of members and the joints?

3. What is a composite beam?

4. Explain the carry ovel: factor, distribution factor andstiffness factor in moment distribution method.

5. Explain the dummy unit load n'rethod of determrningdeflections of a point in a structure.

h

7.

B.

Give the strainsubjected to axial,

Explain how tireshort co].umns.

What is a beam column? Gives€ructures for such columns?

What is the need for knowingwhen a stmctural naemberstresses?

I

energy expressions for a inemberbending, shear and torsional loads.

Euler's column curve rs not valid fbr

(l

some examples in aircraft

the rnaximum shear stressis subjected only norrnal

10. List down various failure theories and explain theirapplications for a particular case.

11. (a) (t(iil

PARTB-(n" tg=80marks)

What is a plane truss?

Find the forces in all the mernbers of the planetruss shown in fig.1. All dirnensions are in m.

Q+)

F ig. 1.

Or

F{ 026

{z)

2

II

tb) Find the forces in all the menebers of theshown in Fig. 2. Atl dirne:lsions are in m.

12. (a)

(b)

plane truss

E-/

Fie,2"A continuou.s bearc. ABCD, simply supported at A, E,C and D as shown in fig 3. F ind the rnoments overthe beam and draw B.M and S.F. diagranns.

Fig. 3.

Or

Determine the values of bending moments at all thesr.rpports of the beam loaded as shown in frs.4"EI isuniform along the length of the beam. Use threemornent theorem or mornent distribution method"

lq'&q fl i* Cc&*r*l!t

Fig. 4.

F{ S?6.)D

I iiir'a

aft / \I < tnE,.1- !-r. \(aJ

I

Cbtain tFre vertical deflection of joint C in the trussshown in Sg 5. Cross section areas of members *nsquare em, AB = CD =2"5, AG = BF = CF'= BE = 3,BG=CE=BC=EF=FG= L"5"

(b) Calcu]atedirectionsectional62.5 mmz

Fig. 5.

Or

the deflection of the joint C along theCE for the truss shown in fig'.6 Crossareas of members Ats = BC = CD =and BD - 125 mm2.

Fig. 6"

4 n 026

-l

I

74. {a) ti,} Give some of the empiricaicolumns.

I

formulae for slaort{a}

(iil calculate the safe compressive load for a steelcolunan 2w long with pin ends if the crosssection is a 100 x 100 x 6 mm I section fiS ?"The reqr.rired factor of safety against failuri is2 and the yield stress is 270 IVIpa. E = 200 Gp*.Use Euler's formula. f,1Z)

Fig.7.Or

Determine the crippling load for a T-section ofdimensions 10 x l0 x 2 cm and of rength 5rn fig gwhen it is used as a strut with both of its *rrd*hinged" ?ake Young's modulus, E = 2 x lO-t Mpa -

H 026

I crrt

N

(b)

gati

I

15. (a) Write sh*rt n*tes cn tlae f*l]owing failure theories '

t4" 4 = l-G)

(il Maximurn shear stress theorY

(iil Maxim-uwr strain energy theory

(iiil Distortion theorY

(iv) FrinciPal stress theory'

Or

(b) A MS shaft of 50mm dianaeter is subjected to a

bending moment of 2000 N-m and a torque T- If theyield point of the steel in tension is200 Mpa, find the maximum value of this torquewithout causing yielding of the shaft according to

(il The maximu.m principaL stress theory

(iil The rnaximum shear stress theory and

(iiil Distortion theorv of yielding-

H 026()

YY rb -* r\trg tff EU

i I.1F).rrr.:h" IlEi;,t',9ir T:-l:-jo,.l-fr\t.,{TIONS, h4=,,1.},r/,_l{jl'JFl 281A"

,3SUH,TF{ Strh,{ES?EH,

Atr F'{} }{,,iu?X CAL H NGINtr tr P"it{G

AE' L254 - AIRCRAF'T STP"UCTURtrS - {

(REGUIATIONS 2OO?)

Tlrne : Three hrours Maxirnum : 100 marks

Answer ALL questions.

PARTA-(trO* 2=2amarks)

1" What is meant by order of indeterminacy? Gi.ve someexamples.

2. Give the relation between the number of rnembers andjoints in a truss and what is its tise-

3. Define Carry over factor used in rnoment distributionmethod.

4" State MaxweLl's reciprocal theorem and what are itslimitations?

5" A cantilever bearn is subjected to a tip load 'P'. What isthe strain energy stored ixr the beam?

6. Define stiffness factor anri clistribution factor

7 " What is the eff'ect, cf eccentricity on the load carryingcapacity of a column?

8. What is neeant by a long coiarrnn? Hornr is it identified?

j

I

SVhat is'rneant b3' 3 c*nstant s'Lrength bear,:?

''fil:s1, ij::e i}!,r.' Ji*tlt;:r,rol:s *{ ir:iaxjl;}um Frincipa} $tresstheory?

PATDTT 1-B -- (5 x 16 = 88 marks)/ \. .', .r 1 ':.j i . rc4l L,. .lr-u!-r L{t t r-i rU rUr uu;:i iijr t'-Lltj irrt

i,lrtijvr, rrl ; r*^ j-.rf UairLrte\,e-{ tJUaiI} Oi leffgi.tr L rS

sulr;ecluil ta a 'r.ransveyse ittad P and a clockw-ise

mi;lreni ]i4 ar 6he rniddle. F ind the slope anC thedeflection at th.e tip using (l) Double integrationmethod. (ii) Area moment theorems"

l.r

5 ktr{

(b)

Or

Compute the forces in all the rnembers of the trussshown in F ig. 2.

n,*r..-61,.."i.;.7

i-

5 kF.lI1.,B&^'

-,-.\/\

...G..rn.....

qjoq*. l}lrfit5/,/i1I

I

2.S kNI

JL-,/P-.

II

I-II6CI''"JS0

ff

i

-t-

F'i<r ,

I F{ *}"S

6 n'l

i2 '. {!, / I]escr;be withi n c,l" c'Le :-':: l ;: a teurethaul.

I

a\) example r,iaei-.eani-, i1sj.t1 tlrrirnent

a:;an1's!3 i:f'Cisiribution

JT' ,^, 11 1 3i1, I,,ir:.. D __.._i ...r rL;, ] ,{-,!ir-t:J

:- -,t1 ,'.-i,-.

,'l

{}r

, f ,l 1 1

- 31::': ' ' "-::' IFA-*rl 9i-"41'. ''-

i:tctilli :-"i: :.1:t c ;: xi "

2 khr 4 khJ

r-Fig" 3

State and prove CastigLiano's theorer:1.

Using energ]' methods for Fig 4 deterneine theslope at the ieft support and tlae midpointdef,lection using Ltnrt }oad method.H = 210GFa | = 25 x 10-10 1I1't. (tA)

B

i,J. (a) (i)

tn)

RY

I

*

t)I

t

dt

t

".^.,,.,...".......'. ".",.....',."'.....*e i.e.4d&,"

Fis" 4

Or

;7F{ *r.*

11i

I

3, i'lez::-r ABC af- iet-:gth 6.5n: and unifo::zn sec€ion isii;,eri at i*:'':r:ds l'' a;:r1 {l A i:lon:.erat cf ::** kiiJ-r:a

t?rlur,= i. icrkwise) is ;lpptit d al B, 4sn f,rcrxn A. cc*rpuiethc :=;-113;3clt reacticcts using Castiigians's thecre*r"

A lrirn; l:-],:;:-,:: .,-,';th h:*ge sr:ppoi:ts at iis ends :rr';;'i-rjcr:tcri lr a::ja-J tr*llp:"tssi-,ir: load P and -;niforrnl:.'

tjjstrrl;iittd iaad (acting norrnal to the axis of the'bea'rr\

e-"{ i:rte:-lsrt3r r;u . Also derirze the expression fqr"

the rxeaxiixaui* Casplacernent of the beanr column.

Or

What, rs Ranki.ne's constant? Flow is iternplo5'gd in colurcn ciesign? {4}

Derive an expr:essioer {or the critica} ioad of aco}ramn of varia-ble cvoss sectron. ttZ)

/-\. (;i'

(b) (*

/. .\{rr I

\AJ15. Wvite short, irotes on -

(il Maxirnurn principal strain theory.(it Distortion energy theory.

Or

(s)

(s)

(b) A solid shaft of c:.rcular section has its diameter100 rnm and is srnbjected to combined brending andtorsion. ?he bending rnoment is three times thetwisting rnornent" If the allowable stress is350 Nlmm2 with a factor safety af 4 catrculate thepermissible twi.sting rnoment using the foilowingtheories. Poisson's rati.o is 0.3" (il Maxlnlutrn stresstheory, (it h4axlrnurn shaear stress theory,(iiil h4axienul:r stvain energl/ theory asrd(iv) Vfaxirnr.am shear strain energy theorS'.

H 01S'4

I Regisier N,r*U."

i8"8," *EGREE EXAIIfINATIONS: APR{L / h.6AV z$n$

Time: T'hree Hours

Fourth Sen-iester

AER.OFJA UTICAL ENG TNtrERING

U07AR403: Aircraft Structures I

,dnswer: A{-L the Questioxls:-

PAR.TA(iSxL:10Marks)

Maximurn Manks: 100

1) Resistance to Deformation is called

a) Safety b) Stiffness c) Strength d) Fa-tigue

2) The support at v,'hich the beam is free to rotate about hinge and also transiaiional

displacement along the piane of rolling

at Rtrller b't Flxed c) Free d) Either (a) or (c)

-1 , -{ b,ean u'hich ha-s more than trvo supports (.OR) more than one span are considereci as

ar Fired beam t'') Cr-utinuous bearn c) Fixed simple beam d )Simple bearr

-i t The product of EI is called

a) Factor of safei-v b t Stitlness lacior

C.; Distribution Factorc) Flexural rigiciity

5) The internal energy stored b-v the material during deformation in loading process is called

a) Strain energy density

c) Work done

6) Castiglianos Theorem is based on

a) Straiir energy - b) Principle of Least work

c) Principle of Stationary total potential energy d) Minirnum potential energy theory

7) Secondary bending rnoments are produced by

b) Strain energy

d) Inelastic strain energy

a) Axial load

c) Transverse load

B) The member which can'ies cornpressive ioad is called

a) Strut

b) Cornpression load

d) Both axial and compression load

c) Column d) Web

c) Rankine d) Tresca

c) Rankine d) Tresca

b) Post

9) Maxiinum shear stress theory was postuiated by

a) St.Venant b) Mohr

10) Maximtim principle stress theory was postulated by

a) St.Venant b) Moh-r

Page 1 oi{

P i F.f B i1* ;. 2 : Z* Mxrilsi- J :\

^" :j Ljelril( i i,li-*. -._.:.

1]) S:l:lr i]t, :,s,.,,::- :,,r, .:. .,. i,; ;'l;u,lLL itt.. :.n(m.Jer iot.ce ;:t iiusS

13) State :he Cas:isii-ili,'5 i-ltcoren:s.

i4) \vrite ihe Clape rrail's ihiee-iloilleiri r;i,rition iir geireraj ia,-*r anil explain the 1Ei11i5.,

1-5) Give expression ioi stiain eneiq\; in (.a)Tersicn anc 1b) Bendi'r.i 6) Define carrv o\/ei facicl.

tr7) Define Euier Coiumn.

18) llefine resilience anti proof resiiience

19) Cieariy explain the octahedral shear stress theorv.

2U) Staie rnaximum shear stress iheorv.

PAR? C {5 x 14 = 7{J Marhs}

2i a) A truss is loaded as shorvn in Fig 1. Find the forces iir the rnernbers of the tness sl,,;Figl

5m. el ,'j&{ \'-

.iI'I

tsTkN

^ 6n ;=A .:- | --'" '-'i *i.- -i t, r f _\ .;...j. u\. -'bo bo \-, '/ &-t\i\, : r.,

aaa.. 1

Iit

a,:lc:

f1

5$s *\if*e n &r $f? * .$

5CIr kF.'

n- ilre ^: O: ,j

fo*;Find ii-ieb) A truss is tcaded as shou'n in Fis 2 fcrces in iriembers cf tlte ir'.r,ss sFrcrvn in Fiq?

2E;:I :::

22 a) State and prove Ciapevron's Three moment equation

(OR;

b) A tr"o span continuous beam ABC fixed ai the ends is loaded as sho-,r,n in fig 3.Find

bending moment and reaction at the supports.

6 kNlm 1?0kNm

:m *{'{ Qitt

I

ie) Loaded be.am

, -- '. ::iJ,

sclr s*o

23 a) Foi the truss shor.rin in rne fig 'i the cross seciicn prea of rhe bars i:r

3*c*'l;' and. r;thers 12 c::i2 .deie;:nine the ver-ticai cispiacenieni of pcir:1

iiisplacernent of point B. Given E-21{}Gpa.

tu',.''--F-*ls.

I

etr )L-._

It hllts ry **-*J

e-vt'' t

cOmt]; e;

L AIi{ I '' I

t1

Fig 4

{oR.)

b) State and pro.ie Castigiianos Theorem.

24 a t Slrcr-l nores (,n:

i) Classiflcation of coluntns. ii) Rar,line's I{ypothesis.

(oR)

b) A bal of lenotir :lm u'lien used as a sin-ipiy supported beam and sub-]ected Eo

iOiiNim over the t'hole span. deflects 15mm at the centre. Detern-iine the er,tt"

r.r'hen it is used as a colurnn lvith loilorving end,condition:

i) tsoth ends pin jointed

iii) Both ends fixed

ii) One end fixed and other end hingectr an,

\Mrat do 1'cu mean b-y- iaiiure theory .Explain any two theories briefly.

(oRt

ln a metallic body the principai stresses are 35MN/m2 anci -95MNlm2,the tL*i:.i ,cipal

siress being zero.The elastic liinit stress in simple iension as rn'eil as i,1 impie

compressioir is equai and 220h4N/m2.Find ihe facior of safety based o* the el;, limit

if iiie cri;-ericn cf lallure for the nateriai is the n:aximum principal stress t}:eory

****5***t t

of

rds

h\

Page 4 cf4

ffi*g" Ho.:

@wes*€erxa Fmp*r ffcde ; ffigSKX.

ts. E ",its.Tech. SEGR EE EXA&dINAT{ cN, NO\IE&{EERiD &CEMBER z0 1 0.

Fourth Semester

Aeronauticat Eng:inee ring

AE i254; A{}tC&\}lT STRUCTURES * I

ffi,egulation 2004)

. Time : Three hours Maximilrn: 100 marks

Required data, if not gi.ven, may be suitably assumed andclearly stated"

Answer,Af,t queotioilo.

. PARTA-(10 x2=28 rnarks)

1. Explain 'method of sections' for truss analysis.

2. When is a plane trues structure said to be statieally indeterrninate?

3. For a composite bearvr section how do you defi.ne an equivalent section made ofone material.

J. W'hat is the biggest drawback of using the rnornent distribution n"rethod?

5. Name the inventor of the rnoment distribution method.

6. Can energy methods be used for statically ind.eterminate structures ?

7. State fufaxweLl's Reciprocal Theorem.

&" What is an ideal cchemn?

S. Fdcw shoutrd the ereee-ceetion of a eoiurnn he designed.?

10. Colurnras ?eadng irritietr curvature wi]-! hend urrder compression even whenF 3P"*- state wh*ther TR{JE or FAX"SE.

PAR?S*{Sx Ld=B0marksi

{a} Obtai.n the axial fcrcee irl t?re srembers of t}"-^T:*state whether ttre forces sre tensile or compressrve'

shown in Fig-1, and

s osdlscr

ffir*fi-" F rs*fi i

lP&

(1)

(ii)

&)

Fig. I

Or

Givetrrycpracticalexarrrp}esofas.Dtrussstructure.Exp}aintheanalysis of 3-D tnrss structilre" (g)

Drarn, the bend-ing zxiomen+" and shear fcrce d-iagrams for the plane

frame shown i* F;: ;-AE = FC = xrn' and CB = 2rr^' P = 20 kN

whileQ=151"N' * (8)

#c

ss&as

Fis. z

II

3 ?. {*.} *btae:: a.il eu.pport r*ections fcr t}:.e bear* sif,*wn in Fig"* g-,*t P = 2S kb{,

Q * $* kN, snd R= I kNi*" OA*AB = BC = f;* * *ffx, and SK = Sa^n.

qrgj& ffi& *-

tris 3

Or.

fCI) Berive and obtain Clapeyron'g 3-rnosrent equation"

iB. (a) Usi.ng energy method, calculate the snope and" defiection at point B in thebeam shcw; in Fig.4, Toial beam length is 4 m and material used is steel(E = 200 GPa). Beam cross-sectiorx is rectangular of dirnensions2crax 1cm.P=9k\i.

g&r

L}

Fig. 4

Or

{b) i* $tate and prcve Casiig}-iano's theorem L W}rat are the conditions.us-rder v,rhich Casiigliano's theorem is a-pplicable? (tO)

(ii) Catrculate t}:e straiil energy stored in a ban si.abject co iinearlyvaryi*g axiatr conipression of 0 kN/m intensity at the neft end and

LE kl.ils:i at the right end. The bar has a lexegth of tr"6 rrq and is rrlade

of, steeL. Bar cross-section is rectangular ofdirueensio&s ? em N l ern./a\\o,,t

C*yrs!.d.er a fixed-&ee colusgn cf Serrgth L subject to compression. Framethe gcvernimg d:.fferezati*X equati.on" Sbtaivr the frrst 2 mcde shapes ofbu:ckling. Wgldt are tke csrresp*Exding criticai loads?

!.4 ict

f-! *

31811

(bi *!se,:ss, wiih rel*vant *quations, ihe f*lL*wing teufr;L* :

{i) Effect of **q:eretrieity an the bu.cHing }*ad ofco].umn

(ii) ?he eonstru*tisln and uses cf a Scuthweil pL*t"

n pir:ned-pi:tcle*(8)

(e)

1K ia) Wri.te notee on tke fcliowirag f'ailure theoriee wi"tie

correoponding fainure envelopes. t

{i} cnaxirulum normal stress failure t}:.eory

(ii) d.istortion energy failure theory

an explanation on the

Or

&) A solid. circular shaft is made of a material whose tensile yield strength is300 MPa. The shafi is subject to a bending momerit equal to 15 kNm anda torque of 20 kNm. Using the following failure theories, ealculate theshfe shaft diameter for a factor of safety of 3.

(8)

(8)

(l) rnaximum ehear stress failure theory

(ii) rnaxinaum etraicl energy failure theory.

(8)

(B)

&1&13

K ffiSA

8.E.iB.?ech. DHGH,trE trXAI\ffNATTCI{S,}J O\EiWBtrft,/B E CEMBE FT, 2* 1 O

FOUR,?F{ SE&4EgTtrR

AtrRO NAUTI CAL E NIGI NItr ERi I\TG

AE 45 - AIRCRAFT STR,UCTLTRES _- I

GEGULA?IOI{S 2oo8)

Time : Three hours Maximum : 100 marks

Answer ALL questions.

PAR? A -_ (10 x 2 = 2A rnarks)

1- where are truss - type strr,ectures found ira an aircraft?

2- what is equivaleni rigidity of a. composite bean? Bxplainwith an exarnptre.

3" write down three moment equation in general form.

4" Define stiffness factor a*d carry-over f,actor in mornentdis trib ution rnetlaod.

5. State Castigiiano's theorems.

6. State Reciprocal theorem.

7.

8.

l

*1ff'ere*tiate between icng and sholt columir.

*raw Eule::'s c.-arv€ f,or a column and Exptrain criticatrsiend"erness rati*.

Hxplain r:raxiiaaum straicl the*ry.

Explain octahedral shea:: stress theorv_

c-)

1a)

PAF"T g - (5 '. 16 = 8{; ;-*aitkc}

il. (a) Setermine tlee forces icl tlxe reeeg'*bers of the tre*.ssindicated in trigure. 1.

&Kru

€ffirq

-t, 1EUre. t -

rJr

I

*d &ae

K $s3

ib) ?he trelss shawn in Figure.cantilever at th.e 3cints A andthe mernbers.

II

9 ic ci rnnn; f pr-i

F{. Find the forces

*e

;*-ttt

! F F 'H, += e,,*f"

1-)

Fipire- 2.

ra) FinC the suppolt moments and draw bendingmoment diagram of the continous tream sh.own inthe F igule. 3. using three moment equation.

F i.gure. 3"

(}r

a

t eeo Nlvn

K SS1

(b)

I

Finri r,he sup-*crt rnorrrents atrc d.;:asr 1:end.ing

moment <iiagram of tbre cor:tt'nous beam shcwn in

t,heFigure.S.usingmcrc}enicistribrrticn*rethod.

A thin circu].ar ring of Radius R and bend'ing ngidity

EIj'ssu}:jectedtoth.esymmetrj'cradialcomprensive

1,:aCs );-:ng.n tiae -q:']ane ^{:lng 3+"';;r'-iu1ie' Ohtain +l^:

exp::ession fol' the b-nd'ing morxrent and ph:t' its

distribution"

-xeii r-r. (a)

Or

(b) Bbterneine aLn support reactj.ons of the beam shown

in F'igune- 4" tlsing en'en:gy rnethods' Then draw

shearf,orceandbendingrnornentsdiagrams.

E=210GPa,l=10-ama'

$eeN

Figure. 4.

4ru

^&dtl u,5 x

i+ \{L } Write $ctes *n the fcll*wing iopics

(i) nn elastic c*l,urnr:- buckf itrg

(aj

i1*)

({trj(ir) The south we3-1 PLot

What, is a bearn-column? Where can a beam-column

type of, structure be found in an atrcraft? Explain the

stru,cturaL anatrysis of a beam-column type of

stru.ctu.re, with an examPle'

Expiain the various theories of faihme and their

relative merits and demel'its-

Or

A cireuiar shaft of tensile yield strength. 300 MPa rs

su;;ected to a coinbj.ned staie of loaciing d'efi*ed by a

bending rnoment N'{ = 15 kN-m and Torque

T - t5 kl{-rn. Calculate the diameter d w}rich the

bar nlust have in order to achieve a f,actor of safety

h.I - .)

t\-4.

th\

(r)/

K SSl

l

A1:ptry t1:e folicwing :hecr':es.

{i} lMaximu.rn str"aj.n thecr"y.

1:i\ l\,{^--.*.,-11 Shear StreSS t}reOnv\ifj lYld.,al.l.l'nLilii Dt-lcGi DL;"<r-D

(rii) &{axirsxum Cistortion ene}:gy thaeory.

K S39