Reg. No. :

T 3009

B.E./B.Tech. DEGREE EXAMINATION, APRILA,fAY 2008.

Fourth Semester

Aeronautical Engineering'tAE 7254 - AIRCRAFT STRUCTIIRES - I

(Regulation 2004)

Time : Three hours Maximum: 100 marks

Answer ALL questions.

. PARTA-(I0x2=20marks)1. Where are truss-type structures found in an aircraft?

2. Define the'carry-over'factor used in the moment distribution method.

3. Transform the cross-section show in Fig 1. to a section made of aiuminiumalone. What is the criterion used?

E= 70GPa

E.25Gra

Fig. 1.

Write down the moment- curvature relationship for the section shown in Fig. 1.

Compute the strain energy stored in the bar indicated in Fig. 2.

A, z. 7Ar

E:TOGPo

3o r*

L2c.r.

T6c'','

l_

4.

5.

Fig.2

State Maxwell's Reciprocal Theorem.

, I r.J 6 b I (J 9.\

Lc^

b

TC rv\

7. What is an ideai column?

8. The load carrying capacity of a column (increases/decreases/remains

unchanged) because of eccentricity.

9. State 2 faiiure theories appiicabie to brittle material.

10. What is the failure criterion fccording to the maximum shear stress theory?

PARTB-(5x16=80marks)

11. (a) Determine the forces in the members of the truss indicated in Fig. 3.

3tN

(b)

' Fig' 3

Or

Look at the 3- element truss configuration shown in Fig 4. E= 70 GPa for

the material used. The cross-section area of each member is 5 cm2 - The

length of member (2) is 99. 75 cm- this member is stretched so that a pin

can be inserted at B to connect the 3 members together. Determine the

forces induced. in the members. Determine also the vertical and

horizontal displacement of point B'

Fig.4

t

2 T 3009

12. (a) State and prove Clapeyron's S - moment equation.

Fig.6

Or

(b) Determine all the support reactions of theenergy methods. Then draw the sheardiagrams. E= 2I0 GPa. I=10-mn.

ft)

Or

Determine ail support reactions for the beam shown in Fig.clapeyron's 3-moment equation. Then, draw the shear force anJmoment diagrams. EI is constant.

6o t r.r $o {,o.<hf

Ltr/\ 8o <-M

5 Usebending

13. (a) (i) State the prove Castigliano's theorems. (6)

(ii) Using energy methods, determine the slope at point B of the beamshown in Fig. 6. E= 210 GPa. I=10+ma. (10)

beam shown in Fig. 7 usingforce and bending moment

*l40 am

Fig.5

Fig.7

t sobg

(i)

(ii )

(a)14. Derive and obtain the first 2 buckled shapes and corresponding

buckling loads of a fixed-fixed colutnn. (10)

Explain Rankine's hypothesis. (6)

(b)

Or

Write notes on the following topics

(i) Inelastic column buckling.

(ii) The Southwell Plot.

(10)

(6)

1b. (a) What is a beam-column? Where can a beam-column type of structure be

found in an aircrafi? Explain the structural analysis of a beam -column

type of structure, with an examPle'

Or

(b) (i) Explain the maximum distortion energy failure theory. Refer Fig. 8.

point A is a,clitical point located on the top surface of the lever

arm. Determine the maximum load Po according to the maximum

distortion energy failure theory using a factor of safety of 1.5. The

shaft is made oi steel with a yield stress value of 300 MPa. (10)

Fig.8

Explain the maximum principal stress theory of failure' (6)(ii)

T 3009

r

{i111" {") Write nctes on the f*ilowing topics

(i) In etrastic colurnn buckling i10)

(6)

&)

(ii) The south well Plot

Or

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

type of structure be found in an aircraf,t? Explain the

structural analysis of a beam-column type of

structure, with an exargPle.

Explain the various theories of failu-re and their

relative merits and demerits-

Or

A circular shaft of tensile yield strength 300 MPa is

su^4ected to a combined staie of loaciing defined by a

trending rnoment hd = 15 kN-m and Torque

T - 15 kN-m. Calculate the diameter d which the

bar must have in order to achieve a faetor of safety

N=2.

15. (a)

(b)

t)K SSl

I

Apply the foll,cwing the*ries.

{u} &€axirnum strain i}reory.

(ir) Maxixnu,ne shear stress theor3r

(iii) &€axicllum distortion energy tlaeory.

r} K #S9

Reg" No. :

.3 SS08

B " E./B.TE Ch. DE GRNE EXAT&INATION, h{.AY/JUNE 2009.

Fourth Semester

Aeronautical Engineering

AE 1254 - AIRCRAFT STRUCTURES - I

(Regulation 2004)

Tirne : Three hours Maximum: 100 marks

Answer ALL questions.

PARTA (10x2=20marks)

1. Expiain the general criteria to determine whether the truss is staticallydeterminato.

2. What are the primary and secondar5r stresses in the analysis of a truss?

3. A 20 crn long steel tube 15cm internal diameter and lcm thick is surroundedby a brass tube of sarne length and thickness. The tubes carry an axial load of150 kN. Estimate the load earried by each- Es = 210 GPa, Et = 100 GPa.

4. Write down three moment equation in the general form.

5 Define stiffness factor in moment distribution method.

6. State Reciprocal theorem.

7. Give expression for strain energ'y

(a) Torsion

(b) Benrling'

8. Differentiate long colut tt from short seltrmn.

9. What is Southwell's plot?

1G. . A solid cubd of steel (E = 210 GPa) is subjected to a tension 150 MPa, find tJre

strnin ener$I per rrnit volurne.{r

\11t B o 6 ! () tt

i o r\ Il

Y./ (a\

5op r't

E

loooN

.<-$

FARTB*(gx16=g0marks)Find the forces ia the mernbers of the truss shownone method.

TIol

Fig. 1

.Or(b) The truss shown tlo*. 2 is supported as cantilever at the joints A and H.Find the forces in thelemberi.

Fig.212' (a) Find the support moments- and draw benrring moment diagram of thecontinuous beam shown in the ng. i "rr"e'&; ;;;;;;;ff;r"r.

2ooor.t 2-ooontl^rn

B

[+t"'.'k- +$. * -l€-- 6tvr"'--l

-

t Fig. B

//0r

{a Find the support moments anf d3w beac{ing nomeat diagram of, t^keconfinuow be,*tn ehow& in t:he fig. s using;lX; dishibutiou method"t,-l

in the fiS. 1 .by any

5oo q

I ooo r,t

looo xl.'tt

-.--

13. (a) {}i Firid the defr.ec*ion st th.e enid-pcht of a simply supporced beara-oftrengtir L, subj*eted to a rrniforrnly distributed Load using unit loadmethod. (8)

(ii) Find the redundant force in the member OC of the truss shownin fig. 4 (8)

Fig.4

/or{y For the truss shown in the fig. 5, the cross section area of bars in

compression are 30 cm2 and others 12 crn2. Determine the verticaldisplacement of point C and horizontal fisplacement of point B. Given:E = 210 GPa

I r.-1

t--Il--'*I

Fig.5

14. (a) A thin circular ring of radius R and bendin$ rigidity EI is subjeft{d tothree synonetric radial compressive loads lytng in the plane of t$eltrif-gstructure. Obtain the expression for the bendrng moment and plot itsdistribution.

Or

(b) Find the fo6gkling sf,ress of a hinged-hinged col.Fmn of length 100 c4r asdhaving T-crosg Bec&icn. The dirnensione of the {langelare 10 cm x 2 cmand the web 10 cm x 2 cw". Oerive th.e fornula used. E = ?O GPat"'

J sm8

A bea'n-cof;** m.acie'of stee]. (E = t10 GPa) simply supported at bothends is sr,rbjeeted. to a a:niformxy distsibuted load of 500 N1m and an axialnoad of 1000 N. F'ind the morneclt at any seeeion and heace frlad themaxiyquna stress" Givem.: L = 4 xn, b * 90 mrn, d * 40 rnm.

Or

&) A circular shaft of tensile ield strength BbO Mpa is subjected to aeom.bined state of loading defined by a bending moment M = 1b kN-nand Torque T = 10 kN-m. Calculate the diam.eter d wbich the bar must,have in order to achieve a factor of safety N = z. Appiy the followingtheories.

(i) Maximum shear stress theory(ii) Maxinaum aistorsion enerry theory(iii) Octahedral shear stress theory.

A ; eJoa

-1

Reg. No. :

estion Paper Code : C 1011

B. E -/8. Tech. DEGREE EXAMINATION, APRIL{\,IAY 2 0 10.

Fourth Semeet€r

Aeronautical Engioeering

AE 1254 _ AIRCRAFT STRUCTURES - I

(Regulation 2004)

Time : Three hours Mnrirnurn : 10O marks

Answer ALL questions.

PARTA-(10 x2=Z0marks)

1. How do you define a truse? Give a suitable example for such a trrrgs in theairplane structure.

2. Explain the difference between a truss and a frame. What are the internalforcee in such structures?

3. What is a continuoug be"t r? Explain how the reactions are determined forthose fsgtn8.

4. Explain how the forces in the statically indeterminate etructures aredetermined.

5. Define strain ener$t in a loaded sbructure. What happene to the structurewhen the loade vanish for a conservative aystem?

6. Explarn the Mqxwell's Reciprocal theorem with a suitable ssarnple.

7. Explain how an ideal eolumn faile.

What ie the need for ghort colnnn formulae?

9. Explain the failure behaviour of ductile and brittle materiale.

[10. What is,the need for studying the gtrength end gtifueas of strufttrres?

qI

(2x- tr\TJ & 1 L} \ ft t^ \\

FARTB-{5x16=80marke}

11" (e) Determine the forcee in atl the membera of the truse showa in the fig.

Fis. 1

Or

A frame ehown in fig.2 cotsists of three pinned bars AD, BD and CD. Thebars are of identical material and croge section and the estimate loadcarrying capacity of each is 30 kN. Determine the ultimate vertical loadP that nay be applied to the system of point D.

(b)

A

{Y)-ra" tt

/t)/ \)-a-

\SW'1,

Fig.2

L2. (a) Obtain the valuee of the reactiong at the supports of the continuous bea"m

shown in fig.3. Aleo draw the shear force and bending moment diagramsfor the bean.

ry c F{-tel.-re"-{*-

Fig.3

Or

o c {Onx

(b) (i)

(ii)

14. (a) (i)

A tinnben beam having 20 x 30 cm rectangular eection ie reinforced

at top a:rd bottom by eteel plates 20 em wide sBd 1.26 cm thick. The

modulii of elaaticity for steel and wood are 200 GPa and 10 GPa

reepectively. The allowable working gtreeees 8re ol, =l MPa and

d, = 0.08 MPa. Find the pa:rimum allowable bendiry moment for

In a composite bearn, what ie an equivalent beam?

the curve.

Or

What are end fixity coefficients?

What ie a be*tn column? Give a suitablestr-uctures

Explain the proeedure to detemin'eexprime::ta3}Y.

e

('1)

(12)

(6)

the section.

13. (a) (i) Define complimentary stt'nin energy. @)

(ii) A cloeed eircular ring of rad.ius R ie eubjected to three radial loads,

each of magnitude P, acting away from the centre. All the loads are

equally placed around tle ri+S. Obtain the expression for the

bending moment at any reaction and draw the bending moment

diagram around the ring. $2)

Or

(b) (i) What is'unit load'method? (4)

(ii) For the.truss ehown in fig 4, calculate the horizontal displacement

of the joint B. Use AE for each member equal 20 x 107. (12)

Itkrt

Fig.4

Draw Euler's column curve a-nd explai-n all the sigrificant points in

(ii) A st€el bar having 4omm x SOmm rectangular eectiou, pinned at

both the ends is subjected to axial cotnpreaeion. The bar is 2m long

and E = 20CI GPa. Determine the buckling load' (10)

(b) (i)

(u)

(iii)

(4)

example in aircraft, (4)

the |uqkling load(8)

t' c I^0x.L

15. (a) (i) and brit$le(6)

(10)

detail the failure behavior of ductile

(ii) Explein the mRr'tt'um strain energy failure theory.

Or

(b) A cantilever beo* of golid circular crosg-eection aupports an eccentriccompreseive load of 60 kl.I applied at the free end 1.6m'n below the qxis

of the bea"' together with a torque of 1200 Nm. ealculate the principal..stresee6 and the maximum ghear gtreeses at a point on the lower edge ofthe beam.

Discuse inmatorials.

trr {tb!1

Reg. No. :

D 4007

B. E./B " Tech. DE GRE E EXAMINATION, NOVEMBER/DE CEMBER 2008.

Fourth Senester

Aeronautical Engineering

AE 1254 -- AIRCRAF"T STRUCTURES -_ I(Regulation 2004)

Time : Three hours Maximum : 100 marks

Asrswer AJ,L questions.

PARTA.*(10 x2=20 marks)

1. Give a relation betweQn the nurnber of members and the number ofjoints in atruss and expiain its sigrrificadlce"

)

2. A soiid cylinder 100 cm lorlg and 5 cm in diameter is subjected to a tensile forceof B0 kN. One part of thisutylinder of length Lr is made of steel (E = 210 Gpa)and the other part of length Lz is made of aluminium (E = ?0 GPa). Determine

length Lr and la so that the two parts elongate to an equal amount.

3- Write down three moment equation in the general form.

4. Define and give the S.I. uniis for (a) Stiffiress (b) Flexural rigidity.' *-

5. A cantiiever beam of length L is subjected to a tip ibad P, find the deflection atthe tip using Castigliano's theorem a

6. State Reciprocal theorem. Give an example.

, 7.. Find the slope at the support of a simply supported beam of length L andsubjected to a uniformll dish"ibuted load by unit load method.

8. Draw Euler's curve for a colunc-n."uli* criti.cal slenderness ratio.

9. Give the Rankinelq formul"a and its significance.2

I fO. A solid'cube of gteel (G = 80 GPa) ig suhjected to a sh&,r of 56 MPa- Find the

q 8i3 C 6 1 C 1 O o 3

PAR?B_-(5x16=B0marks)

11. (a) Find the forces in the rnernbers of the truss shown in the Fig. 1 by anyone rnethod.

."-+iF="35b-

Fio 1^'b'

Or

(b) Find the forces in the members of the landing gear tripod shown in theFig.2.

--irto

--+-I

to e*^

l_iulll,l1

lo

T r€oo

4zoon

Fis.2

l*-?,?tn

4r

iai Fi*d. th.e supp*rt rn*r:a*r:ic zul.d d::aw be;reiing mr:rceni fiagram r.;{ theq:o:rtin$olrs ]:eam shcwn in the Fig. 3 using ihree ncment equation.

&**tqa i*-***ei..rn 4aoo lt

' \ _ _6

ff-?t{F.*-e -:+,1"4x;-a* t'r-rt"l

|"*3 gb'--J-4-

(b)

Fig.3

Or

Find the support rnoments and draw bendi.ng moslent diagram of thec.ontinlrous beaqa shown in the F:g. 3 using rnornent distribution method.

Find the horizontai reaction of the frarne shown in the Fig. 4, usingstrain energ-y method.

r'fI*t

Fig.4

Or

Determi.ne the forces in the systera shown in thre Fig. 5, assuming thecross secti.on area of all ba-rs equa3 and ta-king the force X in the diagonalAD as the statica$y indeieradnate quax.tity.

13. (a)

ibj

drh

&IIt

trl,Y

Fig.5

ga xdadtPf

74. (*i.,7zzl t

The crsss sectio,, of a hi:rged-Si:aged column 1 m long is z with 3 un x 2'nr''

top a:rd bottors {laage *** f em " ? m:n mid'dle web' Derive the formula

used.E=?0GPa'

0r

Abrearvr-cotrumnmadeofsteelsimplysupportedatbsthendsissubject'edtoae*neentratedloadof1000Natadistaneelmfromtherightsuppoltarrdanaxiaiload*'oooN.Fildthed'eflecti"i":^"*d-poiatandthemaxirnurr deflectioL Givea :L= 4m-'b = 20 rnrn' d = 4S t: ' E = 210 GFa'

J;;;oad tb.e colurnn can carry. Derive t"be formula'sed-

"t

A sircply support'ed' bear:: coluron of length L is subjected to a axial load

PandamornentatMatoneofthesupprt.FindthesiopeaithesuPPort*.

15" iai

Or

{b) A eiret*ar shaft' of tensi1e yield strength 300 FIPa is subjected to a

combinedstategfl'oadingdefin'edbyabendiagnaolrrentlE=15kH.reand.torqueT=20kh[-rn.Calculatetr1ogfi*IneLerd.wbichthebarrnrrsthaveinordeito'ehi*oeafactorcfsafetyj{=3.Appiyii:eiciicwingtheories'

ti) Maxirgum shear stress theorY

(ii) Maxisurn distortion erlergy tbeory

(iii) Octahedral shear stress theory' 0

I