Unit II - Analysis of Plane Trusses and Thin Cylinders and Shells

uNtT- n

A un Lvsts oF PLANE TRUSS ,THIN c,yLrNDERs ItuEr-r-s

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iril $-or.*t Re4,otqe Hordzanta\ ' '*RA +FAD tFn" Sin'6P"::o

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ftsf:

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r) trind '+fdBc o[ *\e

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a{.d !q!g1+=, oE rr.-a.tttlaqr1/3 Ac, Ac a'rtSl.rzm,sY1 ol rr H,c_

..j.y

-:-- --'=-j=:=l;;=:--' ,*::s

s\p4: z -

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':

5tsN

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. - .- . --,.F.1

-t

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5 -\-25

IoaA

ff Ke = 3-'15trN

gfe+: g -

caJctplalton oS heze.s ,.l

Tannt - B '

1v =o ',

Re + Fea

3.-T5

.:,! .(f) wa , (t) -v .

sinboa =

t>B

-

Fea SinSo o .

.

Fea : .4,33 KN Ccstr;ynAsiYql

"'' -

--" ^"'t r------rr .,rVd L

a,FK,: =.,.Ail6s lcN -.re.nr1t ! ;- .i .i

-A:

4v =o : (J) +ve , t{) -ve.

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- (- 4'egxSin6a')

-

( - z-'xsin3o' )

=o

-5 + 3'75 + r'z5 =c)-

5 +5 =oO

=O

1w =o ) (--+2 +ve' , (+) -v 'F*s Ces 6ol * o^c. crlsSo' =o

(- 2-S x

in n.F; .-1 , { .*

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4Re =

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^

rg

l8 X 2 -

51

=O

Re --

l3.5PN .

T]er:a) V,Q*.*J cql >te'-ote:ltort

s



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L

T-M.e s:1me=o

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5 X\'L5

= b'z,

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Q- -

c-t.2C

c

!.

-F

!

lsrion6rr fig?. "

cos 6o' '- gAeB?

= cos 6o' XAB

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o* ,eiA-n

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=o

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=-4-g?FtsA

-tt q'.{j+,,{lbtrxtI

n.(.,. \

J\ \f\

! *l ,: {-',-?; -- -i

J'1.--.r //-

Aao"o {----*-l

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acIII

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--ttanssivcC*algl.+a)i')y-

--

B[-

Re

5,tt AB x ,

X BP

sin 6o

a-ba* A

Fec XAP

AX Ax;gAAAX

9.75 x 3.25= Fsc X 2.tEl=-_----.---.--JFsc -- a.rgrc-Nl Crenstdh)

heidc->t t{.\- tn"ial6 e- e) &-7 sez}r'crn @@RcxE * FcaxAB

=O(r-"s x 52 + (Fc*x r..E) - o

2-E Fca ='6'2 5

F.+ : 2-E tsN (rensir-e.1

A

/1

i- Ar^B t-'I

II

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l.Asr Ruy srl poRcF S \N\ TRUSS MEMBFRS

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l) Find' lr',,c-- tqrt{" ry goto.23a-$f36acf+m-aH.+-t{Qct {-ahsion ca -e*f&iurrts

.

,L- . '- +-'--,-.- 9t,

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I,i

_ 5Xt.25 :o

z 6-z9

-gihg: 9?Pt+Yr

Sin 6a. : AP._B

*e = 2.>. x3iin5o'

^? -- 2'l-lrn

:rq

AB = E cos6D'

Ag : L.5rnAc-bS 30' -- ?

A c -- 5xco93o'h e.. z *.33ft

Taian6Le ABP:9P

e-os bo' '- L-haW = e-oJ 6o' *- !L'5

B? > I'z5fiT)

.?c;Bc-tsP?c = 5 -t'29

T.M-@Blwe

=oRex5

FRc

Rc ,= r'25frt

Re+Rc =g

Re+t,25=E

Rg : 15-t,Lg

Re= 3.?5 FN



3 rcP -3 ' h-\tttJslion o* *o>tezs4

3r:inf - B ,

X - d.r,:rc-ctian (raje- ''g" o" a lt-Q*t,:r.enr.e pornt).

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g,

tDvtgt-e.,

Tg.'

Tea

X6

xs7.t-^A

ean O

8o *\a tprretdn aa-el*ici elt q'n 6,

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(Ta*P-" B " f

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+v

A ttzsettexv:z Fdtnt )

Yn -Ysl t Re :o ., . s'{t

Hw Pc=rntS B4f,tde.io

b/,a; Peinfs g art'd' B =-o

b/,o paint*S B arna'A = ArP ?9"11fr

TenSiorr ca-e$*iciA1t a; idnt g a-rt'd c

Terrgion u-el*'tcJent at iarnt e q'rdA

fr

t- aun $ii ah be. wtdt+en *s .

Te. f "-ol + Tee fz'll -ol +3'1 5 --o

2,tl Ts4

Te* : - t.T3- " tivt

9ubl1iptlp TB.* 'in an (i')

5.Tec + t.zFTa*:(,5 Tec + (r- z5 x - r-t})

=o

fg. =

2.16/g

Tge 7 o.+32

Soint - c :

X dla.actiorr (fa*a.- B" 4< ap*e>etva pof.rt)At isrrt c, FcB arra1 Fca loncns aze a'ctln6,

Tha frarrsion ca-Q&&r'cient ear"e.-fion V,

TLa f *"-x.] +Tc'4 txo-x.f =o -..{v:TcB ("

- E) * Tca (r'25 -5) : o-

5 Tcs 3'15 Tc'd = o

_5Tce ;'9.?5TcA =o-5Xo.4gZ- 3't> rcA=D

- 3 -15 T

i,

FoPcE:TQ)Ei6r\ ce

x

+.330

9tlL :

.i

:iI ecrnpacestc,o

jj:i - -.- **

iiil r,TAI)Srort

Ulre!z-.lc-' ,

Joint',.:..t

ans\ac) v>utunt'ali. ,,

Trs f xe - xa] t Tac Ex. -Xal = o l,'

f^e f o - I'z-5f 1 Tra ls -t'zel =6 :i

-t-z|TAB * 3'15Tae =A :-t.L5 (-r-13) + (i--?5 x- o':>1fi=o t

2.41

T*e f Ye -yal +rn.tY.-Y^]-5:oTlc t o - L'l6J + Te-(o. 2're]-s=o

.t 6J_5:o( -

t't3 Y- z-re) i (-o'5t3x -2'3.1+ t\-zg

-5 =t>5

-5 --o

g trr-!



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%and!, r?72-es1JJ12 x'. fra-e-,q

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a.J\aa o\x A )

fbnca A&-e*+a 1T--*; ?l-4s'stu\e)

- v x dxlI

fe.lncr- d.^ra- t'l

oaprako{ t 1

= p-at,[ '"'irt

e-r}r c.rrr-r&p:rcn ifaj *Ve.es;),.otfi

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x F.nz-q

fc { (-txb 4rrt)-* 6e X Lx []tz, e { 6' 'f 't& e(i)

d: !4. -urt*fi

el*ncsrneu-rua-nh'el bt H#P gw&3'

t=j * t'

p.d: *-

d'c :

an-:.rta-] Paz'*uazWh,P^-a-, ? -- td' -- rnrclnal dta*naian o+

ot, g{irr'd ,$na fNq,9ta

6 -tt- rt-- -l^-

N lr.,rnt



o$

tlil " t-on 6;;-rai rtal Stru-s s '..:l

-fVv

*rrLz etrA;nAan,.1',t-n,gg o.fi'

k h-n o','n

"at"dvt6 +t4-a leftfhXlyr'ff".rutLinqj -*,nP-gg

"tts-{j"

,dVY

consiJrart(Y +|,,a t2un4 ti nA 'bD 2l co tphdj nE to

bt\ue-^. fta c"/in4ar\aA)nSqIort-ft \+\-a c^rgr.tlilffi*atvxtLz,

4s"",5 l',is'gfint $'22*e"tuncp- atrrz- h, Ftr:j"l ?Wv " F V x ftne-a ctr) u:Vt'rcrr P

Lv.d

rna-renaar o\ +hs shorr ' tTUL, 9@g s at - tJJitt

ba

*:Yer\atF6p-

\ n dJo*vie4-o-n , Aa =

st-nass C6.i) ineLua-ci \ni., XX Alt pt$on,sln-e.ll" '= 4t

c-rjr cg.mgou.ontrctl 6l ., ; in.dut-od'

g\, A^/w*r'ct-r,

^rtylte 'l-o 6-c-.

,

+-\^,a

i r.. f{"\thr sg

i".

a-r6t^,t

in VoLurwta , Av :

( r tr^)v: 3. P'{ [r-.r 1,'4t 'E

F'do+tE

Aaa- -_

-A

3P.d f '-1 )Av - ;rE (' rn'/

- spd4- (r-trv -- ;4- *{

Mae- glng-n gy-resg t -- ft' *fct

= E-_5 =c)

EFrr c\EL\CY oF A Tc? tt{T ',-ITnaqrind'xlca!gh-[fsuclnovs.xitlltsalfiakta'rnu

"t-n:oW?esokidntq*t**l'dfr'n$ruAiY\alj6\n\a4'1;er! cur*rngar,Jf"*id-l iant ' * -r;* hotl a-rr-a rn4d,e in +vu

z-r'tiq-l olrulagcr.'nt'a^c.r,fidJ Jcvrnt .,s\a **T^^X

*

F :-^' ^ ^ ^c\' aU'f-arrrad

ag' tNgrs-"ly.r(1^ruar'.qj ghrosseg I .'fin rwr6tudrnet)

i)

6iven I -.

Dia. o& ??Q . d = 2aorD r7'rnTlnic*nass a* 6?n,'* : 2a21-n6 .

SoLansnj -

-:

FUric{ ?tLQgstrt13. ? '- t'-a sf,61y4e-

*/^.i i

tsFoe.; .

The

2a,/ztoo

t':'

-".:4loo:i

@nbA 'irdn

t.2-o

:.rin&ost()

til to.n8i&L+in.qj st^4.sS C6'.r )yd.4rl, 5 x 2ooo

fl:

4x 2a

trit cri'crl.msonc.ntial 9\nzss C6.) '

ec.,. v2+1", X zoo o

ZX zo

6c : -?5: Nfcnrm'

Kesur l(l)

c"6ttndarW

L --31'g ltf ;lnn, r



-2)A c!6lindx}td 4 in,tzryng-l , ** I rn ccn tajns ar-aAt a ?neSStine o*, I Nf rnrr, - (Eat]q?q ) ,.Fg. +\4e. rnq'xrr^Jr-rn|rertrni-a"ri 61o gtttp-.sE ind*rc,el "rn V rna-fe;u'a-[ in to c' Nlrn rnf

F\ftd +\ne ' {+i t)c*1-as< & fl^..z 2bnaoa ,

&t\ven'

-Inta:z-rr-e.i A)a:ae-+e:t o* cgl-tnd-o:t, A -- rrn --tooo n'wn.

Mae-iml-rn ?a:r-missiUt' g+l\-a:sl in ++Q' malc:j.o-t Ytt{^9 et\u-rra'*ezps't ft4-t gtnc's.g

,

( Cc).

,. .' , qr; u-e-r Epaar,tta-l sf-n.ess -(6c) : ll}r N f rnm* '

sotruion I -

b-*, t: T\n-trl.ne-ss 4 #ne Sind-r:t

".d21t2. d

L.,L - z-c.

n x looo2x loo

t =

45 rnrrl

RzsuLT : -

l6cxneSS ok nundb "4

4Frntt-t.



- t'yi1.;,-.-.-;f".: --,-r.....:.1 ^.i.r,-.^, l,__ _._l_a_: l_ .,.. 'a

ow'Jf,.V+e)'tce in o;Ab,. ba+l'r xlaltt-?'s nfr bz',.

gamSg+eA #hq. $4.DUY'JLI1 ?@'J:r11SS\bt-Q'tnrc-:zn-a'f

"s eaue) +eP2Q-"t4-Ir\-e- vS e^UJe) fu m\nlrta'-qrrn ob tltt'o UcriJJ-o'1

'

Mqrci rnr.r-rrr ?etLm\ssibta 'in rcrruel ?Sr@asur\'a-

= O.q NfrnmL

sS ? V 4alcon 4 a'q'r't:t-l fu o'{ Nfmtr;r, fueta'.0rrnti,ilA'n4.J sh'Js Co'r) cpi\\ b'

?-4?ot: 4xry..t

o-1 x %oo4xo-3X 2.D

Al 7 15 Alrr,,-..

T"iA V d-lJrz- 14 mo^Q. 'fnan ++le fru q .t irni*rr nflne,wcav. SW4S ,



-- l) A e$nAilca-t' J' iia.in d,xrrrn SooY?nrn }n Aiuaete:ti@Â gel e'b

",., "o ' i*.r{ l.v-t, ;!,.4&{ t{ni ct-r, e+ 9 eE I c> rn rn .

ag- +{g . rfunrr:^n i< .,_ Sqf-'re3ScJad 4-o. *r' lntz;una1 ?â-ssua-a"of 9 .9 Nhr-t . DA_fa-n rni!*

,

(r ) ONaxLta in A-t'am.Bjea.(i\) .CJqlaB?- i ir") , qfkJeu I cha_n.lge \n

Ta-b, E : 2xto" (/lp-" : yoigsantg >ux46 =a -LE ,a rvg-r{ :

Dlam-efen 4 Au-rf,n. A;-*tcofnrn)e-nyh ak Jrurrn , LThlcxness o$ An:sn , t

: : -.. -

Xn,i-M\4-! ?ê-ssutrQ / ? = 2''N f rnrn 2'

Y6W6tl's >rs--tia . '/^ = Q''rypa;-}tgtsrnoAulL|;3. E =

9Xto5 N/mtn'-Reqrl,*l'. : :

lo=*1f+h

\oLrr-m-a .

9otr-r-ftcrn 1 .

r\l oha*no- io &a:nelen , Aa -- .2

drr chan6a in &fi+h , At z 2iirt crnn-rn6o in Vou-r*vt , Au = ?

= 3i:- ( -*)2iE

e.5 xr8oo)L ( ,- -! xo'za)< \'29x toxzxto5 \

dl Cho-rr4a in d.-t,a:note:t, (Aa ) :

Aa



Lox90002.5v tu1I

-

o'25 IIZ)e L-.2-X to )( Lxlo

Au : -0'315 rnro '

o,i) Cvrsrp i n tlaUtmz CAu ) 'Ad+y

vourme-tnjL,,sft- ,-)o (+) = 2' Ta.918Av

- 2Y oE + -

- =l X 7go" 9qooV

.:

A 7 845xto-4 + tzgxto

V

Av A txto-3Fv

-9 xvAv: tXtc' - AY

V= I d,LxL= + x (goo)oxSooo4 lt

V: l'5o8Xtolrnrn3'

-

e r/ l. lag6,r rvAv T lxto -rt':,,ogxto1

Av z l'508xtotrnrn3'

Resul}' ..lr Ar - o, 35t-rr,rn



*ry A ulrinAilca) ue-e.6n&An< eb )usd g\@nfra-- ?r.alas, i4 rnaa-e- e& s+e-e.)Vtaxe '?rnrn ++-icr . T4a iangth atl& 4il9' \ nrre'a-rta-)

8,toxnpfu:t ob th vagee) aes ED cxn o{1d 2 b c rt-->ztasrylkrtc-fu1 " Sc:F;irn\rr-e th.lz *frl*9ne"t es'A ho":7

lu rr44 cd 'gharl A*@t:r 4'-v.)\n +r^4 # et

\ntarrr"e-.lt ktr,dd1 yn'e-\&

t" p.d^tUt -

-

,., 4-t r:3x g-so

C)- -''. 6L,-F N lmmt

\ .* ^r ?t^ I - f. 61Ctmatxntenen$al 9fTabn ; Ac =

-

E m_E+....'

lro,gllmJEL

: -

I-'o" (az'EXo'3)]2xto> LQ.

= 9- gt vto -4

B,-*, (pz t-r'aw fiQxazte-lsf,lt-a)n , e. A

"' I = 5-3lxlo':4d_.L

Aa 7 g-Btxlo-- x d

Aa : r-'gl x lo -+ x ?6o

Aa: o.tg? nnrn

-' ' Tncst-eA,Sa':in d-tax^OlO:t , 44 ':o il33 mrr) -



E ;.J_1 r. .

=' #t L e''5 a" ('t trxa.'l;7

A-i = t'25xto-'t

El^* | urQ-- t-nnt: ++1-Q- ko>t-rnr:-)n $on lort6'i*'rd''rn1

S,ta)n, A.lQ.t= Tl'z1xto-4 =

At '5oo

Al =

o'obz6w\!v''t

AV =

Zq.tSSXlosrnrn

Rgguur lcil :-o*6*4og1-1 p31.! s}^.e-ss ( fe ) -- 62'5 N/mrt'''(il 1+oof 9t^-e-ss C o-. ) :' 125 N/"nr.,' .t"

^ \

ciirT c-haltgz \n dio-rn-e-tur ( Aal : o'193 Yn-rn

LondWUnr=A sb'ln . o, fi _ _i4- :

-,( E rh.r

tiirT t'n cn1ne, \n votu'rno ) - cav)

A = L.Y + A: = 2'8-.{ Qt.v

- d

[4"a"*r]Iv : fC"" E-3rx,o-t) + t'Lexto-41 xL_

4v =

l'18'-7 x Lnl*x(z;o)txraa]



,/-

t**a7'v161 : \nru:r-rreJ djarnc-azl f.rr{ ta-hnrn -g.f?T +ilcxn4-+

Documents

Unit II - Analysis of Plane Trusses and Thin Cylinders and Shells