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f'ec....;l d~j'.-<'tr r~f.t_r : ACf> .. I'll~ I Vi I 'lo..l~

_!::1. +~At 'C:l cJ

6i t M.v,"-/' !tJ .,5up.u,p>o2V,~.,., c/ork/1,.,/ey:,-,""' u ... u:--.e. k.;_r,.:>~t_

olenk.b..., d""/ch..., c/;;2,.., ;~,[r.Jc..

6; ( x, + 6 i,J )(,; + -- . r 6,., Xn + 6i t = 0 t -=-1,2 I - •. 'Z.

f;, X I + S,z X;. -+ - - . ·+- 011'} xll -+ €ut = o J Ao,l 6,, x, -I b;: .Xl -f ---- *1- 02.1') x, -f &.tt = 0 J ljr fl. f/IJLt ' I

rJe,LI/,./tn' cSn, X1 -+ 6n; X2 -1

____ -r 6M' X n -+ 6;t =o

f>~C....l." ... : ~ ltr.

~

I

)

Otk. ~ t:Jg..,IJ.IWI -J..;.b ....... .., ok-h~ onu ot;r"-1.,,.::;~.., kof~(J''"'ndrr.

o},r C!:;,fc. OfM~r:Jtjl fC,/"1 bio =C) a/,,,,,Jt II.

51t .Steokt,~< cJ'l·i.,.,..J,..,c~e., cJot0 , X:::-1 6/t;,,.,t;-e,;,;"'

to-·tlo:'"- no k IQJ lh ,., 0~r d~j i;tt'rnvJiolf,.. .Stc.okftl<_ d(jt>'>~ot' ,jqbrtr ,;.c/'"'' e~~hr.

6zt = jlvli. o<~At clJ +JN: or't·t.olJ::: ~ ~~JMiJ;~Jold:fw;d; -.j5~kf,·,j q/tr. ~t=- 0 iJe. -(,-lui-. .f:.=-OiJt- //11',._(,' -1-eri'..,St/trofvr.

1-f.tJopfP.. ;:;_!~,~-. (}"(

"1- i.ltJJi-.:>-lllt ~Jc:~J s:;h...,., -.j~c,/llr,

2- -x,·:::. I u;:;tc.le ... e.f~r; .. e.. a it !>{[ dtr:.tro-.IDr! \}'- i:fo iJt- J.-h. chyojro...,/"'"' c,;,z.,'l:r,

J - 6; I... •• u.. 6 ; t f.e,. ht-.J.:>pl;:;n.,,,...,

Eic. [},'t ~ 'EI(_ [ _r t;(t.fl'C j!'1:o.IJ + .Iott.tJJ.../lcJJ) d '

h~.JI>f''"'"',..· B~ ~ ... lok. cJ~ '..,:.,., .;0 ,»1 ~t',, o."lr,,J,-.;;,._

>- M,V,tJ o/;y"'Jr"'.,./#-,.1 c,hr7!,, . , b ~ ~rdrof r:JPpJ!tr. {_~poft rj~rl-t../;/,'f.t ole.,kf .. ..,. /1.-t :t~)

_jM.". M ~ ..IJ t E:Zc jf-/1,' ~ olJ + e.Icjl-l;.!l:.J:.clJ = o

6it f>;t

OIL-N 6- ((, l

t =- .3o" C.. v~ LH = ~o->c.

l.:..:n M oJ0. c;l.l ;"";

~t,;. h5 5

.:r.::;. 3.2. cJ...,. 4

E ~ 2.,. 1o' t/..,2

flc_ = 4• 2•1o6-"' 32 .,.,ov = 2S600·t., . .,2.

Uc~t•=- ,,11-f! G. 5 12. ; - lj

Ek. 6.n :;. 102.

,r

"'·0 O.A2S

Uc... ~.t.:::. 25,oo[ott.~o ( 0: 65 • 1 .s .. (-t~a.s)+ d.s ·1·4 .o,s)

+o(t.3o { s,o,o1s _ 3 .,a,•25)J :1r1 9t.~

il(._ blt=256oo .. o<t [1o (-..L · ~··· 5:~ - - £ .. 4•3 -~ ~.i...t3.3) o,&s : O•d o.s 2

+ ..3o ( -'5 ""o,8 - -4" ~-o)J ::::- -152,4113

~,11 Xt- I~ 0 )(l + 11r %~== 0

- i3 x1 ..; fo2 '~2 - 152,416 == o

x,-::. o,323 )(2..::;. -f,'535

~"'trol .. ]M .Mrr;-.J)+flc&>.i ..... o 1o .o7 ~ . s (240,32J ... 1 +0,32J ... o,s - ..,_4,lfv~- 2• o,s .d,Hy )[21 . · .

- .f_.~.,_o,;(:z. .. ~,ftvy.J.4t~os)[-1] t t1,'36S~1g,3148-t'3,311 :::;;.o,ooJ8 & h0 ta:::. o1(:J)'J6j1S,:3'3 = 7o O,OV

-J.... 5 • j ( O,J23 ..;.2fl> 4,ftity) [2) t j_ Lt ,.. 3 • ( 4Mtf.t -+4,6oS) [ -t] b 1 .2. - 3~

+ '"5". 3 . .3 fl -'f,(,o5 [ 4]- 152 ,ft/8 = -/5~ .o33 -+153.f3qr, = o.O v v 1-/oi., , Q 1 0'5'5)5~ 1 01~:::;. "/o 0;02$

:::::t_ --

t-A.-..)"~tl.r.,.;" -b:;,..,,_,,..,.,. I.A.:;j"" ... u"' :;j.._r d~ii'+,r,-11~1<'.rc Ae.Jnet::

q.,;k..,efe,.; ~J, vP.-;1/r,

_j ";,__~ ~- 11 ,'7777""

J" I '1- --' -!tv Vv

v..,v cltr ... s.-( U-tv.ttf") ,,,,tjl'\( t '-t;;/"'-ML~.,-; [b;,;-,.,.; ...,]

lf Q4ts-l '< ..... [ ,, ,.. ... J

6~pu po2.;CJ"""' c:k ... ue....,\~ ... : Hif'n.i-k>•i~ "i>+or-40!.- o•r- e..+1c.~ ol ... ..- ... "- '""'"'.i"'~t c;,o~..,(e.,.;_,.;...,

G?+k_;':"~l:. ha-li .... d... 6::.f"'P'"..2-t:r""' d~.._l,:..l,....,.\.,.,~"'._d~ lo.'r

JeJitol..t,'-1.. cJokh•r, A"'~~'<- ;;2-o~~+.~ .a..}-..) .s..~+-...._...L_

l"e...a"'t ~;~..._LS•'"~~ ""e...::;~- se..le-. ~>\t- -\~ ~\"f ~~ ~

.St f•r 'Ol..l-J ... ""'-'-~ 't-'<o -c \.lo :. '1-lo = '() Uz.1lo.r, 'P::,...-. J;.~

1V1 M 1 X , + M 2 Y-2 -+ - - --+-~""-'\"" X' n N ==- ;...1, x, + 1--iz.. 'tfz. ...,. - - --+- N"" XV~

V ~ \.}, )( 1 -t Vz Yz. -f _ - -+ V"" X'.., ol.......-.

6;:.'~"-l'.l; k c::k"t...l<t~lu;

MJ......t,v

~b

~--> I J Ul.>

'11-Jb t)1114,-"'"""\J

e:I. t-..1 -EA v

=-GA1

+• .....

vir -1!..<"~ \ 't T.,_or~-~--t? c.S<:.r-

s Mi .M ...1> +- fr..t.- 1J ~ + (\I:.V.~ = E.I € A j ' G-.A I 1. "b + e'ltaUca. + tt" .v'" +

MQ (p"" ~ j t

1-'1 ,....J,N """" !>~~rp•l-~l..>r"' d~~I.J,,...I~i.'~~l ~ --U d? b ...... ~,:"' 'i}: u ... r--.... k ... a,Q k d~~IL1 ...... cr~~da.., J::.~,,<,...:'-0'-

s;.,. x1 -+ b~2 X2 4-- -- + bt.., x.., ~ $;G

P:. ... -l.o~t...te_, { ~I I V\ j.,;"" cJ""'? I I I ..-ya.

f,,, '1.1 -+ b,.l X2 + + 6~"1 x.., 8 6-ict J "'''" "'"'""' 62.1 x, + bn 'It + - - -+ b2"l Y.., = 624 d.._~ lL-tLv:

I

6J4 s.,·-i :>Ct +~n-a.Xt. -t- - - -+ -o .. .., "'"" .....

~t~ o/e .. ld.-...,"t:::ll.,f..,., .... ,"' d-,.,.,. ·.;"''-L h~.)c.pl ...... .c., k...+(J''""'

'l:>rcr •, Y[ =I a~ld.t-<Ji"''~ol!' 1&-; o.J? bvJ-eT ve "'-4<)¥\~t-

1 ~"'4J27 ..._\,. .. ,_,, \::rf"''j' ;-1'-t,r,

~; c, ~ - 2 c. tt . q )

~,· ·. c:t'~l{.,.,_ -l-j~ ... t-+-J ... "\.1...

( £ Q 1._ J er- '"I '~ '-'-"-" .f I

?.,...._t{o \ .

~r·', ;..::.r e l...l :t:~ ok-. "-.C-.... ( 1 .... ;

I

Yot::.. J/ .?. -;-;

~

"" Eie- ..:J1 = '25Goo [ 1 x 0 .001 -0./2.5 ~ o.C>OS J = 9. Go

ET, .J.. .. 256oo [ - h o.Oo3] = -76. 8

G. f7 X1 _ 13 'X~ ..,. 9.6o

-/3 'X1 ..j. 102. X-z. -- 76. B

X1.:-o.os

/..2.=.-07

tv\~ DOS M1 ~ 0.76M2. -t2.26

;)-----4 ---,

JCrml?vL + ,

(M)

1.5 (- '2• o.os- O. t;;,. o.os 2 .Z6 •' + 2 .26 x zwo.s) [ -:aJ 6

= - 0 .21 +'9.8~ 9.::.--.!J

HiPEt<STAIIK .6.SIElv1LE.IWt YEmEGqtieML._I-:(~1

~~~~fc... :::>i~h:mkrclc. -.!::Jerclg~4rme he.s-ob i9n , iz~nl:. .$;.1-er,Jierdc.

oldtJv 8 ,.;,; , v...n'Jd i§. ~ore~"Y~i,.,den _y~-.n'ti· ~ Bunun iEin ._yud~!F~firrresi

at&n~ not.J:y<il , oSYaVlOlVl ~.Ji~hrme deJ;~I-Iwvnda birim ~ll~m1f .!::lf''la~ l:. viHtcJ i ;! feo~i '&!}ulsww.

r

( v·,r}Let ~e1Lc:i§~~·mt. du~u)

hpf:rs~.sf-,lc. si~em

M,N,T ke..5i{ ZDrlO>rJ ,

~il ckoi~•~·=mntler, M. ~ , ..6,:J.5 = !:!. .6.v' T c/..5 E!. ~ £F 'd.5 = <5F' - v -

teor enJ

,, ';:_ ,l 7 H , IJ. r

, JJ -:;J_, .... •.

c'='

el:!t. ed; l;r U:o:ms v~ l:~rn~

td-rml~r s 1 ~,. c5ll''l<ll91: r=- - --. ··-- ---, !C,m=JR"-'ids ' L-· ------~-·

(rn)

( .!:JGI:.Rmr:. durJmu )

birim _yWerrre.

;;:;;,;::;-_.:;=-

I •

~

Qlu-.18£:..

'I.e.. ... :,#.., ~ ~1 < ""de,... ,· ... .t~.., "'")"'~~ 4r.

13 o\ ... ~.,.., t->'l d;,::~ , ~i1-~""""~ Or3~

I

e1--"" t;;4oo -~:...,.t. ....,.._ _"'/loco '

' 4"-" ~--

-v o,s.._ )L y

Eic.. 4£! ~ 25,oo -~::;._1-

E l" 2) ,, -:: ,,,?--xz. Elc G~:z. - {~ -- :::

o.5 E1-c:. 0::2z_ """'

A o.2_

E lc ~~ ct :::: 2 5 bOo [ -1 " _L -1 " rooo - 8 E 1c G.z4 - 256co [ - ~ .,. o, 00 ~ J

0 , 005 J = 9, bO

-7b,6

b J1 x1 - 13 ""-.2 - ( S,6o) = o

- 1 3 )(1 +102 >fz. -(-1',8)=0 '>l, = -o. D42 '11 2. ==--o,t- 58

H = -o .o42 .)<. 4 - o,158 X2. o-o4'2.

~...,t,J \ ~ . 5 .( -2• ~"' o.-o42. ~ i .. 2,2.53 -.o, 5" "- o,o'f2. -+ 2 <E o,S-o< " .253 ).[z J b + _L J., o,s 12 .. 2,2S3 -j-2,2:,.¥) L-0 - 8,bD = -5,1-4-5 -t- S,tt-:;. -O.OD5

E.·""t 0 · oo.S o1 0 c:: hQt.o;> = ::: /0 0 ' -"'

5,H25

- t • 5, 3 ( 0,042 .f- Z.,. 2,ZS3) ~)J - ~ • ~[ 2,273 4- 2t 21'1] [Aj- j- .j .. '3,2,2lt- [!!)

- {- =u.l~) ::: - "}t,,-::; 1 + 7&,8 = o.o3

SORU 1: OI~U ve yUkleme durumu ~ekilde verilen ta~ryrcr sistemi KUWET 25p yontemi ile ~ozerek

2 t/m ~

18) E noktasrnrn yatay yer degi~tirmesini bulunuz.

21 Gerekli kontrolleri yaprnrz

4m ~I

t f.-6-s. (.My~"' +o,~-;t Dt 2S e

:Ic;. :f.:t

4m E = 200 000 kg /cm2 I = 40 dm"

Ere. &ro=-~ .s.~.4.r.zj + ~. s .. f. 4.'[2] + ~. 4.·( 8. [3]= S4.'b1-

E!c. ~~~ ~ ~ .S.•L..f. [.2J -r 4.1.1. 1:.3] c::. 15,333

-4·0 X\ = - ato = _ S4.,G.]. ~ /\

~Jil 15/3~ _...; - 11- ~

X, -::. - 3. S65 t""

\-liP· ~i. ~ f'Y1:..

.elc.~"'::::.-! .s.•.(lti-.2"1,·%">) L.U

+ :t· S. ~ · 4 (l) -t-1. It.~ f3,~S+.4•4.1S:». =- 18,SS3- 16,SS .::. 0. 00~ f'L 1 ": I'"".-;;-- 'f L...--

&! .. .2.•1o' •'to"'O'f =-6000 + ... ~

' - /

1/ b t t 1/b + {/g

.Ic.:(,I

Eic. bll::::. ...1- ,.G1'32.5 ~ 1 .. --1"" [3] + .::L . 6· -1 .1 [2j = 1A. b5t5

-3 :3

El-=- ~''2.=--4-· G, 325 .,.~ (2 ... ~+4) [3J =-so,e:,

i.e.s. hlp.~:l.

Elc.. 'i,22 ;:::. 1-· 4 ·4·4· D:.J T i . bt'325~ (2>'-~J.Y -r2-~o4·4;, t2~.£]8J+ ~- (, ,,b,\JJ

Eic.~to= j__ (, 1 '32.5~ ~2"14-1 * [3] +;i. .g .1""lb · [2.J.::o123~ b 3

E:Lc... b2o;::: - ~ ·4· 4. ~2 [bJ- ~- G,325·d2 .(2.~4+t:,) [3J ~- 515,3

[11. (;')6 -50r6] \ l<t]-+ \123 1 2~3] -50 rh 82~,1- L X2. L -5'15,.:)

><'t=- -+,fS4g X2 = 0 1 f>26

3,3o'8

£!c... b--t = j_. G1325. 1 ~ ( ~,466•2"' l(,bf(,) [3]-~ .i . 8-1 "''f,6y_E3 l:2.J b 3

-+ ...i..8.1-< 1(, [2] =- 65, 3214+ 8'5,3333 :=0.0-115 .3

rol=+i.f. h=-l.., = 85,3333- ~5,321(/ =- O,OODILf ~ 8'5, 3'6t3 Oft) C).D14

nc 2)2::;::- ~ A·ft-""5,4f58 [f.]- ~. c,,~z5(2"'4"'3,~e€5-i*·H,r,tc.+G" '3,fJS6 + .1._, 6. (, .'3,1(,& [3J - 2"-b"-'11,(,16) [_..3]

3 -= 303,33(,- 3o3J,/ b = o 126

ro t~+ r;f ha-l-= ~ 3o3,33(, - 3o3r61 b =

3o3 1 4'fC. 0,000<32...

0/o 0, 0.9

I.e .s. -te.. 1-Jip. b: I.

1(,.0

n::::..-1° h:p ol""" .sjyte 1011~ c;.o .1 ·u"' -u "'<Z. .e. .s= > l . 12. • .s. ve. h\p b: li""' ""'~..,le_,-

v.e.- ?(~=-,.f rc.,;"' ~cr..-i"""

~~lc.,le,"'~ cl~"""Q.f'"'""''o...-· 1 ?<-1::.. 1\e.r o:k_ s;.)-k, ... ;l""~fl~"'.

He. f>~~ = .1...,. 6.,.-1 "'~ .. L 3] .3

-+ ~. s(2" 1 .. ~+2*>1"0,{:.+2~>0rl)r3]

+ ~ . bA 01 (,.-:0,G r. [~J::: ~~,2~

Elc blo:=- - j_ .BA- ~b-"~* [3] ..3

-t i... . 8 "" 1 c, ,.... ~ " [ 3] 3

-t f .r:;,.16 (-i+2~o,c;) [3]

+..:L.~.1Q.O,{,. [2] .3

4 j_. ro .. s~o,{,. [ 2J 3

f1c&10 ::=: -1b3,B

+ ~t OIO+f>tt·Xt=V

x,-:::. - z,,"' :;:.. -~,; g,s '4 -I:Nt ~II 1'312~ • •

.5\'i pu p=>2lt:J"' "'\ o

1flo 'VA = G:.+ 1fe,. X1 = 4,~3{, t:. f

'-'fb= 13-.2-.ax1 = 141'315 t- 1' 4o

"~= 5 +_i_. x, ""- 6,~ 4-9 t 1' lo

l-le..:=-4-t: -- ~

2-0

,, ~IP . 11u'fulcluie. \C:o1-.. ne.~w :

~Ic_ ~~ :=:-~ • g. ·1..~1 514 "[3]

-t- ~. 6. -1 ... "b . [3]

-t ~ - 5(~8.514"~ -6,'514-~0/(, +12 1 8~2~ ~ +2"' \2tBS2~o,£) ['3]

-t .i. . e ... of b- 12, e 52 .. l2 J 3

+ j_. c,~ s.-,o, 6 ,._ l:2J 3

= 251,441- -25l,'iS3=--o.ool.2

I. h := "'10 0.0025 .........-

D - ~ . ~of'\{. 2X-== o 2 'i=o

~MI:=:o

l " -1 ~lc_ a£ = 3 . e:,,.. t2,8S'2"'2tv.,.[2J

-+ ~. bt' <3~2,4 ... [2J

+ 1- s ... 214 te·5'4 -t2,.1Zt6<S9 D] == 313,'163

SORU 1: Olc;ru ve yUkleme duru;;;j~~kild;~erire~ ~~~t~~- KUWET - ·l 35p · · 3 t yontemi lie c;rozerek

2 tim . 2 t tllll!lllllllllllllll .. ~:-······· · · · 31 o····, ...... 3,

~ ~ 8

21

A

I• 6m =-IJ~I

0 H E ·)lo-

c...o

1A) M,V,N diyagramlanm c;riziniz.

18) E noktasmm yatay yer degi~tirmesini bulunuz.

Gerekli kontrolleri yapm1z

E = 200 000 kg /cm2 I= 40 dm4

+ (

b~ ;18, b2(, ~I

I ~

I I

I

M ~~ ::::. o, 0023.., "

i

'o~ ::::.0,233 C"1 ( .-!-) I

SORU 1: OI9U ve yUkleme durumu ~ekilde verilen ta~1y1c1 sistemi KUVVET 30p 4 t yontemi ile 9ozerek

4m

6m

:r c. == (, :r .5 ~c:, e.-e.""" .

1A) M diyagramm1 9iziniz.

1 B) E noktasmm yatay yer degi~tirmesini bulunuz.

Gerekli kontrolleri yapm1z

E = 200 000 kg /cm2 I= 40 dm4

E:Ic... b ,, :=. {,. 1 . ~ . [ 3] + 4-. b . . ~ .-1 "'L2J ... 2 2

.E:Ic. bo :=. ..i-.2.4i(-i [3]-+ 4. 4~1 [3Jt1-·b·12.<..{.{_2j :;.

- -5-· 6. go(~ (2] = 12

'!(, = - -:r-z_ ;;= -3,2 :t-3 +vn_ - ,\. e.n:t 22 ).\ir· B~. ~.,-~;-. £lc.6,=1..2.1 (3t2:t1-0,1Z~t ~ + 41l140,"f21-. (3] -t 4. b. 5,.12~1(~ [2] ~

_ 1· b. 9 ,.;(<( [zJ;;: Lt~,t.32-~~.b36::: o.oo.b

!!> 1t " -~ ~-..---------, -"'' ~1 ""2"'lo ... 4o .... lO .,_ 8ooo + f(\'1..

(Mf § ~ ;::.-l~,t-4?. ;:o,ooos E. (, .. Bro,

.Lf,?45t . \~E'::::. o,o~ ~;;q M Elc.6~ == ..... j_.4.0.1·21 ·-A [3]

:;.. + i. 2. f-'2o<.(,,.3,2:f3 -4 ot:r2t3 +0,12-t< b

-t 2.,.o,12.:t ~ Lt]PJ == 24/1-42

(

2t(...,

c. .3"!. - -~

:r. 41\'\.

E>

7f .3"'~ sV\1

I<' 1\

5

8

.Iea 61

~~,~~4.o::t·5·5·S·t"'J-t!·S(2•8 .. S-t-2,.81l5•2•~S).t3] ; ~26,332>

El~~to:::..-~ • s.S.2S[ZJ- ~ .5(2•8•5S-t5S<t-So~- 1~.t-6+2•5·11~)l3] = -4oS5

~lc. ~-\:: _i..- s. 5+-2,6315 t2] u

-t ~ .s. 5" bt25 .. [2J

~ ~ • 5-~2o~lo,ql.•6• 10,4, .. 5

.. e,13~s .. 6 t2"&sm•s) [3J

t,k ~~ =- 0 ·OC.lfiE> ~ 0 V

M

£.1c2>~~ ..i. . .3·3•b [.zJ +.i..s.3 (2•S,831s-lo.~6\[J] .3 6 !I

.... ~0,412.5

t: :::0 1 .... c/ i/rrf.

!.:: -{ 0 d. •. ./t

EI:::. 2 ·•10b ... Ot0010: 2000 tM1...

" ~ E ,;;. 0,00 1-5 ""

A E.

I

f=.

C' , 2 f' 4 ,..,

;t

4t "'t f . "" ! I ~ •VV\ '(1<- 'l '?.d.: \..k._

sb's.k.-;\ ""~~ttY", Srri'M, ,,(__ .SI f· ,-.

C}::_Ul€Mt_tU£.. c;>.~t

..::l.::t... vt- ~~~keVI 4u: •. de~; .l"c_,. (;1:. ~v;it ...... ,·,.i:r,

E:Ie..6w::::- .i... s .. dQ .. (jJ 3

- t · 3.,-i .. IS ... [$]

_ J.... 6. {, ... ~ .. tzJ 6

+ ~ . (.,(lo5)d2.._~.(U

I=k. blo =--~fJT

fTc. S11 ,_ J___~ . >1 . A . C:a}+J.U~J :3

o~..L . $.L~ L3J= -18 3

Ou•t-\t.\i 1:4 dt.M_l.\t.""":V....d.a I

h:P . ""; ' ; "'""'\::r-~ 61o-\- f>ll x, .:=() x,.:::- bla

~~~

x, =- -- ~41--- BA61: t""' tB

~pt.rfo~;~,j<>-"1"'- I

M ~t-Ao+- ')(\ M I e ldt. ~Jitir, I .,._ ~~~\\: kuu-'d\ dl-::f G.lj?;.,..,lo,, : (S-e.'<ilft...-da_ '-f~,...i(~.v.(~~~"', I

1 •

--

K.S.b. 1-l:p . ~tf\tl::~ h·-d:.

Elc. ~" =- S · s . 13,&33 1 . t3J

t ~ . 3 . 1 ..(_-!3,8.33 -t 8,16})· DJ

+ ~ . (,. 1.(2~,161-') · [~

-t 1· b .(~.s) ... \2~.., [2J

=-o.ooooD45 @.oo(,)

f.lc. ~, ~ 0 v b~ :xr cl£,gr,:-+ro."q·, lc,r"

£Ic. s" ..f t> ~ 3

.s . .S/633"'3 ... Ll]

- ~ ._).~~~A118~-18,Hif)l3J

'

I -

... ~ . .... = ...... ~ , . ..;_,_

r.-T ·-- l/800 •ou

6"' 4"' 4"" "'o.sCJ\'1 _,. ___ .:::.._ __ ~-------- ,_ --- . -- - +-

[2)

[6]

; :.;,5T41 i l<' <;jA~

.Si .Y7'iYI v t;

[3]

Hi~I?STAotK B • LiN~\e~Nt'tR

0 -5

\ 1IB_t_

1~-0WS ~~-1/6 N1 ~

-3.0

+ 1.025

E l c S"= _'_,s,to.5>2[3J +..!....G.(f /, I2] +..!...·4· ( 2 , f 2 + 2. f .o.5 + 2..to.5/) \.2] = 9. 917-

3 3 6

EJ, Sn= .!.. 3 . <.-3 )2

[6]+ ~ .5 - <i - 5/UJ +i...4-. <1 5 )~[2J = 71 . 25 3 3 3

E1, S12= _f_ • 5 ~ 1.5, o.s' [ 3] + l... 4 .1.5. ( 2. OS + 1) L2 J = 1- . ~ 5 3 6

9.91'1

i .?50

7. 750 ]

71 250

-- "' - - "> : Lc r oJ d < ~ <- [ N ' ':l c ) = ~ .- O rt =- :: ... c: ' - d ) ~ - t. ... .,. - .... \,. J 1. ..;

E Ic 62t =- 4e;. i o4 , 10- ~~ I ..2.2_ ( ~ ~ (- 3 ) . 3) + ~ ( ..!. .i .s- • 4) + 1 5" ( ~. 1.5. 5) + l o.s 2 o.B 2 o 5 2

+20 ( 1.6+1•4+~ - 025-5)] =1614

L ~ J ix j + L St) "' o 9 917 X 1 + 7 .750 X 2- + f 36 = 0

? .?50 '>< 1 + :f1.25o ><2 + f 6.!4~0

'><1= _50 .?4

><;;~-1+ . 13

10.213

'Cl.4G -D-061

- 11.13 T+

1) [=..:;1 MH.d'S =.!_.f,.1.(-5o . 74)I2J+.L•4•(2..1.(-50 .?4-)+~•(-51.C65) + T J , I ' 3 · 6

+ ( -50 -74)•0-5 .. 2. 0.5·(-51.,:)65)) [~J +.i.... 5•'D.5. (-51 .-065).[3].,;; ...:~35.93 3

:\ \

L '

[h)jMM1ds +ficbft•O -,.. -635.93+636:0.011 rh: 0/o0.DH I

_/- J) MM 2 ds =td· l -3).(51 .39).[6] + {-·4~1 . 5•(-50 ·74-2~51 - 065').[2] +

+ ..L. 5- i .5• (-51 .065). [3] =-1613.?5 3

_(6i3 .?S + fG\4 = 0 .2 5

,,

::.1 3

= == :~ - ::~ .. ~ ~--: / . ::..:.~ -~ -- ...- ... :.. .2__ ) = _ 20 24 5

E1c J"::2 .. 48·-1C"i. ( [.;.00 3· 1 + r.... .Ci0S.c- 375_ o.oo2.. o .3=t5_ 3._i_)= 180 f3CJ)

-4.362

7'.41? XI + 1 .?50X2 =- 20

? .?so x. + ?i 25o X 2 == 1eo

X 1= -4 .362

X 2 : 3.000

'f)[:'] ( MMfdS= ..!...<=>.1·(-4.36 2).[2]+.!.....4.(2.~.(-4·362)+1.2.319+ 1 J 3 c;

+ D.S• L -4.362)•:?.05·:< 31'7 ) ~2] tl_.s.o.s.:? . '.W1.[3J:-2o . 01 3

rhk-:>/<>0,05'

2 ) [lc J ( Ml'- 1odS"' ~-2 •( -3 ) .(.-'1 ) .[6] -t..!...·4•f .5. (-4·3E.2+2•'2 .319).(2J + I ) ~ 3 "-

+ .2_ . 5'·1 · 5 · 2 .3 ~g. I3J-= 1119 .94 3

[j'] ~ M M2 c:ts=~Ic:t; __,. n '1 .94--18o=-D.u6

Tablo 2

Car p 1m Tablosu (f0L Mi · MK·dx)

kr=Jk ...::::::::::J k k1 c:::::J k 2 2J::skm 2" y

221k 2::Jk L l L L L y l

iy; L i k 1 Lik -fl i ( k,. k 21 _L L i k .1... L i k ..!.. L i k T 3 m 3 3

...::::::::::J; 1

...!... L i k 2

...!.. L i k 3

+ L i ( k, • 2 k21 1 L . T I k,., ;2

L i k .!.. Lik 4

i c::r=-- .!... Lik ...!.. L i k + L i ( 2 k1 • k2l 1 . ..!.. l ·i k 1 . ..

2 6 T L 1 km 4 1f l I k

i1c:::J i2 1 .. 1 . . ) +L!2i 1 k 1 •i 1 ~· 1 .. I 1 ( . . ) 1 . . )

TLI11 •1 2 lk 6 L ( 11 • 21 2 k 3l(11 +12 km 12l 31t •512 k U L (It • ~~2 k l • ;2 k, • 2 il kl)

~im 2 l . , . + Lim ( k, • kz) 8 L . 7 . k 1 l . l

3 lmk JL lmk lS 1mkm lS L lm S 'mk

y .2::::J i ]_ L i k .i_ Lik l..Li l3k,•5kzl 7 l . J... L i k .l. Lik

l 3 12 12 lS I km 15 10

'( t .l..Lik ...!.. L i k 1~ L i ( 5 ~~ • 3 k21 1~ l i k,., .!.!_ l I k ~5 L i k i~

l 3 4 30

_2j· ..l ..L l i k 112

L i ( k1 • 3 k21 T L i km .l l . k .1.. l i k '( I Lik l 3 4 10 I 5

t:::s.( i y _!_ L i k _j_ Lik ,; L i ( 3k1 • k2 l ..!.. l . k .l..lik ..!.... L i k L 3 12 5 I m 15 30

~ ..!.. l i k l..L(1oo<)jk .Lti n1·~, k,.

~L(1·«~li k,., 1.. L 1 5-p-,;1; k j_ l (1 ool +J)j k 6

ffl 2 6 • ( 1 • +< I k2] 12 12

LtS. l~~tli

Y yazll1 u'larda L. paraboluniin teget1 yatayd1r.

k

~ 1 . T L-lk

, ) . 6"LI1+ot tk

· +Ll1•flik

..!.. L k U 1 •I' I i1 • 6 •(1++<li2]

tl (1•.c,J)imk

1 ( 2) . "12L5-)I-)Itk

....!.u5-.. -«21i k

12

...!... z 1. I U1•«•• 1kl

12 .

..!.. Ll1•.'•7"2l i k

12 .

..L L i k 3

.1[2- (o<-J ~}i k 6 <>(~

<><)'5

... "' ..,

{ ?24:-lm

l

0 ,.:

2l + .2! 4'1

A e, (t--1~) 1'I771T

"' 2""" ltM t 1/4 T"t'"'

(1 v ... 1 / ~ 11

:rc.= G:L €Icfm:::::..i..5:~.~ [2.]+ 1,.4 ... ~.c [~]~24,~33

.3 clc. bto -=- t· s . .Lf·d .c [2] t -k· 5. 4 .,d ... [z] + 1- ·14 144( t • [3] :=.IS3;·,, t-

?{I = -I '5 ~ ( G ~ T I 2 4 , ~ ;,~ = - b I 31 '5 t n.L .........

-1t IC.oAtto\ ~ E:lc bt :::= - j_ · 5. ~ "l4+ 2.~C.,)I':>) uJ b

+ ~ . s. 1 "q UJ -t i .1 "~ t_q..c.ss-- '-·)'~] C-8 -= -21 ·tl'1 + 21.116'!:,"" Q.ODI1 rh ... (,11(0~ ~

N 1-1 -{ ( ) ' E-lc. b(. """?:· 1-"'+" -b(~t5-+2.··:~&35 ..~-[>J ::::::2.21 ,g415 .. ..

~E~ = 3c,,~15j E1

r · }

2tfWJ

c. .:n --i

:r. 4nl.

.3"'~

Lt .s. vt.. Hip .!.!.; (. t 7~

s""~ XI It' )I

8 (M4)

.J:ea6l

~1,~4fs-3-·5·5·S·t'J-+! ·5(2•8-e+ 2 .. Sil5•2·~S).tl] = ";J28,3:):,

El~E,I0~-1; · s.S.Z5[2J -1·5(2a8•SS -tSS•S+ 1~-.g+2•S•.t!)tl] = --4oS.5

"?.26r3l3 • )(I - ..l,o:>~ =0

I

I , i

flc. ~":::: ..i. . s. ~.-2,6'31'5 t2J V .I

-t 1-·5· S" bt2S " ( 2J

"i ~ • 5+2<~1o,ft~•6•'0.4,•5 • e,IHS,. 6 t2<~&8?1S"''>) tlJ

(1"1) tM. €k br =~o . oo~lb ~ o v

( ~

,I I )

M

f1c. &~: .i.. 3· 3• b [.2J + .i. 5. 3 ( 2~8,8315 -to,~~ [3] 3 6

.. so,H2.S

'J El ~~ ~ 15,0161-5

e ... 2 4.•tl t/rtf.

!~ -iO dt~~t4

e.r::. 2 -.to" .. o,oolo =- 2ooo t M.,_

" ae ~ o,oo 1-5..,

\ b~ ~ oas:. c-..l

A B

( ) d)

) · 1-flb 11/g

"l z.20~t 11'3r51t-

0L4'J ve.._u.:.k.le..,e_ durv.., fe.k; l...k ve..r;\~.., ~j'c.

S 1~-k-,.; l((llN€1 ':;.)~""~ lle.. <f~2£r~

4 m .;1JlCr \cuv.Je..+ (~ v N)

Ic..~b'I

' fJc_ f,ll = .i...c,.1 . ~ [2] + .1..8,3(32 . ~.-f [iJ ..3 ..3

;::: 9>,568

E:Ic..£1o ~_1_.6 , (-f,5).~.('12. [2] 6

- b. 8,362 1( 1 ... 6i2J ..,. 4-· 8,3g2 .. 4 "''" L,2.] :::.103,052.

><t:::. _ ~ =--to3p'52 =-to,t.:e: &11 9,586

fic.. ~I ::= 12S,qoZ5-125, L,o29 =0 .......-

Ill

J;; ~

I )

13,'51 ~

2P 2.zo'3 8·2.61

•1ok-\a_~'-""-1 Sf1 ,j.,-\:<:-; -{'-'' "~S;.;r t ;, .,,,- .~; .. ,~ 1_,.;1" •. ,, '' .

Eic_ 'S~ ==- ..L. 8/~82 .. 4 "(to.'-7C,.6+2~ b) t-

6 ...,_i _ 8,362•db1<-4 [ 2J

J

( ~) + ~ . 4. 4. 8 [3] ;= 6 '9,311

(tv1 t)

l::.oi--\.1 eo L '

~,:: -11 t_552 l---7) er

E:::. 2-~<loG +/""'L. -:r = 2G. .,) ""'t

f'IL S-t ~ - _i_. 6- 1.G,68fL2]- S.. g,3e2 ... 1~6,bb~ [z}-t -bi-l 1 l0:26 3 . 3

fie. b( = 0 v-·

2t/m flllllllll!llllllllllt

2t~~==~~~~~~E

A 8

8 m )lol

d)

Ole+ u ve_ 0 ;:.lc_ le"" e_ durv»~y

;;e_k_; \.J.e. Ve..-;\e..__, +""t~ILI

S r~+e..........: ICuouEr -:::><>.,..,+e""'; l \e.. <fo2ertZ-lc_

d.) I c; \cuv "~ + ( H 'V f'l)

flc. ~~~ = .1...(, .11 [2] + j_.8,Y52 .U [zJ 3 3

IO,'f~ _.,

' ' v':o I ~

1 2. 2o_:'!t T'3·'-''t-

:::: S 15B8

E:Ic..Sto :=oi.b.(1,5).1*-12. [2] 6

- 1· 81362" 1 ... 6 1. 2]

-t ~, g,382_. -f 14 !b [ZJ =- 103,052

><:, = _ ~ :=._lo3p'52 ~-lo,t-:E:' S 11 s,58e>

flc.. ~~ = 12514025-125. 4o29 ==-0 .__.....

MAe.

( ~r-A =-----------=-~=--L-~---==+===--1;~ ~ r---Qq.= 0

~u bu3 u ~CO>* ~ bre.}~ -t~r~ u.;."' "'(. ~ dC>..-.du ... e.~ l'V\o"""C!""'tle..- po2..~tl f+i .... ,

\\I

t

Ill

6A;:.. 9Ao +9AI + 9A2.

66-::.. 9so -t G_.s, -+ 9a.2..

! ;

9A:: ___!::_ (- 2 MAe -t Mo11.) -+ A.o 6e~ ei

66:. ~(MAe, _ 2f.11b.A ) -f- i:>o 6'E:C. E.I.

+ lv1A5

+ M6A, = 6 ~! ( BA - ~)

-L.M&A-= r;.er: (e 8 _ f3o)

; k.:

L 'el-

b E~ ( .2. 9A -reB) -2 ~ (2 GA -r 813) -t

12 ,Ao -t b BQ

L

4 Ao +.2.13o

'-==- 4 Ao -f 2 6o

L

Cf6=-- Be,

MAe = I<. ( 2 t(:>A -t- f 6) + M~

M Jl>A ==- k:. ( ¥=>A -+2 {pg ) + M 16A

; c, ;'?

k.

L

AI k.

f?'\A&

c.) ~ir u,

~& M!!A.

tv1A&~ k.(2lfA~~&)-t~

M15A = k ( ~A-t2 ~IS) -t M!,A

<fe, = 0

ty1 A6 ~ k_ ( 2 ~A)+ \---1A..!!.

MlbA = k.. ~A-+ H~

e (oJ+i'<- 01'\k..,..l-irc..) .J~r uc, m-~-1(,

~ k= o,;zs k 8

~;4 t--.'1 A e. B;'r u-=,

0.., icP.>+ rc.. d ~,... \.l C.,

(Y\~( l1 $\).-te-L o.';" L 0 1'\ '£.o>tt"~lll.. ("C.C.IL.l'i'-fo"' \... r I

,;;:.. t \ 1'\.d •J I -\.:;:. 1£. -1; ,r-1.-

~ j-l4 1-k.)c.p lc.rc.L- ~ 5 :::::. 0

0 \ 1 ""c:> ~ r,.-. ( ~e, -:{=. 0 )

(Goer~ e.-"-.~)

c..~ ~ Q..u ~ c..g 12- ,.11 f!) 'i'l ==; r C ) ~-> )

?crJ ., -("> ~ ?t ,... c. c. " ~ ('S

~ " " .!'> -- c 5 ...) ,< c. '0 j \) ~ "'

Q... \!: .P ll ~ -~ C - CJ cJ, ~ u -f' ;:--~-~ ~ N ~ ~ ~ , ~ ' ~ )

IT . ~' - <:-r t r s ~ ,0 f ( I' c ~ ~- --

l--· ( c.\)";J\

,- -r - o· + v ,..... c ~,

~ c. p " > ~~ ' ~~ ~, c FQ_ ~ "'> " c \I 0 ' \' '--;))

~ j (' F(> ~ ' { ( ,.. \ ~ r.- ~ ~ cl L f;r-f tc_c j)t

r-:"/ F' ~ '---> ( -

()1"'"~ cJ' ~ ~ r f-r ~ r' 5 5 ~ I\

~ ~ r. P-~ 1"1 -tl . \} ,R... ~ ~ 4! f ( J \! r-l + J ~ ~ ~ f ~ ~

f + :, Fl

r•

~ ~

f ~

~ M fd ! ~ Q._ .} q

~

\1 l -€" 0 ..:s .:s ~ -+ I" t

1: v

N ~ K' """ 0

;> ) (tr"" (<_ c ~' p d \) .... -6' CtJ ('> 0 ~ (", ) ~ 0

..!:- \.,.J

) )

(JI (t_ '§ \:;1 " ) (' Q_ f ~· ll II ,!"" ) ~ ~ N t- ~ <f 9 r\~ ! ~ 1'1 J I r-l

~ ;I " ~ ) 5 S- ,---.. - c- ~ - · \ '\ -l- r, - ' ll (\ .... c

o " r ..(' -- ~ :r -::-

:r:. I\ ) () I' v ~ ~ 0 0 ) ~

i) '?. ~

,. ) f"

"-.../

f b ) J ; + ~ g.. -~

r )' > ~ -

::r 1\ (..-

~ I

g_ Q_

~~ 3 ~ (\l ::-' ~ r "' f ~ }'

II'" ct' C...V I) ~

[ ) -1-, """ (,-

~ ~ c - , " I) t ) .> _.) c. lr r:> 3 ('~ 0 0 ~ () u ~ r " §". + ll ., ~ .-r \/' -+ .., ' ~ ll f } ~ ~ '-- ~ • ' 0 r,"( I ,- (\ o-~

0 o ) a ; > 5 ; ) 5 rt {\ > 0 f v , -- "J ~ \ ()-~::..

~ '4',~ )

II l)\ ~' -=-+~ ., ;J ,- ~ f t ' -. ~

"' \)

r il ~ ~

9 l'f'!t~ \l ~ f "!-"'

or

0 f f > 0

\..

r ' ~ t b

; ~t • If ( " ~ t / -~ -.

J"

~

~ CL-

c;,j I,

(

~

~ "> ~ ~ )Q_ -4 ' ~ ,... I)

r a

r]~ r-

12-\YI ~;'

' c ~J'

-; ~ >

~ " t "...__/

fL. .5 ;;-~) ~ 5 ~· {' I o --, ).., lJ 9-

) ~ - )

t (I' t ;-) ~ 5 I'

1 ~ ~ ~ " r ~ -s. ~ r f ~ 1' ~ 0 -r • t rr

<:. ~ tl> 5 '3 f 0 r ~

> 0- c. ~ ~ ~q -.

Q... -§' 0<

• J

~J ') t

\) - . I) - _,

]' f

ct q' .J j

Q.. Cl~~ ~ I :

;- J

u 5 -;:- 0 ~ ,.,. ; r

5

t E,

C'0( ~ v

I t Jy .:;J t-7{ 12-_,d! ~ y a.

~)

~ ~ i I> I\ t ~ .-~ ~

~~ ct) _s -'

~ ~ {. ~~ - rt 7

=- 0 - -.., c '-./ "

0 --i 11-

1-i,

-v

~ (Jl

~ )> s )'

" ~ ("'

C)~

hi -l

2

2

3

L,3

!.-:.,,_ n 1::::., p t 2

k.,1 ( o)

1

.3

k..,~

t>'IL I') 1-:...,1"'~ := k...., ~ ( 2 · <f fl -t- ~~ ) -t )-1("11

~V\2.:::. l:::V'\2.. (2- ~ +-lf2 ) -ttv1"''2.

M""3= ~3 (2 <f"' +if;,) -tNv13

JY'{ .,'t = k""~lt l2 ~.., -t- if4) -+ M., 4

d~.._)'<' -'\o\ -}u-;-...,..;

~~ +u;w,.;

ol., ~ 2 z k. .,_ ~

.S.., = .L M"'~

0..

b,;z_

n.. k.,.!>

it L,l

(b)

IV\ "' ~ c: 2 k..,,; . Cr, + M ,., '-I ( c.)

l"-1\" 'i = o (p~=O c~) k"S =- O

tvt e-j-,.., I ..I.~,__

w.:>-t.-~ o!d-r ... -d-.,

CARPIM TABLOSU I: Mi.Mk.ds !

k I I ......-:::::1 k k L:=:::..... k1 I J k2

L L L L

i I I L.i. k 1 1 1 2L.i. k 2L. i.k 2 L. i. (kt + k2 )

L

~i 1 1 1 1 2L.i.k JL.i.k 6L.i.k 6L. i. (kt + 2. k 2)

L

i1 [ lh 1 1 1 !.r( 2.it.kt+itk2 ) 2 L. i. (kt + k 2) 6

r. k . Cit+ 2. i2 ) 6 L. k . (2. it + i2 )

L 6 +i2 . kt + 2. i2 . k 2

20 im 2 1 1 1 r-1' 3L. i. km 3L. i. km 3L. i.km 3L. im: Ckt + kz) L

20 __,-1 i 1 1 1 1 3L.i.k 4 L. i. k 12

L. i. k 12

L. i . (kt + 3. k 2 ) y L

i~2° 1 1 1 1 3L. i. k 12 L. i. k 4L. i. k 12

L. i . (3 . kt + k 2)

L y

~ 1 1 1 .!:_ L . ( (1 + p). kt ) 2L. i. k 6r(i + a).k "6L(i + p). k 6 .l. +(1 + a).k2

I• a~l• ~l ~1

1

"-41 l>o~u"" ~'-~o~-,,..I.At, .s"'e.'T f,!ll nWl tJe"l ler ({> e. 1 'I) 0 '"~5 E'I. 4 ~~ ,,

bi'fO_ftMo \ Tu; o~V~ \a v-;

de.~2(o,cs+-..{)Er = .3E"I

ciD~2l1-r0•5·+<M5)u::o- 4,'? EJ:

~lcolt<4lll.._ \'•1o W\ eo~~~rr ;

Me,.o ::-MeG:=.- ~l=-.- S.oo-l"" 12. ~t t""'

Me,,a.:::.+b -Ot"'" E__Jf.

,Mc.e.,.-M~'"'- ~,-,3t...,._ -t., 8 g"t

~D~ = •5 l' . t )g .)sS~G. ~ .5

1(,

~·ul(. "{'t.ll.~M L 81,;'"

..S,e,"' 6 +.3 -.8 = 0

..St:> = 8 -5 = 4 'b~o;- ,...,.-._;,.?" d ..... ci be.u. 4.. .

3£:r (elb + e:r cf>p -t"O =o

El <fa. + lt.SG lf>n +4 ""' 0

<fo,._ o,'32 ¥:>t:~===- o,% e.:r e:J.

4w~<>ulz \.l, ""' <:>""'~"'-lle , ;

""e.t> ... t':t l2.tf>.e.+cf..~>)-s =- -s,32-t..,

M!)!l> "'E.-:1 l2~0+ lfe.)+S;:;;. ':f,40t .... t"'\

IY\c~::::. O.S-€.1 (o + lfe.)- 3 =- -2/~4 Moc.-::. o,se.:tl2~.,..o ) + .3 ::::- 2>,~2. t'""

~Pe .. ~.sf.l (.24'oto) + o ,... -o.%t...,

Mt>F .::Oo1St:l{_2.tfo-+o)- 5 ::::. - (,,tf.q t""-

'U:-..11~ \. z~- 0 L.--t,.o ;;;[ Me. = 0 v II" . C.. . D.

r 2+/"" ~ ~

z: 3J: A &I

2.I

c...

7 IC 6"" A'

AI ~ t---

H.'525

'--....!-

.2.t

1t

E

.3"" 3.., 2"" I rv )t

,_

- br1 t-(N)

~

'5r3 2.0 +

~II : <f>e. C{ul.>uk solo:1-tu-',

~A~::. 2~ ~ E:t b

k ~c. - 2 ~ = E:I. 4

ksb,. ]!__ 2~ ~ ,.o,st.:r ~ b '

..j;'f"'J'~a( +~v~ 1

d e, ,. 2 ( 1 + 1 + o ,s ) E1 :::. 5 EI

,A"' IL . 12-e..,.l.c_ .

HA.;=-1-'ft>.A:=. -~z::= -f, -1:.., 12

f~ t'o 4 ;f ~.lo•{,::.~I.2:S .A - 0 25t..., lb rv•B.D~ or

~;:.4 -+e.rj\.....,~

·· Se,.; 8 r2.'5tb::::. 2,2.·~;-h..,

D. N. bt:-u~. :tb'\t..,

5 EI <fe. .. 2 125 = 0

Cfe, ... +o,t.,5/El

CfuloLJI{ \JCj Mo ......

MA6 := 1::1 ( ~I:? )-b :::: -5, '5"5 -t...,

Me,A = Ell2~e.) fb:::: bt'3D t--.,

M5c.""' E1 (2~)~ 0,9 {-.....,

l-Ac. 0 ~ E '1 c ee~ > = o ,45t>.-, .' f ..

M f.2J!) ~ ot5 c1(2~1!>) -g,zs ::: -1,{3

t:D..,trol .~ L"X.~ Lf-==0 ;[)'11~

~· ,, .. :~ I ~-~) Uc~e,:::.- ~ ·b·~.('5,55+2Abt~) [2]

+ ..L.(.. c~.[2] +..1..c..~.(4,s).l5 . £ .3 (,.

• ~ ,(, .1 .(b+.Z.&1r6) .[3)= 0 V

SORU 2 : Ol9i.i ve yi.ikleme durumu ~ekilde verilen ta~JYICI sistemi A<;l 25p yontemi ile 96zerek

I2,Gt C t D

3i" "'" "'"" :

:I A

~ ~m "" ' ""

l

4m

Moment (M) diyagrammt

Not: Gerekli tum kontrolleri yapm1z.

!::>~::- "l<:>'c..~'"""'' s-~o:-tc:t,Jic:aJI(_ s~b:tte..,.:

,., .. , ~ .. Ov-.. {~r 1_ 1

.S~~ -4- f.,S ::: -3/S+....

b~t.. ~LI\lc.,

";€.t~E-),S~o tfE:::.~ E.!

4~hulc llc;.Mo..,,

Msb = o1~EI ( m -to)+4:4/3.~r"" HE~= <1,, E:t ( €1-t ")-1,5:-S,S

M~e • ••'~<I("~ili=6,3 .. Mes-:: tl. ({1)- A.o-\- .... ·~

rc.s.lt£:1 Met-=- -==-o.st""

SORU 2: 25p

r

\tit

OI~U ve yUkleme durumu ~ekilde verilen ta~1y1c1 sistemi ACI 1 t yontemi ile ~ozerek

4 f 'ffi I~ kuvvet {M,V,N) cWIIIIIII t11 Ullllllllll! F diyagramlanm ~iziniz.

31 .............• .... 21 ····'E1····· 21 2 m Not: Gerekli tUm

21

A

6m

;- ;-r--

l1i ~ l/1 -N" r+ t"f

'--::::;

i ~ kontrolleri yapm1z. 1,51

B mrr

)J ~I

~

~

J)i:.J::."" "'\'''k:.{c.IQ .. , s.:>\:.ft

e,;li"'-"'o<--"' ~D

<i.U6UI£.. SABITL.£_r'L·I

kc!) ... :2.-at.r .,_ £I b

- k!)A .. . -_ 2.,..21tl: ,_ ·f'I. • . 4

~t:>t_,..d_,2_.j_Q =0150 EI: ' 't b '

D r')'AGoNAL --rtl2.'r!Yl l_~r2.1

1-.55

-+

Ic.=bL

EI<~t> .. ~ . (, .(ir'>).r.1 .. 2H~J- .i . 6. ~ ( ~~2~13.~ rz_J

-+ j__. " .. 1.. 1'0 l)J - _1__ ~ b • -\ ( 2• fS,C.-t 3) [_'?J 3 '-

SORU 2 : Oh;U ve yUkleme durumu ~ekilde verilen ta~tytcl sistemi A<;l 25p yontemi ile c;ozerek

21

ic; kuvvet (M,V,N) diyagramlannt c;iziniz .

Not: Gerekli tUm kontrolleri yapmtz.

~~~~~~---6_m ____ ~~~~

b .N.' .5.:>\o: t:'

~:\;"'~~"' lfc.

c;u~?uk S"' l" ;l k~ ... . ~2'St

-4- l)o)r---L--

c;, ..J-w.. jt-/..,

)i"EJ{1 g,~+- 1 't-

14r'5 t

~ 8,5

(v/

kAC= 2 ~ -=-E 'I ~

kc. D := 2_ 2 E £!... ::: D15o £I ~ (,

t:>i.:J - s·-, ..... \ , ,; - ~·.

de. -;:.2 (1+o,"J)E.'l ~ 3 E.I

A f'\~. (\)r:,._., t:" I lo·; Jt c

lp ':!l ~ Mc.e,;:::. b t-..,

'3 3-\-l...," +IT) b+..,

f(l A.J ~J~Gz +~ T := 1'3,'5 ~Li) ";'-- \0,5

..:.~·~ -r .. v\. ~" '.'"' ' h

Sc.:= (,-to,s -.::. -Ltr'5

b . \-.1 0 4 . h."J' '- .\)e ... l.,la- :

"QE.I ~c. - ~ ,'5 = G

I'~ Ltr<;> 46 "t'C. === ?:E~ 0

l;u b ut, 11 < ,_( • ~ U 1 I ' \ ,:::>"-"( .,... ·\-14".~,

MeA.~ EJ. ( 2 <fc):::: 3 +M

KAc. :;:o. £.') ( <fc..) :::=- -1,'5 +""' Mc.D .:=. O,SEl\J~c)..:..lo,'?=- -5+"" ~o,,tr :> \ ,j

(~)+"" Zx=-o L'j.:=o .L"~,e.ro V___...

'Ic.=Z:I ~ol\tfo\.2 t.SI)

Erc.~A-=-4- · Lt · {(-3+-1,5)·~ .(:, .CJ3,5

+ 1·~.j (1 ... '5+(,) = J:l.-2-:f. = O ~~

j.:,~<_ \u'1M~

s (. 0:::. "- 3 == .::, {:..., .

b.N.. D . t::>.

::;,g ~l (pc. +.3 == 0

~c.::: - 2.-- = - o,?B /£I :!>I 8e.1

4ubu't. L111 Ho...,. e .... +LL.v; t. ...

M ce,-::: c,(.eil2 C,.c.) +b.=: s.o?3

M c.~.:: El l '2 vc.)- 3>:; -lj .515i"'

M E; c..::. E..:l ( (pc.)-+ 3..:;; 2,1 I I t"'l..

\-.1\c.l>: o,~ f.l (2~);o,4t-1/"'

~,.,+r;:,l ·. 1:"-=0 r~")t""' \.!7' !>f=O _. _ .../ K.s.o - · v

- d:':::; El< b, :::;;~ ,~:2 .~ •. ~ ;,1

E::I, b( ..;-~ . S. 5 .0,4~ DJ + -k. 4 . 5 . ( z"ij ,s~ ...,2,2t1) I:1) - t· 4 (-1r5) • 5 .. '- ,;O.oo3

f Ul;fj ve yukleme durumu jekilde veri/en sistemi Aft yi/ntemi ile ;i/zerek

J t1 V N diyagram/annt 1 ;iziniz.

JOt

A 31 ······; iF

4m 4m --+! ..

( - ·'-t_~f'WI ~olc.~(.g,.., .sobr-t ~ Ctuk>u!c. .Sa 1..\t.l..e.-;

/ 2t/m

31

8m ..I

2 ..c. ..3€'1. k.f'l,(_..... 8 ~ Ot1CS €!.

kc.€:::::. _!!.,..~ ==- o,so €I.. 't ..3

dA = .2. ( 0 11.5 €'1 -t 0. ~67 €'1 + OrrS ei =- 4. 3'33 €'1.

de- 2. (o.1SE::t -to,5o€.t) - ,2,50~ ez.

l }}

~;~~~·-•o• 8 = _ -1ot-. t~ 'j

\ o -•o· 6Eab- 2 .. -s. ~:,,,_ 1

,. l

(

B '2. -t MGC. -::-lv'\c6 S' - ~·8- :=-~O·bEI:J. ""'

12.

\-11e[)--~~>.t.~-4 ... ' =- -3.oo-t.-6 f .

''h:-0::-....... ""o\....b), d~cre... ok"'lt. e-\ru- •

Ll"'& 4, 333 E:t ~ 1> -+ o,":/S €~ (pc. - '2>. {,b:f :.c:» 1 Z1-'le- o,1So n ~b + .2,soo et. ~c.. -t 10.&6-?.::.o)

~

Ac:., I h~"' \c..{ g. ..... I IZ-<>' / 'ilL. \J'f w..OII\A.e.""~'

JY\..a~ o.ne.1. ( o + q:,a.) - 10 =-- S,U'--o., t-'\c. 6 :::. o.soe::rt~~)=Me.tt .. o.?Sel (2•~ -to) -t 10 = 12,so=f-t-..... Mcez. _ .Lf.168/-t"MGJ>: o1 t,t,6f~n(2~~olf9+o) • .3 ==- -o,~l.c-...., t--1 1)~ == o.f:,(.,(J ez. L : o + (f.&) + & =- 4 ,~tit:; .... Ms.c.. =- 0•1-S eL(2 tf>e. -t~) - 10.6€.1 == - H,1J i"" Me.& ~ Or1S t:.1.(.2.{pc,-+ lfs) +IO •bb 1 :::. 4.-:f(,a/

;

l.. 2rt1 ~ If 1\

(

-\:111..

M)

I\0

biGu vL ~::.ld~ ..... ~~. duru"\~ -?e-k; Ida_ vu-; I~ to:-~ 1 q sl~h111','1

M rV1 N d\j:f~""""l"'r'.,' 41t~~l2

<:f-~cJNI •, /::>. NCPic:-k>lo~o ~obit

lo;l;.,n..,:J,..., Cf> c.

G u !bu..:. ::>A.e;, TL€~

k.c€= 2EifLt =- o.s€::r

ke,c"' 0.15,.. 2Wl- )/b::. o,s EI

ole::. 2 ( o.s E1 + o.S~l) =- 2 EI

Al-l t::A.~ T (2 ELi 1C 1-/\.o r.'\2N 'iL-t'll. 1

-~M~.6-=- 2"2::. 4t""-

-lfSt Z \

(a I ' Jl9t:""

Mce,: 3•8o< ~ _ 2 ::= 1-tr"' I~

M c ~ =- -ME c ::: -~ .:. - 2 t M.

Me.. I> = -4 t.""' t3 ~-:::JI.i 1<:. 'Te-a.io...A..;

.5c :::::- '1 - 4 - 2 = ~ -t""

2E! ~c..+-f = o (pc =- - ot5 / E r::

Mce.= o.'5E.1(-;~:~ · 2) +r = GtS i M.

1-Ac€::. 0·'5€1(-;:I )-2 = -2.S-im

~'-"et =- o ,s u t- 2~%)+2= + ~.+s-t"""

Z""f.,.~ ~ .L t-/1 =- 0

14>1-1 112-0L 2 ~ K~ &ar

E! ~~ ==- ~ ·4·4· (2 .. Ao1S+2) [1]

+ ~ . 4 .. ( ~ •5 ) • 4. it ::. =-IC.+Ib::: 0 ~

SORU 2: 25p

~ <D

OI~U ve yUklem.e durumu ~ekilde verile;,;- ·ta§";yl~l si~te~ A<;l

I ,

A

t yontemi ile ~ozerek

21

I~ kuvvet (M,V,N) diyagramlanm ~iziniz. ,

Not: Gerekli tUm kontrolleri yapm IZ.

e.:\. (pc..=?

.b.f-..lol... 5.=>6;-t

~~m» !•3m » 4LJ~ L.ll(_ SA<3i1" ~-E ~

+

~

'* 0

(!-l)t-

">•1:5

lv')-\;

4-0

~6,:. 2 ~ = 0 1 S ~ 4-

k.c.o -=..2... 2. .f:ZI ~o,'5 EJ:. It ~

i:l~'i""to ~..,. \ l<!~~w.·,

ole.-=- 2. (o.s -t-0,'5 )ex:: L£1

A.-.~ . l--"\:o..,.,.

2~.... - ~ gt" 4 t...., ~ 11-------'---z,A J ~8,.6"' ~ Mc.D:= -+_t.-, 1£, ~

~J4t..., ~;:,\,_ ~r:-,..,....;

5c_,;::- -1 +4 = -3t._, h.N.. ~5'- d£-.4.

.2 E :l. lfc. - 3 =- 0

tfc_~ ~ 6 /E:I v-

GuloiJL.._ uc, t---1-.o~.

t-1 C.()"'- O,SEl ( 2 .. 1ft_ -tO )-1 ;5 6t._,

Mu-.::o,'?€1(2-~-t<>) ==AS-l-.,

M...._c. '?-D,')el lo+~) :::.0,15+·

\.._..-/

= L'/<==.:> L MA<=-0

IL. > j) - --1t Ic..=2~

£1c.6~ = ~ ·4 · 4 (-2.<1,5-t-Oo75)[2.J +- '!s-(, .L1(1,'5)-" \2.

~.(;,.4 _ l21(5'.S+~)[1]= 0 v 0

SORU 2 : Oi~iJ· ve yiikleme durumu 2' jekilde veri/en s!5femi c ::4~1 I Yer degljt/rme biiyjjk/iJ!deri y!Jntemi" ile yifz eref 11. V N dlyagromlonm yiziniz. A~tfliftofi mofsimum momentleri belirleylnlz.

8 ' } lim

D

~illNMi';le l'-\ L E i2...

k(!,€~~:;_~I k€~::.}_·~=~ oll:>.= 2. (2~I -t3~r) ~ 2,oEI.

5 5 t 8 Lt A t·l\:CA) 'I eeL IV l ~ IJ '· \ ~t ~ T t.; c;

d € = 2. (~ i- 4Eii- '3EI)~ 4.?:> EI 5 5 4

' \ l'!C f T • ,~ I J1\' ~' ~

Mt>c. =- +4.o-trn. , M ..... P. L 8. IO t. .....

t>E::. -I''Gt>=- 8 =-8 :.-fQ

MEr=-~ =2~2, _ 1 (,* "'-8 , a

l rt ' \ .... , I , I I

2 o EI ~b + o,{. E I ~E. - 6 . 0 = 0 1 O,(.. €I <ft> 4,3 £I (jor=; - {,.O oo. O J

/ / t l

M.AD= ~ . (2"'0+ <f>D) = 1.018 5

Nt>A ,_ 2 ~t ( 2 --.~b + D ) = 1 . ~ '55

Nt>E = ~~I ( 2. <fD + lft )-10 = -b .l55

MEt>-=. 3~J(2~E-+f'D)-t{O "" 12.840

NEF= 3EL(i · lfE -ro )- fb = -14,41-f '-t '

NEe,::: 4~I (2/fE-to) -=-- -1,(;.31

~~~E = ~;'I c2"'o -t-4>E) = O.tslb

, ·I I

Cfo=- 2,65411- /E r

<f:£= -1 . 01:342/EI

k:A PAl I ~ i "i\1

t,r~~lc:. v.-. t-~ ;

+ 5,331

o .641

1

I I ~J,{,~

0,64, Ji E I --r

o,4~

114t418

I

I :L ><=- o 1. L.'l'"'"

'5.~'31 +14,416 -t"b· 1"31

I L-J-8-2""8=0-0 I I 1/ · r ::r f-,1\A I -i . O"ffl -2.<2.,. 8 .5 +0,/31(.

I +2_.,8 ... !4 -iL~t41€-'l~

I I

- <, , ~~~ ... H1 ==-- o.oo4 ~ o .oo

I :r~ .,.\21: I I 1 E~[n:: = _..1-. 8.'5 .141411[3]

I .:>

~ ~ . B.s. H. (.2>] I .

~ ~ . 5 . 5 . (-01SIC-tZ"•WJlcJ

=-0-0-1 ~ 0 \ '

EIS~ ..,- o .oo083 ;.. O . 0

lj)rnimn A If-\ -----------i

L Is

AI!>

~~~r~

'i'A=- <fA 1- f 'trt>:;_ <f~+ f

~B

HAe:. ::::=. k l2.. )fA-t 'te.) -r 1-2\As

H A.;.;:::. k._ (.2.. ~A -t (p~ + ~ ~ ) -t MA.B

1--Ae,A =- ~ \ (f>A +2(p6 +.3'f) -t Mf>~

~llntr,

.6.2 62. .tl.Z. . ~ 1-l 1:...-.(

-> b .-~ '3 \ I

~:~_a) I I

I '+'1 ::. ' ' '-+'2- r A, 'P2..r-~ 1-,'2..

~~ ) r i S L g It- I - l.f 2.. =-

I I I 1 'ft

~ L \f:l r-

h,

j_-1 ___j_+ i

-r

~-L:....I -..J?-

Mv+M ...

V)

5f' + z~ + :r~o -+ :z: 0~ -t- M.,.,

~

( Z'P-r-.L i -r L.'\fv) I"' -t z~.:. -tMG) ~ 0

Ai

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..fo...

M<~~ l :t?' -+vo.

1:- i \.co " 'u \("'"v..,·Hu l'-

1 ~ ,.~..,.r• ... 1 ( -t ) ~~~

A 1--------:zA. !b

"-8 ~ 0 if.'5 I(_

MAIO=- k_ ( 2. {(A-+ V>a. i 3 r AI?;>) -t ~AS

Me, ... : "'" l2 ~~ -r V>A -+ 3 t'Ae.) -t ~A

HP..r? = lc_ ( 2 (pA ...;- 3 ~fA e.)-+ MAJ>

t--1 r3>A =- "- l if A -+ 3 ~ .... ~) -1: HS"

g;....- v ~ """'~~~~ ' ol 0,. ............ e l-~ .s; v"\t.os-t•~

t-:0 :.-........ v'\olc~\a_.-, b~0 b~~l~~v~ 3

"-..,

2 1--------

Z K.,....= o

( M\) -+~a) = k (2<f~ -t (po. + ~~) -tr:ltiJ-+ k (2~o;+~j+3'f)-tr:::i"

==- 3 k_ Cf'ii -t ~ ~ Cfo.. + b ~ \f + (H v +t-il g)

-::>v \uc.., do I..~ c\u-1..-11......1.4.. (j"- ~; "'-0.. ~:lol -'l.a. - _,

~ 0 "-4>~ -t :L 3l <fQ -+ L b l 'f + l2P-t24 t-:?V .. )\-, -t2"lHt>tM+ =o

SV\,_(_.L?-t-.Z~-t2'1.,)~ +2(,::4~ +M-) l!i.e~ k~--'->e-\'· ~--e. -l..., .... ~.-~.-.~ ... z 3 k. y,;:. t 2 J l ~10/ + 2 6 .k. 't' -+ s V) = 0

(t-1\v -+'\·/\ tl ) = 2 \J_6. ( 2 <f J + 2. '1' ) -f" i-/\ ( 9 \IV\ I r,

I 5 ) - - I sr')=-\.._"Lr~2'1-r-;;\Jo ~"'+/~tJ..r.-tl-1~)+2 Y\.e ,, "" ()

V\ oL~f~"""""~~<Z. 0

1V\ n0 = ~~ ( 2 lfn -r 2 'f11G ) -t M -<J' i ~,..,

c

1--,2-

d"' ... 2 .I ( ~..,l+lc .. 6 )

St1.==:.2Jr-t.,;: +2'/Y'f.:,f-

h

'fA(?.: 6. 'fcc.""~ h, hz.

'-V C:.l) = \-,, • ~Af!,

h~

Mbc: o.tSO (.2.. ... <f~>) "'';, .... I'S,34I+t'll. ~DA~O t15£1l2~E~i1.'f)i"o"" 6 125-h>t MoE:: El (2Cfo+Cfe) -lb ::-2~,-;,qJ+"'l ME!)::; l:l l ~b-t 2~)-1-lb = o,()b +1'1\ M£e.$ o,sul2fr~+3't') +o ::=. -0,13l;~ ~~?>~ = o ,5cll CfE --t ~ 'f ) -to:::; ~, ~ -fw\.

___, 1-.:)t

"""' v ---7 [ " t v•• VI>A =[oil5~!)+2 'ft)-4-o] 't;. "•~{ o.su\24o,...3'1')<o t ~~~·31

.!: 1-\ =-~ 1,5£l 4'e +..,6aCf~: -t 4.s~I '\'-1•4::o

E

Crbc 0 1 22~ /E! 1(6 =-~,04'5/ E.I

~:. s,2:Jl/ t:-1.

1

.:J.-. Ltl

J;-~~ I 1

')

-P S "L

' '

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I ::¥ ()t• ( .or ll_ ,

;.I: -:::; Vf -t''J'

~ lv"' 3 .. . -?

qc LUll... t

L I ·Lf'~ 11? -=- < 34-=- c.:,

k _<2~(-":_t,I_ '2~ 1 ~ - -3

I <.,!1!: •

* 0~y--;;).5::d I ~ rt~ '~~· .

?~T 2~r z-T 2_ H =-c -"'> 3 '!' - ~ -+-'?"' -- 9;; ..L F2v ___!::_- /'f.J-+ -1'?.!:] == Q s- z s- ?. <s

b-o,/c_ latA!/ la.t~h crf"" (c c,.~ l u 11 1 H·. 1 '.::...

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17_.

1-. 1 'ZET(·+/I~~vo ? s.<r;; ·.)-,., .oP? _ ~ l ,""" ~ ~ ... - J"" ~ o-> -+-/1.(;,0 • H.>

,_ L.:;;> =- E"7. )

(1 )

.L ''>, c;y

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l

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= - lo b ''

-?1.<- Culu lt 1 < c; ktt t.Vl-+- bt0 (e;

/,)..t.L.~ t t..ci ("-C 2/l.._:, ''-~' G ttl;' 1" 1 ll€

~c...J.t ~ IG-tvJ d~. 5'<C 1~.dit.t..dc. \._~Ltl ~ttt\:"-'rli~,

* bLtLfe clef?/(. l c.tt 1 V"&L•~ c YL ::- ~ ')

~·-' ~-'/._

2-t--vl,~L) \ \ I

} "' c-' r

~ e,A=. 3~::t ~.8

~ = S,1s . 4e.! L

6.. MA.r;. _L, f"'A&= lter1

lfA.c..:::::. MAc. . L2.

C 3E.I: 1 )A.b::. 0

(pAE

CfA & = CfAc_ = ~A.~ e,

4EI1 r-f -=-M-Ae. . L, tv'Ac. • ~ Lr q_:C::I I 3E.I2... r .2. =- 3 Eir -L2.. MAs ~A C. Z"t..A.

f<- r , ~""--- - --("l r.2.. ~r- :rr- ~I)(

-r, . --rM MAe,.= L.. ~ z,-

~ t~""r

q ... b .. ]~ ~ ;~_...)'• 2-,..w,

1- b::f~-----oc:~>yh..-,\, •.

m t ' b~l I "" I J .. "' \ • /l o"'e"' ~"\I , ""'e."":J 1 lA 1'2. l>J';j -""'"' no c.~..._..- 1

I'Y\O"'""''t d~(f'c<2"".c c "'--k d::: S::.::: ""'I<L..--

7.- qubu~ vc-d~..-le.~: lo......t;v-\~~,"v-.

(= :r L

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d :::. J:; '-"' ck.._

h =- _!i_ L I r

b - r" ~~ .r ..... ..J- -"';-..., t.. - 1)1-::>"VVe_~ rta -: cJ.=, i' f"A- /c- fru' r~ ~ ( r.~J-F'p ')I r.

r- _ Jy0 ::.......,fc.r-cJ.._ o1~0iJ: 6o2"""~ q:,d~ 1-Y')o""~"~,.. -/-erJ (~Or~f-&.... c:JJ/ ffh.,._ '=-=·Nv/ k.-1 oro")/" ...t-_

oJ:f,.fr /,r. Hod~;'--' )r,.,(c_p.rfre.. =i:;_J-;::""1~ ~yd~~ IYI=-m~""--f,~ (Jo..-tJ 1 ;'fe-..1-//Fr.

{; ~ De2Jp{L--.I'CI-{,.._ -/oz (~ "')o,..,.,., f- c/J.rfLr,' btzf!t• br'r--

frl&,.--k o~f..- D · Oo1 / 0. 01 , p,~,' ,£.::c.,=."/ ~~c_J~ IL--k--- J e: :__re {,;._r:r- J:: ~ <;>--. ~ J. 7 ,~ r

1

g ~ c;yh ... k_ ..,c_ .... ..., .kt; -/:;:"'-"' ,..,....:;:_,,..__,...._,!~~ ~.p;--~-0-:L.......

~2. ~,...;:::-,..L ~"'<:>~ 4r/.:::>,-.,tr_ T:,,ri='VJ yv b ..... !.__ <-<c:....,~

3t ~t-/"'

c. l"L- ~- -1& .3!.

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(v/

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roe • E ::. o,5o ~

" DAf.rTMA IC.AT:>A--trLAotJ

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fw'-C>E"" o, So~ : o,.t, o

( ... > AN~A>T~~Lik... fYIOHIC',.._ITLEe.;

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Z--1 = iJ,,287 -t- 18,~31-+~· !31,- 35 • 0

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o.z~5

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SORU 3:

25 p D ~~.u..u.:.:..:..:.~..u.:. ... :..:..:.~..u.:..~.J..

21

8 31

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A

I "" 4.5 ~ I ""' 4.5 m-.1

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e:J: t:H 1 4 c. OA ::. 3 • S. {; it5. [zJ

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OI~U ve yUkleme durumu ~ekilde verilen ta~tytct sistemi CROSS yontemi ile ~ozerek i~ kuvvet (M,V,N) diyagramlannt ~iziniz .

Not: Gerekli tUm

kontrolleri yaptntz.

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't-IHh',l II\\ ! t

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f'-li::>E:-::o. 0 t333 . II.

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l \'• I '.I - llt'.)O t3,S o

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j _:; ,, ,? •. , o,

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(_ (If6t-1J fAc.f) ,_ -z./v ""o,6o

(_ )

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(_:rfc, ~ ~: <;l)

f1 E':::. 3I(/l, ""O,JD

(_ )

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f' L tM Me.{) =-M~(_;; 8, tb

~ 1l JAjN\

NlJ ~-A~.,-!£-Mt.E-:::. ~ ::::.-5 <tM

2..-

N~e:, :::-1..... 'P.L::::. JtM-Ib .

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2 , 0{,2.

l

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SORU 3: Olc;U ve yUkleme durumu ~ekifde verilen ta~ryrcr sistemi CROSS 25p yontemi ile c;ozerek

12 t ic; kuvvet (M ,V,N) 4 t 3 t lm diyagramlarrnr c;izinizo

'flllllllllllllllllllf. C .. .. .. 03 1 D 31

1.51 I """1 'E""

121

~

31

- DOSoo =-

Not: Gerekli tUm kontrofferi yaprnrzo

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\').e "S 0 b~:.~ \u D~ E ~ '

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rce "" ru'::. 3 'I ::. Or31-)'J. 6

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SORU 3: Olc;U ve yUkleme durumu §ekilde veri len ta§IYICI sistemi CROSS 25p yontemi ile c;ozerek

8 t 3 t lc; kuvvet (M,V,N)

c flllllllllliflfWIIIIItE 21'""' rU""JI ............. .

121 l1,5I

A B

-·

djyagramlanm c;iziniz

Not: Gerekli tUm kontrolleri yapm1z.

Dtf:.""' "'o\c...-"'l..-..- 1 S':'~o;t

~~e"'Le,A d.:::f~lt..- 'D ,E

4LI IOU IL e..E£)0 12.l:Ee...l

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D AG;.I(""' A. \LA'( 5--f I L A 2-J

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4,5 4rst- 12

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. ~:::1!>,5

TT\jo J 4 tv{ I>~= -4 {-""-

o .oo r-; o.OO'f -o.ol8, _ o,J4o · o.oJO -o,~Sol -~.2oo 1 -o. £.oo - &;.ottJ, ,s .ooo

V"

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SORU 3: Olc;U ve yUkleme durumu ~ekilde verilen ta~1y1c1 sistemi CROSS 25p yontemi ile c;ozerek

21

A

Sm

12 t lc; kuvvet (M,V,N) diyagramlanm c;iziniz.


D'(f;:; -. 1'\o'c:.-k>.fa..-1 ..Sea b \t

b . D~~n - "'-.:>~..... • c. 1 0 eED8,2Lt:a....

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12 .~5 t \ (,~S 5,~'? t rt>E"" '3; - o ,3> l-5

1<3,~t DA'b\TMA ~'1SI'\-l\LA/(.I

'

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¥of-1.'1•LoL 1 : 'LX::o.a L'i:="' L MA•O

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:r~:: 3I

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~/ ~ . . .. .. . -· ....

S.U. t-1UH. MIM. FAK. IN~MT MUH. BOL .. YAPI STATIGIII BUTUNLEME SINAVI 29.01.2002

SORU 1: OI<;U ve yUkleme durumu §ekilde verilen ta§IYICI sistemi KUWET 30p yontemi ile ~ozerek

21

A

I• 2'1!1•4 m •I•

1A) Moment diyagramm1 ~iziniz.

18) E noktasmm yatay yer degi§tirmesini bulunuz.

4 m Gerekli kontrolleri yapm1z

E = 200 000 kg /cm2 I= 40 dm4

SORU 2: Olc;U ve yUkleme durumu §ekilde verilen ta§IYICI sistemi A<;:l 25p 1 t yontemi ile c;ozerek

i~ kuvvet (M,V,N) C diyagramlanm ~izinlz.

21

A

6m

B

• ~I

2 m Not: Gerekli tUm kontrolleri yapm1z.

SORU 3: OI~U ve yUkleme durumu §ekilde verilen ta§IYICI sistemi CROSS 25p yontemi ile ~ozerek

B

21

A

llrl.i..:

SUre 140 dakikad1r.

12 t ic; kuvvet (M,V,N) diyagramlanm c;iziniz.


Soru ka-Jtlan temiz olarak iade edilecektir. BA~ARILAR DiLERiM Yrd .Doc;.Dr. Nail KARA

2.2.1.6. ANKASTRELiK UC MO~lENTLERi (EI Sabit) ALt 1

iKi lJCU AHKASTRf KiRi~LER Viikleme !)ekli ~All

P.l --s-

P.oll-n) --L-

Pn.!L -n) +---L

Tablo ?

BiR UCU ANKJISTRE- aiR UCU MAFSALL1

Yiikleme ~!i MA<!

I /

k .. ,

j

I

-~{l·b) I I

J.P.L l -16

I I

Degi5ik konumlu/iki ucu ankastre ya da bir ucu ankastre diger ucu maf

sall1 c:ubuklann degi5ik yukler alt1ndaki ankastrel ik uc: momentleri, ac1 i5a

ret kurallar1yla tablolar halinde verilmi5tir {Tabla 2).

S.U. MUH. MIM. FAK. IN~AAT MUH. BOL .. YAPI STATIGIII FINAL SINAVI 02.062003 '\) ~--------------------------------------------~ ( SORU 1: Ol~u ve yukleme durumu ;;ekilde veri len ta;;Jy1c1 sistemi KUVVET 30p 4 t yontemi ile ~ozerek

Dfjjjjjjjjjjjjjjjjjjj i'fE (),II

31 ---- r·--- 31 ----- ---

1 ----- --------> I.

c 2 tim

. I '

21 8

6 m

1A) M diyagram1n1 ~iziniz.

18) E noktasmm yatay yer degi;;tirmesini bulunuz.

Gerekli kontrolleri yap1n1z

E = 200 000 kg /cm2 I= 40 dm4

SORU 2: Ol~u ve yukleme durumu ;;ekilde verilen ta;;Jy1c1 sistemi A<;l 25p yontemi ile ~ozerek

8~ T t ffl i~ kuvvet (M,V,N)

c ~ 1111111111 IIIIIIIIIIIIIIII~E diyagramlar1n1 ~iziniz. 21

21

A

12m 2m

....... =-1011( )loiOII( 6m

SORU 3: 25p D ,....~....,.,j,j,,,........_~....,.o~o~o~o~--...

21

8 31

21 4m

A

I• 4.5 111.,1.,... 4 .5 m,..l Sure 110 dakikad1r. Soru kag1tlan temiz olarak iade edilecektir.

Not: Gerekli tum kontrolleri yapm1z.

Ol~u ve yukleme durumu ;;ekilde verilen ta;;Jy1c1 sistemi CROSS yontemi ile ~ozerek i~ kuvvet (M,V,N) diyagramlar1111 ~iziniz.

Not: Gerekli tum

kontrolleri yap1111z.

8A$ARILAR DiLERiM Dr. Nail KARA

-K M Ottrl_:, ~uvvet- Cf"'+e..""':' ,c. ..c- 1'-1\otv.'> ci~pl"'>""-a-, ..:j;""+e""';

,, ' DEPLA~r--1-Ar-....\ ~'Slf'l\E"--{1

olup 1

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q u ~.>tf'""'1 s+-r~ef (r:-drtH~ ) c:~.-"1\a_le..,__;

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+-... ~ '? \.e..__.le.r Je_

aAt""""~ d.,,._

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b:t~; e~b~

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k "" !:SA l.~ = L

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EA L

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he.)~p IQ..,, '11.

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tl~:sj ?'

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A IJGCJ"- j.;rc... mo..,e"'t-

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k.33:: i!! L.

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t;311ll'~ D 7tl..£N/}1£'

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ru=- Pr. c.o~a( + P-r:. !>i"' 01.

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r" p5 p,

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in ~-H= == r.. ~J~ ... i~ . \t:l~-,c......,i;

1?~ ?CU e\:. -:: ( \1:] 71-(J ~ '{ d ~~ lr-

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I ~

H~t "7-t

lt> ..... 0/3t l.

(4,1")

(1o, s)

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r, P2. f.s rtf ::

P:s

f'- X-'it:

lo- 4 lo

s -I(. I~

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o,, +o.g c o,s o,, 0

0 0 1

O,l,

- o,s D

t_"T]T

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o,, 0

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o\ ' ... , r ~ ....

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I<+~ 1 lf>~)C.ic

b~ .. i4p~(J H -- t .J:-f t> l> t"i ~ - :L \.f J = lV ~

l"'-1 L t>~ - \ F}

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l {,

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k2., ku l::2.s bj l!tr k~ o

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b., b.L "'-~ b.~ '4.s ~ ~

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j.s-1 ~s z. sn ~t"'1 .Srs- Ss- o

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(_s- ·1) +~ = ~ ((4-2.)+-11*3 := ~

$ekilde yiikleme ve deformasyon durumlan veri/en iki ucu elastik ankastre kiri§lerin t;ubuk ut; kuvvetlerini bulunuz

~ ~ ~

31/m

WIUIIITIIIIUIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIt 10 t 0,003 rad

~001 d 002 em

~

Io,5 em _f1 em

0,002 rad 8m I~ 8 m ·I

EA 0 0

EA - --L L

0 0 I= 0,008 m4 A= 0,2 m2 E = 2800000 t /m2

0 12£/ 6£/

0 c y 0

6£1 4£/ 0 -

12£/ 6£1

L' y [p] = [k].[d] + [f]

6£1 2£/ (A) (B) -

(C)

L' [kJ= I L EA EA

y L

-- 0 0 L

0 12£/ 6£1

L' -y 0

6£/ 2£1 y -

L

70000 0 0

0 525 21 00

[k] 0 2100 11200

-70000 0 0

0 -525 -2100

0 2100 5600

- 0 L

0 12£/

u 0

6£1

L'

-70000 0

0 -525

0 -2100

70000 0

0 525

0 -2100

0

6£1 -y 4£1 -

L

0

2100

5600

0

-2100

11200 l[f]

5 0

+ =

0

.-----a- fl . (jJ

100 kN 2A -~21

[1]

Ol2_1 ~· · .. 0 ,, ,,, U2 I U2 I 6 . .., ~ .., ~

0 1 0 0 0 0

[1] Nolu <;ubuk

-1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 -1 0 0 0 1 0 0 0 0 0 0 1

[2] Nolu Cubuk

C05U: : 1 s1nu: = 0

L

1 0 0 -1 0 0

0 1 0 0 -1 0

1 0 0 -1

0 0

0 3 3 0 -3 3

-3 0 3 3 0 3

/' -

~ekilde verilen ta§1y1c1 sistemin Matris Deplasman yontemi ile <;ubuk u~ kuvvetlerini bulunuz.

A= 1 I = 1 L = 1 E = sb.

Cubuk dugum numaralan [1] -> 1 -> 2 [2] -> 2 -> 3

[k1xvz=[T] T.[k]xyz· [T]

C05U: : Q 51n U: = 0 -1 0 0 0 1 0 0 0 3 0 -3 3 -1 0 0 0 0 4 0 -3 2 0 0 1 0 0 0 1 0 0 0 0 0 0 1 -3 0 3 -3 0 0 0 -1 0 2 0 -3 4 0 0 0 0 0

0 0 0 0 0 1

0 0 0 1 2 3 -3 0 3 -3 3 0 -3 -3 0 -3 0 -1 0 0 0 1 0 0 -1 0 4 0 -3 2 -3 0 4 3 0 2 3 0 -3 3 -3 0 3 3 0 3 0 1 0 0 0 -1 0 0 1 0 2 0 -3 4 -3 0 2 3 0 4

2 3 0 0 0 0 0 -1

12 6 0 6 4 0 0 0 1

-12 -6 0 6 2 0

0 -12 -6 0 12 -6

0 6 2 0 -6 4

1 2 3 0 0 0

Cubuk ankastrelik tepkileri

-50 0

25 -50 0

-25

0 0 0 1 2 3

0 100

{f2}xvz={f 2}xyz= 25 0

100 -25

0 0 0

2 3

1 2 3 0 0 0

15

3+1 0+0 3+0 [K]=E 0+0 12+1 0+6 =E

3+0 0+6 4+4

4 0 3 0 13 6 3 6 8 1 2 3

1 2 3

Denklem tak1m1 ~ozumu [K].{D}={F}

4 0 E 0 13

3 6

3 6 8 I 3

= ~ rn

[F]=OO DDEY

I =1/E 3

Cubuk u~ kuvvetleri {P}xyz=[k]xyz·£T].{d}xvz +{f}xyz

1 0 0 -1 0 0 0 3 3 0 -3 3 0 3 4 0 -3 2

E -1 0 0 1 0 0 0 -3 -3 0 3 -3 0 3 2 0 -3 4

1 0 0 -1 0 0 0 12 6 0 -12 6 0 6 4 0 -6 2

E -1 0 0 1 0 0 0 -12 -6 0 12 -6 0 6 2 0 -6 4

200 kN 17,581

10,32 -r -

- -,58 ·( ·· ....... 10,32

100 kN [1]

-----89,68 · .... ..(61,77 9, 3

0 1 0 0 0 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 -1 0 0 0 0 0 0 0 1

1/E

190,97 '\ 10,32

7{39

- 9,03

89,68 +

(N) kN

fd1l 0 0 0

10,323 -9,032 2,903

{d2} 10,323 -9,032 2,903

0 0 0

9,03

- 190,97

10,32

(V) kN

0 0 0 1 2 3

2 3 0 0 0

9 032 39 68 36 77

-9,032 -39 68 42L58

10 32 -90 97 -42 58 -10 32 90 97

-48 39

61,77

.2o

-50+0

~ 0+100 -25+25

=

10 323 -9 032 2 2 903 3

{f1l [P1}xyz 00 9 03

50,0 89 68 + 25,0 = 61 77

0,0 -9,03 50,0 10 32 -25,0 17,58

{f2} [P2}xyz 0,0 10 32

100,0 9 03 + 25 0 = -17 58

0,0 -10 32 100,0 190 97 -25,0 -73 39

73,39

(M) kNm

SORU 10: Ol~u ve yukleme durumu verilen sistemde B noktasrnrn, (1 Op) yatay yer degi~tirmesi os H ve donmesi <r>s degerlerini bulunuz.

Jm 21,5 t/ml D 2~1 3 Urn T ~ -[ siii!I!IIII!I!!UII!!IIIIII!IIIIII!!IIc

A AI A I

I• 3 m .. ,. 4 m .. ,. 4m

T:.A 0 0

EA 0 -

L L

0 12£I 6D

0 12£/

----u 1.' -f)

0 6El 4EI

0 6EI

[k 1 = L' L L' EA F:A

0 0 -- 0 L L

0 12£/ 6FJ

0 12EJ

J} J} -----,y-0

6D 2El 0

6£1

L' L -IT

[F] = [K].[D] = [DDY] - [ >:f]

[p] = [k].[d] + [ f] 1 0 2 0 0

50000 0 0 -50000 0 0 375 1500 0 -375 0 1500 8000 0 -1500

-50000 0 0 50000 0 0 -375 -1500 0 375 0 1500 4000 0 -1500

[K] = '5000~' 800~' [F] = rn 1:: Hua -

[D] =

0,0001 m

-0,005 rad

~:..;..;;..;.-1

0

6EI

1.' 2/o"/

L

0

6FJ

L' 4 /:J

L

0 0

1500 4000

0 -1500 8000

E = 2000000 t tm< I= 0,008 m• A= 0,2 m<

f1 0

21 ,5 35 0

21 ,5 -35

d1 0,0001

0 -0,0050

0 0 0

p1 5 5

-7,50 14,00 -40,00 -5,00

-5 -5 7,50 29,00

-20,00 -55,00

KAFES KIRI~ 1

6

1 I

L I EA Vi I 8,4853 2 >Q

0,2357 0 -0,236 0 0 0

k -0,236 0 0,2357 0 0 0

0,7071 0,7071 0 -U, I Uf U,{Ufl u

T 0 0 0,7071 u u -u,rur

0,7071 -0,707 0 0,7071 0,7071 0

TT 0 0 0,7071 0 0 0,7071

3 I L EA Vi I 1 0 dt 0,1 0 -0,1

0 0 0 k -0,1 0 0,1

0 0 0

0,8 -0,6 0 u ,o u,o u

T 0 0 0,8 u u u,o

0,8 0,6 0 --0,6 0,8 0

TT 0 0 0,8 0 0 -0,6

1 2

-30 kN 3

Zi ,.1.

Vj }Q m

0 0 0 0

0 u

0,7071 U,(Ufl

0 0

-0,707 0,7071

Zi I Vj

~= AA :::·:

0 0 0 0

0 u

-0,6 u,o

0 0

0,6 0,8

(4)

<I

.·.•.·

'

8

Zj <I Jt :::::::

0,1667 0,1667 -0,167 -0,167

01 0 0 0 0

-69,73 1 -51 ,58 2

Zj :I :Jt 0,08

-0,06 -0,08 0,06

03 -69,73 1 -51 ,58 2

0 0 0 0

0 0 0 0

0 u 0 0

-0,167 -0,167 0,1667 0,1667

d1 0 0

-85,78 12,834

sin cos -0,6 0,8

-0,08 0,06 0,08

-0,06

d3 -24,84

-83,1 0 0

F~1 - 2

0 0 0 0

0 0 0 0

p1 20,219

0 -20,22

0

p3 -2,484

0 2,4837

0

0~1 - • 2

2 L EA Yi )I Zi :(I 6 2 J! {Q

0 ,3333 0 -0,333 0 k 0 0 0 0

-0 ,333 0 0,3333 0 0 0 0 0

0 -1 0 0 TT 1 0 0 0

0 0 0 -1 0 0 1 0

4 L EA Yi I Zi (I 8 1 ( ~ ( ~

0 ,125 0 -0,125 0 k 0 0 0 0

-0,125 0 0,125 0 0 0 0 0

1 0 0 0 TT 0 1 0 0

0 0 1 0 0 0 0 1

Yj I jj\

Yj

rl j j

Zj :(I sin cos (jt 1 0

0 0 0 0 0,3333 0 -0,333 0

0 0 0 0 -0,333 0 0,3333 0

0 0 1 2

02 0 0 0 0

-69,73 1 -51 ,58 2

Zj

··= ~ { ~(

0,125 0

-0,125 0

0 0 0 0

d2 0 0

-!>1 ,58 69,731

sin cos 0 1

-0,125 0

0,125 0

0 0 0 0

1 2 0 0

D4 d4 -69,73 1 -69,73 -51 ,58 2 -51 ,58

0 0 0 0 0 0

23

p2 17,193

0 -17,19

0

p4 -8,716

0 8,7164

0

,,,,,,,

~m 40 kN A= 10.0875 30 kN I 30 kN/m

31 ..,.A,.. 31 ~kN

30kN }m A= 0,125

~ekilde verilen ta§IYICI sistemin Matris Deplasman yontemi ile «;ubuk ug kuvvetlerini bulunuz.

1 = 0,0009 m4 E = 2,00E+07 kN/m2

0

[1] 0 , .. ~

[21

3 4 .... J -

(3) T 42 (2)

1 r·L x ;Lv ..... ~. [41 ....

5 r·t:..-o [ k 1xvz=[ T ([ k ]xyz·[ T]

\'0 _c:

1 Eteman=t A 1 E j L i ~ 1 JjP;Q~l$ ·••• t®Q(W® / . 3 Ji :t>)®f?

0 1

T 0

1 yi ' zi I » 1 zj 1 cos I sin I ··-· J) . ( !t u >~ u Jf < 0 -1

0 0 0

583333,3 0 0 -583333 0 0 0 0 8000 12000 0 -8000 12000 8000

k 0 12000 24000 0 -12000 12000 kT 12000 -583333 0 0 583333,3 0 0 0

0 -8000 -12000 0 8000 -12000 -8000 0 12000 12000 0 -12000 24000 12000

0 1 0 0 0 0 I 8000 -1 0 0 0 0 0 ! 0

TT 0 0 1 0 0 0 T1 kT 12000 0 0 0 0 1 0 -8000 0 0 0 -1 0 0 0 0 0 0 0 0 1 12000

0

f D1 T*D 0 0 0 0 0 0 0 0 0 0 0 1 Qi.PAA-~~ 0,00053923

-1 0 0 0 0 1

0 0 0 0 0 0

-583333 0 0 12000 0 24000

583333,3 0 0 -12000 0 12000

0 12000 583333,3 0

0 24000 0 -12000

-583333 0 0 12000

0 0

k*T*D 0,00 6,47 6,47 0,00 -6,47 12,94

0 0 0 0 0 0

0 -1 1 0 0 0

0 583333,3 -8000 0 -12000 0

0 -583333 8000 0

-12000 0 ---

-8000 0 0 -583333

-12000 0 8000 0

0 583333,3 -12000 0

0 0

0

0 0

0 0 1

0 12000 12000

0 -12000 24000

12000 0

12000 -12000

0

UU ~4qoo • .. ••-1

0 0 0 0 0 1

~

"'

k

TT

1 Eteman-{ A ~ ,; 1 l. 1 ' 1 2 o::::· ·-·:: _:. ·. :·::< ' ";::0:::::\::0::- . . .· . . . ;: >:::O:.:<:o;:o 4 : ,, .. : .· :. : .. o:,' JM~6 : . . ~f)J!O.®® ,.-.,.,.,.-.,.,.,._ -P.tJQZ:"f. .

I yi l zi I yj r zj I cos r Stn~ 1 < ~ ) u >~ ) \4 < :·:~·· > 1 0

625000 0 0 0 10125 20250 0 20250 54000

-625000 0 0 0 -10125 -20250 0 20250 27000

1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0

f I

0 !

40 !

26,6667 0

40 -26,6667

-625000 0 0

625000 0 0

0 0 0 1 0 0

0 0 1 z 3 4

0 0 -10125 20250 -20250 27000

0 0 10125 -20250 -20250 54000

0 0 0 0 0 0 0 0 1 0 0 1

1 0 0 0 0 0 0 1 0 0 0 0

T 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1

625000 0 0 -625000 0 0 0 10125 20250 0 -10125 20250

kT 0 20250 54000 0 -20250 27000 -625000 0 0 625000 0 0

0 -10125 -20250 0 10125 -20250 0 20250 27000 0 -20250 54000

TTkT I ----- I I ------ - .

T*D k*T*D 0 105,53 0 15,06

0,00053923 40,39 -0,0001688 -105,53 -0,0008525 -15,06 -0,0002218 19,84

N I!'

IE/eman[ A 1 E I 1 L 1 t 1 3 . Q/Utf ••• ••••••••••••••••·•~®QQ®Q < s • JM~1<t ) T

yi zi yj zj cos sin I F - l -- --t ··-· ~ ) ' · ••••••••• ..,. i L )~ ) q y ) Q ) 0,8 -0,6 I

450000 0 0 -450000 0 0 0 3456 8640 0 -3456 8640

k 0 8640 28800 0 -8640 14400 kT -450000 0 0 450000 0 0

0 -3456 -8640 0 3456 -8640

~-- 8640 14400 0 -8640 28800 ---- ----

0,8 0,6 0 0 0 0 -0,6 0,8 0 0 0 0

TT 0 0 1 0 0 0 0 0 0 0,8 0,6 0 0 0 0 -0,6 0,8 0 0 0 0 0 0 1

f 03 -36 48 40 -36 48 -40 5 @;J!QN~

0,8 ·0,6 0 0,6 0,8 0 0 0 1

0 0 0 0 0 0 0 0 0

360000 -270000 0 2073,6 2764,8 8640 5184 6912 28800

-360000 270000 0 -2073,6 -2764,8 -8640

5184 6912 14400

T*D k*T*D 0,00037642 169,39 -0,0007833 -16,64 -0,0002218 -33,18

0 -169,39 0 16,64

-0,0013902 -50,00

0 0 0

0,8 0,6 0

-360000 -2073,6 -5184

360000 2073,6 -5184

0 0 0 0 0 0

-0,6 0 0,8 0 0 1

270000 0 -2764,8 8640 -6912 14400

-270000 0 2764,8 -8640 -6912 28800

- -- _.__ -----

N "i-1

1 2 3 4 5

2 [K] = I A~Q~$.q l+.U.~t I 174:J:J(;;~ I }1~~IJ: <l .-.•. fl!l1~ / I 3

4 5

1,5E-05 4,4BE-07 1,84E-06 -5E-06 1,96E-06

4,48E-07 1,5BE-06 2,04E-06 2,4E-07 -8,9E-07 [K]", = 1,84E-06 2,04E-06 8,6BE-06 1,2E-06 -3,1E-06

-5E-06 2,4E-07 1,2E-06 1,53E-05 -BE-06 1,96E-06 -8,9E-07 -3,1E-06 -BE-06 3,96E-05

{F}=dd-Ef

53,33333 --w

-130 -13,33333

-

d_d_~_v Lf

tv ():)

0 6,47 t ·f \ 6,47

lkN6,47l~ 12,94 '···l ·l

······. 0 )-so 0

20 kN/m

105,5~~111111111111111111111~ ~·· .. 105,53 ; t t )6 82 67,06 ~ 55,06 24,94 '

105,53

(N) kN

30 kN 30 kN/m

·· :~

205,39

~'''''"'""'

''''''''-'X ----.::::::

(V) kN

(M) kNm

"' ~

J Eleman

1

k

Tl

Eleman

2

k

Tl

I 'I(

yi 0

EA "I

0,1 0

-0,1 0

il 01 0 0 0 0

-78,655 1 -329,26 2

yi 10 EA

1

0,125 0

-0,125 0

!I

02 -78,655 1 -329,26 2

0 0 0 0

10

zi yj 10 10 L sin lU 0

0 -0,1 0 0 0 0,1 0 0

~I ~I d1=T.01

0 0

-78,655 -329,26

zi yj 10 18 L sin 8 u

0 -0,125 0 0 0 0,125 0 0

!I !I

d2=T.02 -78,655 -329,26

0 0

3o

4 zLv

I x/ 5

:tiE 8

~I

Tl il ll il il

zj 10

cos 1

0 0,1 0 -0,1 0 0 k"T 0 0 0 0 0 -0,1 0 0,1 0 0 0 0 0 0

0 0 1 2 0

"I -~!1 ~I ~:il ~ll 0 0

p1 7,8655

0 -7,8655

0

zj 10

cos 1

0 0,125 0 -0,125 0 0 0 0 0 0 0 -0,125 0 0,1 25 0 0 0 0 0 0

1 2 0 0

!I "1_;:;~1 ~I -; :;~1 ~I!

p2 -9,8318

0 9,8318

0

Eleman 3

k

T '

Eleman 4

k

T'

K

yi zi yj zj 0,7071 0,7071 0 0 10 10 T -0,7071 0,7071

EA L sin cos 0 0 2 14,142 0,7071 0,7071 0 0

0,1414 0 -0,1414 0 0,1 0,1 0 0 0 0 k.T 0 0

-0,1414 0 0,1414 0 -0,1 -0,1 0 0 0 0 0 0

0 0 0,7071 -0,7071 0 0 0,7071 0,7071 0 0

0 0 0,7071 -0,7071 u U U,(Ufl U,(Ufl

03 0 0 0 0

-78,655 1 -329,26 2

yi zi 'IU 'IU

EA L 2 10

0,2 0 0 0

-0,2 0 0 0

0,8 0,6 -0,6 0,8

0 0 u u

D4 -78,655 1 -329,26 2

0 0 0 0

1 2

d3=T.D3 p3 0 40,792 0 0

-288,44 -40,792 -177,21 0

yj zj '10 "' T sin cos -0,6 0,8

-0,2 0 0 0 k.T

0,2 0 0 0

0 0 0 0

0,8 0,6 -u,o u,o

d4=T.D4 p4 134,63 26,927 -310,6 0

0 -26,927 0

F ~1 ~2

0

0,8 U,l>

0 0

0,16 u

-0,16 u

D

~1 ~2

-0,6 U,ll

0 0

-0,12 0

0,12 0

3\

0 0 0 0

0,7071 0,7071 -0,7071 0,7071

-0,1 -0,1 0 0

0,1 0,1 0 0

0 0 u u

0,8 -0,6 0,6 0,8

-0,16 0,12 0 0

0,16 -0,12 0 0

A::-0,25

I A=Ot15

.2 5 .£. 2 1-----¥----- --~-------· ----)( -···-----·----~···-*-------;)(

0

0

£>1

~0 ~ lot

/.10 1 1.:::

2_

1' 2..

1

'5o roo -

- 15oo - 3000

-5ocro -

- -1500

- 3MO 0

1i 3t/,.,

"' Jj ~

~J:.o - -5Qoo) -

3ooo - ..Asoo

80fl0 - - _3000

- 50000 --3{))o - ~soo

4000 - -3000 0 0

0 +0 - 0

1:2r E~.2..t.to6tf.,). A""" 0,~""'2. I-== O. oO Y ""' 4

"' 1

-3ooo

Ltooo -

-3ooo 'BODO

-~

1-~ 2

'l-

0

0

0

0 -

l lbOOO 2- 4000

-o,gs-f-+5 -4 .14) b. d2 +.fz -1.143 -t5 ::o 3r851-

-z,265-5 .;1,2.85

0 .;-o =a ~ \ o,S51-t-5 ::::5r6S+ Jz;:: t>~l

3,e51- -;;r,2e,5 '!>?-

( -------rf: {-----x1 b.D 14,44~t '5,65-7-t 1~t'32/ 2rb1'5

S.U. MUH. MIM. FAK. I N~MT MUf-J. BO~_vAPI STATIGi II TEK DEr<S SINAVI 05.03.2008

Ad1 Soyad1 : No : SORU 4: OlctU ve yUkleme durumu verilen sistemi matris deplasman yontemi 20p ile ctozerek M,V,N diyagramlanm ctiziniz. E = 2E+06 t lm<

I= 0,008 m' A= 0,12 mL

11 t 0

EA

L

0

0

0

12E/

L' 6EI

0

6E! L'

4EI -

EA --

L

0

0

0

12EI L'

6E!

I 0

6EI L'

2EI

[k]= L' L EA

- L' EA

L

0

2 3 4 5 6

[K]I

--L

' 0

l 0

0

12E/

L' 6E! L'

0

6E! L'

2E! -L

- 0 L

0 12EI 6E!

L' -[}

0 6EI 4EI

-[} L

[F) = [K].[D] = [DDY] - [ I:f]

[p] = [k].[d] + [ f 1

0 0 1 0 0

30000 0 0 -30000 0 0 375 1500 0 -375 0 1500 8000 0 -1500

-30000 0 0 30000 0 0 -375 -1500 0 375 0 1500 4000 0 -1500

0 0 2 0 0

80001 ~mm

40001 ~sooo:

[F]=rn

[D)=

o}-o I c

4 ~ f1 f2 0 0 12 5,5

16 11 0 0 12 5,5 -16 -11

d1 d2 0 0 0 0

-0,00175 0,00075 0 0 0 0

0,00075 0 2 p 1 p2

0 0 0 0 0 1500 -1,50 10,5 1,13 6,625 4000 -11,00 5 6,00 17

0 0 0 0 0 -1500 1,50 13,5 -1 '13 4,375 8000 -1,00 -17 3,00 -8

0

v 1 A

M 1~--------,:ts:-------~

SORU 10: Ol~u ve yukleme durumu verilen sistemde Ave B noktalarmm, (10p} CJ>A ve cp8 donme degerlerini bulunuz.

E = 2000000 t /m" 27 t I= 0,006 m•

4~1 A=0,2 m'

s 2,"11'''11'''''''''~'M,m,,,,,,,lllll~1 ~ c A, I ~ 0

J A,l

5 m '///-' 1 0 m _ I t 0 ·I>E o ~ r 2J-o f1

0 f2

EA 0 0

EA 0 0 - - 0 0

L L

0 12El 6 EI 12EI 6t:J -----;; u 0 - -----;; u

13,5 33,75

15 25

0 60 4£1

0 6U 2U

u -u -[k]; L L

FA 0 0

EA 0 0

L L

0 13,5

-33,75

0 15 -25

0 12U 6/::t

0 1'2 U 6 U

------;; L' -----;; -u 0

6 / :"/ 2 "'

6U 4 "' -,!- 0 - .

J.' / , I .

d1 0

d2 0

0 0 [F] = [K].[D] = [ODY] • [ }:f] -0,0090 0,0040

0 0 [p] = [k].[d] + [ f 1 0 0

0,0040 0 0 0 1 0 0 2 p1 p2

40000 0 0 -40000 0 0 0,000 0,00 0,000 0,00 0 144 720 0 -144 720 -3,621 9,88 2,882 17,88 0 720 4800 0 -720 2400 -33 ,750 0,00 19,214 44,21

-40000 () 0 40000 0 0 0,000 0,00 0,000 0,00 0 -144 -720 0 144 -720 3,621 17,12 -2,882 12,12 0 720 2400 0 -720 4800 -2,464 -36,21 9,607 -15,39 ...

0 0 2 0 0 0

[K] =

a= -0,0090 rad ~) Me= -36,21428571 tm

S. U. ~UH. MIM. FAK. I N~MT MUH. BOL..YAPI STATIGi II BUT. S!NAVI10.09.2004

Ad1 Soyad1 : No:

SORU 4: OI<;U ve yUkleme durumu verilen sistemin 20p <;ubuk u<; kuvvetlerini bulunuz.

E = 2000000 I= 0,0125

0 A= 0,25

ot n 3t/m }--o 2~ 0 eJIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII~~ c

A , l :X:: A , l

, 3_,...,.,.,___---'1;...:;0--'m;.:.;_ ___ _.~+ol•t------'1;...:;0--'m~-~·1

[k] =

EA L

0

0

EA

L

0

0

0

12El ----v-6£1 L '

0

12El L'

6EJ I }

0 EA --L

6EI 0 L'

4El 0

L

0 EA -L

6EI 0

L ' 2EI

0 L

[F] = [K].[D] = [DDY] - [ ~f]

[p] = [k].[d] + [ f] 0 0 1 0

50000 0 0 -50000 0 300 1500 0 0 1500 10000 0

-50000 0 0 50000 0 -300 -1500 0 0 1500 5000 0

0 0 2 0

0 0

12EI 6£1 - ----v- L' 6EI 2EI L ' L

0 0

12EI 6EI ~ L'

6El 4El - -;y- L

0 2 0 0

-300 1500 -1500 5000

0 0 300 -1500

-1500 10000 0 0

[K] = [F]=~ -25,00

[Kr'= [D] = 0,00300 -0,00200

A B

d1 0

0

0,0030

0

0

-0,0020

0 1,5 20

0 -1,5 -5

rad rad

B

f1 0 0 0 0 0 0

p1 0

1,5 20

0 -1 ,5 -5

0 0 1 0 0 2

d2 0

0

-0,0020

0

0

0

0 -3

-20

0 3

-10

0 0 2 0 0 0

t lmL m• m"

f2 0

15 25 0 15

-25,00

p2 0

12 5

0 18 -35

c

A B -------------------

s _____________________ c

SORU 9: 01~0 ve yukleme durumu verilen sistemde cpA= -0.03 rad ve cpS = 0,02 rad (10p) olarak veriliyor. AB ~ubugunun, u~ kuvvetlerini bulunuz.

0 E = 20000000 kN lm' 2 I= 0,008 m~

3 0 A= 0,16 m' 80 kN 120 kN )-.., 2

j~llllllll~~~~~~~~~lllllllllf .)

0

1c ,}---1

)-o I • 8 m :'f 4 m •I,. 4 m •I f1 f2

1 £A 0 0 _EA 0 0 0 0 L L

0 12£/ 6£1

0 L' -----;}

0 6£1 4£1

0 [k]= -----;} L

EA £A 0 0 -

I, L

0 12£/ 6£1

0 L' ------;}

0 6£1 2£1

0 L'

-L

[F) = [K].[D] = [DDY] - [ ~f)

[p] = [k).[d] + [ f] 0

400000

0 0

-400000

0 0

2

[K] =

0 0

3750 15000

0 -3750 15000

0 1

80000 0

40000

1E-05 0

-4E-06

0 15000 80000

0 -15000 40000

3 2 0

800000

2 400000

0 0

400000

0 0

0 3

40000 0

0 160000

0 -4E-06 1E-06 0

0 7E-06

Cj>a = -1 E-04 rad

12£1 6£1 -[} -----;}

6£1 2£1 ------;} L

0 0

12E/ 6£1

L' L' 6£1 4£1

L ' L

0 3 0 0

-3750 15000 -15000 40000

0 0 3750 -15000

-15000 80000 0 0

[F]=~160 -80 200

-0,003 [D) = -1 E-04

0,002

( ~)

120 60 160 120

0 0 120 60 -160 -120

d1 d2 0 -0,0001 0 0

-0,003 0,002 O,OOO f 0

0 0 0,002 0

p1 p2 40 40 -40 -40

-15,00 105 30,00 90 -160,00 0 160,00 280

-40 -40 40 40 15,00 135 -30,00 30 40,00 -120 80,00 -40

-120 kl\

/

SORU 9: Olc;u ve yOkleme durumu verilen sistemde q>B= -0.0024 rad ve q>C = 0,00035rad (10p) olarak veriliyor. BC c;ubugunun, uc; kuvvetlerini bulunuz.

E = 2000000 tim'

2Im 12 5 t/Am 17 t J- I = 0,009 m•

'

0 A= 0,25 m' 2 3 t/ m

c@lllllllllllllllllllllllllllllllllllllll~~ o e A,J ::::2S: A,J r5t~.o -t - w///' 5 m 5 '/////• 1 0 t 0 ~ 1~~~~~--~~~~E~-m--~~~~E~------~~m~--~~ ~~

[p] = [k1.(d1 + [ f 1 0 f1 f2

EA 0 0

EA 0 0 --

L L

0 8,5

0 15

0 12£/ 6£/

0 12M 6101

----;! L' -~ I! 0

61:'1 4£1 0

6El 20

(k]= u [. - I! / , F:A

0 0 / :"A

0 0 L I.

21,25 0

8,5 -21,25

25 0 15 -25

0 12£/ 61::1

0 12/:1 6£1

-~ ----;r- / ,' -.,.,- d1 d2 0

6/:"/ 21:"/ 0

6/J 4/:l 1.·- - - --·

1.' -

I. I. 0 0 0 0

-0,0024 0,00035 [F1 = [K1.[D] = [DDY1 - [ :Ef] 0 0

0 0 [P1 = [k].[d] + [ f 1 0,00035 0

0 0 1 0 0 2 p1 p2 50000 0 0 -50000 0 0 0,000 0,00 0,000 0,000

0 216 1080 0 -216 1080 -2,250 .6,25 0,375 15,375 0 1080 7200 0 -1080 3600 -16,250 5,oo· 2,500 27,500

-50000 0 0 50000 0 0 0,000 0,00 0,000 0,000 0 -21 6 -1080 0 216 -1080 2,250 10,75 -0,375 14,625 0 1080 3600 0 -1080 7200 -6,250 -27,50 1,250 -23,750 -

0 0 2 0 0 0

[K] =

cp.= -0,0024 rad ( ~)

Me= -27,5 tm

SORU 10: Olc;tii ve yiikleme durumu verilen sistemde 8 noktasmm, (1 Op) yatay yer degi§tirmesi o8 H ve donmesi cp8 degerlerini bulunuz.

16 t

I 4m

A , I 4m

EA 0 0

EA 0 0 --

L L

0 12£/ 6£/

0 12£/ 6£/

L' L' L' 7 0

6£/ 4£/ 0

6£/ 2D

7 -L'

-[k] = L L

EA EA -- 0 0 - 0 0 L L

0 12£/ 6D

0 12£/ 6£/

L' L' L' L'

0 6D 2£/

0 6£1 4£/

L' -

L' L L

[F) = [K).[D] = [DDY] - [ Lf]

[p] = [k).[d] + [ f] 1 0 2 0 0 0

12500 0 0 -12500 0 0 0 375 1500 0 -375 1500 0 1500 8000 0 -1500 4000

-12500 0 0 12500 0 0 0 -375 -1500 0 375 -1500 0 1500 4000 0 -1500 8000

[K] = 11250~1 800~1 [F]=rn -40

[D] =

0 "-B - 0,001 m ( ____. )

<j>a= -0,005 rad ( ~)

E = 2000000 I= 0,008 A= 0,05

f1 0 8

16 0 8

-16

d1 0,001

0 -0,005

0 0 0

p1 12 12

-7,50 0,50 -40,00 -24,00

-12 -12 7,50 15,50

-20,00 -36,00

t lm" m• m"

SORU 9: Olc;u ve yukleme durumu verilen sistemde q>B= -0.0005 rad ve q>C = 0,00175 rad (10p) olarak veriliyor. BC ~ubugunun, u~ kuvvetlerini bulunuz.

E = 2000000 t 1m' I= 0,008 m•

0 A= 0,12 m'

.)1:7t4m ~~~ ;J:;J-- 1

~1·------· j.t---------t~---+1 f1 f2

~ 0

o 3t/m 1)-0

Af11111111111111111111111111111111~ A , l

8m

FA 0 0

EA 0 -

L L

0 12£1 6£1

0 12£/

L' u ,; 0

6F:t 4£1 0

6EI

[k] = L' L -u Erl

0 0 EA

0 L L

0 120 6E!

0 11f,]

L' L' L'

0 6{:'/ 2EJ

0 6D

L' - -?-

L L

[F] = [K].[D] = [DDY] - [ :Ef]

[p] = [k].[d] + [ f 1 0 0 0 0 0

30000 0 0 -30000 0 0 375 1500 0 -375 0 1500 8000 0 -1500

-30000 0 0 30000 0 0 -375 -1500 0 375 0 1500 4000 0 -1500

0 0 1 0 0

[K] = [F] = c:::::cJ Q!J

<pa = -5E-04 rad ( ~)

M8 = -20 tm

0 0 0 12 8,5

61:-1

rr 2U

16 0

17 0

L 12 8,5 0 -16 -17 60

J'

4~-l J d1 d2 0 0 0 0 0 -0,0005 0 0 0 0

-0,0005 0,00175 1 p1 p2

0 0,000 0,000 0,000 0,000 1500 -0,750 11 ,250 1,875 10,375 4000 -2,000 14,000 3,000 20,000

0 0,000 0,000 0,000 0,000 -1500 0,750 12,750 -1,875 6,625 8000 -4,000 -20,000 12,000 -5,000

2

S.J. HUH. HIM. FAK. I N~MT MUH. BOL. YAPI STATiGI II EK SINAV 29.01.200.1.

Ad1 Soyad1 : No:

SORU 4: Oh;;U ve yUkleme durumu veri len sistemin E = 2000000 t lmL 20p B mesnetindeki donme ve momenti bulunuz. I = 0,008 m•

0 0,15 mL

~;1111111111111Md11TI111tA· ,}-' A , l

of-o lA

10 t

I A , l

I• 4 m

E4 0 0

EA L L

0 l2El

L' 6EI

0 L'

0 6EI

[k] = L' EA

0

4EJ 0

L

0 EA -

L L

l 0 l2El 6EI

0 -~ L'

0 6EI L'

2EI 0

L

[F] = [K].[D] = [DDY] - [ ~f]

[p] = [k].[d] + [ f] 0 0 0 0

37500 0 0 -37500 0 375 1500 0 0 1500 8000 0

-37500 0 0 37500 0 -375 -1500 0 0 1500 4000 0

0 0 1 0

0

l 2El -~

6EI L '

0

l2EI

~ 6El

- L'

0 0

-375 -1500

0 375

-1500 0

[K] = [F]=~ c::J!J

-0,001 rad ( ~)

M 8 = -18 tm

8m f1 f2

0 0 0

6El 5 12 L' 10 16

2EI 0 0 L

0 5

-10 12 -16

6El - ""L'

4EJ d1 d2 L 0 0

0 0 0 -0,001 0 0 0 0

-0,001 0,0025 1 p1 p2

0 0 0 0 0 1500 -1,5 3,5 2,25 14,25 4000 -4 6 2 18

0 0 0 0 0 -1500 1,5 6,5 -2,25 9,75 8000 -8 -18 16 0

2

S.U. 1'1UH. MiM. FAK. iN;,MT MUH. BOL .. YAPI STATIGII I FINAL SINAVI 07.06.2002

SORU 1: 30p

OI9U ve yUkleme durumu ~ekilde verilen ta~JYJCJ sistemi KUWET 2 tim 4 t yontemi ile 9ozerek

tllllllllllllllllllllllllll ~ 1A) Moment diyagram1n1 4 t . .....,.E-.,..,__ 9iziniz.

D E

~r·:n······ 8~

~~<~-6?•~l<~~12~m~--~·-~

C noktasmm dU~ey yer degi~tirmesini bulunuz.

Gerekli kontrolleri yap1n1z

E = 200 000 kg /cm2 I= 40 dm4

SORU 2: OI9U ve yUkleme durumu ~ekilde verilen ta~JyJcJ sistemi A<;l 25p yontemi ile r;ozerek

4.25t i9 kuvvet (M,V,N) 3.5t 2 tim diyagramlanm 9iziniz.

'flllllllllllllllllllllllt' . E C D .. ·······21

B :}

l-<2)1ool...c:: 9 m

31 Not: Gerekli tUm kontrolleri yapm1z.

SORU 3: Olr;U ve yUkleme durumu ~ekilde verilen ta~JyJcJ sistemi CROSS 25p yontemi ile r;ozcrek

12 t ir; kuvvet (M,V,N) 3 t /m diyagramlar1n1 r;iziniz.

tlllllllllllllllllllt; 4t

C ·······31 D 31 ·······~E·· · 31 F 4I 121

~

1.51 I Not: Gerekli tUm kontrolleri yapm1z.

SUre 130 dakikadJr. Soru kagJtlan temiz olarak iade edilecektir.

BA!?ARILAR DiLERiM Yrd .Do9.Dr. Nail KARA

AD! SOYADI:

SORU 4:01~i.i, yUkleme durumu ~ekilde 20p verilen kiri~i matris deplasman

yontemi ile ~ozerek i~ kuvvet diyagramlannr ~iziniz.

-

r2t : 3 t1 m 2 !I . . :llllllllllllllllllllllllllt I~ I

E = 2000000 t /m2

I= 0.008 m4

A = 0.16 m2

K

L zs

6

8 m ~ I

31L DDEY

I (V) t

I (M) tm

NO:

F

E4 0 0

E4 0 0 - - -

L L

0 I '2El 6£1

0 12£/ 6El

i! L' -y L'

0 6£/ 4£/

0 6£1 2Ef

i! -

i! -

[k]= L L EA E4 - - - 0 0 - 0 0 L L

0 12£/ 6El

0 1'2£1 6£/

i! i! i! !3 0

6£/ 2£1 0

6£/ 4£1

L' - -L L' L

[p] = [k] .[d] + [f]

[K] .[D] = [F]=[DDY -}:f]

d

0

p

+ f------1 f------1

6

(N)t

SORU 1: OI<;U ve yUkleme durumu ~ekilde veri! en ta~JYICI sistemi KUWET 30p 2 t/m 4 t yontemi ile c;;ozerek

'fllllllllllllllllllllllllll ~ 1A} Moment diyagramm1 4 t,.......~y....,_ <;iziniz.

D E

~r·:n··· ... B~

~~~~~6~~~~~~~12=m~--~~-~

1' t6,1St-

C noktasmm dU~ey yer degi~tirmesini bulunuz.

Gerekli kontrri yapm1z

E = 200 000 Kg /cm2 I= 40 dm4

t1(12

Ic. ~{,I sLc,: lt''r~

£:1c..Gt, -= ..i-.10 l2J'-{,Sz t2~>~.'5,..{+2~..l)f?J (,

-t.1-. ~3-~-~ (2] ?-56,4-{,f-3

£1c. b1o::-~ . IQ.,3S,5(2 ... 15+~) [f)

+ ...i.. 13. ~ 41 ~ '[2.] .3

... .L . 13. ~ . g . [2.] :=-Lj3 -:r -b

x,==- -~?-- -.431 . ~t-,;e~4 &u 5&,lbi-

£1c. tq := .i. .1~. 3t, .~ (zJ J

... ~-13-1l2,t.Jti6-~)[0 -t .L.rot2 ... te.ft.~ . .,.~a.~ ... 1-\-~t.y.~lo

b '· •)r>1 -:::::: 3l.t0.42(,-349~.:; -tz~u,,~~ L~ ~

-~ v rV1= ?11.\0

'Ere.~~ _-.i..,o. bl-2""23.@S-t+•w)[~J 6 = ·1~q(,,4

?Jl = ~= o. o2:5""' ~ ~

SORU 2: Oh;U ve yUkleme durumu ~ekilde verilen ta~JyJcJ sistemi A!;l 25p yontemi ile c;ozerek

4.25t ic; kuvvet {M,V,N) 3.5t 2 t/m

till I II 111111111111111/lt .. · E C D .. ·······21

8 31""" r-········· 31

21

diyagramlann• c;iziniz.


b.N . .s""b: t-

e,: 1\"" lY\ i ;:¥.. "' (e c... Ct-ueu\(. s;.<~\ 1' L~\' k,o..c_ =2 2 :EI _::_E::L -

't kc.t.=.1..2.~- o,c:,E::r:.

It <3 -)~-jACi;>ONAL Tt.a.";'.- Lt:~~

c::J.c.~2( E.'J +OrSEr)= 3€I Al-t\l.A\ia1tdt<. \l..~.A~cJ'r-lcNlM f

~~J ~;::.)Si-2,':{--h t-4r'l..5 + l.\ - A-)8,'3"' ~ z +m

¥..::-2o,zs+--- ~CD== -\C.

~~ ~ ~ r v'-'l.z l C.Q \M. \...ttl..,

5c.., 1- lb-"'" - g +-""" I

A<;. I 1>£1'-\.IL l..f:M. I

3 E.I Cfc. -5 =O cfc_== 3-EI

~\.l.;VI(. \.)~ MO""'-er-I.TLttl\

MA6 :::: c:l ( /fc. -tO) = 3 {f">\

Me,A:: EI (2~ -tO)= b +-..,

Mc..b::::. ~(2Cfc..-t0)-\6::::.-13-+m._ :£-!-~ Zi""" o zM.;....~ o v

SORU 3 : Oh;U ve yUkleme durumu ~ekilde verilen ta~ryrcr sistemi CROSS 25p yontemi ile 'rozerek

12 t i'r kuvvet (M,V,N) 4 t 3 t lm diyagramlarrnr 'riziniz.

tiiiiiiiiiiiiiiiiiiiV. C ·······31 D

1.5. I 31 ······1E ... 31

j 21 Not: Gerekli tUm kontrolleri yaprnrz.

D~~ Nol..-k 1,..,, $ob.-l-

b~ r.s. 1)~::.~ t~r DVIZ. E ' Y.ulo ... t._ f'c_d~rt~.

r AD:= ~ ='Dt 3t'5 '!.. Lf-

rDt ""' r€.f""'-3 :r :=. Ot31-}l. 6

(~.p=o rc.o,_o

b~s, + ....... - ~+,..,.a,\= .... ,

~ f'vi~A-= /4DE -=- 0,)

"'5 0

.------r.l----'+~+-----rf--~:::----fl t__ \ot

-D. Soc =- -1 .boo

'LSJ::> . ~ot--1 Teoi...U Ic..::: 6T.

£Ic. ~A =--.i_ ·4.1,..(o,a-i,(.).[.ljJ-1·8(-irS).1A[2]

-t f· g_1 (2,.~,6o -t- i~,3~'5]. [zJ ~

()

ADISOYADI : C€.. 0 AP Al-.l.A\o-\"TAI'l.J NO:

SORU 4:01c;ii, yiikleme durumu §ekilde 20p verilen kiri§i matris deplasman

yontemi ile c;ozerek ic; kuvvet diyagramlanm c;iziniz.

I2t : 3 tl m , 11 :llllllllllllllllllllllllllf •

!"······:~·~··~·· I f-o 2. i.J .... , ...

E= 2000000 t 1m2

I= 0.008 m• A= 0.16 m2 31L

K DDEY f F

4000~1 800~1 01 = ~.0003

02 = 0.001

40000 0 0 -40000 0 0 0 375 1500 0 -375 1500 0 1500 8000 0 -1500 4000

-40000 0 0 40000 0 0 0 -375 -1500 0 375 -1500 0 1500 4000 0 -1500 8000 .. 0 0 0

E4 0 0

E4 -L L

0 I 'lEI 6EI

0 I! r;

0 6EI 4EI

0 r; -[k)= L

E4 E4 - - 0 0 -L L

0 11£1 6£1

0 r; r;

0 6£1 2El

0 -r; L

[p] = [k].[d] + [f]

[K].[D] = [F]=[DDY -l:f]

d -0.0003

0 0.001

0 0 0

-12 0

1.5 12

8 16

12 + 0

-1.5 12

4 -16

~2.oo

zs

0 0

1'lEI 6EI r; r;

6£1 2El r; L

0 0

17£1 6El r; I! 6£1 4£1 -r; L

-12

p

-12 13.5 24 12

10.5 -12

(N)t

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