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Transcript of L-----U-'i./Y' - Konya · PDF filesell'"' sJ,r ~ Sio -+ bi1 Xr +
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YAP/ STATi&i li DE.R.S NOTLAI2.1 (1'793- eA.)
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I (Vi d:..e I ~e.t..: I Jtf' ir HI""' cJ &Jr., ... IJ)
l-liPEI2-HATI 1.L !o;J'Te. ~ f.2o.s-ko-f.; l..t.
'Xi::1 ~~sit: 2o rlor rt r-.J\ 1 \/ 1 ~
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 .!::l<i>f''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-:...,<i 4
Co
1
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 <p ~ <tobsJ k. ~t..:tle" ~
ke.c..::::.2.€L:I)= D,SEI it
~&n"' 2 H:!o'I) =- EI. ~
k:()€~~ . 2 ~ .... o,sE! ~ b
k:D+:::. ~ . 2. € l?>'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
I-ll
6z. -\-1'2,.
I~
..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
' '
,~ I l '.,;;. L l tc... 1). c; t' t ' ' • I) ~-
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 '.::...
~ -==-+/1S.6Cto/Er ; Vz-::o-Ab. ·'bSkL; r'f::-3,y-:f"]kr l:u. .. lutot~<'"' * Q,.u&uit.... uc;- L'LU:tlt:P-f..·Lct,· N,1 ;~ lc!.{c('2rf;,+cr;-+g"'-P)+0
17_.
1-. 1 'ZET(·+/I~~vo ? s.<r;; ·.)-,., .oP? _ ~ l ,""" ~ ~ ... - J"" ~ o-> -+-/1.(;,0 • H.>
,_ L.:;;> =- E"7. )
(1 )
.L ''>, c;y
1-1 ..1----1 +
g,-z<)!
- - 7 -+------- ·;- --,
l
\ (~l)
= - 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
V\ e)"" f' I-"\ r .
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!.
2!.
A
~ Y- 8 ,..,
-4----- - --f
10.t.U - -1'-r:SZ5 41.14/ =--o.oo~ -o.oo.f .ll....Q.Q.l_ o.oo6 o. ool. ~o.-04o - -O.o.2.:) O.o.sj .- O-IlS O-Il~ -o.goo -... ·0·45o -4,5oo - J.ooo .3-ooo
:C:OOo - ·3.ooo -'-·~l&.ooo -ll..ooo S,ooo
(v/
( t~ M)
r l
('{-~
"' ..:t
~u&u~ rZ.Eo012-LEe.·,
0A!'b"" ~-~ = 0,2SI 4 b
reo=-~ ... o,:HSI 8
r~ :..1- .U ~o/H5 J: ~ (o
roe • E ::. o,5o ~
" DAf.rTMA IC.AT:>A--trLAotJ
@ t:,;~-:. ... .:;
~ _ Ot2SI .,. 0•-'fO SA -(o,~s_.o, 3~S) 1
r'e.!>= 0• 3~5 I ::. o,,O ( u )
@ Di'j'C...,,.-J
u _ o,H·S! : o,.;o rt.e.- (o,ns+o,3~S +o.So)r
JA-C>l' o, '?>~S I ,. o,3o
:.
( ...
fw'-C>E"" o, So~ : o,.t, o
( ... > AN~A>T~~Lik... fYIOHIC',.._ITLEe.;
M e.c = - 3 -£ 2 :::. - '- t "' +- J Me.t>:.-M!>&.:. ~ _ -4 b-t..,
\.I. -
,._,., l)t =- ~. s .. ' ==- s-t"" 16.
IC..o N 'T .Z..ol-
.!'>C=- o.~~z--f.o2l. r0,z.5.::: 0 v-v
Z--1 = iJ,,287 -t- 18,~31-+~· !31,- 35 • 0
~~rtfp.,-coO ~"l. -r 18,?3~ .. g -+-1.S~'"' '4 + 2,or;t, - o,ts .. & - s,.B .. q- 8 .. -it :::o,oo.t,
-----o.1=12
o,Zf-5 r:= - · .... l
o.z~5
- ~ -(N)-t t"+-
<:sS ...__ ...___
SORU 3:
25 p D ~~.u..u.:.:..:..:.~..u.:. ... :..:..:.~..u.:..~.J..
21
8 31
21 4 m
A
I "" 4.5 ~ I ""' 4.5 m-.1
,_
ll\ <5 f
t:- (-+)5 •Ob25 I V\ 0J c:C'
\!'1) t-" ~
v (!0 /"1
L" '/... -;..0 ~ 'i "''"' Z 14 N'· 0
VoN\~2 IL,S_i)
Ic"' (.:.t
e:J: t:H 1 4 c. OA ::. 3 • S. {; it5. [zJ
- ~. s .lj.5.~,s).[2J = "b2 - < b2 = 0 ~
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.
DuJ:.'"""' "'ct:.-{..:.\<=>r I Sol,:, \ t
'D~ '"'\ . i)::J::.-I c.r ~I D L\ I l I ' II~ : I ) ' I'' ' ( , 1
rA&::c ~ ==o,<st. 4
In" 2"! c-\01J = - ::o.OJ.> ~
i- '1 rrbL:;:: It> E ::=- - .
't-IHh',l II\\ ! t
• ' ('I '. I
(S) f-Ar!>"-"' ~ :::. O,lt 1,1S
r!bD= o,y 1"'12>c=-D,2
(b) j1oe,-::. <2.2-:=o,C,br o,-=ts
f'-li::>E:-::o. 0 t333 . II.
·, I •l I I I ,,. I
M DE-== .2 "' "3 \::20,2 S +-"" 8
~Be= ~ -4*='5 = c,a-sf-..o 1(:,.
l \'• I '.I - llt'.)O t3,S o
-13,'50 -C,,15
j _:; ,, ,? •. , o,
o\~u ve.. Qo;::,\_\"w-.4-- ,d._tru~ va_.r;la...-, <:;.e.<c,e.vCLQ ~ V'r'\C>\1\L'\ t- ' • ' d<=>f't""'"" 1 c..r-o}) _,s"'-~-e.-:u t£- Ctatu.e-k k);-t 1c_t.J-.~ ... ~.t. d':''f. Cy·2•"~ 1 2.,
2..I
- 7 ,00Q -+1•000 -1 000- o.soo 'I ~ O·iO~* - o.6o4 0.00.3
-O.Oift j -(),(),20 --7' -0.010
· ·~o.o.34 - +o.ob6 ~.osT - 0.22h -0 . .338 - -O .I(,S
_;_.:...:..::~--
--.,.---~---0-·S_"_,lt - 1.12S .f,4f.
~.MO
-o.oo:r-- o.ll-3 -.cs6o
.:;.ooo
(T
. ~ -2.8.2.o
~t.lj .soo ·~b.boo -\o.ooo - s.ooo
4-UIOU \L Q:E;i)~ol.L~:
r;...c_:::. .I b
l(_J)~ ¥ ~ ~ rD~;"' ~ . !:1:-~ ~
~ 5 (b :3 2-:Z: _ 3I
1c.6 "'" -zt · 5 -16 t::>A0t T MA ICAT.)A"-fliMI
{~A::::. I/(, ::=. O,Cfo
(_ (If6t-1J fAc.f) ,_ -z./v ""o,6o
(_ )
tAt>c. = _! /Cf ~ ;: OtlfD
(_:rfc, ~ ~: <;l)
f1 E':::. 3I(/l, ""O,JD
(_ )
t18 =- Ot3 0 A"-ii(A5 Ttlf L(LL 1>{ol{
9-L l tM MAC.= -MtA:::: (2,;. j
f' L tM Me.{) =-M~(_;; 8, tb
~ 1l JAjN\
NlJ ~-A~.,-!£-Mt.E-:::. ~ ::::.-5 <tM
2..-
N~e:, :::-1..... 'P.L::::. JtM-Ib .
· S-oo "5. 00
.z_ () O
o.osz
-10.0 0
2 , 0{,2.
l
~- -5 .. 00
-
Z.'"( =- s.oo + 3-600 + 6.313 -10-S ~ O.oo
'-~ 2: x ==- 2. - o.o62 -t2 .o62 -t2. -1" 6 ==- o.oo
i21-11A ,.,-~ .OO-t-1.t.b~3 ·H0<~.4 -2"'2 -6,313l4lb
- 2.062"" b - 2,.bge_.g_O.Ob2-'2. -tS~It;
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
D0:...-... Nol..-k !.,.,, S,.:,b,-1-
\').e "S 0 b~:.~ \u D~ E ~ '
Y.ob-..t._ r-~~rl.v-.
rAC.: ~ = 'Do3'.f-'5'I.. lf
rce "" ru'::. 3 'I ::. Or31-)'J. 6
(e~ =-o leo:::.- a
bc:os' t..,_- ~~0 .to ... ,
~ f'vi~A-,: finE =- 0,)
'LS.!:> 0 ~oN TeoL..iJ Ic...::::. ~'I
£Ic.. ~A =<l -4-1 .. (o~e-i , (,) - l4J - 1 - B(~6) . 1 . z4(_2] -t f o 6 .1 (2,.'3d,o -t 1Lt , ,~'5J [zJ v:;
::: .g(, t S'5,~T51 = - o ot>l.3 rt.-r= ~.ct-.<1°
J I ,. ~~~\l.lr-'lt- duru.....,u >' \c.ild"'- ..;e..-i\e..., c,ert,e-.~ ... V; o"Ylo,....,_...,.t
~0""-l-t'-'\j\e. c,O.H .f"t\::._ \l'c.)it tl.\J'-'~et.; ..Ji".:j....,f""Q""'\o:o ..-.,....
oiQ.,
.. r:lJ Q ~~~ :f.
6 t '1 r . :L : •
_ _:.5::.~ ___ -t-----8-~---- t -.)5 ~ '1
·o.~ o
I/~ =:o----- 0-Jo .,
~ o.Jo
~ Cro~~ ~t". \)t"\o-... e~~ ·~.:.rE\oro.~ 'lo ... lu..,o --1
lj~ """"'""-"•'('-.\-\l':¥'"'•u\'t. c.lft!j;,. ~£.c k.._._\h.H•- \-\f'r;
Vi! ke1~t l.:vvv" \--; d,..i;,.,J{Q ...... to .. •
,L, ~~;\\1"!,.-de. ..;p.-',\...,.;~ti .r. {i?.
~Xi r 0 .:~
:z-:~; ~- 0 .
·~ ~,._,, =0 ii leu 1\.Jo'\~.-.
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
~A~ -:=. ;!l.._ • 3:,!_ :.Q 1 "5 :r:. 't ~
n~E.= ~ = o,5 :r. b
re~ <=- ~ ::::..06 1.. ~
re:F =;l. -~ =o,2'5I ~ !3 .
D AG;.I(""' A. \LA'( 5--f I L A 2-J
fi.A=~£= o,-s
t1o =fAw = o,'f f"-EF ::= o,2..
A~/!UJ.-J Ttl£ Lil( mom_ . Moe=-fvfiED =2 "- (,l ::=. 6 f..,._
4,5 4rst- 12
(n ~ A }l MH= s-k \,;_ . .3 .. 8... ;:I
. ~:::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"
!OC..fJSl:::.- _ of~Li ~ (jG1J.uu.e clu!Iunrr ~c7&-r1d~<'. v~rn !cu
~~~ 1;-tlt ,· <rfvto tUOL j _b-2(1 ~ ~wJ/Cf'll-~S '!~~Ill; 'l 1Le cp 2.e I y L ~Lv.Lt' t- (L-u~.f- t d LJ (f C,/2 lt!l l .
-t tT i ;3 VJ)
- - Jr.
, o ,yo l -::- 0/-;o , 0 II.,. tf,o
~ o,-zo I J
-1. :f.vo.oj-+ 3o, '333 - 0 I 00 5 - 0 I oo 3 +o. 01'3 - 0,1~'2~8, -1- -0 .0 {,y _-i.Q1J~-- '3 . 1o~ - ;f 1 boo - 7' ,0001 -'2o .ooo +3<2.~
\
.J.O
Z1
'c.
II!) ~ 0
t D
2.1
E
2t(...., r ~ r e.ol.:.rle.r
J:t rBc.== E_ =OoS :t: 4
!51>.,.~ = Oo'5 1-b
It>€-:::. 1... ~- o,:Hs ~ <t ~
r0 ~ ..,.._ \ • ~ = o,31-'51
D~J'' +""""' l:::o ·b""'(JI Ia ~ 1
f112>c.. .,. o,5 fooD== o,5
' Cl!.oS.) DtN.~L.C'-l.C)I
-1SS3 f.2t1-6tl341 = o.oot o.oo/ -o.oo') ....,.-o.oo3 ~ o.oiB o.otj -{). 0gg ~ -o.oq~ o,r1-5 Ot35 0,20 -Ot15o __,-o,315
-(,.oo ?,Soo -1,5oo 7·0o
-0 ,e,~, - -
Elc.~~ ==-!. ft.lt . (0 1 C,.ZI-b·OrB~1) [3] (../""
+ ~·4.4 - o,zH,.oJ .. ,;_ .'-4 .. ~-;, .. u.J t ..1... ~ "4<~(f..B'l I+ toS'53) (.2J ==-;, 4'5 ,'112 + '34~, B€8 :-0.a>~
,.2. o.h"' o.oooo f-
o't"'~c'<.
tst _9-4:;
t A (!,
~ l.I I ,:)!.
l.
2,"
-[-
~. '525
2tf..,_ i cf l~ 41. 7
1 ~tS~
S,t.O
., . Y.ll"3UI<._ IZ..E'O-o't.LEILt
lA(!. = ~ ... £ = o, ~I. 4- 5
r JI -=-- o.S r. (!,C.=- c;-rco=-~-~-:;..o,sr
4 b
() AG I T H A lLA. T!':,A'i l(.ll.~)
{
fe,A= _!3!1_ '> 0,375 5 o,J rO,s
lie. = _E!2.. =- 0 ,&25 OdJ
o,s _ 0 ..:: ___.- J..,l
o,S+O,S
0,5
- e-,%1 -t Lj,:S'3"*3:: b.2o3 -11f.S(; .,_ '=~'~4 :: 5,60
2-
.:L>l:=O
"'1:......,= q,18 r 11,g5 +2,t;l -r4.1l
-€-~-z .. b- o
.2)-.;fA-= ~ ... z,s -t '3• s -tZ .. '-~'4
- '3,78.,. 5 -H.&~" il -'-t,?-2•11-
G<>z.\JN\.
b..JJ~ "'""~\-co(la.-1
rcJ<>rl.~,.:
rP.>E ~ If 4
,A'\1.<.. y-y{O"''c"' +Uz...-~
M~e,::. -K•;E= ~~2. .... ,z.o-t.., 12.
2 :z+/....,., ~ ftl---__,.A J ~ t._,
~~~ t-4e,L= 1 t.., 8 ~~MBA t--'\•>-"':::.-4-t._,
-o,2s +2.~
- lj .o 4 -o
.L,.o rc.= r De..~~-= _ 1.. ·4 ·'i (2-'lrt5+~S)
6 + ..L . 4 . 4 "3:::: 0 .00
.3 v · l 1
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.
Not: Gerekli tUm kontrolleri yapm1z.
D'(f;:; -. 1'\o'c:.-k>.fa..-1 ..Sea b \t
b . D~~n - "'-.:>~..... • c. 1 0 eED8,2Lt:a....
15·4'6 15·4"1- f2_+ IO .K~. +-.., fA(.,.,~ . g:::. 0,31.)
J!""AJ (-_,--"-1--t.~~r,-4bftr \~it- o,3t-5 I I t H!.t>: B-
12 .~5 t \ (,~S 5,~'? t rt>E"" '3; - o ,3> l-5
1<3,~t DA'b\TMA ~'1SI'\-l\LA/(.I
'
r'CA= ~c.t> = o,-::.o
¥of-1.'1•LoL 1 : 'LX::o.a L'i:="' L MA•O
'<:::-eN. 'TQ 0 l. l-- ·. i-. ),P . L---"
:r~:: 3I
l=1.c..'fD= l·~.1.(HB{.'fi2.r.l5r£tll)[1) - ~. s. A. 24. w - ~. g.w>).1A2H1J
-f ~. 6.-1 .. ~V. -I 'S , 4 bln- 10,ZQ) v::;-. , ""''"'"' , •"' ""·"" "~ r 1 ~ "'"''
~~--" "
(v)t
4t11
o,so -1.2 .00
~oNT~Ol-
t2t ~1---
c2-t:l..,
lc 3Y .2X
'l .I, I'll y b;\1 ,v "'
'10 ,2;) -10,20
- -1,So ..f • .lo -12.00 s.oo
Z.'l-= u
t::..:Ogu"" ""olc.-4>1.a ... r ~l.lt-4UBUIC.. 2.eo0o2.~
r...,..e.,. 3X = o.~'J-5 'l: 8
re.c.~2 .. .2.r - or25 I 4 6 -
I>,... E), THA ~AT~"11 LALI
u o.~~s"l 0
, ,-·SA: -. .~
(Orl15tO.tS)l
..A o,2S :r 0 h. r·f2>c. = - ,., l .. )
A~I£Al>T12~t.ik. MOM.
oue M -12•8·. 2 t"'" fYIA~-- e"= - = f 8
Mr;c.._ 2~6z. gt...._ -s=-
Z'f = c;.,-?>3':l-5 + 13,.3625-+ 4,~- .f2 - 2"""' = 0
D[;~m f../oSC.TALAt2..l I-/Ai2€~ETL.i .si.sTEmt..€-12_
C.ll.oss 'fo N r~;;;m!
Dttii.JI (J:..,;; .JI!!t•f !~eJ; ferJ/ /u. J+)
Jc:aj'"' t:lifr"' Itt~'"~ ku Vv~ +!._,..,' ( +} e /, "'~"' ·
1~- 6/'Jk.ltt? J'(j;;,.., nol£ .. :f•/•rl JQb/t SiJ.fe..,.0 (.o,· C,.o.2.;,{&ir . V.,i le.r- bulv,ur. ( I:H~ y:./:1~ "1 ~1:.1.;)
.2c- .S.Je.ce.. b~ 1 ""JU .. (j~ r:IJ"l";-1/rwtc.krit-ti,.,
her bfr,' j~;.., Q.(Jrl ~(jrl o/m,p." v..2..e.r'
1
~.~ ... c.c.. CJ'r J';j ''r f; ,..,.,.,..(e rd6.... eo/ "r o..., 1'11o,,,. f-/u--
c:J,~ (/~'- of-..--4. V ::;lc./~,lr uc. V /J le.r- buliJIItu.
V11 . A 1 -+ \/.z. 1 A.2. + Vo 1 = 0
\1-12. A 1 -t V2.2. A2. T Vo.2.. = 0
t:>c.,.,k.J,_,., q~~;:,t,:;,.... /..A; fer bulvnur
~ t.k.ll,.,Je.. d~per po.2. ;J""/o.-.1-. ,,eflce mo,.,~,.,-rlLr-
b ulum.J,.. , f>;te:/'Q...,/a..- <;i.L,'{,',.. ,
n : :::J~,.. riff'"; .;.,-,c J:.,'l~.... d~ ;;...., .SU '.J 1
C; KQpwlt f>-'i,ro-. .Joe/ I.J I .
1 2..
1\ :.2. C.= .f
N = .2. -1 -= -f
A ~ -1
I -,. ---r * vu ,~y2.4.)
\ --r
~v
r'\-:. 4 c.= .3 t-.1= 4-31 = -1
· 2.
n =..lt c.- 2
jl..b Lt -.2 .. 2.
,
---L
L
L
6/c;,jj "L.U~k_U""'L. dt.JI"IINI.I.I ,5t.lt..f/.k_ ve.,.,'/~ ~Ut;ev-fjf li>o">\4(:-
/:).Jif"'~#o - CrDJJ c:J5,.,.ft;-..,• f/4-. ~.;~ ~~f: k<-tvvc,'f:-,'
c:J.[JaJ,..._,....f.,.,../111 Qi.J../"l/..2..
c. .l.l-
A
y 4 y 4 y
-tS.2.ool -t 7- ,goo 1-.3 . 000 1- 1o.ooo
_ o. o9~ J -O •Olo 101234 1
8""
st~,-----------~,r---------Ar-
--r 1r38~ .......- Oolrat-
st- ((02..";;""~ .t>:cr:;- 1'\•lct--L..-, ho.rc.fc.L+U ~i~+c-.nr. ~ ~l.>v k.. rd:;,.l~.·
lAC.=~
" rc.b::: ~
lb
~~,t~
r~c= .:£ '1
roe:=~ ,, ~o-b0 ,1coo,.1
f"'llc. = o,Lfo /'t 8 = fLe =q3o
1 . .5AFHA ct&JJ"Wtl} (AQo) Afl~ut-,s~U"- t-A,o,.,t-af!~/
£___.&.,.* -~ to . a_ 10 ,-- 1o
I -~ ·-0.838
-: o.oolf l-o.ool o.o~o •
-o.oO I-o,o4'f 0,1'58 I
- ~.oSo ;-o,l8B -- -J.OOO,
5
2. ~HA (A:f=.o) Q.'O.w4
c:)"J v,.., ""'" h> /,,.,, ,_ { A) (:11!- r
dtji.JI-i rm./e-<>~ v~ r ,'fir.
~ .Ac
' t:> I
' ~J1f't-l!l... mo~;rffv,
.E :c = 6 o , A = 1 r 4 ;,
MAC: MeA: 6 E-(f) .A= '"'0 ·.( z/ot-.1 L2. (,L
fvfba • J~ =- 3·2·(,0 •4:::: S. '25.,_. LL gl.
loulvnvr. en,J .Jcf'e-~e-r/
~ptllr. (1-t)l£.qfN./'t..t:U
\}u h4JIUnWI".
Z~= o "o' + \Ju. A=o
.A:.. Vol :- _ ~
'./u .2,581-0. a - If 18Cj~ Ioiii &J"I¥ .
~/ ~ . . .. .. . -· ....
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.
Not: Gerekli tUm kontrolleri yapm1z.
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
~-\r-\-l''' -ru• '"'-/
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lSL c..)e"'-~1" VV\CP'\""-l\ t \e._ b~trl,' b~r d~r-.. l-h...do...
~(;h'\ 02-piD).VV'\.O) t.e.-~ .e.-dLb~~ ~ \'c,~V) tO?\:) ILl
..5~~-\--2-........_e._ 0 d"'jrv l+v.d...,._ tot ~.::,;~z_ eo'• '"""'e.~~ cs.e.·-~-'c~
k.u,h./2-t ola.,-o~ tov-~ .e.d~\et.o~llr.
Ta~I<JICI 5\S.-1-e'-'\ de.JL7 ~ u~Pwk..(cu-- \£.e.-"'d'~'---12__
.e...t-~ ed ~ d-:= \t.L e..- ._) e... U::: \c. .LQ....r ~ e.. +lq_ :-'
d " \J\ ·• ' - 0 rrl; c:::le_ol=~~.v>.=,\=-~1 ~· ... "" =----\-'"\ .,__ 8"'y-e_ ~ '
<JD f'o .to...-. ~ u \o u ~ 6'5 c ~ U. 'i l=.r '"' 1 \'7"1 d.e.f'\.->~ ""al
J f"" \,; lcl~ \c. [e_.,.; d~ .-... I ~ la__,· \_, -tor'=-""" .S~\.) I <\.a,
0 ylllo~'-"1 ,S.e.rbe)-t-Clt.. ~e.c_e..)~ ~~r.
-~======:::~ ------')>- 2._
Ct- LIB U \(_ ..SE e._ e.E:sT Ll k:_
be e. E C E l£. ti;
?, - k..H do~ -t b2. cl.2_
p2 = k:z.., cJ' -+ ~22.. cJ:L
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q u ~.>tf'""'1 s+-r~ef (r:-drtH~ ) c:~.-"1\a_le..,__;
1 f' 3 ~.:. '<.. \(e.- (e_ ~ ('~
~ c:l) d e.r 1.2) ""- .._, \.L ~.Jd·O' ..-.::
\:.~] st~.f~~} (n(jit\;4_) ~~-tv-~~
e.L.e~, \..{'1 ~uv~~ bJI'(J-~:...1 lo.'r ""'?h~+lr-.
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+-... ~ '? \.e..__.le.r Je_
aAt""""~ d.,,._
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b.... ..ele.>e.--._ -t=~~~~ cS~zs"'::.."'e....
2
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Ad 1"'' "1 : An \::...~i: ( e \', \(.
Q.e-\elbO""\ ~-~ ~
2
kuvve.-t~ -1::.~+1..:1<.. ed;ld(f; DloJru\1---.. l J L:,;r~
clep\9~""'""..._,..., o\u?i-u]..., c:-Jofr-..... \4-'-'i J- ;--~e._
k r'ct .sltf r,~ 4e-slr ..5 U 1 J 1
k to To?l.jtC.I e_(a""'a-"' 1 ..., -b::>r~ e..d\1"'-"i( b0+CV)
...5er loe.j + t~ ~ der.ecel<L..-; d..oJ r._. I-t-..~ ........... d=- \:...,~
de.p\a.s""o-, l.:a.r- .:Sif• ..- ik~ 1
2:30\ "".\.2... cr o\c.v..
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EA ..-1 - t:=:=========:::::J '}-<\\.1 6-.u.eov--L ~
cl= ~ = ~ ~
b:t~; e~b~
b= ;{ ~~"! p =
k-1~ =- EA L
k "" !:SA l.~ = L
~~
- -·- ========tt ~ t-21
EA L
me.hH~.t- ?Qr+~P .... , 1"\e.. olor~- olsw...., -\-u"-1
ct u bu \c:. I.., ..- t "' u '1 I c.,... 1 -\-.:;.""" tl V'\ \: ... ~-\ r <.. o \d~'"'
o.\~~;:,"':.:,\<:,el.!:._; ;l.::.i uc.,u Qo"'\::-c:>~-tr~ Cfui.:>IJk:lc:::>.-
i'Cj""'"' \.,o2 '" lo "'\\"11 f' Q 11 k=..o~f-r c.J.l ~ i ~c:> b.l'tJo""' l ~:or· I
.foblolo..-1 u ... l"'d·-.~1~ ; \/efi\e...., ~::.\::.\e..-
5
Q \ +· ""a.l-. Ct u bu k:.. Q"' "-.)+r..J.r ~ f"@q ~ s b"""""" t ... 1
poz :-t ~ f U ~ ..-...1a.- dik k-+e. o t l "'co.-Qk_
he.)~p IQ..,, '11.
3
,f L
f3 ::. - {€;. =: 'f. Co)~ • S 2. =.
12
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'f.l2. 12
b'"0 ~ "'- Co.l o(
i IL. 'r .., r f>' 1 P r"" ~
Cf .sf"'o( l•.) I(. ._s 2.
4:{, S {'.,ll(.. (o.) ~ • ~
2. Cf • C.o}o{ • S
~ (~----
t k2.3
/ kS3
*A> ~v~LE,....E'- DLlll..U"''J,J "' hj
E f 1~.., \ "- I:: ~ .. ;r ~.:;"'-e""". \c_..., I 1- ""' \ ...... -\.::. m u bo:o -
\.1 e.~G+ ~o: 1si ,~,v k - El. A } t k.23
L
k33-\- ~l.~ + k:.53 . L -= 0
\l.s3=- ~ 1,..2.
tl~:sj ?'
.5:::.1 u c,4- J;."' """IZ.
. EiA: A 1 = -1
. .SQJ u~~ dc.""....,e..
9e,:::.-~=0
E ~lb-14.. k.:rl; .Je. ~ LJc.u, ... ~ 1"&. ...., ... .,e..,"t-
k6J L L k3J L 2L er. . :2 · 3- E..1 '.i' 3 -...41-L=o
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A IJGCJ"- j.;rc... mo..,e"'t-
j_f k,J .!=... ~ - I::.JJ. L ._h)-p, L :::-a e:r ~ :J. .3 ..z.. J7 ' .
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k.33:: i!! L.
k"-£ -----~ ~~5,
joL UC, 7A
St'J.k-W~ /8oo J;......,,,JU,-u'l;;p ..$-..1 ..., (j.;.... b:,;..... cJ ;....., --//e.. J::.G.r~//o;-fulj,,J..._
k.3(..= 2€! -r
kt.6 ;:: C.., EX -c
k5l. = - t:. ex. -L1.
k2. 6 = 'EI. LZ.
t;311ll'~ D 7tl..£N/}1£'
b uli.JIIWf',
,5olll4~ -t:i- cJ~..,...,, L
-. ,.( ,. \1~ ~J lA$~ +:: tf....,.,..,,
'b /-(f- og}; It:. J:-k. el trw J~
bulu,ur.
,A 'blm S n' ' ol)~.,...,
1(L )'4,.5
"-ss 1 -- t I ----------···
k..2. s = - -11 E.l:
L..l
k ss ::: ;fl€I.
t=l
k3S.::- 'e:r u.
k,-s = -~ bulu'\Ur"'
L1.
..S0J-JU Cf l
8
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olc.lj- cJ/k~-1<. o/1,,,.Jo.
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Ps =- k.3.2. d:J. + i:::3.3 .J3 +- k:Js J5 +I::J!ud{. -fh fs = ks2. J.2. 1- k:sJ d:> f k:.)s d5 +- k:.s, di, + fs P(. ::::. k6J. J2.. f k.,j d3 f 1::.65 ds + ~' -db -t ~
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ru. ,..., b ,'(j,'le..-
p, .b, bz. 1.:::,3 kcc, k-1,5 k,, P.t. k.u. l::::..lt. ~.l.l k.t~ k25 k2' f'.3
J.c.3r k:.s2.. k33 lq~ k.ss lcJ'-Pct -k.'i ' "-4t. k4J kc,¥ k4s k:c,L
~ ks1 k:52. ks3 kS'<t k~s ~£~' p, ~I k,z k'J k,y h-s b"
t>clc.t '"' ~~t- c~2..1 I("~~
c:1, +, d2. +'2. d.1 tJ
>< d't -t *4
cl.s -fs ch -+"
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~P?
fd~ 1-f:'~ . c.u\.oulc. .... 7 Ql'\\(•.>h e.- l ~ lc. re.-\::l':j"""'\
\o
1!,/)J,t,., .kje/le.- ~62,/tt'"J.oo.
1 2 3 4 s E:A €A : - 0 0 0 0
L -- I L-
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2
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s
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6.e:r 4 ET. L1 -;:: --- -c Lt.
11
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(A) LioJ (c) P, 0 +0 = 0 0 +- 0::::. 0
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f> • P<. ~L '1 L2. - -:1·6 12 J..
12..
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olo.Jrutf~.su...,oJ-.. Px ~ Py ~ Pr cf:~o: us- ~r' b,·l~;<...,;
bullJrt•'? kuvve"t~r", r:f'",~ U n 1 '1t::>lt:.-l-c:Jo...., ~$1!:'?
c:;ere( ?t.. 1 tj 1J i!..l.Je:..,/~,.,· -c/~ .. ,f-!v..Jv.,f::l-=- ~~~~~
J;J:.: ..j-Jo-f,"kt;~ e1r J:J,?~~.,It!/~ (Jr,/cJ,;,,"I/rl~,...
PxJ ~-e)
{Yr,2..J)~
J 1\ /<o Y.~ p~J ~
L = ~ (:::IJ- Yi )t-r (~J-~~~ 'o.s o{ -= ('ls-i:) I L
.s i , o{ = l ~J - :e ·, ) I L
ru=- Pr. c.o~a( + P-r:. !>i"' 01.
'f'~ ... - r"(.~i"'O( + r~ .c.o.)..:(.
ll1 = r:: ~:: :1 u:1 [t]
~ -t-~ O~ 4- I le.,t"\- \ r; 1; I~'-
'P, p.2. r?>
r" p5 p,
C.Ol oe. $'"'a( 0 0
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0 0 0 Co~ a(
0 0 - li\,ll(.
0
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fi>~1tJ3 =- [T] . 1 P1')('"<7:
1d3xJ~ =- [T] . ~d~>l..""fc
1FS?(z:1d~ [TJ ~f\')("ft-
0 0 f\ 0 't:> fl 0 0 PJ .sil.,o( 0 p'i Co~o( () Ps
-1 ?t. "j .. :tt-
0
-trQ ... ~i>"'>~~ ....... , e.('~-t. -o\d-J- b-.Jlu.,..uf" . '&u-clw.,... ..... "'"'-
1~ \e"""" le, ..I.e.. \.::...,l-..:J \,'<._ .s....::f l- .r •
~P~x'-lr .. ~1]1 1 f~?-j"=
)d~ X-t2-. = [T]T ~ dS?C.a}-
1 t~ >l--ft -=.. (. T]T t .f.~~~
in ~-H= == r.. ~J~ ... i~ . \t:l~-,c......,i;
1?~ ?CU e\:. -:: ( \1:] 71-(J ~ '{ d ~~ lr-
tkJy.-;~ . ~dS>l---t-t - L\f. t.~c.J"tla l..J{"'u6: ~}""...,t ~.J))(.'it.-= trJ,.Lic.]?\.U~ '[:rJ1o3)(.·H:
Lk1 )(.'{ t ... ( T]T [ "] 1\:j~ [ T]
I ~
H~t "7-t
lt> ..... 0/3t l.
(4,1")
(1o, s)
Co.) o( =
r, P2. f.s rtf ::
P:s
f'- X-'it:
lo- 4 lo
s -I(. I~
= - o,a
o,, +o.g c o,s o,, 0
0 0 1
O,l,
- o,s D
t_"T]T
4o.o ..,_
-+-o,a 0
o,, 0
0 ...,
11 .9
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[P]~6 \ 'Pl >C. '"it-
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. 'R:1J i I L\ ~ M .,..._ICZ. t ~'
o\ ' ... , r ~ ....
1:.1f'~~~ ~ = 2 [~]')C..'fe . 1: t t1~~~ -t 2:.. ( .f~.,c.."'r [~1 i,. bJ
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}
1 g~ ::: [~J-1 l l='3
~ -l
l {,
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f-0i-t.l~lc._ """-+.--i~lc..,- ~ / e..\e"""•"'"' koc:l V\U...._,.._\cu' lf'"\
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LK] ~
1)J
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0 c:> 1 2 :!, 't k,, 1:::,~ \c.,l "''1 k,'S k,, 0
k2., ku l::2.s bj l!tr k~ o
kl 1 ~.32. s.s ~J~ lc1r "kl'c. 1 kt,l ~l I "iJ b,r, b,.s ~ 2.
"-l1 "-fl. ltn l:::r~ ltSJ' lc.n. 3
b., b.L "'-~ b.~ '4.s ~ ~
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C9 .l{,lj k3s
"-43 k:.'~4€0 k4r +St.t
k~.3 ks<.t t~ 1 ksr+51L
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:s,, s,1 s,li s,"f s,> s, 2. ~--.........5.2.--, S.u ~u \ St1.1 $2r S.2.L l
[k-) = SJ1 SJJ.. S'J.\ S'l'f Slr S:" 't 2. Sif4 S41.. s;;J 5411 S ~t'f ~ o
j.s-1 ~s z. sn ~t"'1 .Srs- Ss- o
S" ~z. $(.,) .Suf ~'f St' o
@ k.3(. CD
ktt" -t St.J ® lc:rc. +$.t.J CD
k'-3 lc"<.t tS,, IL,'f +S.32 k''" -tS3.3 GJ
11-
0 0 0
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c-a ~J
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0 5
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riJ;-t!;i<_ Mgrr;~; v"'' bo"''"t 0 a .... ~) \~ j ',
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e.~:t-t:Y. .
(_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] =
<i>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.
Not: Gerekli tUm kontrolleri yapm1z.
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