^'{Alno f. ./rv i i*rc, r a i q ) *;rn|r in/U{

i i o*ios {o{ , {u , fo Pr*v*r ,3, 01 v t*'t;'):A Daioir. F=s[nl, "fta, {*7=@ttPa,8=2tztt'tt /$', i+a /lp,* s D

ry{=9 + J.6.Psmd,=4,

ij#r.flfft7q

L\ i'^o'";cni:q:{ {ri1r.{a ze) Prryrranyrfa{Lest S$ fi iqq,r, ,**o/,;l; ry*,ooD:+U

.y e.

l.0 ril - ,{i, L!}J5 : @-4so.9

-=-lg- -rA

^ {;-"a;'-:= -?- J-*tJ{pqr _ ,rqP( - t$:2.s_ = {e saE i. - {d2W ';n7; ;E

,tt1,3nr,.Jnn> n t fi,9, 4c = i J'r= 7,15,,,,"2

Fcryinagg&*es: &= * t& * 3r58t')n

r&Druqi(i

.4

.t

'i /ni'

--\ r lJ t \ t, ,

=) ! Jafo/' a f,1. ZSrpa AB * 9: l.!" c'r fal/rrra t.

3grr: . 4 uro

L-zalmm'

g

fr lg'cct?co: F{s)o6o'.4 y:EF*, = !?"' r'z : *d-:44'= Y:gi4

"(r* qz.l| 'tgz IFil f= tr#=rffi'=zl3ar,/

{l*/rrA{i^* z*rrr{x; t-r,cr/ r,?!;t: !* A.- g,u*As4ZqJqlql-lA . *o/u,jb '- ;"gr/,'{ F= 8o OP

ELs/,r/r/;lo * zavr-ipi isp;t zfli'inl r*^-rri,4,;Z&*aL3A, /q{o-1o, Q*eadkt l-!**l h=4*, Q=am, u ta oV

a=2n o; reJu La ita sp{prpefeotb mA-/ 'rro? W -*lffi .;f= -'Fof =--pff*z, tr"- */{rLl Aer:i,:lt?I?, ax= r,p*rpr jp:,#*:SJ.f{= (1.{'r.r{.,g_ ,_;5 * 1+s)14*l = $o {Y,. {e.e)= {;g'J*=u,qJ

#m' I e"rir a * # =' *":#4j*V:\N.=ff8*:T*"i:*#rr*g:Ww1i -l*

-fi :&F =-fr,!fn,E , #;,f;*y*{'PrsjekA

Qaa. t !=fu;**t*roqastlPo, - 7. xY 2 d'rD,i*t= ttq l-!+* *=ff=znra

fr

Za dio za&ita (d)

Vi= Jffi*ff:JWrA?ilPaa e,st{.ro= Gidl za Teprsini rreljp1 &,1^ frs/enq - le$r>o s/*en{s I {Jo{" {F=taort%,)

r; = S"# -ff-iil-g = EQ- t#Si = drd {rpa) , tretadreJ,/, k -Ti * Ta/2 = e# k-wr) t G,, - -E- Hr { = ttLdu-- ttz$zx;= lL{"*.=[.'"rffi^.'=7-''ffii = 4sx#

Phu /70 L't *el r, , o. d- rlii- : Ri*r*rqu - {rora& $g, SoQPa , {&z = SoN&, l= s}s o\k, , ^ n$ ilapoo,bo

^ u \T, f,r^U aQ*u

){rfdu*r,{* ai*- ll{t =e4,*{r$=s,gb .,V/'

7 sttl {: fiSLxpr,5'

a) s,y'*

+H

"$UsaAr9,="ry1!"

; !orfrs/"/rir -2"/a{nk-48, ?alo jrt fi =

i,/1/."/u

ffH':ffiffil'{p.{, 8"1g, rs rii

.rr#&.9.*/&n* a{**,laSnd =#}ul

ffYav'"* i 5r stnsa*-{ *Ses,nd't=llt&) , {a} rrf{is .

{S.*r *: # =r{, &=* *W=W,fi rutrXktAtrfu{}i,**aeirooagb} ! {* *n* ,,r,,r*_: W%= 6i*fr rr"!n,.;r,P

,\ T""Jf:o' F = t,'/!r='## : 7,,8 rtp^aa* . frai{s, Att lsr*a.zr>e . Az. *t*pm"^! {aqlenage **t&aff; s,u =-rr.*.1/1 =.' ** =* ffi ir:*r,d) S,lq uA, {,c= srcarF*&co+{

=,tt,.t,k,,f; + As*{ttft =q;4Lr,t, S,c=&sip*feszox =iSiaf*apl$3e = /, { g [nJ / F.,q __ JEI fi] = !!f.*zoJqt'q I

.2 E, **y'CI. Jb : rYs = 2 Lrtn ,

tbiIt3

iola,.i.

i%ttL

nf. -

tr._ -lH.-

dlCI= 2/s , TJ;*= gc ll fa,, S = d*o &fq , L = Zn .-i' t,zt :2igs i--s1a ig : A * C : 53g =-$.= *.{g = -iL**

u) ,,n *oL da ?.a = o

L) n. - t t, -:Q 1'./!!idr.4 -/ - -' ! \__Z-lt;*:-"l L't 9;17o, mortr,./a !r*)llnn r'aqlq2,2{.e:at*. e=$d =83,2w

{{usf**{oz*J*tqAeg.

/,to-zavriri isyi*,r-r. .--

34

a) j-r- lo;io ,r/r'roa7o Pa A'A -f:*l. il? TrF= F,l = Q,soilor,t!=**,uf ffE*

+ \ ,J,#;lJ, L\ jr'^;trrrbo*'apit: r* = r9- rP t{ , llgf.t:l .

r* = ryi-. 34.5,, ,^ 7gi.iNiS ; A Svelgnt^,rPa?sqr

T Ta"'z4oq

i(

,r ],Zq;a1aLl

l,'no\

Y

{5o

4.=.2- 9J_ ^. ti\ir = Ti { = zz,*?i17 t** $*l1* ,,,na, =- _llxn,o^ ,r;y;, * *; a / s

, {r ,_;,rt---/ >,s ltLenq-'

-sWEq - 43,5n^ -7-Y

\'('-rY --e#rr'5{-5r;='ri

e.' : 7.^--fi.' c'Di 6d \ {,S. 6o*;^ =:_:II ,l* -.--1Afl1

.'1ji n'i'i{i -il.' 1a-g7to, i,?;r,r? a.' -, -.1, )lr?ger{ i (, !-,t } .r.c,z,s.;1;t

i I *1rs/u/, lo *,1:V r ssor t :,'b/n,,,3igr,;6 - *.lt,pa"i s.'

;ri.,* ,i. #f1=2Pg rt ":,, -^,1--rr'3

?\,tl- =r? i{f = ZGi*} F j.;:L - ry#d* f,rr= r{r = #f = r}Ern}L.* = 3-4EHE Yit!

"u * %= lyrf = --AiE '?= --7;n -

rv i |nti-,1*.5v:*

uritrt{*,, tt, D* *,{,

,-:e#-xr*,

q

{s*

E/rEl5e/o/,/o -

Jrug, f*rc)ybln; tsp,l ,zc,v,j*ur { }ero }b, j:fi{ 7: ;.: - .= gs N?a

of {,.9r>,t1.-J'

ct] :6*- f*

bi !trf qzr9o4 q,t sgar,siw

-s a${acrj) lr ,r,r,rami/

\& FtfupcEa\ +s/[r* ryir'*rb. *7o t

', #" ].'--.--,*- /":#e {!,4ini,..4,*?3e uza i ix}

!**a'- Ft-.lol, fu"2rt &=3F; "

,./ ---jj{.r/- F - j* f, ft., c= E*rr,s.Q=w $ ifi pr^: -" 4 i*:

't@rnht ssf= ico{lfuo , ,,,;d-.r,*./1 ,ltb) 'ttkupp i .*rzrri :*.,tiah,ra J .'riL' Fov2,li gs,1o-,o s,

^-'La./\ -(.-'j :+-r'e ^.ri\ tr-tV=\-_ Lv;*rd;r

;';r = -tGT:a; , Ts , -YELI*: *$,:g {= ,,oe

'))]'yir.*' ncnazsip;b.aapo*q je r/of *c.:.l.it, ,aJ {.,, $4*so fi L It==..;IF=1J,6.r: 7gilpq - --;,-.:5

JetYnrn'-:t" ":,,.o,' SdJeJo 65='vrt dr?r, -*:!-1!!!E, ii.^1 =-+t - 4sze.+i*E,pzrtlrd= {i?,{pa 4.r*F

o''.,;{] ,f,

?fr **___1_'/;?+,rso;

u,r-.

^\^'rI ',-l-.,., , , !:* .-''' --'rj Iq .*\t*%",,/"'tt'?'j i 1'/cb2*1!.;t,g-'".,j *ai,afo lc-,sJs li {p-e,t1} ,::,i?i

,^^r^:W^rt-*,t1"5;ro,r).)("'rr='-,oi!''lf i 7l{xl,-ir-41+ f }.

{: j *:,*::f"t' ylu , }{ t, , !* {'; ili,lno /. -r{,*p,ostr:/t' /frf ?tii* yr,' Z-u',, ,q."^ .-A^2.

J 9gr LI:z-----

&-iX,rtk (P L b= '-1,35r*.{g,t;+ *c*- tn}*6-

- _4 1 ,*

xzlz1a P-* **ffi t)l i/r)

,r{^1,.:"

r1'J,,

-

31?1e4 tr+ *--- --.rlI*ry*-

- {.,Ta,-ryf{= *T,t.ca-'ll'+,. Lah

- 'tt3.,l L '.Rn*i

"{"4' =

1rta"36 3EInzlz=*t-t**tf,

.7n "-:*:Ltir=-,4or^,>o,'r*..*},*p*/?d ::4!*o,rtv$ryr

i l **zzczi i2 ,oo7,t;n;) ve:f*a -

a. {e5 rie

t . 2,t -\.1 i ,l _y? r,.e i q= +L 4 6?oz- -) 4{; 1;-= ## = 7'8 -'' 1 Pi'ou/uter4: "- fi;= ty';*"r'!ito. A, ^ o*e Ja N,l>11fr-z {?* =} .'lr= }Ss{'">a2' 4." 2$3nn2

.' ir.-,p--...s --":'ici . r.s: lp e .fg= / [r;= g:#= ? ,f#**tgtVr'.''.Ul L : *;' 2S,3grri =:

Jr = yls = gSfF> a .'^ oo,- y r. z \,1/. ! n- Lttd] sridtt oi/ontu l,xa-ilco's(+'szcaJ,a=s{?-ttft]:e'ez!-*2'13'#)i'=6;s;Ft't;uttL4 4*= 94sin,{-s2linp =r**-srfu =;t,ee.?- Jlg fu',;,r= .t,2? vtlr-';-r,t-{'l-A=ixi+g, , /,65 lu

,:*.n., hqt, ..,E ; ilu -3lovn, 7d.,.' ao:^: 3= 3o*?o, r:."'o, 7;='/s _:*.t t. J

o, i {.Qo a t'vD' .">orDtr? '; :)- . . - 4ir^ ill ,'' r!r* H;1 = M's { t} : ;::.;=

"t''' ,

/t, ror, ,.bIo!-2 .LiJo3l ,*' * *Z t; '

ilr,-t-lq . y.* - Ltt,', P/d\4 - o 3) "u' :3L . ''Ltla= l'!'l

--

i'!l -C.v,.,=orz.t,iivn;ir - tT,r wy; = zGTt = i+"t't .- -Ijr*_j_

,, ^ ft " #" = !'lfi L^]'D io

bi r;thrsElbhqqge t ..t., iLt-l,-o, =

I ,Y!:J O : -_*_J.-*.- y;' * TJez* zoH.zr- EJ-*z JrysTqzn, F-

|aflPa, b=3-, {=

-*.'---{igb

n - -

.-

-.'-r-i J/a i.1{6' +'J 4 i,4.vt- :@ * sqg r.zz7,j=fu,uLiuZs?r^)k-J_ z,^.;'-:** ! 7r-'zo$;i.- ;*;*,**" j- ;r'5 1{{tnr\.

,3,r,f: - .

?;ott-.jret .Tt4nan= #; !=;lir?ae},'/y** rglcrrc y,,*,o1h iriri;r,; '"&2- L

a\n; r./ ' t / t ,_t Kt.! *ltlzf\,9Jt'+".v

Y9dno b',N^/

L.r

-te

n(l,Fto

P,'

.1\.1=d)F t

tc/e.J r*;

ir-*i jar)$ . +**r ,"1 :j y'rpl$i.,35

r-, c.lt!t^,/ *Y*;#;:*_.'

e)

rj

{7o;,{td, i"lu, g.4.Xrd1' * t;'*i*n;* $oro E.

#=;;k i i * :44 ;:{:,,-:*'* :", j) i:Yrua;'-"':::-,r*r,=ffi- *frj q.'= |;-r,rr,a1r,,{. u, ; + :::'jr,,'_*',J? *;::,':i': i *. :"'* Qs,tapT'z :i * 'JS{,{ tnl

_,7-; ,,,- ,* :. )*

ni

t'?i"* ,d;,:::u' Q'** Eaftp$t 6=2a" {= $AN' *u'=o,o' vgr*r-

..4*-s ^:rr"l Y,*,i ^'{ l;Aro{..,;q;

&- i5 ={,L i;, ie\ .3d=S--r,sl t +e i Po'*,,,

=s st.at= "@= T=7i

ioi{:A !"o{r=l*rrrtra1?1 .

a{, * -t,.c,^-/ - n--*- -i 4u- 4- L :> sio|= :L=?, u*2.*atsv!'/^ -rd{-S-::- I 4t' m-i ' '''t,\ 'r(z) \ !_ -ttn9tr)'2&{&,{.,, A _ -: =4 fpl 4' 1ts{' r W'5 t

*t" {-\-LL :a[.=$s,rp

*Jc.= #^ _i'"' io= drjs 7, tr) {siu fti, :,go!r=7'nlrsi,( {q)rf,-- *lt "'o=q;

*:n,= -s.('. :;-*" ).-

rt' tt[Ar lFA,

,, .c4z , H "{s)q&}' sF;:k{= dr. *- + :X:k fe)z.ild;,c +'"k; LT I .-\ e 2 4'F ut-u / 31 s,a a zi"+.^-r-iyt'- r ii it; *,# *""* * = 2F r) ,h;u661 . + +rl* *sr= 2F =) .a= =2F = = /,NLt/_.Sr= C3gtxt

,_, G*t ':o/ 9,ag4 z 1't porrec'nii rr esieLa -'rs rf = *"r 0,* + 0,, *= $ffi= tS,inot', rr1pr,: dy=+===4:t.51Az $, itlr;6-= 35lflfq )6?or =) J,***,ro,e*a1c TrtiyetaA2, &?#=##4=23t3/hm1g At, 1A.r^ Sir S mmz. v -r a -W flp * zrtt=o gs) t ffo= p&, *- _?, u,.1'4rbta1

, ,,0=q+,tvrilt4= ,|,?2gL+tm, $r=g,,1-_ ^_^_,4 - ::=_':-'l ,,u &fU= ors& i&. i,inU **L) !'ry"zicn,i-rar,1e .

(prcUbr u ltr ,1yp/"n{rr;gftgs,L*tn T< = *r,Ld.'= _1"._ -t:'l ilt_ ", ri^o

t . -Lot-t 2- qW/ = Jry* ? -uu-a/,f{tq4 I I dr,:rw#4 :t- 4w4.v -;87*= vvL

-\ ffi = 86,7 n'4 ': D= 3/ra= 4rc tntz>$on*,-*a{nAe.:elir/a 1* C),-Dr1\rao a3{ova u,t(aty {,** s{,t;; ,,-;{*'"u'tnr*

"J]'.,4 I* L-*ffi-.4- strNPq=4*nax '?ulp,u= 4** = i,ori-ra$ , %=?trv*.= c,*,air$t'o

' W -6ro= $,Tt-:mr- lxnr^. *rcr-t f": s,oo6 ra4

,.tl t

/,tt;/r iN-\

:.

--> tr., t ' Ltll)

"l Xn

,'*. it.''L.:- 1-,

3 Y:J I

,71

i:\/?t,/l,/t/

i t,'

,/:/' l.-?. ir-,' i;stu

v| -=)| !-,l,'La4v

iou'r-

j t*it, ,j,- r {t)t ?,- ,*/:* k fi.ritZipil,r,ir. - ,);l,201 A')

-JA l-

LLru\F' " '

rs=(ff i(4,,t, I z,l.

l-)

^"I:il -- flon' 3'. = 4oo ltn = Plcx

' vlv

l- = i-i+u t F,-o^ -- 1.162 t)- lr?..--4 "'c.*-"

,--:1[\,l "'.,

" \e J,. - ir=_ "+: ->,-.it'@ : t,,.:r_---_t;hl"a)

-.#Y.Y-

dZ; t^ ike prgsTgo po,u.ic r+ ,rorr_;r.) {u (dafnos/;c; )

F7*^ a ,-l ,L'L\ : r\-J-y, \ 1/

F-l-J _ir

^ -

f> fl4!z

6'4 t d /7),r4;:-..6

,* ^ :/"'sotffiFo,r# fr66(' YM'.L

4e,7si < Ll

^:i.., ?;'-r.J,|r '

.1'/: )

bz-"Eu

---->

*? =\8,s'ie

i= y,s,:ru

:-5otl&

o,oZr,$!,;a4rc,nz

rz

2q

D' -O

-sq ru. n, da^!*,,zqx

-

= lrl'I-.l,JI n/f2-o a #- ,rP,

tt-l . if / n'-tn rL- r v"-J \J2

F;-zkrl , cl= 4ooni',1 4L li, ii .r:.: ir . t !- r llrr,{t) l,-toz,coi:a,yje, fx= + -':d=i = *(r-W,, , A=

"L,d_r;;r= irfi ,&

q) RerL L, ill, c t!''^'!iin ',', no f;-g

,,/n;ir L i-'irfx't)

4o6zit y',rr.

.i i,' ^- t'i'/'*'7r!u*i:';rlliJeZnA'lDC?"x-

-) Dr 'agrqm /24/;Or;q rezuifor -r

o,L\ 7,a . -

/, . , ac*3*,a-2,'s-S- = '-a f;a l'T

{r'*, $\=i ' ,^, Fr=Gl:=l',, =o + - 1+rz,F,L,.' 'i 5el'+ /='fiffi^, ==i''

= i) + a' 7a * =f

a,-:----r-in-- i i) i/e,/"ol ,'!'""i'Ar-';;-_],.l.i \ ,'.'' *;:'-' ,,olr. Y= ?--- ft= k''irc"iA,--$,-it-o i <

-

--

- i- l- -- -i -*J{'-S i - t:ez t :,?z' \zt ::!i!*ili:. .,-.{= 3.2_,na=6,::l-='--f; i i ,r.. ,, i- - ..' " ./' ia-ce .,.;r;;r; ? JrZ,n {,Yu

----

I . ..t "-^:"

fewrti kolokvij iz Elastostatike,09.5.2014 - Rjeienja

Zadatak (grupa A) Dato je: F = 8kN, a =2m ,4 = 4kl'{/m , 6do,=60MPa .

/'|4

nl

-

{Ltuno treewrti kolokvij iz Elastostatike,09.5.2014 - Rjeienja d fb

Zadatak (grupa B) Dato je: F=5kN, c=3m, q {kN/m, 6do,=80MPa fb

I

q)

r?tt o

/'t oI/!3,',*Fo -

- Zz,zr*rt.

----F

'r[*rP;]

LL- 5q.{ez-i- t.a2.3q4qL+ z.eqz

4

z{i=*ai) Fs 4= S-ry',

= !31,r (srfi"fA|, F-"- Oqffiq--:, ? -.,&-f .iio.l, zf$ 4a_i$Ajlf

= 4 *p/z a.\ = {S,s at

4\

tfuv= {t,zflLnnl)'^rrzicn,sarfe {nq r*ou,t n;,:;';; t1'ot- u ){hox= $_i;g-,x: !,1#Ir

d

Itn't,s,td

r I nun i; tlrg{1

--^?- T -T1 rP *- llt'-rl* * u

-JJ-,l,ltA

t_Il,t

t6

?7 ?t-urr$rawq

Dipgnzl6u satt|l*u

.o

*bi) no -Dqfo-1-e; fi;Tlc*sn, * *!z ,T/,20 = 3O0 Pq" 612 t'to '

al il*m rn / ;,/$l $"e;{ryie*af{e+rva- llr*0 (4)\an+ ?rd= fe* = g {z}fari= W, \ru= iZi G)

(ll { {e} uz llt4a= rYs 'N+ , lf tr', - -Na 'Ua*rl^)q -lr4,g--= o &1 1'*bWn oo]f;.. ! "i.b,rr){rrx-ro) = t'tt {'-{f} 6>

r{x = n^ {z- *} 5 t# fi ntt ; '{),o=

-S zlpo = #b* f+)t7) u tt].;

tls= Nx-n^= #il*, =# Lh

= nfg

-

4=- g7;r6es:, 4l' \l I H4-lzl - lr

ile ! eozIELT *

J: Jf,3 @=*

__ot

Hg

_

t4x- Htq

q

LH rng.* - 4t-t Z - gtt'T-1p:,

D>-= 7o,5 l"o /

--:!-

2_L

'*#ru eresishz'z: Tr-2^o*= 4r_ 4:_ = izh+..1oNn-ot ,4g =,f{ tlpd =TJrt .-b*{,,-z- -A{/r-.,rD;1a}ftn aghva,{"rJq?o

.. Lt, _ -

ar\'"t"taloYq t-'ffi-o g

-?nn=- #:--H=**f*o = Vax = 6{nr- g $trfu sfu.4tffiW-w,WA JosYH = 44e "id31qd ='1rr" {alj

Y L_ turc

148

)*-i

I

1_"il-,tt

*

1rid

I

z4&

t- 8o,7nQt d=fu,4*ot{r**1w-a prgsrelq L-2: Tz-zora r=Ti-z*ox= 2O H P*,= TJoz '

, (A,jagra,n Je,Ai no:!;p;1.

d) Ras o,i,e/q nn P o r\q,ae:;rl*t 4Qcr*aNh/t/t

fr. F-\zl

-rX./\t.,,l-l

0=9obP"s A"2ha) {!na*nf, q ul/;t.-/e7'**

{ tl'$**t np:-(n7g z{A/ ttz zay,'tgrta -u l{7,1 ,

-' tls-rYa , ilu -+ /vk)f{Nw #*:+4w** */n*S,{ 3t&stl*n*W) * t1.= -6g.:pny*a s{

t)N*a.{-rrT

$i,z**ieoka3reD+__ : lltu D __ lla, ,ffi:xt

,"* V _6,rJE 2-z_

G+ lrJefluiY*

-fr>r9Td"zT 4{

T-a='{oflp

Jnos sld : $lY+ ?*A- o :

|Ts*ry, {*}{ z}t (s} * {,a) '

sffi= ;'' 3,fJW

/*$-u 'tl*;4

c) n ) iaqrqlr2 Lt qo'"/ 4

72r-

fbAz

I

1 F. I ,r-iti5at,HJ---..*

I'.t

-

.2.41a

q,,

q

Zfihq '$\na

! Ua:?rqm r?aPh4 Lr,i rTepaoq :4_t= - +?ftPq t {i_t= {aorlfq ft*afe

LQuoo F.)q{o.*1i * F= ;lN,

*

7= ,/lo t{fa 1 F= 4oa yfo,=+

,3t

frt

0 is,/a

J}-/'-t S0=-3ta

a) grole]ilFx+A * F* aa{*a*a{rc*a{u=a {.}A{an = -Fa.\q-, at,ap fu-g

FaaAAtco = F"-s QrA7 )

{u = fu ^F,, 6-r= fi-q E*={E-r) a$EAz

r"r3

E*lt

+ FsqgEAzSF,-r)tr-r)r Fa=p g)fr- 9F- t.ql^/

$ jtnenztaorsanp fr- #= 4/t/{

.r FH=t=orrFdz-z= f=f**A,,

* = ffi = $0,9maL, &= * : 10,2b7o2/ Ar: (a,9n *rz,

Ponfnayt /"{le n/n*t

=-z,g /r?bZ ---g-brLF

uno{oa{r} ,qr.#N=

=- {!.2r,lg

4ar97zr.f .ig0g;gro* Jf &qra4 ,oa s& ril, jy,an fw.rcn(fr rq{olqfn=

- u{r, =" - rtfr-q - -

h1jagr.n .f /ot na siei,

fiq=-rlr = -$3a+

I7,AA/ ratot/*s*^* Aq - K,MqT-tu.n4,

r( t\_/' cln c F.

X,r= ZYttA;Ax*=@*

fi,4+7;12*u*./vc : AraZ F-n

^,=T,'i-if.' reX H**lw-ffia&, = z+1e*t, Lsoxriox:W$ w,,,.,^ | lr a,n cnIS,. 3g,l WlIP

= s4ecrrl

V *58,{ent {4.rebq erui>t;et,{i dq-cAr&y.=-Jt;-ffi' ='38,tul uzidt*J*/ aftakr'a*e;

ilrl

il l rf ;t, {, { i, Jq . ! x. ; y* I tbe ersy !t'> e{' i; e.fP *Sl,{ero* Q*1Sl y,*,ie{,/i Jq.L*n; rr#l itq e-szt-rt>P/r7ie,r",ya---f-r-r-r - ='18,1t^1 uzfdred*,t' "rr:k,:?n r:q. + 4 *z ,^ - ^^^ #.TJ,t,* = fg+ f3 = (srgrr 4e)*,r* =u*ospA\ lz,^t= Ji %- fia* .Q& . {92 SSS a";

t2

a ,tqIe1>r'--Z

*r-&,*,-

* /r5/ov{*.,_i p ftri",ii'

K-( tit noKolokvij 2 iz Etastostatike, Malinski fakuttet S *^/ilri.| i, .4.Zadatak2 (grupa A)' spremnikpravougangg popreinq presjeka prikazan na slici, sadriigas podpritiskom F=2Mpa. Ako je I = 2 m, a-= SO i*, Ir

= g0em, 6 = 1 0 mm, F' = I 20kN, odrediti:

(a) naponsko stanje na erementu D (bpienito ravno naponsko stanje je prikazano, odreditiprikazane napon, 20 bodsva)(b) glavne normalne napone i priavce ovih narcna {lg bodova),(c) glawre smifue napone i ravni na kojima ovinaponi djeluju, treba skicirati oriientisanielemenari oznatiti uglove (I0 bodova),(d) makimalni pritisak ako 1.e dat dozvodeni napon na zatezanje o a = IAAWa{t 0 bodova).

Trn=To

Napomena: Srnatratf da sila F uzrokujesamo akijalna naprezanja u praycu x.

*K

o

4 = terk*1.

&tr= -Wqru-z|-=-sqrcn+\

-4 = 4)*r?, #- r-9'7

-T-r = $.t?r #. rY I r*= 4"'{*25'n14= ;. A,-r,fr;{zx* $,ou-s,p)1nil,}= n+*l Slt rrr*,*{* =fu,n *ttv.{-t,+}f *,Ad= 4a4e o'e+

S=&"*{e,.+liu=Wrb,s cufd*|,= t33,3w+ lrt=iy,o{*u-^')tr,"f#*b*rrYb}ut= "a"tH=;r:'u!,T,fo{#* {o,s-r,ql.uk, = Q.czg* .lg=ry,* (**}'t,={# r P,s-1q1f7}';= rssh*ir* = r,{ ;r$,-{.r{- = i: *i *. i Ii - e effi=npl * = ry+ { rca- wh,, = {'$ * P o, rf r Fa = s's t;S =fsx,e *t*,t* Zttp+k,q]r*t = als,'t c.* I $=Lr*,r+ re**sg* qe1*\ = @It l : Fr,yr r(ra, -rrXru.{J{ d * ffir f *- xcY,t o*}AJ - S g * * J' {Y{. & *Wq g l'Jk; =fnr* (-r,s5+tdXs0r-q r4r,4,b+{qs*,r1;E-a'4$*fi*(es**4Yqs-qn4d*F- {*tl'rlY# *rtIs; =- rl\fl-s t 3o 4'8] cd = ,'s*,+rn*{) f,>t7wor nomen/i' ut = fu= ##-= 4, ry=fu=#,=:'''u}

At,"*Xlra4r= ,ts,leoz

I;rt= Z+ctmlT,11= g&r*n\4= 3te*,,

c) *hvni -o-rn/r'n. :Ir,z.= W*

T,t,L = -{i*,L b\

Kolokvij 2 iz Etastostatike,

t L JffiEt,tqr =

ifakurtetsarajevo, rr.(.fu'|.n0 F'xc = eW; , *L* f,*r.ji

xr=-t,98'?,trq*B-y:7!, O

-^- Aers +6aly@*@LL=

-4i w

I,tr@,ei

LA_^ ^ ^..,i 32tr3*' , Zq= 858$ cnb r ry

r-E]sr,z*>ol Tuur. e{= 1,7" {P"}'o"o'adr;)Cas7.*>o J

d) v,g{; rja r4A [q,av, t*?= {ax,t*ltz,z;*a = 4oeflfi b>+ 6"s{e'"t'=r"o*c1;rs)lt,ixt = +* S = bs',; 2t,-.2 - **)d= {ao{r*"f {tr)g) v,{e+; rjei. E4A

/- [-i u noKolokvii 2 iz Elastostatike, Maiinski fakultet Sarajevo, ,r.r.r,16/

Zadatak2 (grupaB)' spremnik pravouganog popreinog presjeka, prikazan na stici, sadrii gas podpritiskom p=2Mpa. Akoje: r = zm, d = s0;, & = g0cm, d = I0 mm, F = I0k].{, odrediti:(a) naponsko stanie na elementu D (opdenito rtlvno naponsko stanje je prikazano, odreditiprikazane napone, 2O bodoVa)(b) glavne normalne napone i pravce ovih napona 1tO bodova),(c) glavne smiiude napone i ravni na kojima ovi naponi djeluju, treba skicirati orijentisani elernenatioznaiiti uglove (10 bodova),,(d) makimalni pritfsak ako je dat doaroljeni napon na zatezanje oa = l(}LfuIpo (.t 0 bodova).Smatrati da sila F uzrokuje samo akijatna naprezanja u prave u y.

B-Bsas ood

debrjina ,,ffiitiskomP

4

t,'fu'qpo,>3tc

-:!an;f*, P r|')qL

Y F"o"o.'

ZFq,'=a

e {qrni oap*>i su f7= ti: {ortftPq, dz-- } =3ares*,o" ,, O !, K S,s frewtl gfur;$n */"rlnqPOrTa( jr T**o,

-{{, er"Jsf*r$i *P.ryel u:{ou.q eAs{rino rn--abltoyerq}.*tqLsrnaln,/nrin. sniiuc?' Hpcrts sq nonquainq 7d aSfrnt{s" QJnorq a7o'r7;g{aurtAnoPha/oif] naPw)e.

ft\bJr'}-1xr'l'.i *\ 'f tx= lsY = *,.:letsr'o' j55&'fi '."-Y'tflf,. -J_

*\\.4 -zi,itlPqL"s"-

$a;si*tq{,t; fr&sql, y - M 1{d =t r < ee&$*r - ":*%:*,r#*re?'4,*!3:-w. t z\r=# , d,*=fifu= ffi=r{,snr4#

'{pv ? {t "J.)

Ird]

Zadatak (grupa A). Za zadani sloieni presj,ek na stici:(a)

.izratunati aksijalne i centrifugalne momenteinercijeza teii$ne ose presj,eka fg-* ZO boaova),(b). izratunati otporne .momente inercije za dvije

.

teiijne ose (2 x 5 bod} - -'r- '(c) izraiunati glavne momente inercije i polo2ajglavnih centralnih osa inercije (gcrtati glavneose), (10 bodJ,

(d) objasniti kako se pozicioniraju glavne ose (t) i (2)u odnosu na raspored eteminarnr,-pJ#j,lrJ. .

popretnog presjeka oko ovih os" (S boOJ,(e) kako bi trebalo oriientisati pop*e"i presjek uodnosu na opterefenje da Ui nor.iir"o na,iveCu.- .nosivost prema savijanju (5 bod.),(0 kako bi trebati postaviti profile (L u odnosu na Uprofil) da bi znaiaino povecali moment inerci.l.e

za jednu od osa (skicirajte) (10 bodova).^r

J#lestnre:

iI\ '.1, -.J, J'n J\) ALsi ialni, terfri{uga/nt lryldnfr'At= l1,l t z

Ir,a= LiluilQr= 38,lcn1

EP= 31{un\,IP = sq4 c"11

T*,11= ^5,4 U'?

_ . dimenzije su u centifieirima/hfut1g

vr. &t,* t t tlg.Az -ftzAa-ktfi + ^AttAz-Az-A,t

.rc= qgle{44,es}fi,t *a-a-t/.2-i3,,{ *$c 4-2 Ch

-_\ r -' L-I5= i:ast{sJ{ -{lr2-D}r5}#= 'lo5l cn'

-ig=4'.d'-'8 &&u:tr{fH,\ r.o)c,},= -3#

6ar -b

-frf' = ryu{q'- !r+-ri}('{tt; Y"ll!= ' i q'u s(c * i+-epj(C-6fr)'2)rn1= -\tn'

!L=1clttiler,4r-UctLs-il.rilq-@+vlfit+&siyv'3*1At* Az -Az*Ai ,t'3i1+l3c-gt-Z

jfe = G,* th

ffi-'f '*f$'l=wct4 = r'rt+ {u^^oP'{r =Pal* i{-dss !

ff = & * {q,- NJ' ar= {4 r fu- qo tf rx'S='l4ll',1'g = 4, + { *,' x"k): (1$ r{n*t): e a)= n' e "!tF = 4,, + &rS* = (+ r(a- *uf''S = L+ u'!

e= (rx+a*-5{-tE7'} = E3{ cni

J.Q = T.xt,,t+ {ret-xrt{P,-(tifla= ,'u

= (rql + c-;;;'i,i,1['!r*' E'i){l,i='ic''?+16, "r. rto r,

7-*i-s.

lf,l-,*=

TP* =lai

IilftIqx

g) \Lavrr t7)ornrr/r' i 6io,trt oJe[,,r=B*Lt+ =nfiY,fi * Ty = {ost cr$ t -Ts * 2"= sssrl"tgzA= j{L}_*o {l)*\ , (r)ohv lf

- l3 (p* f j'e 7r,li,ir* c-tq si;,,s/rlu ) '"

d) Po, icior*o(/ r 4h,i"i/t'*1 f"',n!,^ {:r5'1) o.u.f,I v6 /L/O/?//'.rrr7.4*'1v"'. ', _, ; I ^/.._'n' r = s4 i/o y.rrt?javrq eia {t) se ,oez)t)cntr44" ,& u/r-foAt* 7>c'urszn(*, ,

_,1 !.,. , t ie/r. au Na t2).u,)aiiene tt cJP. Ck-nafo tr1|1r 'l

e ) ci it'/Cr1pnt' o:a]yt sa*'/ : ',*'*' l - {: /^1, A ,uo {D;e oLori,,i;sn/i:nn1t /"hg 1lJ&Le t , tv - )-) t-J ^i l^^Fl/Fn/rJQftrp lfarr.u'i **"soaA *" ,flf './ / / /n* sile saiian/q ainc;no Tcraleln+ scr,.t {/

t) Po:{or$of/u prrfi/o L q Jnastt /"q U -

a)&ra ?q A

Cfpernf mop>enft'r#s =

7e,.J n\:-!u

Tn-+

612txc

tl- naslata L

__ 4*sV cd =,5+

rqA e^V{* aA-

Ll./

5+O,g{

rbl,o46L un'

,14 rn'

AL

\t'lx

nrc(b

b4F!1uoo b'

PM kolokvij iz Elastostatike, Maii nstfakultet Sarajevo' 08'03'20 1 4'

Zadatak (grupa B). Za zadani sloieni presjek na slici:

(a) izraiunati aks'tjalne i centrifugalne msmenteinercije za teiiine ose presjeka (3 x 20.bodova)'

(b) izraiunati otporne momente inercije za dvijete2i5ne ose (2 x 5 bod.),

(c) izra(unati glavne momente inerc'tje i potoiaj:-- giirnirt cenlrdnih osa inercije (ucrtati glavne

ose), (10 bod-),(d)objisniti kako se pozicioninju glavneose (1) i(2)

u odnosu na raspored elementarnih povr3inapopreinog presjeka oko ovih dsa (5 bod')'

(e)'kiko Ui ireUato orijentisati popretni presiek.u'-'

odnoru na optereenje da bi nosai imao najvedunosivost Prema savijanju (5 bod'),

(fl kako bi tiebali postaviti proftle (L u odnosu na U" profil) da bi znaiajno pove(ali moment inercije

za jednu od osa (skiciraite) (10 bodova)'

$ble'ft '{a) A Lsii'*/n;' *rr/"r{a7ab; n>cmtntt ttnrory(

Ar 41,1tnL *e=_$+us)fl{+Y9w

4,4+lso-s*-zx",*+xs?}.^Y$As'X4Aqfutaz-As-l*

ir< = Zico?i;:* 31,tot .k= - a,eA *4 = 1fi cn' a = gtr tu + fuA,2- h:As-k+A+ _{jt-+l4k,l+eF'.ls+"wG

-R r^L'

-

'Ular{A -qL -'/i l i AY = r1c!"' , t[= 9ttAt+5{242-Ytj^3'};1t'1

-_ll \"r''i-iij -1?=;e,td'+ ''r' W- 43,tt{3o-e-LI ii : ,*t t. ,r .,r,t,r* ii ir,u=+144cr't+ le - Erof cn f\nurq, i i

&r= V3#,'

{= ;1":,r};^,:t;;. -'

fi = -4,,r;,;

=$n{t,"v-rq*faFrzt+u}

tf :r*u+ iq..-eu)12=@-rr-ro! =uu,\ ry^**.&r-ff -rr-, c,tti:i *oli +Bt'T;i,

n I R =tuu+{to-&ir =(*+ro -{-qs{f' n}t}

: *' v'? tn'r /^ , \ r. ..

-i1 .\ i n'

fgu+(*t*iau=(#+lo-{-qsd '812}to: J1

' t

1p"*rr{4$*=#rp-q'#uV =1555,tmt ly;, -

r, -,\zr - {tn.r ,{-L-r',iy.2\d=lz,+rrn6.ffi T.,l -:;;:r ;:";' * ?. \' q:,=,,,*:::,','r! :):= ;{,;;i=*ff:5 y,:Y;': E,* ii4=^(4tnr,{tz{ v-4?,t'ts,,),A,= 3t'^-

* -o-)-92 #r id :#,,;;,f;J.||,li,n-flli 4n,ft5,sa3ISy- -l.r}r}

,i\-gi -r tt? -. roo, - rq[gsn-g-);41 =, I L- 1 - 7ta)*{:1,:)r,i = ??fyLi!= t21*,,:(*' ^.1;: il'li"i.,.l ._ t\qcn\ i f*,. = i35,i -1221

= (, * ft-f',n0)(6-'ic5)2Jc'at= 119i.n\ i f:5 = (35': -122;

. CrupaE -nt;s/qvaL

D{ prrnino menf i et 't/ -tu / tc\a' L1 rL' +

ry unc f" 5 l\i*,*- Uc ,a{

B2q

c) &Lq,.tni ****r/''' ,'g/"'rtP c58 nfr'*?&T,n c il+T*J-1lt-

---=-

t = za4i *,Etqtd,= -JEL-