Lectura Control de Deflexiones

 

  8 Flatrlk ig k`s

flaimfmlags ig sgrvmfml

Fu`ail gk imsgðl ig flafrgtl flafrgtl `rb`il sg g gdgftu`e` dgftu`e` ` tr`vís igk bítlil bítlil gkàstmfl kls d`ftlrgs ig sgcurmi`i gr`a gkgv`ils gkgv`ils ig blil qug gk gsdugrzl gsdugrzl ig tr`e`jl tr`e`jl igk `fgrl gr` e`jl e`jl y plr kl t`atl t`bemía kl gr` su igdlrb`fmöa. igdlrb`fmöa. Kl bmsbl sufgiâ` fla gk f flafrgtl lafrgtl plr kl qug gk gdgftl igk r g g p al gr` flasmigr`ekg. E`jl gst`s fmrfuast`afm`s gk flatrlk flatrlk ig igdkgxmlags y r`j`iur`s al g gr` r` ig b`ylr matgrís. K`s imbgasmlags imbgasmlags y f`r`ftgrâstmf`s f`r`ftgrâstmf`s ig kls gkgbgatls gkgbgatls imsgð`i`s plr flasmigr`fmlags ig rgsmstgafm` rgsmstgafm` gr`a sudmfmgatgs p`r` c`r`atmz`r c`r`atmz`r gk `igfu`il `igfu`il flbplrt`bmgatl flbplrt`bmgatl ig k` gstruftur`. Ga k` `ftu`kmi`i gk bítlil bà bàss gbpkg`il plr kls prlygftmst`s prlygftmst`s p`r` gk imsgðl ga flafrgtl `rb`il gs gk bítlil ig imsgðl ` k` rltur`. Gstg prlfgimbmgatl prlfgimbmgatl flasmigr` flasmigr` gk flbplrt`bmgatl flbplrt`b mgatl magkàstmfl t`atl igk flafrgtl flbl igk `fgrl kl qug pgrbmtg rgiufmr kls flgdmfmgatgs ig sgcurmi`i k`s sgffmlags ig kls gkgbgatls. @sâ bmsbl gk usl f`i` vgz bàs bàs flbúa ig flafrgtls ig `kt` rgsmstgafm` rgsmstga fm` y `fgrls `fgrls ig gsdugrzls ig dkugafm` gkgv`ils gkgv`ils rgiufg `úa `úa bàs imfh`s sgffmlags . K` imsbmaufmöa ig k`s imbgasmlags ig kls gkgbgatls lf`smla` k` k` pírimi` ig rmcmigz ig k`s gstruftur`s cgagr`ail igdkgxmlags qug pugiga pugiga rgsukt`r rgsukt`r gxfgsmv`s y qug ` su vgz `fgatú`a `fgatú`a gk `crmgt`bmgatl ig k` gstruftur`. _lr kl `atgrmlrbgatg gxpugstl gs agfgs`rml agfgs`rml flbpkgbgat`r gk imsgðl ig ua` pmgz` ig flafrgtl `rb`il fla ua ` `igfu`il igfu`il flatrlk ig igdkgxmlags ig r`j`iur`s p`r` c`r`atmz`r qug imfhls gkgbgatls fubpk`a k` duafmöa p`r` k` fu`k dugrla flafgemils.

8 0

LAYULK IG IGDKGXMLAGV

Gk flatrlk i g igdkgxmlags igdkgxmlags gs ua` gt`p` buy mbplrt`atg ga ga gk imsgðl ig gstruft gstruftur`s ur`s al sökl ga gk f`sl igk flafrgtl `rb`il. Wa gxfgsl ig igdlrb`fmlags pugig lf`smla`r k` d`kk` ig `kcua` bàquma` qug vg `dgft`il su duafmla`bmga duafmla`bmgatl tl plr gkk`s l gk igtgrmlrl igtgrml rl y ` vgfgs mautmkmz`fmöa ig gkgbgatls al gstruftur`kgs flbl pugrt`s vgat`a`s fmgkl r`sls t`emqugrâ` gtf. Fu`ail k` gstruftur` gs augv` gstls gkgbgat gkgbgatls ls pugiga duafmla`r emga sma gbe`rcl igspuís igspuís ig ua tmgbpl pugiga igtgrmlr`rsg igtgrml r`rsg l igj`r ig duafmla`r duafmla`r igemil ` k` igdlrb`fmöa igdlrb`fmöa fla gk tmgbpl qug prgsgat`a prgsgat`a k`s gstruftur`s gstru ftur`s ig flafrgtl `rb`il. Gstg gs gk f`sl i ig g pugrt`s flrrgim flrrgimz`s z`s qug qu g al pugiga igskmz`rsg l vgat`a`s qug sg dkgxmla`a dkgxmla`a ga gk pk`al vgrtmf`k. vgrtmf`k. Ga cgagr`k ua gxfgsl ig igdkgxmla igdkgxmlags gs gstrlpg` k` `p`rmgafm` ig k` gstruft gstruftur` ur` y ga bufhls f`sls `k`rb` ` kls usu`rmls usu`rmls sma bltmvl y` qug ua` igdlrb`fmöa gxfgsmv` al agfgs`rm`bgatg gs sâatlb` ig d`k d`kk` k` mabmagatg. Ga kls`s k`s igdkgxmlags igdkgxmlags pugiga lf`smla`r k` dlrb`f dlrb`fmöa möa ig gst`aqugs l pgqugð`s k`cua`s ig `cu` prlvgamgatg ig k`s kkuvm`s l ig `kcúa mbpgrdgftl ga k`s mast`k`fmlags s`amt`rm`s. Gst`

 

slergf`rc` mafrgbgat` k`s igdlrb`fmlags igdlrb`fmlags ga gk gkgbgatl k`s qug ` su vgz `fgatú`a gk gst`af`bmgatl sm al sg fugat` fla ua `igfu`il smstgb` ig irga`jg. Gst Gst` ` rg`ffmöa ga f`iga` pugig kkgv`r `k flk`psl ig k` gstruftur`. K` b`camtui ig i g k`s igdlrb`fmlags gs `dgft`i` plr k` f`kmi`i igk flafrgtl pgrl eàsmf`bgatg eàsmf`bgatg plr gk fumi`il fumi` il qug sg tgac` ga ler`. Gk fur`il masudmfmgatg l flbp`ft`fmöa flbp`ft`fmöa ma`igfu`i` mafrgbgat`a k`s dkgfh`s ig kls gkgbgatls, igk bmsbl blil, qug gk igsgafldr`il ig vmc`s `atgs igk tmgbpl gspgfmdmf`il y gk `kb`fga`bmgatl ig b`tgrm`k ig flastruffmöa slerg kls`s qug `úa al h`a `kf`az`il ua` rgsmstgafm` bâamb`. @ pgs`r ig kls d`ftlrgs d`ftlrg s qug tmgaiga ` `ubgat`r k` igdlrb`fmöa ig kls gkgbgat gkgbgatls, ls, sm k`s rgflbgai`fmlags prlpugst`s plr gk F M sla tlb`i`s ga flasmigr`fmöa, al igegrà gspgr`rsg b`ylrgs maflavgamgatgs lf`smla`ils plr gk gxfgsl ig igdkgxmlags.

8 0 0

ítlil igk

FM

p`r` gk flatrlk ig igdkgxmlags

Gk föimcl igk @FM prlplag ils bítlils p`r` gk flatrlk ig igdkgxmlags ` amvgk ig f`rc`s ig sgrvmfml. Gk prmbgrl ig gkkls gs `pkmf`ekg ` gkgbgatls slbgtmils ` dkgxmöa dkgxmöa qug al gstàa kmc`ils ` pmgz`s al gstruftur`kgs qug pugi`a sgr `dgft`i`s plr igdkgxmlags gxfgsmv`s. Gstg bítlil flasmstg ga i`r ua gspgslr l pgr`ktg bâambl ` kls`s y vmc`s, qug c`r`atmfg qug k`s igdlrb`fmlags igdlrb`fmlag s sg b`atgac`a igatrl ig ua r`acl `fgpt`ekg. Ga Y`ek` 8.0 sg bugstr`a kls pgr`ktgs bâambls rgqugrmils,, ga duafmöa ig k` klacmtui rgqugrmils klacmtui ig imsgðl, kls fu`kgs igpgaiga ig k` a`tur`kgz` igk gkgbgatl y ig sus flaimfmlags flaimfmlags ig `plyl @FM-=.7.5.0). @FM-=.7.5.0). _gr`ktg bâambl, h Gkgbgatl

Vmbpkgbgatg `ply`i`

Wa gxtrgbl flatmaul

@bels gxtrgbls flatmauls

Tlk`imzl

Gkgbgatls qug al slplrt`a am gstàa ga flat`ftl fla t`emqugrâ` u ltrls bmgberls qug pugiga sgr s gr i`ð`ils plr igdkgxmlags gxfgsmv`s Kls`s b`fmz`s `rb`i`s ga ua sgatmil

0/5?

0/59

0/58

Tmc`s l kls` Tmc`s kls`ss agrv`i`s `rb`i`s ga ua` imrgffmöa

0/04

0008.7

0050

000

008

Y`ek` 8.0 _gr`ktgs bâambls ga kls`s kls`s y vm vmc`s c`s sucgrmils sucgrmils plr gk föimcl igk @FM p`r` gk flatrlk ig igdkgxmlags igdkgxmlags @FM-Y`ek` =.7 `.). Kls v`klrgs ig k` t`ek` `atgrmlr h`a smil prlpugstls prlpugstls p`r` flafrgtls ig pgsl alrb`k ig 56?? ` 59?? nc/b6 y `fgrl fla gsdugrzl ig dkugafm` ig 95?? nc/fb5._`r` flafrgtls kmcgrls, fla pgsls

 

gatrg 097? 0=7? nc/b nc/b6, 6, kls bâambls bâambls prgsgat` prgsgat`ils ils sg buktmpkmf buktmpkmf`ràa `ràa plr 0 . 4 7 - ? . ? ? ? 6 ~ ~grl ) gstg d`ftlr d`ftl r al sgrà bgalr qug 0.?=, ilaig wf gs gk pgsl igk flafrgtl ga .nc/b6. .nc/b6._`r` kls flafrgtls fla pgsls gatrg 0=7? 0 =7? 56?? nc/b6 nc/b6 al sg igdmag d`ftlr d`ftlr ig flrrgffmöa flrrgffmöa pugs ístg sg `prlxmb` `prlxmb` ` k` uami`i

plr kl t`atl sg igsprgfm`. @igbàs, sm gk `fgrl `fgrl tmgag ua gsdugrzl ig dkugafm`

imdgrgatg qug 95?? nc/fb5, kls pgr`ktgs pgr`ktgs bâambls sg buktmpkmf`rà buktmpkmf`ràa a plr ?.9+d93???). ?.9+d93?? ?). Gk sgcuail bít li lilp lp`r` `r` gk flatrlk ig igdkgxmlags flasmstg ga gstmb`r su su b`camtui vgrmdmf`r qug al gxfgi` kls kâbmtgs prlpugstls prlpugstls plr gk föimcl @FM-=.7.5.4 @FM-=.7.5.4). ). K`s dkgfh`s dkgfh`s bàxmb`s pgrbmtmi`s sg prgsgat`a ga k` Y`ek` 8.5. mpl ig gkgbgatl

Igdkgxmöa flasmigr`i`

0. Ygfhls kk`als qug al slplrt`a am gstàa kmc`ils ` gkgbgatls al gstruftur`kgs qug pugi`a sgr sg r i`ð`ils plr igdkgxmlags igdkgxmlags gxfgsmv`s.

Igdkgxmöa mast`atàag` mast`atàag` igemi` igemi ` ` k` `pkmf`fmöa ig k` f`rc` vmv`.

5. _msls qug al slplrt`a am gstàa kmc`ils ` gkgbgatls al gstruftur`kgs qug pugi`a sgr i`ð`ils plr igdkgxmlags gxfgsmv`s.

Igdkgxmöa mast`atàag` igemi` ` k` `pkmf`fmöa ig k` f`rc` vmv`.

6. Ygfhls l pmsls qug slplrt`a l gstàa kmc`ils ` gkgbgatls al gstruftur`kgs qug pugi`a sgr i`ð`ils plr igdkgxmlags igdkgxmlags gxfgsmv`s. 9. Ygfhls l pmsls pmsls qug slplrt`a l gstàa kmc`ils ` gkgbgatls al gstruftur`kgs qug al sg i`ð`a fla igdkgxmqags gxfgsmv`s.

_`rtg ig k` dkgfh` tlt`k qug lfurrg igspuís ig k` flklf`fmöa flklf`fmö a ig kls gkgbgatls gkgbg atls al gstruftur`kgs.

Kmbmt`fmöa

0098?

0059?

Y`ek` 8.5 Igdkgxmlags bàxmb`s bàxmb`s pgrb pgrbmtmi`s mtmi`s plr plr gk föimcl i igk gk @FM @FM-Y`ek` =.7.e.). K` igdkgxmöa kâbmtg prlpugst` ga gk f`sl 0 al gs sudmfmgatg p`r` gvmt`r gk gst`af`bmgatl igk `cu` ga tgfhls. _`r` kls f`sls 6 9, k` igdkgxmöa ` flasmigr`r sgrà f`kfuk`i` f`kfuk`i` rgiufmgail k` dkgfh` ` k`rcl pk`zl igtgrbma`i` plr gk bítlil gxpugstl ga k` sgffmöa smcumgatg bgals k` dkgfh` qug lfurrg `atgs ig k` flklf`fmöa ig kls gkgbgatls al gstruftur`kgs. Ga gk f`sl 6 k`s igdkgxmlags pliràa gxfgigr kls kâbmtgs prlpugstls smgbprg qug sg igbugstr igbugstrg g qug kls gkgbgatls al gstruftur`kgs al rgsukt`ràa i`ð`ils. K`s gstruftur`s `slfm`i`s `k f`sl 9 t`bemía igegràa vgrmdmf`rsg p`r` gk f`sl 0. 805

Fàkfukl ig igdkgxmlags

K`s igdkgxmlags igdkgxmlags ig kls gkgbgatls ig flafrgtl flafrgtl `rb`il `rb`il sla sla duafmöa igk tmgbpl plr kl t`atl pugiga sgr ig ils tmpls tmpls:: mast`atàag`s mast`atàag`s ` k`rcl pk`zl. K`s prmbgr`s prmbgr`s sg igega duai`bgat`kbga duai`bgat`kbgatg tg `k flbplrt`bmgat flbplrt`bmgatl l gkàstmfl ig k` k` gstruftur` sg prliufga mabgim`t`bgatg mabgim`t`bgatg igspuís qun k`s f`rc`s sla `pkmf`i`s. K`s sgcuai`s sla flasgfugafm` igk rg g p flatr`ffmöa igk flafrgtl sla lf`smla`i`s plr f`rc`s slstgami`s ` kl k`rcl igk tmgbpl. K`s igdlrb`fmlags ` k`rcl pk`zl pugiga kkgc`r kkgc` r ` sgr gk ilekg ig k`s igdlrb`fmlags mast`atàag`s. mast`atàag`s.

 

  gdkgxmöa mast`atàag `

K`s igdkgxmlags mast`atàag`s sla igdlrb`fmlags gkàstmf`s y plr kl t`atl k`s gxprgsmlags ig Ugsmstgafm` ig i g B`tgrm`kgs p`r` b`tgrm`kgs gkàstmfls pugiga pugiga sgr utmkmz`i`s. G a k` dmcur` 8.0 sg bugstr`a `kcua`s dörbuk`s p`r` gv`ku`r k`s igdkgxmlags ga gkgbgatls prmsbàtmfls prmsbàtmfls fla imdgrgatgs flaimfmlags ig i g `plyl slbgtmils ` imvgrsls gst`ils ig f`rc`. Gk v`klr igk böiukl ig gk`stmfmi`i igk flafrgtl sg gstmb` ` tr tr`vís `vís ig k`s gxprgsml gxprgsmlags ags 5-4) 4 5-3).

Dmcur` 8.0. @kcua`s dörbuk`s p`r` gk fàkfukl ig igdkgxmlags ga vmc`s ig b`tgrm`k gkàstmfl

Gk flafrgtl gs ua b`tgrm`k qug sg `crmgt` `k sgr slbgtmil ` ua blbgatl supgrmlr `k blbgatl frâtmfl qug gs flbl y y`` sg igdmamö gk qug lf`smla` gsdugrzls ig tr`ffmöa ga k` sgffmöa qug

 

gxfgiga gk böiukl ig ruptur` igk b`tgrm`k. Gk blbgatl dkgftlr qug `ftú` slerg ua` sgffmöa madkuyg ga su dmsur`bmgatl y ístg, ` su vgz, ga su blbgatl ig magrfm`. _lr kl t`atl, k` magrfm` ig ua` sggfmöa gstà imrgft`bgatg rgk`fmla`i` f fla la gk blbgatl dkgftlr `k qug gstà slbgtmi`. slbg tmi`. Er`asla prlpusl ua` gfu`fmöa gbpârmf` e`s`i` ga gk `aàkmsms gst`iâstmfl ig cr`a aúbgrl ig gas`yls p`r` k` igtgrbma`fmöa igk blbgatl ig magrfm` gdgftmvl ig ua` sgffmöa. Gstg p`ràbgtrl tlb` ga flasmigr`fmöa gk `crmgt`bmgatl qug gk gkgbgatl prgsgat`. Gk föimcl igrmv` ` p`rtmr ig gkk` k` smcumgatg gxprgsmöa:

ilaig il aig::

B :

Blbg Blbgat atl l dkgf dkgftl tlrr fr frât âtmf mfl. l.

B`

Blbgatl dkgftlr bàxmbl `k qug gstà slbgtmil k` sgffmöa, e`jl k` flaimfmöa p`r` k` fu`k sg gstà gv`ku`ail k` dkgfh`.

Mc:

Blbgatl ig magrfm` ig k` sgffmöa erut` ig flafrgtl, sma `crmgt`r, rgspgftl `k fgatrl ig cr`vgi`i, igsprgfm`ail k` prgsgafm` igk rgdugrzl.

0

Blbgatl ig magrfm` ig k` sgffmöa r`j`i`, rgspgftl `k gjg agutrl.

Gk blbgat blbgatl l ig magrfm` magrfm` frâtmfl, Mfr,gs Mfr,gs gk blbgat blbgatl l ig magrfm` magrfm` ig k` sgffmöa `crmgt`i` flasmigr`ail k` prgsgafm` ig rgdugrzl. _`r` igtgrbma`rkl sg gbpkg` gk flafgptl ig sgffmöa tr`asdlrb`i`, gk fu`k gs gbpkg`il p`r` `aàkmsms gkàstmfls y qug gs `pkmf`ekg ga gstg f`sl ga gk fu`k gk flafrgtl gs `a`kmz`il `a`kmz` il e`jl flaimfmlags ig sgrvmfml vgr dmcur` 8.5).

Dmcur` 8.5. Vgffmöa tr`asdlrb`i` p`r` gk fàkfukl igk blbgatl ig magrfm` frâtmfl. Gk blbgatl dkgftlr frâtmfl sg igtgrbma` h`fmgail usl ig k` rgk`fmöa smcumgatg, qug t`bemía gs prlpugst` plr gk föimcl:

 

5 5

ilaig:

dr:

Ygasmöa ig ruptur` igk flafrgtl igtgrbma`i` ` tr`vís ig k` gxprgsmöa 5-9). _`r` flafrgtls flafrgtl s fla `crgc`ils kmcgrls, gk v`klr ig d sg igtgrbma`rà sustmtuygail Jd f plr dJ0.33 dJ0.33 smgbprg qug ístg al gxfgi` m al sg s g flalf flalfgg gk v`klr ig dmt, k` tgasmöa ig ruptur` igtgrbma`i` ` tr`vís ig 5-9) sgrà buktmpkmf`i` plr ?.37 sm sg tr`t` ig flafrgtl fla `crgc`il kmcgrl, crugs crugsl l y dmal, y plr ?.87 sm sg tr`t` ig flafrgtl fla `crgc `crgc`il `il kmcgrl dmal.

.

Imst`afm` igk gjg fgatrlmi`k ig k` sgffmöa erut` ig flafrgtl, igsprgfm`ail k` prgsgafm` igk rgdugrzl, ` k` dmer` gxtrgb` ga tr`ffmöa. Ig k`s gfu`fmlags ig gqumkmerml y flbp`tmemkmi`i ig igdlrb`fmlags sg igiufg:

ilaig:

a:

Ugk`fmöa bliuk`r mcu`k ` G V f

f:

Imst`afm` igk ig k gjg agutrl ` k` dmer` gxtrgb` ga flbprgsmöa e`jl flasmigr`fmlags gkàstmf`s.

Gk blbgatl ig k` sgffmöa dmsur`i` sgrà:

Ga k` dmcur` 8.6, sg bugstr` k` v`rm`fmöa igk blbgatl ig magrfm` gdgftmvl ig ua` sgffmöa ga duafmöa igk blbgatl `k fu`k sg gafugatr` slbgtmi`, sgcúa k` gxprgsmöa gxprgsmöa 8- 0). Flbl sg `prgfm`, imfh` rgk`fmöa igdmag k` v`rm`fmöa igk blbgatl ig magrfm` ig ua` sgffmöa sma `crmgt`r ` ua` sgffmöa sgffmö a `crmgt`i`.

Dmcur` 8 6 T`rm`fmöa igk blbgatl ig magrfm` gdgftmvl ig ua` sgffmöa ga duafmöa igk blbgatl dkgftlr `k qug gstà slbgtmi` kl k`rcl ig i g ua gkgbgatl flatmaul l smbpkgbgatg `pl `ply`il, y`il, gk blbgatl dkgftlr v` v`rm`ail flbe sg `prgfm` ga k` dmcur` 8 9 y plr kl t`atl, t`bemía su blbgatl ig magrfm` gdgftmvl. _lr gkkl, k`s k `s rgk`fmlags prgsgat`i`s mam mamfm`kbgatg fm`kbgatg p`r p`r`` k` k ` igtgrbma`fmöa ig k`s dkgfh`s bàxmb`s al pugiga sgr utmkmz`i`s imrgft`bgatg pugs kls gkgbgatls ig flafrgtl sla ig magrfm`s v`rm`ekgs.

 

Dmcur` 8.9. T`rm T`rm`fmö `fmöa a igk blb blbgatl gatl dkgftlr ga gkgbgatls flatmauls

_`r` supgr`r gst` smtu`fmöa, gk föimcl igk @FM prlplag qug gk blbgatl ig magrfm` gdgftmvl ig ua bmgberl flatmaul sg` mcu`k `k prlbgiml ig k`s magrfm`s gdgftmv`s ig k` sgffmöa ig b`ylr blbgatl plsmtmvl y k`s ig b`ylr blbgatl agc`tmvl. _`r` gkgbgatls gkgbgatls prmsbàtmfls smbpkgbgatg `ply`ils, gk blbgatl ig magrfm` gdgftmvl sgrà gk flrrgsplaimgatg ` k` sgffmöa fgatr`k igk gkgbgatl y p`r` kls vlk`ils, gk blbgatl blbgatl ig magrfm` sgrà flasmigr`il ga gk `plyl @FM-=.7.5.9). @ktgra`tmv`bgatg, sg pugig gbpkg` @ktgra`tmv`bgatg, gbpkg`rr k`s smcumgatgs gxprgsmlags p`r` igtgrbma`r k` magrfm` magr fm` gdgftmv` ga gkgbgatls gkgbgatls flatmauls ga ual l kls ils ggxtrgbls xtrgbls Ugd. 59 : _`r` bmgberls flatmauls ga `bels gxtrgbls:

_`r` bmgberls flatmauls ga ua gxtrgbl: 0,

ilaig:

?.870,

?.070,

Mgb: Blbgatl ig mag magrfm` rfm` gdgftmvl `k fgatrl ig k` kuz. Mg,, Mg,: Mg,: Blbgatls i igg magrfm` gdgftm gdgftmvls vls ga kls gxtrgbls flatmauls igk gkgbg gkgbgatl. atl. 0 : Blbgatl ig magrfm` gdgftmvl ga gk gxtrgbl flatmaul.

Gk blbgatl dkgftlr, B`,gbpkg`il p`r` k` igtgrbma`fmöa igk blbgatl gdgftmvl gs ggkk qug flrrgsplaig ` k` gavlkvgatg i igg gsdugrzls, gs igfmr, `k b`ylr blbgatl prlvgamgatg prlvgamgatg ig k`s flbema`fmlags ig f`rc`s `ftu`atgs utmkmz`i`s. Vm sg h`fg usl ig kls blbgatls igtgrbma`ils ` tr`vís igk bítlil ig kls kl s flgdmfmg flgdmfmgatgs atgs i igk gk @FM, prgsgat`il ga gk smcumgatg f`pâtukl, k`s igdkgxmlags igdkgxml ags tmgaiga ` sgr slergstmb`i`s. Vm utmkmz`ail gstg prlfgimbmgatl al sg s`tmsd`fga k`s dkgfh`s bàxmb`s pgrbmtmi`s gs g s agfgs`rml gdgftu`r ua `aàkmsms bàs gxh`ustmvl.

 

5 9

gdkgxmöa ` k`rcl pk`zl

K`s igdkgxmlags ` k`rcl pk`zl sg vga madkugafm`i`s plr k` tgbpgr`tur`, hubgi`i, flaimfmlags ig fur`il, fur`il , gi`i igk flafrgtl `k `pkmf`rkg k` f`rc`, f`atmi`i ig rgdu rgdugrzl grzl ` flbprgsmöa, b`camtui b`camtui ig k` f`rc` pgrb`agatg, gtf. Ig gstls d`ftlrgs bgafmla`ils, ual ig kls bàs mbplrt`atgs gs k` prgsgafm` ig rgdugrzl ga flbprgsmöa. K` `pkmf`fmöa ig f`rc`s iur`atg ua pgrmlil bàs l bgals prlklac`il lrmcma`, plr gdgftl igk frggp igdkgxmlags flasmigr`ekgs. Vm k` sgffmöa fugat` fla `fgrl ga flbprgsmöa, plr flbp`tmemkmi`i ig igdlrb`fmlags, igdlrb`fmlags , ístg sg igdlrb` f`i` vgz vgz bàs `eslremgail b`ylrgs gsdugrzls y igsf`rc`ail gk flafrgtl flbprmbmil. @k imsbmaumr gk gsdugrzl ga gk flafrgtl, gk frggp imsbmauyg y plr kl t`atl k` b`camtui ig k`s igdkgxmlags. K`s igdkgxmlags ` k`rcl pk`zl sg mafrgbgat`a ràpmi`bgatg ga kls prmbgrls iâ`s ig `pkmf`fmöa y fladlrbg tr`asfurrg gk tmgbpl, tmgaiga ` mafrgbgat`rsg ` ua rmtbl f`i` vgz bgalr. Gst`s igdlrb`fmlags sla lf`smla`i`s plr plr k` f`rc` bugrt` qug rgsmstg k` gstruftur` gstruf tur` y plr `qugkk` p`rtg ig k` f`rc` vmv` slstgami` iur`atg ua pgrmlil sudmfmgatg flbl p`r` pgrbmtmr gk igs`rrlkkl ig igdkgxmlagss flasmigr`ekgs. igdkgxmlag flasmigr`ekgs. K`s dkgfh`s ` k`rcl pk`zl sg igtgrbma`a buktmpkmf`ail k` igdkgxmöa mast`atàag` prliufmi` plr k` f`rc` flasmigr`i` flasmi gr`i` plr ua d`ftlr h mcu`k `:

ilaig:

7:

p:

D`ftlr igpgaimgatg igk tmgbpl qug `ftú` k` f`rc` flasmigr`i`. Gs mcu`k `: _`r` 7 `ðls l bàs

5.?

_`r` 05 bgsgs

0.9

_`r` 4 bgsgs

0.5

_`r`

0.?

bgsgs

Fu`atâ` ig `fgrl ga flbprgsmöa `k fgatrl ig k` kuz p`r` gkgbgatls flatmauls y smbpkgbgatg `ply`ils y ga gk `plyl p`r` vlk`ils.

_`r` v`klrgs matgrbgimls ig

4

g gbpkg` k` cràdmf` prgsgat`i` ga k` dmcur` 8.7.

Gk p`ràbgtrl h igpgaig igk tmgbpl, ` tr`vís igk tírbmal tr`vís igk tírbmal p .

7

y ig k` cglbgtrm` ig k` sgffmöa, `

Gk bítlil prgsgat`il p`r` gstmb`fmöa ig igdkgxmlags gs `prlxmb`il y plr kl t`atl sm íst`s flastmtuyga ua prlekgb` ga gk imsgðl, gs flavgamgatg gdgftu`r fàkfukls bàs rgdma`ils. Vm fla prlfgimbmgatls bàs gk`elr`ils, `úa pgrsmstga k`s igdlrb`fmlags gxfgsmv`s, sg igeg flasmigr`r `kcúa prlfgimbmgatl p`r` gvmt`rk`s. Gatrg gkkls sg tmgag: mafrgbgat`r igk pgr`ktg ig k` sgffmöa, mafrgbgat`r k` fu`atâ` fu`at â` ig `fgrl ga flbprgsmöa l prlvg prlvggr gr `k gkgbgatl ig ua` flatr`dkgfh`. flatr`dk gfh`. Gstg úktmbl rgfursl flasmstg ga i`rkg ua` kmcgr` furv`tur` `k gkgbgatl ig blil qug `k sgr `pkmf`i`s k`s f`rc`s, k` igdkgxmöa tlt`k al sg` gxfgsmv` (vgr dmcur` 8.4).

 

Iurlfmöa

Dmcur`

87

T`klr ig

g

l f`rc`

a

b

s

s

p`r` gk fàkfukl ig k`s igdkgxmlags ` k`rcl pk`zl

Flatrldkgfhl

f

Dmcur` 8 4 Flatr`dkgfh` ga vmc`s

85

F L A Y U L K IG U J IWU V

K`s r`j`iur`s sg prgsgat`a ga gk flafrgtl fu`ail sg gxfgig su rgsmstgafm` ` k` tgasmöa. Vu prgsgafm`` gs magvmt`ekg y plr prgsgafm plr kl t`atl gk prlygftmst` prlygftmst` sökl eusf` kmbmt`r su `afhl. Wa `crmgt`bmgatl gxfgsmvl gxfgs mvl pugig lf`smla`r k` pírimi` ig kâqumils kâqumils ga rgsgrvlrmls l pgrjuimf`r k` `p`r `p`rmgafm` mgafm` gxtgra` ig k`s supgrdmfmgs supg rdmfmgs qug rgqumgrga rgqumgrga ua `f`e`il flbpkgt`bgatg kmsl. kmsl. @sâ bmsbl k` prgsgafm` ig dmsur`s dmsur` s `dgft` gk rgfuermbmgatl ig k` `rb`iur` y plr kl t`atl t`atl su duafmöa ig prltgffmöa `k rgdugrzl. K`s mavgstmc`fmlags h`a h`a igblstr`il qug k`s crmgt`s gstrgfh`s ga flafrgtls ig euga` f`kmi`i y emga flbp`ft`ils al rgiufga rgiufga flasmigr`ekgbgatg flasmigr`ekgbgatg k` gdmfmgafm` ig imfh` prltgffmöa. _lr gk flatr`rml flatr`rm l k`s crmgt`s `afh`s pugiga `dgft`rk` alt`ekgbgatg. alt`ekgbgatg. _lr gkkl gk prlygftmst` prlygftms t` prlfur` qug gk dmsur`bmgatl sg s g b`amdmgstg ` tr`vís tr`vís ig ua` euga` f`atmi`i f`atmi`i ig r`j`iur`s gstrgfh`s `atgs qug ` tr`vís ig ua`s plf`s ig crlslr flasmigr`ekg. K` flrrlsmöa ig k` `rb`iur` smgbprg sg h` `slfm`il `slfm`il ` k` prgsgafm` ig dmsur`bmgatl. Vma gbe`rcl sg h` igblstr`il gxpgrmbgat`kbgatg gxpgrmbgat`kbgatg qug gk `afhl ig k`s crmgt`s al al madkuyg imrgft`bgatg ga gst` rg`ffmöa smal ga gk pgrmlil ig tmgbpl rgqugrmil p`r` qug gkk` tgac` kuc`r. Ltrls d`ftlrgs

 

qug p`rtmfmp`a ig blil smbmk`r ga gstg dgaöbgal sla: k`s f`r`ftgrâstmf`s igk bgiml `bemgatg, gk rgfuermbmgatl ig k`s v`rmkk`s, k` pgrbg`emkmi`i igk flafrgtl, gtf. K`s crmgt`s cr mgt`s sg cgagr`a plr kls gsdugrzls qug lf`smla`a k`s slkmfmt`fmlags ig flrtg, dkgx dkgxmöa> möa> f`rc` f`rc ` `xm`k, tlrsmöa, `sâ flbl k` flatr`ffmöa ig dr`cu`, frggp, flrrlsmöa igk `fgrl, gtf. K`s r`j`iur`s cgagr`i`s plr flatr`ffmöa ig dr`cu` dr `cu` sla buy buy mbplrt`atgs mbplrt`atgs plrqug plrqug cgagr`a ua p`tröa mamfm`k ig dmsur`bmgatl qug igspuís gs `cuimz`il e`jl k` `pkmf`fmöa ig ltr`s slkmfmt`fmlags. Gk `cagt`bmgatl mamfm`k igemkmt` `kcua`s sgffmlags k`s fu`kgs sg vugkvga bàs vukagr`ekgs ` k` `ffmöa ig ltrls gdgftls. _lr su p`rtg, k`s dmsur`s cgagr`i`s plr flrrlsmöa igk `fgrl sg igega ` qug gstg b`tgrm`k mafrgbgat` su vlkubga `k lxmi`rsg. Iur`atg gstg prlfgsl, `krgigilr igk rgdugrzl sg cgagr`a tgasmlags r`im`kgs r`im`kgs qug supgr`a supgr`a k` rgsmstgafm` rgsmstgafm` ` k` tr`ffmöa igk flafrgtl kl `crmgt`a. 850

@afhl ig k`s dmsur`s

Gk `afhl ig k`s crmgt`s gs kmbmt`il ig `fugril `k tmpl ig gxplsmfmöa qug tgairà gk gkgbgatl imsgð`il. Vm al gstà gs tà gxpugstl ` k` matgbpgrmg gk `afhl ig dmsur` ige igegrà grà gst`r plr ige`j ige`jl l ig ?.?9 fb. sm kl gstà, gk `afhl ig dmsur` igegrà sgr bgalr bgalr qug ?.?6 fb. Gxpgrmbgat`kbgatg, Gxpgrmbgat`kbga tg, sg h` igblstr`il igbls tr`il qug gk `afhl ig k`s dmsur`s ga gkgbgatls ig flafrgtl `rb`il gs duafmöa ig k` imstrmeufmöa imstrmeufmöa igk rgdugrzl. rgdugrzl. K`s v`rmkk`s v`rmkk`s ig imàbgtrls imàbgtrls pgqugðls plfl gsp`fm`bmgatl sg flbplrt`a bàs gdmfmgatgbgatg qug k`s v`rmkk`s bàs crugs`s y bàs `kgj`i`s gatrg sâ. Y`bemía sg h` igblstr`il qug gk `afhl ig k`s crmgt`s gs duafmöa igk gsdugrzl ga gk `fgrl ig k` imst`afm` imst`afm` igk elrig ig flafr flafrgtl gtl ga t g a s m h ` k` prmbg prmbgr` r` dmk` ig rgdugrzl rgdugrzl.. _`r` flatrlk`r gk `afhl ig k`s dmsur`s gk @FM 6 08-?5 kmbmt` k` imst`afm` bàxmb` gatrg dmgrrls:

V

=44??

8-8)

5.7 FF.

@FM-0?-9)

V

ilaig:

Ff: gk g k rgfuermbmgatl rgfuermbmgatl ig kls dmgrrls V:

imst`afm` gatrg dmgrrls

Dörbuk` gbpârmf` e`s`i` ga gxpgrmgafm`s gxpgrmgafm`s

5

qug v`kg v`kg p`r` gstruftur`s matgrmlrgs

6

9

7

4

3

Flafrgtg F`vtr. F, m a. )

Dmcur` 8.3. Gsp`fm`bmgatl igk rgdugrzl

 

8

gxtgrmlrgs.

@igbàs maimf` qug: s M 6 ?

575?

ds Gst` rgck`bgat`fmöa gs `imfmla`k ` kl qug b`ai` gk kls`s ga ils sgatmils V 5 h.

b.

8-=)

FM p`r` kls`s ga ua sgatmil V

6 h y p`r`

GJ gsdugrzl ig tr`e`jl igk `fgrl sg gstmb` ` tr`vís ig k` smcumgatg gxprgsmöa:

ilaig B gs gk blbgatl e`jl f`rc`s ig sgrvmfml, gs igfmr, sma `bpkmdmf`r `bpkmdmf`r y sg gstmb` ` tr`vís ig k` gxprgsmöa gxprgsmöa (8-6). @ktgra`tmv`bgatg, sg pugi pugig g `submr qug `fgrl tr`e`j` `k 4? ig su gsdugrzl ig dkugafm`, gs igfmr, d ?.4dy. Gst`s dörbuk`s dör buk`s gstàa e`s`i`s ga r`j`iur`s bàxmb`s bàxmb`s ig w

?.?90 fb. p`r` gstruftur`s matgrml matgrmlrgs. rgs.

@uaqug gk @FM al kl maimf`, p`r` ltrls `afhls ig r`j`iur`s sg pugig tlb`r:

_`r` gstruftur` gxtgrmlrgs ......................................................................

w

?.?66 fb.

_`r` gstruftur` slbgtmi`s ` `t`qugs quâbmfls .................................... w

?.?08 fb.

_`r` gstruftur` slbgtmi`s ` `cu` ig b`r l s`kpmf`iur`s ig `cu` g b`r ..................................................................................................... w _`r` gstruftur`s rgtgagilr`s ig kâqumils ga flaimfmlags lrb`kgs .................................................................................................

w

7?.?07 fb.

?.?57 fb.

_`r` gstruftur`s rgtgagilr`s ig kâqumils ga flaimfmlags gvgr`s .................................................................................................... w

?.?5? fb.

_`r` gstruftur`s fla prgsmöa ig `cu` ................................................... w

?.?0? fb.

855

Tmc`s ig cr`a pgr`ktg

Vm gk pgr`ktg pgr`k tg gdgftmvl ig ua` ua` vmc`, i, gs b`ylr l mcu`k qug =? = ? fb. gk gkgbgatl igegrà igegr à sgr prlvmstl ig rgdugrzl rgdugr zl `imfmla`k ga sus f`r`s p`r` gvmt`r gk dmsur`bmgatl qug sg puimgr` prliufmr ga gkk`s igsprlvm st`s ig `fgrl. Gk föimcl sucmgrg qug gstg rgdugrzl rgdugrzl sg rgp`rt` ga k` bmt`i madgrmlr `k gst`r igsprlvmst`s igk gkgbgatl (vgr dmcur` 8.8), ga `be`s f`r`s ig k` vmc` y su gsp`fm`bmgatl V gatrg e`rr`s klacmtuima`kgs `imfmla`kgs sgrà:

 

V V

ilaig @

ik4

6? fb.

àrg` ig ua` e`rr` ig @ .

Al sg rgqumgrg qug gk rgdugrzl tlt`k ga `be`s f`r`s f`r`s ig k` vmc` 5@sn sg` b`ylr qug k` bmt`i igk rgdugrzl klacmtuima`k igk gkgbgatl.

Dmcur` 8.8. Ugdugrzl p`r` flatrlk`r dmsur`s ga vmc`s pgr`kt`i`s