Ensayo de Compresion No Confinada

 

[NU]A

FKJ. CK Z[KBOZ DD

JONSKNDCO DNS]OC[JJDO N.................. DNS]OC[JJDO N.................................... .................................... .................................... .................................... .................................... .................................... ........................... ............... ........... ......... = OMLKSDPOZ....................................... OMLKSDPOZ..................... .................................... .................................... .................................... .................................... .................................... ............................ ............... ........... ............ .......... : FG]JO SKO SKO ]DJO.................... ]DJO...................................... .................................... .................................... .................................... .................................... .................................... ............................... .................. ..... 3 KW[DUOZ T HK]]GFDKNSGZ................. HK]]GFDKNSGZ................................... .................................... .................................... .................................... .................................. ..................... ........... ........... ......... 0

7.

FG W[DNG CK JOFU]KZDO FG JOFU]KZDO N.................. N.................................... .................................... .................................... .................................... ................................ .................... ...... 0

=.

KXS]GJSO] CK F[KZS]GZ..............................................................................................................0

:.

FDJ]O FKS]O CK JG]AGZ.................... FDJ]O JG]AGZ...................................... .................................... .................................... ................................... ...................... ........... ........... .......... ..... 1

3.

FDJ]O FKS]O CK CK@O]FGJDONKZ......................... FDJ]O CK@O]FGJDONKZ........................................... .................................... .................................. ...................... ........... ......... .... 1

;.

MGBGN\G KBKJS]O KBKJS]O NDJG..................... NDJG....................................... .................................... .................................... .................................... .................................... ....................... ..... 1

0.

J]ONO FKS]O...................... J]ONO FKS]O........................................ .................................... .................................... .................................... .................................... ......................... ............ ........... ........... ....... 8

1.

PK]NDK]......................................... PK]NDK]....................... .................................... .................................... .................................... .................................... .................................... .......................... .............. ......... ... 8

8.

KZS[@G...................................... KZS[@G.................... .................................... .................................... .................................... .................................... .................................... .................................... ....................... ..... 8

U]OJKCDFDKNSO.......................................... U]OJKCDFDKNSO........................ .................................... .................................... .................................... .................................... .................................. ...................... ........... ......... .... 4 CGSOZ DNDJDGBKZ...................... DNDJDGBKZ........................................ ................................... ................................... .................................... .................................... ............................. ................ ........... .......... .... 75 CGSOZ OMSKNDCOZ KN BGMO]GSO]DO..............................................................................................77 J[]PG KZ@[K]\O CK@O]FGJDO CK@O]FGJDO N..................... N....................................... .................................... .................................... .................................. ...................... ........... ....... 7= JONJB[ZDONKZ........................................... JONJB[ZDONKZ......................... .................................... .................................... .................................... .................................... .................................... ........................ ........... ......... 7: MDMBDOA]G@DG............................................. ........................... .................................... .................................... .................................... .................................... ................................. .................... ........... ........... ..... 73 GNKXOZ........................................ GNKXOZ...................... .................................... .................................... .................................... .................................... .................................... .................................... ............................... ............... 7;

KNZGTO CK JOFU]KZDON NO JON@DNGCG

7

 

[NU]A

FKJ. CK Z[KBOZ DD

DNS]OC[JJDO N DNS]OC[JJDO Kb knsgyo ck jofprksdon no jon`dngcg, bbgfgco tgfmdkn knsgyo ck jofprksdon sdfpbk o knsgyo ck jofprksdon undgxdgb, ks fuy dfportgntk kn Fkjgndjg ck Zukbos, y kn nukstrg jgrrkrg, yg quk pkrfdtk omtknkr un vgbor ck jgrag ubtdfg ckb sukbo, kb jugb, sk rkbgjdong jon bg rksdstknjdg gb jortk ckb sukbo y kntrkag un vgbor ck jgrag quk pukck utdbdzgrsk kn proykjtos quk no rkqudkrgn ck un vgbor fgs prkjdso, yg quk kntrkag un rksubtgco jonskrvgcor. Kstk knsgyo pukck ck`dndrsk kn tkoræg jofo un jgso pgrtdjubgr ckb knsgyo trdgxdgb. Kstk knsgyo ks fuy dfportgntk, porquk pkrfdtk jofprknckr kb jofportgfdknto ck bos sukbos sofktdcos g jgrags, yg quk ks kn kbbos o somrk kbbos quk sk vgn g uncgr bgs kstrujturgs, yg skgn pukntks, kcd`djdos o jgrrktkrgs, quk rkqudkrkn ck ung mgsk `drfk, o fgs gun quk pukckn gprovkjhgr bgs rksdstknjdgs ckb sukbo kn mkn knk` k`dj djdo do ck su prop opdg dg jg jgp pgj gjdc dcggc y kst kstgm gmddbdcg bdcgc, c, sdkn sdknco co kb ks kstu tucd cdoo y bg kxpkrdfknt kxpkr dfkntgjdo gjdo n bgs hkrrgfdknt hkrrgfdkntgs gs pgrg jonskaudrbo jonskaudrbo,, y `dngbf `dngbfkntk kntk pockr prkckjdr, jon jon un ungg jdkr jdkrtg tg gp gpro roxd xdfg fgjdo jdo n, kb jof jofpo port rtgf gfdkn dknto to gn gntk tk bgs bgs jg jgra rags gs ck ks kstg tgss kstrujturgs.

KNZGTO CK JOFU]KZDON NO JON@DNGCG

=

 

[NU]A

-

FKJ. CK Z[KBOZ DD

OMLKSDPOZ Omtknkr bg jurvg ksukrzo ‚ ckorfgjdon.

- Omtknkr kb ksukrzo fgxdfo ck roturg q fçx.

- Omtknkr kb focubo ck kbgstdjdcgc Q

KNZGTO CK JOFU]KZDON NO JON@DNGCG

:

 

[NU]A

FKJ. CK Z[KBOZ DD

FG]JO SKO SKO ]DJO Bg ckorfgjdon undtgrdg λ  sk jgbjubg ck bg fkjgndjg ck fgtkrdgbks jofo< λ6

  γ   B5  

...7

Conck<

-

  γ  ks

-

  B5 ks bg bonadtuc ordadng ck bg fukstrg kn ff.

bg ckorfgjdon totgb ck bg fukstrg (gxdgb) kn ff.

Kb ksukrzo dnstgntgnko ckb knsgyo somrk bg fukstrg sk jgbjubg jon bg sdaudkntk kxprksdon< ϊ 6

 U  G ' 

…=

Conck<

-

  U

 

ks bg jgrag somrk bg fukstrg kn jugb gbq qudkr dnst stggntk pgrg kb jorrksponcdkntk vgbor B, kn ia.

  G '   ks kb g r kg ck bg skjj skjjdo do n tr trgn gnsv svkr krsg sgbb ck bg fuks fukstr trgg pgrg pgrg bg jg jgra ragg

jorrksponcdkntk U, kn jf

=

Kn fkjgndjg ck sukbos ks prgjtdjg jonvknjdongb jorrkadr kb grkg somrk bg jugb gjtug bg jgrag U. Ksto no sk hgjk jugnco sk knsgygn fktgbks kn tknsdon. [ng ck bgs rgzonks pgrg kstg jorrkjjdon ck grkg ks bg ck pkrfdtdr jdkrtg tobkrgnjdg somrk bg orfg jofo kb sukbo ks rkgbfkntk jgragco kn kb tkrrkno. Gpbdjgr kstg jorrkjjdon gb grkg ordadngb ck bg fukstrg ks gbao jonskrvgtdvo tgfmdkn puks bg rksdstknjdg orfg skrg fknor qukjonsdckrgnco bg quk sk pocræ  G  sk jgbjubgr utdbdzgnco u kbbtdfg grkg jgbjubgcg ordadngb. Kbckgrkstg kg ordadngb jorrdak qukg kb vobufkn totgb ckb sukbo pkrfgnkjk jonstgntk. Kb vobufkn totgb dndjdgb ck bg fukstrg ks< 5

P S 6 G5 ¿ B5

...:

Ukro ckspuks ck gbaun jgfmdo B kn bg bonadtuc ck bg fukstrg ks< P S 6 G ' ¿ ( B ¿¿ 5 ∝ B) ¿

…3

Daugbgnco bgs kjugjdonks (:) y (3), jgnjkbgnco tkrfdnos y ckspklgnco kb grkg jorrkadcg G', sk omtdknk<

KNZGTO CK JOFU]KZDON NO JON@DNGCG

3

 

[NU]A

 G ' 6

FKJ. CK Z[KBOZ DD

  G5 7

∝λ

Sgmbg 7. ]kbgjdon aknkrgb ck jonsdstknjdg y rksdstknjdg g bg jofprksdon sdfpbk ck grjdbbgs

Jonsdstknjdg ck ckb su sukbo kbo

Jgrag uu b ttdf dfgg ((iia/j /jf f=)

Fuy mbgncg

25,=;

Mbgncg

5,=;-5,;5

Fkcdg

5,;5-7,55

@drfk

7,55-=,55

Fuy `drfk

=,55-3,55

Curg

>3,55

KNZGTO CK JOFU]KZDON NO JON@DNGCG

;

 

[NU]A

FKJ. CK Z[KBOZ DD

KW[DUOZ T HK]]GFDKNSGZ 7. FG FG W[DNG CK JOFU]KZDO JOFU]KZDO N.  Kstg fgqudng fkjgndjg nos pkrfdtdrg jofprdfdr bg fukstrg hgstg un punto conck bg fukstrg gbbk, pgrg ksto sk nkjksdtgrgn cos fdjrofktros uno ck ckorfgjdon y uno ck jgrag9 kstg fgqudng fdck jofprksdonks fknorks g bo boss 75 755 5 iUg iUg (7 (7ia ia/j /jf f=) y ck ckmk mkn n skr skr jg jgpg pgjk jkss ck fkcd fkcdrr bos bos ks ksu ukr krzo zoss = jofprksdvos jon ung prkjdsdon ck 7 iUg (5,57 ia/jf ).

FÇW[DNG CK JOFU]KZDÚN

=. KXS]GJSO] CK

F[KZS]GZ.

Ks un kqudpo fkjgndjo jgpgz ck sgjgr kb tkstdao ck sukbos9 sd bgs fukstrgs bbkagn gb bgmorgtordo kn tumos no gmdkrtos bonadtucdngbfkntk, ks prkjdso quk procuzjg pojg gbtkrgjdon kn kb sukbo.

KXS]GJSO] CK F[KZS]GZ

:. FDJ]O FDJ]O FKS]O CK JG]AGZ. KNZGTO CK JOFU]KZDON NO JON@DNGCG

0

 

[NU]A

FKJ. CK Z[KBOZ DD

Nos dncdjg un nufkro quk gb fubtdpbdjgrbo por su jonstgntk nos rksubtg bg ukrzg quk sk bk kstg gpbdjgnco g bg fukstrg ck sukbo.

3. FDJ]O FDJ]O FKS]O CK CK@O]FGJDONKZ. Kstg argcugco g 5,5=ff, y jon un rgnao ck fkcdjdon ck por bo fknos un =5% ck bg bonadtuc ckb kspkjdfkn pgrg kb knsgyo, o gbaun otro dnstrufknto ck fkcdjdo fkcdjdo n, jofo un trgnscujtor quk jufpbg kstos rkqukrdfdkntos.

;.

FDJ]ÚFKS]OZ

MGBGN\G KBKJS]O KBKJS]O NDJG. Cg kb pkso ck bg fukstrg jon ung prkjdsdon ckb 5,7 % ck su pkso totgb.

0.

J]ONO FKS]O. J]ONO

Zd kb ks fgnugb.

jontrob ck bg prknsg MGBGN\G KBKJS]ÚNDJG

KNZGTO CK JOFU]KZDON NO JON@DNGCG

1

 

[NU]A

FKJ. CK Z[KBOZ DD

J]ONÚFKS]O

1. PK]NDK]. Jgpgz ck fkcdr bgs cdfknsdonks æsdjgs sdjgs ck bg promktg jon gproxdfgjdon ck 5,7 ff.

PK]NDK]

8.

KZS[@G.

Fgntdknk ung tkfpkrgturg ck 775 · ; µJ.

KZS[@G

KNZGTO CK JOFU]KZDON NO JON@DNGCG

8

 

[NU]A

FKJ. CK Z[KBOZ DD

U]OJKCDFDKNSO 











Zk tofg ung fukstrg ck sukbo, tdpo FDS (Fukstrg dngbtkrgcg kn tumo ck pgrkc ckbagcg)9 ck kstg fukstrg kxtrgkfos ung pkqukng promktg jdbæn ncrdjg crdjg juygs cdfknsdonks son ck 3 jf. ck cdgfktro fkcdco ckb dntkrdor y ung gbturg ck ;.88 jf. Bukao ck omtkndco kb fobck jon bg fukstrg, pksgfos gfmos kn ung mgbgnzg kbkjtrondjg ck ung prkjdsdon ck jkntksdfg ck argfo, omtkndknco pkso ckb fobck fgs pkso ck bg fukstrg. Jon kb kqudp kqudpoo kxtrgjtor kxtrgjtor ck fukst fukstrg rg sk rktdro rktdro bg promktg (jdbdncro pkqukn pkqukn o) qukcgnco bg fukstrg no jon`dngcg y jon bgs cdfknsdonks dntkrdorks ckb jdbdncro. Bg fukstrg uk jobojgcg kn bg fgqudng ck jofprksdon, kn kstk fktoco ck knsgyoo sk gpbdjo knsgy gpbdjo ; ckorfgjdon ckorfgjdonks ks ck 5.55; bkjturg bkjturgss kn kb fdjro fdjro fktro ck ckorfgjdo ckorf gjdo n, bukao ; ck 5.575 y kb rksto ck 5.5=5 jon dntkr dntkrvgbos vgbos ck tdkfpo ck 7; skauncos. Jgcg ckorfgjdon gpbdjgcg sk trgcujk g ung jgrag gxdgb gpbd gp bdjg jgcg cg bg ju jugb gb sk to tofg fg bkjt bkjtur urgg kn kb fdjr fdjroofk fktr troo ck jg jgra ragg y pgrg pgrg trgnsorfgrbo kn ung jgrag tknkfos quk fubtdpbdjgrbo por ung jonstgntk ‒i‖ quk ks propdg ckb gmrdjgntk ckb fdjrofktro ck jgrag (i 6 :4.144), kb vgbor quk nos sgbk kstg kxprksgco kn ia. [ng vkz bg fukstrg gbbk, o skg jugnco vkfos quk kb fdjrofktro ck jgrag jofdknzg g cdsfdnudr kn bgs bkjturgs y jugnco vdsugbfkntk vkfos quk bg fukstrg hg gbbgco kn su orfg dndjdgb, pgsgfos g fkcdr bgs cdfknsdonks jofo kb cdgfktro ck bg pgrtk jkntrgb ck bg fukstrg y su gbturg. Bukao vgfos g jgbjubgr jon opkrgjdonks fgtkfgtdjgs kb ksukrzo fgxdfo ck roturg, kb focubo ck kbgstdjdcgc y bg johksdon ckb sukbo.

CGSOZ DNDJDGBKZ

KNZGTO CK JOFU]KZDÚN NO JON@DNGCG Jontkndco ck Hufkcgc< ]kjdpdkntk Nro. Ukso ck Fukstrg Hüfkcg + ]kjdpdkntk (ar.) Ukso skjo + ]kjdpdkntk (ar.) Ukso Gaug (ar.)

KNZGTO CK JOFU]KZDON NO JON@DNGCG

; =7=

Jofprksdún< Cdg fktro Dndjdgb (jf) Cdg G rk rkg Dndjdgb (jf=)

3 7=.; 1 ;.88 1:.4

Gbturg Dndjdgb (jf) Pobufkn DDn ndjdgb (jf:)

4

 

[NU]A

FKJ. CK Z[KBOZ DD

7

Ukso ]kjdpdkntk (ar.) Ukso ck Fukstrg Hüfkcg (ar.)

;4.84 7;=.7 7

Cdg fktro @dngb (jf) Cdg

3.7=

Ukso ck Fukstrg Zkjg (ar.)

Grkg @dngb (jf=)

Jontkndco ck Hufkcgc (%)

Gbturg @dngb (jf)

7:.: : ;.87

Cknsdcgc Hüfkcg (ar./jf:)

Pobufkn @dngb (jf:)

108.=

Cknsdcgc Zkjg (ar./jf:)

CGSOZ OMSKNDCOZ KN BGMO]GSO]DO

t Sdkfpo trgnsju rrdco 5s

Fdjrofktro ck jgrag 5

U

γ

Jgrag gxdgb

Cdgb ck Ckorfgjdon Ckorfgjdon ckorfgjdon Sotgb [ndtgrdg

ia

5

 

jf

5

KNZGTO CK JOFU]KZDON NO JON@DNGCG

jf jf

5

ə

5

 

' 

G6

  G5

 

( 7 ∝ə ) Grkg Jorrkadcg

ϊ 6

 U  G ' 

Ksukrzo =

jf

7=.;1

75

 

ia / jf

5

 

[NU]A

FKJ. CK Z[KBOZ DD

7; s :5 s 3; s 7' 7' 7; s 7' :5 s

5.557 5.55: 5.553 5.551 5.57 5.57=

5.535 5.774 5.7;4 5.=14 5.:48 5.318

5.55; 5.55; 5.55; 5.55; 5.55; 5.57

5.55; 5.57 5.57; 5.5= 5.5=; 5.5:;

5.5558;5 5.557157 5.55=;;7 5.55:357 5.553=;= 5.55;4;=

7=.;87 7=.;47 7=.05= 7=.07: 7=.0=3 7=.03;

5.55:= 5.554; 5.57=0 5.5==7 5.5:7; 5.5:18

7' =' 3; s

5 5..5 5= =5 ; 5.5:3 5.53: 5.50= 5.58: 5.77; 5.70; 5.785 5.74; 5.=7; 5.=:5 5.=;5 5.=0; 5.=1; 5.=45 5.=4; 5.:55 5.=81 5.=85 5.=1;

5 5..1 44 40 ; 7.:;: 7.177 =.308 :.:5: 3.;11 0.;01 1.703 1.107 8.;;1 4.7;3 4.4;5 75.;31 75.43; 77.;3= 77.137 77.435 77.3== 77.733 75.43;

5 5..5 57 7 5.57 5.57 5.5= 5.5= 5.5= 5.5= 5.5= 5.5= 5.5= 5.5= 5.5= 5.5= 5.5= 5.5= 5.5= 5.5= 5.5= 5.5= 5.5=

5 5..5 53 ;; ; 5.50; 5.51; 5.54; 5.77; 5.7:; 5.7;; 5.71; 5.74; 5.=7; 5.=:; 5.=;; 5.=1; 5.=4; 5.:7; 5.::; 5.:;; 5.:1; 5.:4; 5.37;

5 5..5 55 51 40 :; ;: 3 5.5775;3 5.57=1;; 5.5707;0 5.574;;8 5.5==4;4 5.5=0:07 5.5=410= 5.5::70: 5.5:0;0; 5.5:4400 5.53::01 5.530104 5.5;5715 5.5;:;17 5.5;041: 5.505:13 5.50:110 5.501711 5.515;18

7 7= =..0 00 81 4 7=.177 7=.1:= 7=.110 7=.8=7 7=.80; 7=.475 7=.4;0 7:.557 7:.531 7:.54: 7:.735 7:.781 7:.=:3 7:.=8= 7:.:=4 7:.:18 7:.3=0 7:.31; 7:.;=;

5 5..5 50 1= 88 3 5.750; 5.7:33 5.74:7 5.=;11 5.:;;8 5.;580 5.;;:5 5.;404 5.0;;8 5.0447 5.1;1= 5.1448 5.8=15 5.8045 5.8858 5.84=; 5.8;51 5.8=15 5.854=

=' 7; s =' :5 s =' 3; s :' :' 7; s :' :5 s :' 3; s 3' 3' 7; s 3' :5 s 3' 3; s ;' ;' 7; s ;' :5 s ;' 3; s 0' 0' 7; s 0' :5 s 0' 3; s

Conck< 

U



  G5  

   

λ γ Bo   ϊ 7

Jgrag gpbdjgcg. G rkg dndjdgb. Ckorfgjdo Ckorfgjdo n undtgrdg. Ckorfgjdo Ckorfgjdo n o ckspbgzgfdknto. Bonadtuc dndjdgb ck jgbdmrgjdon. Ksukrzo.

KNZGTO CK JOFU]KZDON NO JON@DNGCG

77

 

[NU]A

FKJ. CK Z[KBOZ DD

J[]PG KZ@[K]\O CK@O]FGJDO CK@O]FGJDO N

CDGA]GFG KZ@[K]\O - CK@O]FGJDÚ CK @O]FGJDÚN N 7 5.4 5.8 5.1 5.0 5.;

      Z       O       \       ]       K       [       @       Z       K

5.3 5.: 5.= 5.7 5    1    7    4    0    :    7    8    ;    =    7    7    5    1    1  3    1    0    0    0    0    ;    ;    ;  3    ;    5    5    5    7    :    ;    1    4    7    :    ;    1    :    4   3    1    5    1    5    :    0    4    :    0    4    =    4    ;    :    7    5    0    0    ;    :    :    =    7    7    5    5    5    5    5    5    5    5    5  3    5    5    5    5    5    5    5    5    5    5    5 .    5 .    5 .    5 .    5 .    5 .    5 .    5 .    5 .    5 .    5 .    5 .    5 .    5 .

CK@O]FGJDÚN [NDSG]DG



Kb fgxdfo ksukrzo o ksukrzo ubtdfo ck jgrag ks daugb g 5.84=; ia / jf .



Kb focubo ck kbgstdjdcgc omtkndco ks<

=

 K 6taη 6

 K 6

  5.55:70:; 5.5558;5:3

6:.1=5=1=3 ia / jf

ϊ 7 λ7

=

JONJB[ZDONKZ 

Ck gjukrco g bos rksubtgcos omtkndcos kn bg tgmbg prkskntgcg, juyo vgbor fgxdfo ck ksukrzo ks ck 5.84=; ia / jf , sk hg bbkagco g jonjbudr quk bg fukstrg ks ck jonsdstknjdg fkcdg. =

KNZGTO CK JOFU]KZDON NO JON@DNGCG

7=

 

[NU]A



FKJ. CK Z[KBOZ DD

Bg arg`djg ck ksukrzo ‚ ckorfgjdon nos fukstrg jofo kb bæ fdtk fdtk ck proporjdongbdcgc y kb bæfdtk fdtk ck kbgstdjdcgc kstgn fuy cdstgntks ksto ks ckmdco quk un sukbo no sk jofportg jofo fgtkrdgb kbgstdjo. 

MDMBDOA]G@DG 

M]GLG F. CGZ @uncgfkntos ck Dnakndkræg Akotkjndjg, skauncg kcdjdon, Fkxdjo, =575.

KNZGTO CK JOFU]KZDON NO JON@DNGCG

7:

 

[NU]A

FKJ. CK Z[KBOZ DD



NSU ::4.701< Fktoco ck Knsgyo Kstgncgr pgrg bg rksdstknjdg g bg jofprksdon no jon`dngcg ck sukbos johksdvos.



GGZHSO S =58< [njon`dnkc Jofprkssdvk Ztrknath o Johksdvk Zodb.

GNKXOZ

KNZGTO CK JOFU]KZDON NO JON@DNGCG

73

 

[NU]A

FKJ. CK Z[KBOZ DD

KXS]GJJDÚN CK BG F[KZS]G

FÇW[DNG CK JOFU]KZDÚN U]KPDG GB KNZGTO

U]DFK]GZ @GBBGZ CK BG F[KZS]G

KNZGTO CK JOFU]KZDON NO JON@DNGCG

7;