Ingenieros Civiles
I N D I C E
Ca p itulo tulo 1 1.1 1.2 1.3 1.4
Dis Diseño d e ed ific fic ios en hormigó hormigó n arma d o Introd Intro d uc c ión ................. .......................... .................. .................. ................. ................. .................. .................. ............... ...... O b jetivo jet ivo .................. ............................ ................... ................... ................... .................. .................. ................... ................... ......... Norma No rma s d e d ise ise ño ............... ....................... ................ ................ ................ ................ ................ ................ ............. ..... Doc Do c um e nto nt o s d e un p roye c to ....... ........... ........ ........ ....... ....... ........ ........ ....... ....... ........ ........ ....... ....... ......
3 4 4 4
C a p itulo itu lo 2
Ba se s d e c á lc ulo .................... ............................. ................... .................... ................... ................... .................... ..........
6
Ca p itulo itulo 3 3.1 3.2 3.3 3.4
Estructur tructu ra c ión y p rec á lculo sísmic o C o nc e p to ................. ......................... ................ ................. ................. ................. ................. ................ ................. ............... ...... Co nd icione ic ione s d e d iseñ iseñoo d e una e struc tura ..... ........ ..... ..... ...... ...... ...... ..... ..... ..... ..... ...... ... Siste iste m a s e struc tura tu rales les ................... ............................ .................. ................... ................... ................... .............. .... Eleme ntos nto s estr estruc uc turales típ típ ico s en ed ificios ificios de hormigó n a rma d o d e m e d iana ian a a ltura ........ ............ ........ ....... ....... ........ ........ ....... ....... ........ ........ ....... ....... ........ ....... ... Func ione ion e s d e los e lem e nto nt o s e struc turale tu raless ....... ........... ....... ....... ........ ....... ....... ........ ........ .... Pred imens ime nsiona iona m iento d e los elem ele m ento en to s estruc estruc turales tura les ..... ....... ..... ...... ..... .... ..
9 9 9
C a p itulo 4 4.1 4.2 4.3
Aná An á lisis lisis sísm ic o C ub ic a c ión d e p e so sísm ic o ............... ....................... ............... .............. ............... ............... .............. ....... Disp Disp o sicion ic ionee s d e la no rma NCh 433 o f 96 ...... .......... ........ ........ ........ ........ ....... ....... ........ ...... Re sulta ult a d o s d e l a ná lisis lisis sísm ico ic o ............... ...................... ............... ................ .................. ................... .........
12 13 14
Ca p itulo 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7
Aná lis lisis y d iseñ iseñoo d e losa losa s Des De sc rip rip c ión ................. .......................... .................. ................. ................. .................. ................. ................. ................. ............ Co m p o rtam rta m iento ien to e lás lá stic o ........ ............ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ .... Tipo ip o s d e los lo sa s ........................................ .................... ........................................ ........................................ ......................... ..... Tipo ip o s d e a p o yo ................ ......................... ................. ................. ................. ................. ................. ................ ................ ........ Determ Det ermina inacc ión d e l e sp e so r req ueri ue ridd o ...... ......... ....... ....... ...... ...... ...... ...... ...... ...... ...... ....... ....... ... Det e rmina c ión d e e sfue rzo rzo s d e d ise ise ño e n losa losa s ........ ........... ....... ........ ........ ....... ..... Dia Dia grama de fluj flujoo p ara e l diseño diseño d e losa losa s rec tang ulares ulares c on c a rga unifo un iforme rme .............. ..................... .............. ............... .................. ................... ................... ................... ................ ....... Disp Disp o sición ic ión d e a rma d uras ura s y no m e nc latura la tura ..... ........ ...... ...... ....... ....... ...... ....... ....... ...... ..... Arma Arm a d ura m ínima nim a ................ ........................ ................ ................ ................ ................ ................ ................ ............. ..... Se p a rac ra c ión m á xima e ntre nt re b a rra rra s ........... ................. ............ ............ ............ ........... .......... .......... ......... Se p a rac ra c ión ió n m ínima nim a e ntre nt re b a rra rra s .............. ..................... .............. .............. .............. .............. ........... .... C o ntrol nt rol d e d e fo rma c ione ion e s ............. .................... ............. ............ ............. ............. ......... ....... ........ ........ ....... ... Diafra Dia fragg m a d e tra nsfe nsferen rencc ia .............. ...................... ................ ............... ............... ............... ............... ........
3.5 3.6
5.8 5.9 5.10 5.10 5.11 5.11 5.12 5.12 5.13 5.13
M.K.C. Sem es estre tre 2006/ 2006/ 1
8 8 8
16 16 16 17 19 19 22 231 24 24 24 24 25
1
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Ingenieros Civiles
Ca p itulo itulo 6 6.1 6.2
Aná lis lisis y d iseño iseño d e viga s, c olumn a s y mur mu ros M é to d o s d e d ise ise ño ............... ....................... ............... .............. ............... .............. ............ ............ ........... ........... .......... Méto d o d e los los fac tores de c arga y res resiistenc ia seg ún có d igo A .C.I. .C .I. 318 ................................... ................ ...................................... ...........................………………….. ........………………….. 6.3 Difer Diferenc enc ia c ión p rác tic tic a p a ra viga s y co lumna s d e hormigó hormigó n a rma d o ................. ........................... ................... ................... ................... ................... .................... ................... ................... ............ 6.4. 6.4. Deta lla lla m iento d e a rma d uras p a ra m a rc os sismo ismo rresis esiste tente nte s …… 6.4.1 6.4.1 Deta lla lla m iento d e a rm a d ura p a ra c olum na s sismo ismo rresis esiste tente nte s ... ... 6.4.2 6.4.2 Deta Det a lla lla m iento d e a rm a d ura p a ra viga s sismo ismo rresis esiste tente nte ..... ....... .... .... .... .. 6.5 Cua ntía ntía m ínima d e a rma d ura transve transverrsal en c olumna olum na s .... ...... .... .... .... .... .. 6.6 6.6 Cua ntía ntía míni mínima ma d e a rma d ura ura long itud inal en c olumna s .... ...... .... .... .... .. 6.7 Cua ntía ntía má xim xim a d e a rm a d ura transve transverrsa l en c o lumna s .... ...... .... .... .... .... .. 6.8 Cua Cu a ntía m ínima nim a d e a rma d ura trans tra nsve ve rsa rsa l e n viga vig a s ...... ......... ...... ...... ...... ...... ..... 6.9 Cua ntía ntía mínima mínima d e a rma d ura long itudinal itud inal en viga s .... ...... .... .... .... .... .... .... .... .. 6.10 6.10 Cua ntía ntía má xima xima d e a rma d ura long itudinal itud inal en viga s .... ....... ..... .... .... .... .... ..... 6.11 6.11 C o m e nta nt a rio rio s ................ ........................ ............... ............... ................ ............... ............... ................ ................ ............... ........... 6.12 6.12 Anc An c lajes la jes,, e m p a lme s y g a nc ho s ........ ........... ....... ....... ....... ........ ....... ....... ....... ....... ....... ....... ........ ....... ..... 6.13 6.13 Dise Dise ño d e m uros uro s sism ism o rre rre siste iste nte nt e s .......... .................. ................ ................ ............... ............... ............
28 28 30 31 32 34 35 36 36 36 36 37 37 37 41
Ca pitulo pitulo 7 7.1 7.2 7.3
Dis Diseño de fundac iones Introd Intro d uc c ión ió n .................. ........................... ................. ................. .................. .................. .................. .................. ................ ....... Esta b ilida ilida d g lob a l d e las la s fund fun d a c iones ion es ...... ......... ....... ....... ...... ...... ...... ...... ...... ...... ...... ...... ...... ..... Ejem je m p lo ................................. ................ ................................. ................................ ................................ .............................. ..............
44 44 47
A ne xo A Ane An e xo B B.1 B.2 B.3 B.4 B.5 B.6 B.7 B.8 A ne xo C A ne xo D
Noc ione ion e s d e d ibujo ib ujo té c nic o ........ ........... ....... ........ ........ ....... ....... ........ ........ ....... ....... ........ ........ ....... ....... .... Info rma c ión c o m p lem e nta nt a ria ria ....... ........... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ..... Hormig Horm igóó n p a ra e lem e nto nt o s sism ism o rre rre siste iste nte nt e s ................ ........................ ................. ........... Ac e ro p a ra e lem e nto nt o s sism ism o rre rre siste iste nte nt e s .............. .................... ............ ............ .............. ........ Re siste iste nc ia m á xima a la c o m p resión resión ........... ................. ............ .............. .................. .............. .... Re siste iste nc ia a l c o rte d e e lem e nto nt o s sism ism o rre rre siste iste nte nt e s e sp e c iales iale s... ... Mó d ulo d e e lasticida lastic ida d d e l ho rmigó rmig ó n ........ ............ ....... ....... ........ ........ ........ ........ ........ ....... ...... ... Co efic iente d e b a lasto lasto en func ión d el tipo d e terreno terreno .... ...... .... .... .... .... .. Re siste iste nc ia a l c o rte d e m uros uro s ................ ......................... ................. ................ ................ ................ ........ Punz un zo na m iento ien to d e losas y za p a ta s ............ .................. ............. ............. ............ ................. ........... Ta b las la s p a ra e l d ise ise ño d e losas .............. ..................... .............. .............. .............. ............... .............. ...... Instruc nstruc c ione ion e s b á sica ic a s d e uso uso p rog ram a ETABSve rsión rsión 8 ....... .......... ...... ...
55 61 61 61 61 62 62 62 62 63 65 68
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Ingenieros Civiles
C A P I TU L O 1 D I SE Ñ O D E E D I FI C I O S E N H O R M I G Ó N A R M A D O 1.1 I N T R O D U C C I Ó N En el desarrollo de un proyecto, el arquitecto define los espacios y sus terminaciones de modo d e sa sa tisfa tisfa c er los los req uerimient uerimientos os p a ra los c ua les el ed ific ific io fue c onc eb ido. ido . La e struc tura, tura, esqueleto resistente del edificio, debe desarrollarse dentro de los espacios disponibles sin interferir con el proyecto de arquitectura. En este sentido, el diseño estructural está subordinado al diseño de arquitectura. Sin embargo, la materialización de este esqueleto impone algunas exigencias al diseño arquitectónico en cuanto a los espesores y dimensiones de los elementos resistentes (losas, muros, vigas y columnas). En el caso de países con sismicida d a lta o aún mo d erad a, e sta s exige exige nc ias pued en ser muy seve seve ra s. Históricamente en Chile, país de alta sismicidad, los edificios han sido concebidos como estr estruc uc tura tura s de hormigó hormigó n armad o o d e a lba ñil ñilería ería . Esto se se d eb e p rinc ip almente a su su bue n c om po rtam iento frente frente a sismo s d e gran intensi ntensid a d, d ond e se han obser observad vad o da ños meno res, es, y a la disponibilidad de mano de obra de bajo nivel de capacitación. El uso del acero, que requiere de mano de obra calificada, se ha mantenido principalmente en el ámbito de los e d ific ific ios indus ind ustri triaa les. les. Los muros de albañilería resultan efectivos como estructura sismorresistente en edificios bajos, de hasta 5 pisos. Los muros de hormigón armado son efectivos hasta 20 o 25 pisos, según la longitud de los muros principales. Para alturas mayores, por si solos, no logran controlar las deformaciones de entrepiso. En este caso es necesario acoplar los muros con dinteles, o a g reg a r ma rc os ríg ido s. La estructura de un edificio se deberá diseñar de modo de satisfacer los siguientes requerimientos:
• Resistencia: -
Ca pa c id ad d e resi resistir tir c arga s Esta b ilida ilida d d e la estruct estruct ura ura
• Rigidez -
Ind eformab ilid ad frente frente a la s c a rga s Co nd icione s d e uso uso d el ed ific fic io
• Durabilidad -
Ma ter te riales inalterab les en el e l tiemp tiem p o Ma ntiene n sus sus p rop ieda ied a d es resis esisten tente tess
• Ductilidad -
Ca pa c ida d d e d isipa r energía energía Esta b ilida ilida d d el ed ific ific io frente frente a c a rg a s sísmic a s
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Ingenieros Civiles
1.2
OBJETIVO El ob jetivo d e esto estoss a p unte s es mo strar la la s d istinta istintass eta et a p a s y p roc ed imiento s a seg uir en el desarrollo del proyecto de cálculo de un edificio, basado en la experiencia profesional de los autores. Está orientado a edificios de hormigón armado de altura me dia y d e c a ra c terís terístic tic a s reg ula ula res. es. Deseamos enfatizar que cada proyecto presenta singularidades que le son propias y q ue en a lguna s oc a sione s p ued en req uerir uerir de a ná lisis esp esp ec ia les, les, má s p rofund os q ue los d eta llad os en e ste m a nua l. Por Por lo lo a nterior, nterior, el bue n c riteri iterio y c ono c imiento imiento s d el ing ingenier enieroo a c a rgo d el p royec to serán serán indisp indisp ensa ensa bles p a ra su c orrec orrec ta c om p rensi ensión y uso. uso.
1.3
N O RM A S D E D I SE Ñ O El diseño de los edificios en hormigón armado deberá satisfacer los requerimientos esta esta b lec ido s en las siguiente s norma s vigente vige nte s en Chile:
•
• • • •
Norma NCh433of1996 NCh433of1996 “Dis “ Diseñ eñoo sí sísm ico ic o d e e d ific ific ios” ios” En esta esta nor no rma se es e sta b lec en las a c c iones sísmic a s q ue d eb e sop sop ortar orta r una estruct estructur uraa , la la s deformaciones laterales admisibles, los métodos de análisis que se pueden usar y la c oo rd inac ión c on o tra tra s nor no rma s d e a ná lis lisis y diseño diseño . Norma NCh1537of1986 “Diseño estructural de edificios – Cargas permanentes y sobrecargas de uso”. Norma Norma NCh431of NCh431of 1977 1977 “ Co nstr nstruc uc c ión – Sob re c a rg a s d e nieve ” Norma Norma NCh432 NCh432of19 of1971 71 “ Cá lc ulo ulo d e la ac c ión d el viento viento sob re las co nstr nstruc uc c ione s” Có d igo A CI 318 318-9 -955 “B “ Build uild ing C od e Req Req uirem uirem ents ent s for Reinforce Reinforce d Co nc rete ” Mientras no se oficialice la nueva versión de la norma NCh430 “Diseño de edificios de hormigó n ar a rma d o” , deb en usa usa rse las d isp osi osic ione s d el cód c ód igo A.C.I. A.C.I. 318318-95 95 p a ra el d iseño iseño (no e l aná lis lisis) is) d e los elem ento s d e ho rmigó n a rma d o. En En p a rticular, ticu lar, los elem entos ent os estructurales que forman parte de marcos de hormigón armado destinados a resistir solicitaciones sísmicas deben dimensionarse y detallarse de acuerdo con las disp disp osi osic iones p ara zona zona s de alta sismicida d d el c ap ítulo tulo 21 de d ic ho c ód igo . Nota: En estos apuntes se han incorporado algunas de las disposiciones establecidas en las versiones p osteri osteriores ores al año 1995 1995 de l c ód igo AC I. Asimi Asimissmo se m enc ionan las rec om end a c iones p rop uestas para el apéndice “Adaptaciones al código ACI 318-05 para ser utilizado en Chile”, el cual se encuentra ac tualmente en estudio estudio..
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Ingenieros Civiles
1.4
D O C U M E N TO S D E U N P R O Y E C TO D E C A L C U L O El d esarr esarroll olloo d e un proyec to d e c á lc ulo ulo estr estruc uc tura tura l d e un ed ific fic io d eb e inc inc luir uir los siguientes do c ume ntos, ntos, que d eb erán ser ser entreg entreg a do s a l ma nda nte:
•
Plano s d e estr estruc uc tura: Los p la nos d e e struc truc tura tura d eb en c onte ner tod os los d eta lles nec esa esa rios p a ra la ejec uc ión de la obra gruesa del edificio, así como la calidad de los materiales a usar, la zona sísmica y el suelo de fundación de acuerdo a la clasificación establecida en la norma NCh433of96.
•
Bases ases de c á lc ulo: Las bases de cálculo corresponden al documento que incluye todos los antecedentes c onsiderad onsiderad os en el d iseño iseño estr estruc uc tural de l ed ific fic io, a sí c om o los p rincipa les resultad esultad os d el a ná lisis lisis sísm ic o . Esp ec ific ific a c iones ione s Téc nica nic a s d e Ob ra Gruesa Gruesa (E.T (E.T.O.G.): La s E.T.O.G. .O.G. corr c orres espp ond en a l d oc ume nto q ue incluye tod a s la s rec om end a c ione s nec esa esa rias p a ra la c orrec orrec ta e jec uc ión d e la la o b ra g ruesa uesa . Memo ria d e c álculo: álculo: En c a so q ue sea sea req ueri uerid o p or el ma nda nte, se se d eb erá ge nerar nerar la la me mo ria de c álc ulo ulo d el ed ific ific io. En En ella ella se d eb erá d eta et a lla lla r el aná a ná lis lisis sísm ico rea liz liza d o y e l d imens imen siona miento mien to d e los d istintos istintos elem entos ent os q ue c onfo rma n la la e structur truct uraa .
•
•
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Ingenieros Civiles
C A P I TU L O 2 : B A S E S D E C A L C U L O La s ba ses de c á lc ulo ulo d eb en c onte ner los los siguientes ant ec ed ente s: 1. Id entifi entific ac ión d el ed ific fic io 2. Estruct ura ura c ión : Breve d esc esc ripc ión d el sis sistem tem a estr estruc uc tural utili utilizza d o e n el ed ificio. ificio. Debe c ontemp lar: Ø Siste istema ma d e c a rg a s ver ve rtica les. les. Ø Sistem istem a d e c a rg a s late ra les. les. Ø Siste istema ma d e p iso. iso. Ø Alc a nc e d el diseño diseño sísmic o (ob jeti jetivo, vo , d efo rma c iones, iones, fis fisura ura c ión) 3. Ma te riales : Id Id entif ent ifica ica c ión y ca lid lid a d d e los ma ter te riales utiliz utilizaa d os. os. Ø Hormigón Ø Acero Ø Albañilería Ø Madera 4. Tensiones ensiones a d misibles misibles:: Refe Referrenc ia d el mé tod o d e d iseño utiliz utilizaa d o, nor no rma c onsi onsid erad a y resi esistenc ia s b á sic a s d e c á lc ulo ulo p a ra c ad a m ate rial. Ø Métod o d e d iseño Ø Norma Ø Hormigó n : Resis esiste tenc nc ia esp esp ec ific ific a d a Resis esiste te nc ia a la c om p resión esión Resis esiste te nc ia a l co rte Ø Alba ñilerí ñileríaa : Resis esiste tenc nc ia b á sica a la c om p resión esión Resistencia básica al corte Ø Ac ero : Resis esiste tenc nc ia a la trac c ión p or flexi flexión Resis esiste te nc ia a l co rte Ø Ma de ra : Resi esistenc ia b á sic a a la c om p resi esión p aralela Resis esistenc tenc ia bá sic a a la tra tra c c ión p aralela Resis esiste tenc nc ia a la flexión flexión Mód ulo ulo d e elasti elasticc ida d m ed io Ra zón d e resis esiste tenc nc ias 5. Solic olic itac iones : Des Descc ripc ión d e la s c a rg a s norma les y eventu ev entuaa les c onside onsiderra d a s en e l d iseño iseño , Referenc ia a la no rma q ue las esta esta b lec e. Ø Pe so Prop io Ø Sobrecarga : estática y sísmica Ø Sismo ism o Ø Viento Ø Nieve
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Ingenieros Civiles
5. Comb inac iones de c arga : Defini Definicc ión d e las c omb inac iones de c arga p ara el diseño diseño sismorresistente .
6. Antec Ant ec ed ente en tess d el a ná lis lisis sísm ico ( Seg Seg ún NCh433 NC h433of of 96 ):):
Ø
Zona sí sísmica : Tip o d e suelo: Pe río d o s :
Ø
Co rte ba sa l :
Ø Ø
De a c uerdo a la la ubica c ión d el ed ific fic io. De ac uerd uerd o al informe nforme de mec ánic a de su suelos. elos. Se e ntreg a n los tres p rimeros ime ros p erío erío d o s d e la estruc estruc tura, tura , c orres orrespp o nd ientes ent es a la traslac traslac ión en las d os direc direc c iones princ princ ipa les y a la rotación. Se entreg entreg a c om o porce nta je del p eso eso sí sísmico d el ed ific fic io, en las las do s direcciones principales, tanto a nivel basal (último subterráneo) c om o en e n el prime prime r p iso. iso.
7. Dis Diseño d e fund a c iones : Definic Definic ión d e las p resiones esiones a d misibles misibles d el suelo, suelo, seg seg ún informe informe d e me c á nic nic a d e suelos suelos.. Ø Ø
Pnormal ( kg/cm ²) : Pa ra c a rga s está está tica s Peventual ( kg/cm ²) : Para c arga s d inám ic a s
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C A P I TU L O 3 E S TR U C T U R A C I O N Y P R E C A L C U L O S I S M I C O
3.1
C O N C E P TO Extra xtra er d e los p lano s d e a rq uitec tura los elem ento en toss nec ne c esa esa rios y suficiente ufic iente s p a ra de fini finirr una estr estruc uc tura tura c ap a z d e d a rle esta esta bili bilida d a l ed ific fic io frente frente a las solic olic itac iones esta esta rá som som etido d ura ura nte su su vid vid a útil, útil, y de a c uerdo a la normativa vige nte.
3.2 3. 2
C O N D I C I O N ES D E D I SE Ñ O D E U N A E STR U C TU R A Ø
Ø Ø
3.3
Resis esiste tenc nc ia: Los Los elem entos ent os estr estruc uc turales d eb en tener ten er una resis esistenc tenc ia a d ec uad ua d a frent frentee a las solic olic itac ione s d e d iseño . Rigidez: Deforma Deforma c ione s d e la e struc truc tura tura de ntro ntro d el ra ra ngo p ermiti ermitidd o. Dura Dura b ilid ad : Durac Durac ión d e la estr estruc uc tura tura , a través de la selec c ión d e m a teria teria les q ue ga rantice n sus sus prop ied a de s me c ánic as en el tiemp tiemp o.
S I S TE M A S E S TR U C T U R A L ES
• Siste iste m a d e p iso: iso: Ø Ø Ø Ø
Losa osa d e H.A. H.A. c on v iga s d e H.A. H.A. Losa osa p osten ostenssa d a c on o sin sin viga s d e H.A. H.A. Losa osa p ostens ostensaa d a má s vigas viga s p ostens ostensaa d a s Losa osa c olabo rante má s viga viga d e ac ero. ero.
istema ma d e c a rg a s ver ve rtica tic a les: les: • Siste Ø Ø Ø Ø Ø
Muros d e H.A. Ma rc os d e H.A. H.A. Columnas de ac ero ero Columnas compuestas Retic ul d d
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3.4 3. 4
ELEM LEM ENT NTO O S ESTRUC UCT TUR URA A LES LES TIPICO IPIC O S EN ED EDI FICIO IC IOS S DE H.A ., DE M EDIANA IA NA ALT A LTUR URA A Ø Ø Ø Ø Ø
3.5
3.6
Losas Vigas Pilares Muros Fundaciones
FUNC ION IO NES DE LOS LO S ELE ELEM ENTO S ESTRU RUC C TUR URA A LES LES Ø
Losa osa s:
Ø
Viga Vig a s:
Ø
Pila ila res: res:
Ø
Muros: Muros:
Ø
Funda und a c iones: iones:
Sop ortar c a rga s d e oc upa c ión está está tic tic a s. Ac tua r c om o d ia fra fra gm a s rígid os en su su plano . Dar Da r sop orte a las losa losa s. Fo rm a r ma m a rc os ríg ido s c o n los pilares. pilares. Trab ajar c om o eleme ntos d e trans transfer ferenc enc ia. Dar Da r a p oyo oy o a viga s y losa losa s. Fo rm a r m a rc os ríg ríg ido s c on las viga s. Transm ransm itir itir las c a rg a s ver ve rtic a les a las fund a c ione s. Dar rig id ez y esta esta b ilida ilida d a la estr estruc uc tura tura frente frente a solic itac ione s e stá tic a s y sí sísm ic a s. Dar Da r sop sop orte a las losa losa s. Tra sm itir itir la la s c a rg a s ver ve rtic a les a las fund a c iones ione s. Eleme nto s d e transferenc transferenc ia d e fuerza fuerza s d esd esd e la estruct estructur uraa al suelo d e apoyo.
PRE PR EDIMENS IM ENSIO ION NA M IENTO IENTO DE LOS LO S ELEM LEM ENTO S ESTRUC RUCT TURA URALE LES S 3.6.1
LOSAS Pa ra la losa losa m á s c rítica , generalme gen eralme nte la d e m a yores d imensiones imensiones,, se se d eb e verificar: •
Esbeltez: e ≥ luz efec tiva / λ + rec rec ubr ub rimiento imiento
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Ingenieros Civiles
• No tener arma d ura ura a c om presi presión. 3.6.2
VIGAS Se rec rec om iend a q ue la a ltura tura d e la viga , h , c ump la c on lo si siguiente:
• viga viga ap oyada-apoyad oyada-apoyad a • viga viga empotrad empotrad a -emp otrad otrad a viga en vol ad izo • viga en q ue: 3.6.3
h ≥ L/10 à h ≥ L/15 à h ≥ L/ 5 à
h = altura altura de la viga viga . L = Luz Luz lib lib re d e la viga entr ent re a p oyo s.
PILARES En e llos c ontrola la c om presi presión, d eb iénd ose ose c ump lir lir:
σ = N/ N/ A ≤ σad m en q ue :
3.6.4
N = fuerz fuerza d e c om p resi esión en el p ila r, A = área d e la sec sec c ión tra tra nsvers nsversaa l d el p ila ila r, σadm = esfuer esfuerzzo d e c om presi presión a dm isib le, que d ep end e d el hormigó hormigó n (se (se p ued e esti estima ma r c om o 100 100 kg/ c m2 para H30).
MUROS En ellos controla el corte, producto de las fuerzas horizontales (sismo), debiéndose c umplir umplir pa ra c ad a m uro: uro:
donde:
•
τm = Q m / A m ≤ τa dm → espesor requerido τm = esfuer esfuerzzo d e c orte en el muro, muro,
Q m = fuerz fuerza d e c orte en el muro, Am = área d e la sec sec c ión tran sversa versa l d el muro, τa d m = esfuer esfuerzzo d e c orte orte a dm isible, que d ep ende de l tipo tipo de ac ero ero y de ho rmigón. El esfuerz esfuerzoo d e c orte me d io de los muros se ob tiene en forma a p roxima oxima d a , pa ra c ad a una d e las direc direc c iones en las que el sisismo ac túa, c omo :
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Si se asume
τmedio ≈ 6.0 6.0 kg/ c m 2
q = 1.0 1.0 t/ m2 c =6% =6% à A muros = A tota l edificio edificio / 1000 con A total edificio = n * A
área nec esari esariaa en c ad a dire dire c c ión
Notas: uros solo c uenta n los muros “ largos” largos” y de d e long itude s p a rec id a s. • En A m uros osible se se d eb e d isp isp one r muros en la p eriferi eriferiaa p a ra tener ten er una b uena rigide z tor to rsional. iona l. • En lo p osible • En lo p o sible se se d eb e b usc usc a r d isp isp o siciones ic iones simé tric tric a s.
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C A P I T U L O 4 : A N A LI S I S S I S M I C O Hoy e n d ía e xis xisten e fic fic ientes herra herra mienta mient a s c om p uta c iona les q ue p ermiten rea liz liza r el aná lis lisis sísmic o d e una estruct estructura. ura. A co ntinua c ión ión se se d efinen a lguna s d e las c a ra c terís terística s b á sica s d e un e d ific fic io, la la s q ue se req uiere uiere en la utili utiliza c ión d e los p rog ra ma s d e a ná lisis isis má s c om unes. unes. 4.1
C U B I C A C I O N D E P E S O S I S M I C O ( m éto ét o d o simp simp lific lificaa d o )
4.1. 4. 1.11 PE PES SO SESPE PEC C IFIC IFICO O SM A SUS USUA UALE LES S • Hormigón armad o 2.5 2.5 t/ m ³ ñilería 1.8 1.8 t/ m ³ • Alb a ñilería • Estu c o 2.0 2.0 t/ m ³ • Relleno de piso piso ( so b relosa relosa ) 2.0 2.0 t/ m ³ 2.0 2.0 t/ m³ • Enluc ido d e c ielo • Tierra jard ja rdine inera ra 2.0 2.0 t/ m ³ lso 50 kg/ m² • Cielo fa lso nita 50 a 100 100 kg/ m² ( esp esp eso eso re s d e 5 a 12c 12c m ) • Tab iques d e volc a nita • Tec humb hum b re 30 a 100 100 kg/ m² ( piza piza rreño a teja ) 4.1.2 SO BREC A RG A S ESTA TICA IC A S DE US USO ( NC N C h 1537 153 7 of o f 86 86 ) • Ed ifi ific ios ha b itac iona les 200 200 kg/ m² p iso iso t ipo, ipo , 100 100 kg/ m² último último p iso ( te c ho ) • Ed ific ific ios d e ofic inas 250 250 kg/ m² p iso iso t ipo, ipo , 100 100 kg/ m² último último piso piso ( tec ho ) 500 500 kg/ m² • Esta c iona miento s • Areas d e uso uso p úbli úb licc o 400 400 kg/ m²
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4.1.5 CUBICACION DE PESO SISMICO Pa ra c a d a p iso c ub ica r tod to d os los ele me ntos nto s a ntes nte s d esc esc ritos, itos, suma r la sob sob rec a rg a sísmic a , y dividir p or el área en p lanta d e d icho p iso. iso. Los Los va lores lores usua usua les q ue se se o b tienen va ría n entre e ntre 1.05 1.05 a 1.20 1.20 t/ m ². 4.1. 4. 1.66 PR PRO O PIEDA PIEDADES DES EN PLA PLA NT NTA A Para c ad a piso piso d el ed ific fic io, d eterminar: eterminar: • Area Area en p lanta , A. A. • Coo rde nad as de l centro centro d e g raved ad respe espe c to d el sisistema c oordenad o q ue se se usa usa rá pa ra el mod elo a a naliz naliza r, Xc g e Yc g. • Mom entos de inerc nerc ia de la planta respe espe c to d e c ad a uno d e los ejes ejes c oordenad os, os, Ixx Ixx e Iyy. Iyy . ísm ic o * A / g (supo • Ma sa traslac traslac iona l: MT = q sísm (supo ne peso peso unifor uniforme me me nte distr distriibuido )
• Ma sa rota c iona l : 4.2
MR = MT / A * ( Ixx + Iyy )
D I S P O S I C I O N E S D E L A N O R M A NC NCH H 433 o f 96 Zonific onific ac ión sísmica
Ubica c ión ge og ráfica
sector cordillerano franja franja c entral de C hil hile, ap roximada roximada mente entre la co rdillera lera d e la c osta osta y la c ordiller ordilleraa d e los And es zona co stera Zona on a 3 Nota: g ac eleraci eleración ón de gravedad = 9.8 9.8 m/ s2
Zona on a 1 Zona on a 2
Ao 0.20 g 0.30 g 0.40 g
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Ingenieros Civiles Méto do de diseño diseño
Comb inaciones de ca rga
Tensiones ensiones a dm isibles isibles
Ca rga s p erma nen tes + sob rec arg as d e uso uso ± sismo ismo 1.4 1.4 (ca rgas perma nente s + sob sob reca rgas de uso uso ± sis sismo mo ) 0.9 c a rga s p erma nen te s ± 1.4 1.4 sis sismo mo
Factores de carga y resistencia
Defo rmac iones sísmic as En el ce ntro de ma sas
En c ualquier punto
Parám etro de diseño diseño Espectro de aceleraciones
Req uisito uisito
Inte rpreta c ión
El desplazamiento relativo máximo entre dos pisos co nsec nsec utivos utivos,, medido en el ce ntro ntro d e ma sas en c ad a ? CM = 2 ‰ h una de las direcc iones de aná lisis, is, no d eb e ser ser ma yor que la a ltura ltura d e entrep iso iso , h, multiplic multiplic ad a p or 0.00 0.002. 2. El desplazamiento relativo máximo entre dos pisos co nsec nsec utivos utivos,, medido en c ualquier punto de la planta en cada una d e las direc direc ciones de aná lisi isis, no de be ? pt = 1 ‰ h + ? CM exce d er en má s d e 0.001 0.001 h al de splazam iento relativo co rres rrespo po ndiente med ido en el centro de masas masas..
Fórmula Sa
=
Co me nta rios rios
I Ao α R * P
Fac tor de amplificación
Tn 1 + 4.5 To α= Tn 1+ To R* = 1 +
Fac tor de reduc c ión
Tn : períod períod o d e vibrac ión del mod o n
3
T *
T * Ro
0.10To +
Ro : p a ráme tro relativo a l sis sistem tem a estruct estruct ural = 11 11 edificios d e H.A. H.A. T* : pe ríod o de l mod o c on m ayo r masa masa traslaciona traslaciona l equivalente en la d irec c ión d e a ná lis lisis. is.
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Ingenieros Civiles
: O I C I F I D E ) A C I T S A L E A T S E U P S E R ( O C
* R o / m 1 i n í m o Q s = e % P l % a s a b Q Q
) g / o ) A I ( ( . A T I C C E N F E A T A N R O C I O I M O P P C S I A I M R S T I . E A O F E L E N L E O C O U Z S C A
* R 3 / 3 1 4 h O C N o S n s e P A ú g % e C s = * * R R / e Q
* R
o s e P 0 . % 1 =
9
8
7
6
5
4
3
= = * * x y
x y o o m s m s : a c i t s á l e a t s e u p
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Ingenieros Civiles
C A P I TU L O 5 A N A L I SI S Y D I SE Ñ O D E L O S A S 5.1 DES DESC RIPCION: La s losa losa s c orres orrespp ond on d en a elem ento en toss p lano s, es d ec ir c on d os dimensiones mayores y un espesor pequeño; apoyados en todos o a lguno s d e sus sus b orde s. Res Resiisten p rincipa lme nte c a rg a s vertic vertic a les norma les a su p la no, y está está n som som etida s p rinc ip a lme nte a flexi flexión ón fuera d el plano . En cierta cierta s oc a sione s a c túan c om o eleme nto d e tra tra nsfer nsferenc enc ia d e fuerz fuerzas paralelas a su plano, viéndose así sometidas a esfuerzos de corte importantes. 5.2 C O M PORTA M IENT IENTO O EL ELA STICO IC O : q lx
Fuerzas ho riz rizon ta les
ly 5.3 5. 3 TIPOS IPO S DE LOS LO SA S:
Igu a land o las deforma deforma c ione s en a mb a s d irec c ione s, se se ob tiene la siguiente ec uac ión d iferenc ferenc ia l que rige el co mp ortam ortam iento elásti elásticc o d e la losa losa :
∂ 4w ∂4 w ∂ 4w q + 2 2 2 + 4 = * cte ∂ x 4 ∂ x ∂ y ∂ y EI
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Ingenieros Civiles
∆=
Px × lx
48 × E × I
Como
• Franjas:
3
ly
=
Py × ly
3
48 × E × I
> lx ⇒
ly lx
>1
3
ly ⇒ Px = Py × lx
Entonces Px
> Py
ε ≥2 La losa osa tra tra b a ja p rinc ipa lme nte e n una d irec c ión, la la m ás c orta.
Ø
Losa osa s d e forma irr irreg ula ula r: No siem pre la ge om etría etría en planta de un ed ific fic io p ermite ermite definir losas perfectamente rectangulares. La existencia de losa losa s d e e ste tipo c orres orrespp ond e a una si situac ión ó p tima tima , puesto puesto que su c omp ortam ortam iento y d iseño es c onoc ido . En En c am bio las losas de forma irregular como triangulares, en L, o con perforaciones, tienen un comportamiento que debe “ ima ginarse” ginarse” c on m uc ho c riterio, terio, o b ien deb en ser ser ana lizad as con herramientas especiales como programas que utilizan
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La rig rig id ez a l giro giro d el muro muro e stá d a d a p or: KØ m = ( 3*E* Im ) / (h m /2) en que,
Im
= b m *e m ³ /12 / 12
(Inercia (Inercia a flexi flexión) ón)
y d ond e,
E = mó d ulo ulo de elasti elasticc ida d d el hormigón. hormigón.
Por otra otra p a rte, la la rigide z al g iro d e la losa losa está está d a d a p or: KØ L = ( 3*E* IL ) / L en que,
IL =
b L*e L³ / 12
(Inercia (Inercia a flexi flexión) ón)
Nótese que si la losa en su apoyo izquierdo fuese continua o tuviese p or ap a p oyo un muro, m uro, su su rig rig ide z a l giro giro serí seríaa : Como
KØ L = ( 4*E* IL ) / L bL= bm = 1 (los (losaa y muro muro po r unida unida d de anc ho)
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Comparando las rigideces de la viga y de la losa, y considerando q ue e n la la p rá c tica es p osi osib le d em ostr ostraa r q ue la inerc inerc ia torsi torsiona l d e la sec c ión fisur fisuraa da es muc ho m eno r q ue la inerc inerc ia teó ric a , se se d ed uc e que Kt v < KØ L lo cual confirma que la viga solo apoya a la losa, sin empotrarla. Ø
Borde lib re:
Se p rod uc e c ua ndo un b orde d e la losa osa no se ap oya sob re elemento elemento alguno. En la la prác tic tic a esto esto o c urr urre p or ejemp ejemp lo e n b alco nes, nes, o en to rno a las p erfora erfora c iones d e a sc ensores ensores,, o en los desc desc a nsos nsos d e esc esc a leras. eras.
Ø
Pila ila res c on c a p iteles: iteles: En oc a siones los bo rd es d e losa losa no tienen tiene n un a p oyo d efinido , y se generan campos de losa apoyados sobre pilares. En torno a los p ila ila res se d isp isp one n ca p iteles, iteles, q ue c orres orrespp ond en a un eng rosa osa miento mient o de la losa, osa, y que p ermite ermite evitar prob prob lem as d e p unzona unzona miento . En la práctica esto suele darse en campos de losas de grandes dimensiones, como zonas de estacionamientos, o bien cuando se quieren lograr plantas libres de vigas.
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Ingenieros Civiles
5.5 DETERMINACION DEL ESPESOR REQUERIDO En general las distintas normas de diseño establecen que el espesor a usar en una losa d eb e ser ser tal ta l que sa tisfa tisfagg a las sig uientes c ond icione s: I. Esb e ltez: Se d efine una esb esb elte z d e la los lo sa , λ, tal que la s d efor efo rma c iones q ue se se producen bajo las condiciones normales de uso no sobrepasen el limite esta esta blec ido . Así Así d eb e c ump lir lirse: • Métod o ap roxi oxima do : e m in = li / λ + recubrimiento en q ue, li = ϕ *lx *lx long itud efec tiva(d ista nc ia entre p untos d e infl inflexión) exión) λ = 35 p a ra losa osa d e p iso tipo 40 pa ra losa osa de tec ho recubrimiento = 2.0 cm (considerado como la distancia entre la cara inferior de la losa y el centro de gravedad de la armad ura ura de refuerz efuerzo )
donde,
ϕ : fac tor d e esb esb eltez (ver ta b las p a ra d iseño iseño d e losa losa s)
• Seg ún ACI 318-9 318-955: El esp esp esor esor a usa usa r d ep end e d el tip tip o d e a p oyo d e la losa losa y d e su rig rig ide z rela tiva a flexió flexió n (ve r ACI ca c a p .9.5 .9.5.3. .3.2). 2).E En fo rm a
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Ingenieros Civiles Ø
Losa osa s c ruza uza d a s:
Ø
Losa osa s irr irreg ulares: ulares:
La ec uac ua c ión d el c om p ortam iento ent o elástico elástico ha sido resuelta esuelta numéricamente por varios investigadores, obteniéndose ta b las a travé s d e las c ua les se d ete rmina n los esfuerz esfuerzos os en las losa losa s en func ión d e sus sus d imensiones imensiones y tipo d e a p oyo . Las tablas más conocidas corresponden a las desarrolladas p or Ma rc us y Czerny Czerny (Ver Ane xo C). En este este c a so, c om o ya se se me nc ionó, ionó , se p ued ue d e mo d ela r la la losa mediante programas computacionales tales como el SAFE o el SAP, los cuales utilizan elementos finitos, y entregan una informa informa c ión m uy c om pleta de de forma forma c iones y esfuer esfuerzzos en la losa losa . Si no se dispone de esta herramienta, lo más recomendable es estudiar la losa con varios modelos simplificados, tales c omo una losa losa de forma forma rec tangular ap roxi oxima d a o una viga viga , de modo de “acotar el problema”. Los esfuerzos de diseño se p od rá n esta esta blec er pa ra las c ond ic iones má s d esfavo esfavo ra bles de cada modelo, o como algún promedio de las situaciones analizadas. En cualquier caso se recomienda usar valores c onser onservad vad ores y m uc ho c riterio. iterio.
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Ingenieros Civiles
diseña diseña r una viga viga em be bida en la losa losa , lo lo que se m a teria teria liza reforzand eforzand o c on b a rras long itud inale s y es e strib trib os (si (si se se req req uieren), el sec sec to r en c ues ue stión. • Una solución si simila mila r deb e a do pta rse e n el c a so d e un bo rd e libre. libre. 5.7 DIA DIAG G RA M A DE D E FLUJO LUJO PARA EL EL DIS DISE EÑO DE LO SA S REC TA NG ULA ULA RES C O N CA C A RG A UNIFO UNIFO RM E Determ Determ inar el esp esp esor esor d e losa losa a utiliz utilizaa r co nsiderand nsiderand o para ello la losa más crítica, i.e. la de mayores dimensiones y/o con apoyos más desfavorables.
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Ingenieros Civiles
5.8 DIS DISPOS POSIC ICIO ION N DE A RM A DUR DURA A S Y NOM NO M ENC LA TUR URA A Armad ura supe supe rior or o suples
Ba rra rra sup erior → F’= φ8@20 (s) (armad ura ura p rincipa incipa l)
Ba rra rra inferior → F’= φ8@20 (i ) (armad ura ura secund aria) aria)
p r r
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Ingenieros Civiles
5.9 ARMADURA MINIMA La c uantía uantía m ínima nima de armad ura ura de tram tram o a proveer en la la losa osa de pe nde d e la norma d e d iseño iseño utili utilizza d a . Seg Seg ún la no rma ACI 318-9 18-95: 5: Am in =1.8 ä *b*e *b *e .... ...... .... p a ra losa losa s d e ta ma ño reg ular. Am in = 2.0 ä*b*e ....... en franjas de grandes dimensiones, para evitar problemas de fisuramiento producto de la retrac trac c ión d el hormigón. hormigón.
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Ingenieros Civiles
5.13 DIAFRAGMA DE TRANSFERENCIA Ø
Concepto: Co mo ya sa b em os, os, la la estr estruuc tura tura de un ed ific fic io e stá c onformad a po r do s sistem as e struc turales tura les b á sicos ic os : vertic a les • Sistem a d e c a rga s vertic • Sistema de cargas laterales Los elementos resistentes de la estructura pueden formar parte de uno o de ambos sistemas, como en el caso de las losas. Estas tienen como función primaria
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Ingenieros Civiles
• Elementos de borde: Son los elementos perimetrales del diafragma, que resisten
esfuerzos de tracción y compresión de manera equivalente a las alas de una viga en p osición osición ho rizont izontaa l. Siemp re d eb en e xistir istir y pued p ued en ser ser de sd e simp simples les a rma d ura ura s d e refuerzo refuerzo p erime erime tral co ntinuas, ntinuas, hasta hasta viga s y element elem entos os esp esp ec iales. iales. • Elementos recolectores, puntales y tirantes: son desde simples armaduras de refuerzo, hasta vigas o elementos especiales embebidos en el diafragma que tienen por misión recolectar las fuerzas de cizalle en la losa y transferirlas como fuerzas a xia xia les a los elem entos ent os vertica les q ue fo rma n el si sistem a d e c a rg a s late ra les. les. No son son
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El factor de reducción de la respuesta φ
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Ingenieros Civiles
B.4 RE RES SIST ISTENC ENCIA IA A L CO C O RTE EN EN ELEM LEM ENT NTO O S SÍSM ÍSM O RR RRE ESIST ISTENTES ESPE PEC C IALE IA LES S (AC (A C I 318 318 -95) 95 ) 1. Arma d ura tr t ra nsve nsverrsa l en viga s y c o lumna s sísmic a s (c .21. .21.3. 3.4. 4.2): 2): En las zona s identifi iden tificc a d a s p or “ lo” en c olumna s y “ s1” en vi v iga s (pá g. 26 26 y 28) 28) la sec sec c ión debe estar dimensionada para resistir el corte asumiendo Vc=0 (resistencia al corte del hormigó hormigó n) c uand o se prod uzc uzc an las sisiguientes c ond ic iones sisimultánea me nte: • La fuer fue rza d e c o rte sísm ico / c orte está está tico , en e sa s zona s
•
La fuerza axial de compresión mayorada, incluído el sismo, es menor que Ag.fc’/20 (Ag=á rea d e la sec c ión tra tra nsvers nsversaa l) 2. La resistencia nominal al corte de segmentos horizontales de muro y vigas de ac oplamient oplamientoo es [ 5 Ac p √ fc ’ / 6 ( = 1/ 6 del hor hormi migón gón + 4/ 6 del ac ero) ero) , d on d e Ac p rep resent esentaa el área d e la sec c ión tra tra nsve nsverrsa l del de l seg seg me nto c onside onsiderra d o. (c.21. (c.21.6. 6.4. 4.4) 4) Luego 1. + 2. à en d inteles
nom .máx.= = 4√ fc’ / 6 τnom.máx.
3. La resi resistenc ia nom ina l a l c orte de to d os los ma c hone s q ue c om p a rten una fue rza late ra l común (segmentos de un muro con perforaciones), no debe suponerse mayor de 2 Ac v √ fc’/ 3, dond e Acv es la sec sec c ión transvers transversaa l; y la resis resiste tenc nc ia no minal mina l al c orte d e c ua lquiera lquiera de los machones individuales no deb suponerse mayor de 5 A c p √ fc’/6, donde Ac p rep resent esent a el área d e la sec sec c ión transver transverssal d el ma c hón c onsi onsid erad erad o. B.5 MODULO DE ELASTICIDAD DEL HORMIGÓN
• •
Mó d ulo d e elasticid elasticidaa d está está tico (A.C.I. (A.C.I. 318 318-99 -99 cap c ap .8.5 .8.5.1 .1)) Ec = 4 700 700 vfc ’ Mp a ( x 10 à k g / c m2 , x 100 à t / m2) Mó d ulo de elasticida elasticida d sí sísmic o Ec = 19 000 vR28
(kg/cm2)
B.6 C O EFICIE IC IENT NTE E DE BA BA LAST LASTO EN FUNC UNCIO ION N DEL TIPO DE TE TERRENO (Hah (Ha h n , p g .315) .315)
• • • •
Suelo d e a rc illa a renosa enosa húmed a Suelo d e a rc illa a renosa enosa sec a Suelo d e grava a reno sa fina fina
: 2 a 3 kg/ c m3 : 6 a 8 kg/ c m3 : 8 a 10 kg/ c m3
Suelo d e g ra va a reno sa g ruesa uesa
: 15 a 20 kg/ c m3
B.7 RESISTENCIA AL CORTE DE MUROS De a c uerdo a lo e sta b lec id o e n 6.1 6.144 la resi resistenc ia má xima a d misi misib le a l c orte esta esta b lec id a e n el A.C.I. A.C.I. 318 318-99 -99 está está d a d a p or:
√
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Ingenieros Civiles
Por otra otra p a rte seg seg ún lo esta esta b lec id o 6.2, 6.2, pa ra el mét od o d e los fac tores d e c arga y rres esiistenc ia se d eb e c ump lir que :
? Resis esiste tenc nc ia d e d iseñ iseñoo ≥ Resis esiste te nc ia req uer ue rida φ Vn ≥ U Donde 0.6 p a ra c orte en zona on a s d e a lto riesg iesg o sísm ico φ = 0.6 U ˜ 1.4 1.4 Vs
pa ra c om binac ión d e c a rga s está está tic tic a s y sísmica s
En q ue Vs : Resis esiste tenc nc ia p a ra c a rg a s d e servicio Por lo ta nto en el c a so má s d esfa esfavorab vorab le se tiene: Vs máximo = φ Vn / 1.4 1.4 En la siguiente siguiente ta b la se se resum resumee e l valor de Vs máximo pa ra d istintos tintos tipo tipo s de hormigón, hormigón, de ac uerdo uerdo a los c riterios d e V.Berte V.Berte ro y d e l A.C.I. A.C.I.
Hormigón
Berte ro Vs máximo A.C.I. Vs máximo V. Berte
(Kg/cm 2)
(Kg/cm 2)
H 25 H 30
13.2 14.4
9.9 10.8
H 35
15.6
11.7
H 40 H45
16.7 17.7
12.5 13.3
H 50
18.6
14.0
Nota: Se ha c onsiderad onsiderad o fc ’ = 0.85 0.85 R28
B.8 PU PUNZ NZO O NA NAM M IENT IENTO O DE LOSA LOSA S Y ZA PATA PATA S (A.C (A .C.I. .I. 318-95 318 -95 c a p . 11.12) Pa ra losa osa s y za za p a ta s no p rete nsa nsa d a s Vc d eb e ser el meno r de:
• Vc = (1 + 2/ βc )* √f c ’ *b o *d/ *d / 6
(ec . 1111-35) 35)
βc = razón azón del lad o lar largo go a l lad o c orto orto de la columna, la c arga arga c onc entrad entrad a o el área
de reac reac ción. d = 0.8*h 0.8*h h = altura altura tota l de l elemento b o = pe rimetro d e la sec sec c ión c rítica p a ra losa losa s y za za p a ta s (mm 2) *d / 12 • Vc = (αs*d/b o + 2) * √f c ’ * b o *d/
αs
= 40 p a ra c olumna s interiores nteriores 30 para c olumna olumna s de bo rde 20 p a ra c olumna s esq esq uina
(ec . 1111-36) 36)
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Ingenieros Civiles
B.9 RESISTENC NCIA IA A TRAC C I Ó N DE DELL HORMIGÓ N (A.C (A .C.I. .I. 318-95 318 -95 c a p . 10.2.5) De acuerdo a lo señalado en el comentario C10.2.5, la resistencia a tracción del hormigón sometido a flexión es una propiedad más variable que la resistencia a la compresión y es a proxi proxima d am ente d el 10 10 al 15 15 % d e e sta. Por otra otra pa rte d e a c uerdo a lo e sta b lec id o e n el ca pítul pítuloo 22.5.2, ec uac ión 22-6 22-6, se se de duc e que para elementos de hormigón simple (sin armar) sometidos a flexión simple (sin fuerza axial) la resi esistenc ia en la c a ra trac trac c ionad a de l elemento elemento de be satisfac atisfac er: s tra tra c c ión nominal nominal = (5*Ø*vf’c ) / 12
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Ingenieros Civiles ESFUERZOS DE DISEÑO RECOMENDADOS PARA LOSAS CON ε >2.0 (franjas) (Seg (Seg ún Ren Ren é La La g os y Asoc Asoc .) Los valores indicados a continuación no consideran la alternancia de cargas. Mex
Mex
lx
Mey Mx
Mex = Mey =
Mx =
q ⋅ lx
Mx
2
Mex =
12 q ⋅ lx
2
Mey =
17. 5 q ⋅ lx
lx
Mey
2
Mx =
17(19)
q ⋅ lx
Mey =
q ⋅ lx
2
8
2
Mx =
11.25
q ⋅ lx
Mx
2
8 q ⋅ lx
lx
Mey
q ⋅ lx
2
8
2
10(12)
EQ UIL UILIBR IBRIO DE D E M O M ENTO NTO S NE NEG G A TIVOS IVO S (seg ún Re né La g o s y A so c .) M1
Dif=(M Dif=( M 1-M 2)/ M1 (%) (%)
M2
Si: • • • • •
f 1.08
à M -=(M1+M2)/2x 0.9 , f=1.0 Dif<25% 251.0 >1.0 à M -=0.7x max(M1,M2) dif>100%
Donde f: facto r de am plifi plificc ac ión de l mom ento +
1.05 100
70
Dif
ARMADUR ARMA DURA A M INIM INIM A EN LOSAS LOSAS FL FLO TAN ANT TES(se S(se g ún Re né La g o s y A so c .): Am in =5.0 =5.0 ä *b*e co mo armad armad ura ura total,
con b: unida unida d de anc ho y e: espes espesor or
Ejemplos:
• • •
Losa e=10 cm Losa e=12 cm Losa e=15 cm
DM φ 8@20 à DM φ 8@16 à DM φ 10@20 à
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Ingenieros Civiles dond e no ha y dilatac dilatac ión (permanente o temp oral) oral)..
A N E X O D : INST INSTRUCC UCCIO IONES NES BA BAS SICA IC A S DE US USO O PR PRO G RA M A ETA BS v. v. 8 Ac tua liz liza d o p or Enz Enzoo Fighe Fighe tti (Ene (Ene ro 2004) 2004) La venta na p rinc ipa l de Eta bs v.8 v.8 co ntiene las barra barra s de herram herram ientas Ma in, Dis Dispp lay, Point Point a nd joint joint a ssigns, She ll a nd a rea a ssigns, Fram e a nd line line a ssigns ign s, Define , Design Design,, Draw , Sele Sele c t y Sna p .
Main
Frame line assign
Point an d joint assign assign
Shell an d area a ssign
Display Define
Design
Draw Sistema de coordenadas Select pc n e asignación po r niveles veles
Snap Ba rra rra d e e sta do
Define Definir Definir prop ieda de s de l ma terial
o o r e na a s de l cursor cursor
Draw Selec ciona r Ob jeto
Unidades de trabajo
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Ingenieros Civiles Main Nuevo mod elo Ab rir arc hivo .EDB .EDB exis existente
Display Mostrar Mostrar mod elo inde inde formad o Mostrar Mostrar mo de lo de forma do
Guarda r mod elo
Mostr Mostrar ar formas mod ales
Imprimir Imprimir grá ficos
Mo strar d iag ram a de esfuerz esfuerzos os
Imp rimir imir tab las de da tos
Mostrar Mostrar diag rama de energía y traba jo virtual
Deshacer
Mostrar
Reha ce r
Mostar Mostar curva de pushover pushover
Refresh Bloquear / Desbloquear modelo Co rrer rrer a ná lis lisis
Point a nd jo int assigns assigns Asigna Asigna r d iafra g ma rígid rígid o
Co rrer rrer an álisis álisis de la sec uenc ia de c onstrucc onstrucc ión
Asigna Asigna r pa nel zone
Co rrer rrer a ná lis lisis estát ico no linea linea l
Asigna Asigna r restri restricc c ione s
Zoom área
Asignar Asignar Fuerza uerza o mom ento
Zoom todo Zoo m ant erior
Shell and area assigns assigns
Ac erca miento
Asignar Asignar muro o losa osa
Alejam Alejam iento Desplazamiento Desplazamiento c on el mo use use
Asignar Asignar una pa sad a en losa losa Asigna Asigna r dia fragm a rígido rígido
Vista Vista en 3 d imensione one s Vis Vista en planta
Asigna Asigna r ejes loca les Asignar Asignar etiqueta de Pier
Vis Vista en elevac ión (por ejes) ejes)
Asigna Asigna r etique ta de Spa ndrel
Rota r vista vista 3D Ac tivar tivar / Desac Desac tivar perspe perspe ctiva Mover uno hac ia arriba b a en una lista Move r uno hac ia ab ajo en una lista
Asignar Asignar ca rga uniforme uniforme Frame and line assigns Asi Asignar secc ión del frame frame
Contrae r / de sco ntraer elemento s
Asignar Asignar restri restricc cc iones de l frame
Fijar ijar op c iones pa ra ver el mo de lo
Define rigide gide z po r pe netrac ión (ca cho rígido rígido )
Asi Asigna r no mb res d e grup o
Asignar Asignar ejes loca les de l frame Asigna Asigna r ca rga d istri istribuid buid a d el fram fram e
Select Selecc iona todo Selec ción ant erior erior
Design Diseño Diseño en ac ero
Limpia selecc iones
Dis Diseño en co nc reto
Selec ciona r usand usand o línea línea de inters intersec ción
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Ingenieros Civiles
1.
Crear nuevo archivo archivo y gua rdar como archivo de trabajo File à New Model /
/ ALTFN
Es impo rtante q ue est est én d efinida efinida s c orrec orrec tam ente las unidad es en la ba rra rra de estado antes de escoger new model.
Altura Altura d e en trepiso trepiso
Estructura cione s de piso piso prede finida d a s. Usar Usar o pc ión “g rid on ly” para losa de H.A.
File à Save as /
2.
/ ALTF ALTFA A
Generación de la grilla grilla Edit à Edit g rid da ta à Edit g rid / ALTED ALTEDE E
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Ingenieros Civiles
3.
Generación de la elevación Edit à Edit story d ata à Ed it Sto Sto ry / ALTEY ALTEY (E o I o D)
a b c
a
Notas: • Se ingresan los pisos de abajo hacia arriba. Debe incluirse el nivel “base” (el nivel v el de empotramiento de l ed ifici ificio). o). • Para usar usar planilla planilla “ salida w aller” aller” los pisos pisos de be n tener una e tiqueta tiqueta solo numérica numérica . • La opción “similar to” permite que al asignar en el nivel de referencia (ej. Story 8) estas asignaciones se repitan automá ticam ente en los niveles niveles relacionados (ej. Story 1 al 8). Para ello es necesario que además este seleccionada la alternativa “ similar imilar stories tories”” en la la op ción de a signac ión po r niveles.
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Ingenieros Civiles
c
4.
Definición Definición de m ateriales Define à Material prope rties rties /
5.
/ ALTDM ALTDM
Definir el espectro de aceleraciones Define à Respo nse Spe c trum Func tion s /
/ ALTDE
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Ingenieros Civiles 6.
Definición de sismos a analizar
Define à Response Spectrum cases /
/ A LT DR
Se d ebe n a gregar 2 e spec tros, tros, uno pa ra sismo en X (SX) (SX) y otro p ara sismo smo en Y (SY) (SY)
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Ingenieros Civiles 7.
Definir Definir estados estados de ca rga e státicos
Define à Static Loa d Cases /
Indica Indica en c ual estad estad o de ca rgo se se incluirán incluirán los pe sos propios de los eleme ntos asigna asigna do s, y en que p roporción.
/ ALTDL
Es import ante que e l tipo de ca rga quede bien d efinido, efinido, c uand o se utiliz utilizarán arán las combinaciones de carga predefinidas por el programa programa . Sobrecarga Peso Propio
8.
Definir combinaciones de carga
Define à Load Comb inations /
/ ALT ALT DB
Solo se a ct iva si se se escoge escoge un “ type” de ca rga ho rizontal
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Ingenieros Civiles
9.
Definición Definición de m asas
Define à Ma ss Sourc e /
/ ALTDA ALTDA
Opción recomendad recomendad a
De los pesos propios de los elementos asignados, más masas sísmicas adicionales asignadas sobre las losas (opción Assign à Shell/Area à Ad ditional Area Ma ss). A partir de las cargas asignadas a través de los estados de carga independientes (incluido los pesos propios de los elementos, con la op ción self self weight =1 en el estad estad o de Combinando las opciones anteriores.
Impide que se generen modo s de vibrar vibrar con vibrac vibrac iones fuera de l plano d e los diafragma s (verticales).
10. Definir Definir tipo d e a nálisis nálisis Analyze à Set ana lisis lisis Options / ALTNS ALTNS
Al especificar las masas a través de las cargas asignadas, es necesario definir que p orcenta je de estas estas ca rgas se d eb e considerara en la determinación de la masa sísmica (25% o 50 % para la sobrecarga, dependiendo de la imp ortanc ia del edificio, edificio, de ac uerdo a lo estab estab lecido en la NCh433of96 NCh433of96). ).
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Ingenieros Civiles 11. Definir Definir sec ciones de vig as, co lumnas y diago nales Define à Fram e Sec tions /
/ ALTDF
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Ingenieros Civiles 12. Definir secciones de muros y losas Define à Wall/Slab Wall/Slab / Dec k Sec tions /
/ ALTDS
13. Asignar Asignar co lumnas, vigas y diag onales (elementos de línea)
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Ingenieros Civiles 14. Asignar Asignar m uros (eleme ntos de superficie) Para asign asign a r un mu ro, se se d eb en seg uir los os siguient siguient es pa sos: Permite ermite ge nerar muros muros desde desde la planta o en elevac ión definiendo definiendo nodo inicio, c io, nodo final o hac iendo un solo clic clic e n la linea linea de la grilla la
Selecc ione el muro , y luego
El usuario debe especificar una etiqueta identificatoria para los elementos de área. Se debe usar la misma etiqueta para todos los elementos de superficie que
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Ingenieros Civiles 16. Asignar diafragmas Seleccionar las las áreas áreas que c onforma onforma n un d iafragm a d e p iso iso
Assign à Shell/ Area à Rigid Diafrag Diafrag m /
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Ingenieros Civiles 18.
Trozamie nto d e losas y muros.
OPCION OPCION 1: MANUAL Edit à Me sh Area s / ALTEH
Opc ión muy útil útil
Opc ión muy útil útil
Notas: El objetivo del trozamiento (meshing) es lograr la conectividad
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Ingenieros Civiles
Lueg o de hac er el aut o Me shing, es nec esario esario aseg aseg u rar la c one ct ivida da d e n de tod os los elemen tos. tos. Para Para e sto, se se d eb e selec selec ciona r
Se de ben selecc selecc ionar las opc iones indica indica da s
19.
Asignación Asignación de ca rga en losas losas
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Ingenieros Civiles Otras Observac Observac iones
• • • • •
Si se usa la opción de asignar masas adicionales, estas se deben asignar sobre las losas considerando el porcentaje que aporta la sobrecarga, más las masas producto de los pesos muertos (Masa adicional = (PM + % SC)/9.8). El programa trae inco rpo rad a una c alculadora. Para Para usarl usarlaa b asta asta ha c er dob le clic clic en el ca sill illero do nde va el resultad resultad o. Pa ra ve r solo a lgun os p isos: isos: View à Set Build uild ing view limits limits à Set Sto ry Ra Ra ng e Para a larga larga r un elem elem ento en p lanta o en eleva c ión usar usar el botó n “ de splazar plazar elemento ” (res (reshap hap e). Se selec c iona e l elem ento y se se estir estiraa d esd esd e un extremo . Sec tion Cu ts: ts: