FACULTAD DE INGENIERÍA CARRERA DE INGENIERÍA
CURSO: CONCRETO ARMADO
TEMA: DISEÑO DE ZAPATAS COMBINADAS Autores: BALCÁZAR ROJAS, REINER ALÍ HERAS SALAZAR, KRISTIAN FERNANDO Profesor: JOSE RAFAEL MEJÍA CHATILAN
Cajamarca P!r" #$%&
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INTRODUCCIÓN D!'(r) *!+ m'*) *! +a c-m!'(ac-.' (!'!m)/ a +a/ /0!r1-c-a+!/ 2 a +a/ 0r)1'*a/, *!'(r) *! +a/ c-m!'(ac-)'!/ /0!r1-c-a+!/ (!'!m)/3 +)/ c-m-!'()/ c)rr-*)/, +a/ 4a0a(a/, 5-6a/ *! c-m!'(ac-.', 0+a(!a/ *! c-m!'(ac-.', (-+-4am)/ !/(! (-0) *! c-m!'(ac-)'!/ /0!r1-c-a+!/ ca'*) !+ !/1!r4) ) +a/ c)'*-c-)'!/ *!+ (!rr!') a c)'/(r-r !/ 7!')8 E' !+ /-6-!'(! (ra7aj) /! *!/arr)++ara !+ *-/!9) *! ZAPATAS COMBIANADAS, !+ ca+ /! !'c!'(ra !' !+ (-0) *! c-m!'(ac-)'!/ /0!r1-c-a+!/8 U'a 4a0a(a c)m7-'a*a /! carac(!r-4a 0)r /)0)r(ar m:/ *! ' !+!m!'() /)7r! 'a m-/ma 7a/! 2 (am7-;' 0)r (!'!r ' !/0!/)r <! !/ mc=) m:/ <! +a *! 'a 4a0a(a a-/+a*a ) +a m-/ma c)rr-*a8 C)m) a+(!r'a(-5a 0)*!m)/ '-r +)/ !+!m!'()/ a /)0)r(ar 0)r m!*-) *! 'a c)'(ra(ra7! a/> r!*c-r!m)/ !+ !/0!/)r *! !/(a +) <! /-6'-1-car>a ' 6ra' a=)rr) !' ma(!r-a+ c)m) !/ !+ c)'cr!()8
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OBJETIVOS:
E+ )7j!(-5) *!+ (ra7aj) !/ a0r!'*!r ac!rca *!+ *-/!9) !' c)'cr!() arma*) *! 4a0a(a/ c)m7-'a*a/8
A 0ar(-r *! +)/ c)'c!0()/, r!a+-4ar ' !j!m0+) !j!m0+) c)' +) a0r!'*-*)8
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CAPÍTULO I CONCEPTOS CONCEPTOS GENERALES 1.1. APATAS La/ 4a0a(a/ /)' m-!m7r)/ !/(rc(ra+!/ <! /! /a' 0ara /)0)r(ar c)+m'a/, mr)/ 2 (ra'/m-(-r // car6a/ a+ /!+) /72ac!'(!8 E+ c)'cr!() r!1)r4a*) !/ ' ma(!r-a+ m2 a*!ca*) 0ara +a/ 4a0a(a/ 2 /! /a a/> !' !*-1-c-)/ *! c)'cr!() r!1)r4a*), *! ac!r) !/(rc(ra+, !' 0!'(!/, ()rr!/ 2 )(ra/ !/(rc(ra/8
F-6ra $%8 Za0a(a a-/+a*a *! c)'cr!() arma*)8 F!'(!3 B)+!(>' C)'/(r2!'*), Ac!r)/ Ar!<-0a8
La 0r!/-.' 0!rm-/-7+! !' ' /!+) *!7aj) *! 'a 4a0a(a !/ ')rma+m!'(! *! 'a/ ca'(a/ ()'!+a*a/ 0)r 0-! ca*ra*)8 L)/ !/1!r4)/ *! c)m0r!/-.' !' +)/ mr)/ 2 +a/ c)+m'a/ *! 'a !/(rc(ra )r*-'ar-a 0!*!' ++!6ar a /!r *! c-!'()/ *!
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/)7r! +a /1-c-!'(! :r!a *! /!+) c)m) 0ara <! ;/(! /)0)r(! +a/ car6a/ !' 1)rma /!6ra8 N) /.+) /.+) !/ *!/! *!/!a7 a7+! +! (ra' (ra'/1 /1!r !r-r -r +a/ +a/ car6 car6a/ a/ *! +a /0! /0!r! r!/( /(r rc( c(r ra a a+ /!+ /!+) ) /72ac!'(! !' 1)rma (a+ <! ') /! 6!'!r!' a/!'(am-!'()/ !?c!/-5)/ ) *-/0ar!j)/ 2 r)(ac-)'!/, /-') <! (am7-;' !/ '!c!/ar-) 0r)0)rc-)'ar +a /1-c-!'(! r!/-/(!'c-a a+ *!/+-4am-!'() 2 5)+(!)8
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Para +)6rar !/()/ )7j!(-5)/, !/ '!c!/ar-) (ra'/m-(-r +a/ car6a/ /)0)r(a*a/ a ' /!+) *! /1-c-!'(! r!/-/(!'c-a 2 +!6) r!0ar(-r+a/ /)7r! ' :r!a (a+ <! +a 0r!/-.' '-(ar-a <!*! *!'(r) *! ' -'(!r5a+) ra4)'a7+!8 S- ') !/ 0)/-7+! !?ca5ar a 'a 0!<! 0!<!9a 9a 0r)1' 0r)1'*-* *-*a* a* 2 !'c)'( !'c)'(rar rar ' /!+) /!+) /a(-/ /a(-/1ac 1ac()r ()r-), -), /!r: /!r: '!c!/ '!c!/arar-) ) /ar /ar 0-+)(!/ ) caj)'!/ *! c-m!'(ac-.' 0ara =ac!r !+ (ra7aj)8
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F-6ra $@8 E*-1-c-) c)' c-m!'(ac-.' /0!r1-c-a+ 0)r 4a0a(a/8
F-6ra $8 E*-1-c-) c-m!'(a*) /)7r! 0-+)(!/8
1.!. TIPOS DE APATAS E'(r! +a/ *-5!r/a/ 4a0a(a/ *! c)'cr!() r!1)r4a*) *! /) c)m"' /! c!'(a'3 +a/ 4a0a(a/ c)rr-*a/ 0ara mr)/, +a/ 4a0a(a/ a-/+a*a/, +a/ 4a0a(a/ c)m7-'a*a/, +a/ +)/a/ *! c-m!'(ac-.' 2 +a/ ca7!4a/ *! 0-+)(!/8
U"# $#%#t# &orr'(#) !/ /-m0+!m!'(! 'a am0+-ac-.' *! +a 0ar(! -'1!r-)r *! ' mr), c2a 1-'a+-*a* !/ *-/(r-7-r a*!ca*am!'(! +a car6a /)7r! !+ /!+) *! +a c-m! c-m!'( '(ac ac-. -.'8 '8 La/ La/ 4a0a 4a0a(a (a// c)rrc)rr-*a *a// ')rm ')rma+ a+m! m!'( '(! ! /! /a' /a' !' !+ 0!r>m!(r) *! ' !*-1-c-) 2 a 5!c!/ 7aj) +)/ mr)/ -'(!r-)r!/8
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/a*a/, !' 0ar(-c+ar ca'*) +a/ car6a/ /)' r!+a(-5am!'(! +-6!ra/ 2 +a/ c)+m'a/ ') !/(:' m2 c!rca'a/ !'(r! />8
L#s $#%#t#s &o+,'"#(#s /! /a' 0ara /)0)r(ar +a/ car6a/ *! *)/ ) m:/ c)+m'a/8 c)+m'a/8 U'a 4a0a(a 4a0a(a c)m7-'a*a c)m7-'a*a 0!*! 0!*! /!r !c)'.m-ca !c)'.m-ca ca'*) ca'*) *)/ ) m:/ c)+m' c)+m'a/ a/ 1!r(! 1!r(!m!' m!'(! (! car6a* car6a*a/ a/ !/(:' !/(:' /!0ar /!0ara* a*a/ a/ !'(r! !'(r! /> a 'a *-/( *-/(a' a'cc-a a (a+ (a+ <! <! // // 4a0a 4a0a(a (a// -'*-'*-55-* *a+ a+!/ !/ <!* <!*ar ar>a >a' ' (ra/ (ra/+a +a0a 0a*a *a/8 /8 G!'!ra+m!'(!, +a/ 4a0a(a/ -'*-5-*a+!/ /)' ca*ra*a/ ) r!c(a'6+ar!/ 2 //! !m0+!ara' 0ara c)+m'a/ +)ca+-4a*a/ !' +)/ +-'*!r)/ *!+ (!rr!'), /! !?(!'*!r>a' m:/ a++: *! ;/()/8 U'a 4a0a(a 0ara (a+ c)+m'a, c)m7-'a*a c)' )(ra 0ara 'a c)+m'a -'(!r-)r, 0!*! *-/!9ar/! *! ma'!ra <! ') /)7r!0a/! +)/ +-'*!r)/ *! +a 0r)0-!*a*8
U"# %*#"&-# (e &'+e"t#&'" ) +)/a *! c-m!'(ac-.' ) c-m!'(ac-.' 1+)(a'(! !/ 'a +)/a c)'(-'a *! c)'cr!() r!1)r4a*) /)7r! ' :r!a 6ra'*! <! /! /a 0ara /)0)r(ar mc=a/ c)+m'a/ 2 mr)/8 E/(! (-0) *! c-m!'(ac-.' /-r5! ca'*) +a r!/-/(!'c-a *!+ /!+) !/ 7aja ) +a/ car6a/ *! +a/ c)+m'a/ /)' 6ra'*!/, 0!r) ') /! /a' 0-+)(!/ ) caj)'!/ *! c-m!'(ac-.'8
L#s ,e$#s (e %'*otes /)' +)/a/ *! c)'cr!() r!1)r4a*) <! /! /a' 0ara *-/(r-7-r +a/ *-/(r-7-r +a/ car6a/ *! +a/ c)+m'a/ a 6r0)/ *! 0-+)(!/8
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F-6ra $8 T-0)/ *! Za0a(a/8
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)(r)/ 1ac()r!/8
F-6ra $8 C)'*-c-)'!/ *!+ /!+)
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()ma*a c!rca *!+ c!'(r) *! +a 4a0a(a8 S- !+ 1)'*) *! 'a 4a0a(a !/(: +)ca+-4a*) a c-!r(a *-/(a'c-a *! +a /0!r1-c-! *!+ (!rr!'), ' /!+) ar!')/) 0r)5 0r)5!! !!r: r: ' /)0) /)0)r( r(! ! 7a/( 7a/(a' a'(! (! '-1 '-1)r )rm! m! 0ara 0ara +a 4a0a 4a0a(a (a,, 0!/ 0!/ / m)5-m-!'() +a(!ra+ !/(: r!/(r-'6-*)8 La /-(ac-.' j/(am!'(! c)'(rar-a )crr! 0ara 4a0a(a/ /)0)r(a*a/ 0)r /!+)/ arc-++)/)/8 La arc-++a 7aj) +)/ 7)r*!/ *! +a 4a0a(a /! 0!6a ) (-!'! c)=!/-.' c)' !+ /!+) arc-++)/) *!+ !'()r')8 C)m) c)'/!c!'c-a, m:/ car6a !/ ()ma*a !' +)/ 7)r*!/ <! !' !+ c!'(r) *! +a 4a0a(a8
1.0. PRESIONES PERMISIBLES DEL SUELO La/ La/ 0r!/ 0r!/-) -)'! '!// 0!rm 0!rm-/ -/-7 -7+! +!// *!+ *!+ /!+ /!+) ) <! <! /! /a' /a' 0ara 0ara *-/! *-/!9a 9arr +a c-m!'( c-m!'(acac-.' .' 0ara 0ara 'a !/(rc !/(rc(r (ra a 0ar(-c 0ar(-c+a +arr, /! )7(-!' )7(-!'!' !' /a'*) /a'*) +)/ /!r5-c-)/ *! ' -'6!'-!r) !/0!c-a+-4a*) !' 6!)(!c'-a8 /(! *!(!rm-'ar: +)/ 5a+)r!/ *! /!6r-*a* c)' 7a/! !' +)/ 0r-'c-0-)/ *! +a m!c:'-ca *! /!+)/, !' +)/ r!/+(a*)/ *! +a/ 0r!7a/ *! +)/ /)'*!)/, !' 0r!7a/ *! car6a 2 !' )(ra/ -'5!/(-6ac-)'!/ !?0!r-m!'(a+!/8 O(r)/ a/'()/ 0!*!' !'(rar !' +a *!(!rm-'ac-.' *! +a/ 0r!/-)'!/ 0!rm-/-7+!/ *!+ /!+), c)m) +a /!'/-7-+-*a* *!+ marc) *!+ !*-1-c-) 0ara ac)m)*ar +a *! *!1+!?-.' *! +a/ 4a0a(a/8 Tam7-;', !+ a6r-!(am-!'() *! +a /0!r!/(rc(ra <! r!/+(a *!+ a/!'(am-!'() *! +a/ 4a0a(a/ /!r>a mc=) m:/ -m0)r(a'(! !' ' c!'(r) *! ar(!/ !/c;'-ca/ <! !' ' a+mac;'8 C)m) (a+!/ -'5!/(-6ac-)'!/ ') /-!m0r! /)' 1ac(-7+!/, +a ma2)r>a *! +)/ c.*c.*-6) 6)// *! c)'/ c)'/(r (rc ccc-.' .' 0r)5 0r)5!! !!' ' c-!r c-!r(a (a// 0r!/ 0r!/-) -)'! '!// a0r) a0r)??-ma ma*a *a//
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Ta7+a $%8 Pr!/-.' m:?-ma 0!rm-/-7+! *!+ /!+)8
F!'(!3 D-/!9) *! C)'cr!() R!1)r4a*), Mc C)rmac8
La /!cc-.' %8#8# *!+ c.*-6) ACI !/(a7+!c! <! !+ :r!a r!<!r-*a 0ara 'a 4a0a(a *!7! *!(!rm-'ar/! *-5-*-!'*) +a car6a ()(a+ 0r!5-/(a, -'c+2!'*) !+ 0!/) *! +a 4a0a(a, !'(r! +a 0r!/-.' 0!rm-/-7+! *!+ /!+) ) +a ca0ac-*a* 0!rm-/-7+! *!+ 0-+)(! <! /! *!(!rm-'a' /a'*) +)/ 0r-'c-0-)/ *! +a m!c:'-ca *! /!+)/8 S! ')(ar: <! !/(a car6a ()(a+ !/ 'a car6a /-' 1ac()r-4ar 2 <!, /-' !m7ar6), !+ *-/!9) *! 4a0a(a/ *!/cr-() !' !/(! ca0>(+) /! 7a/a !' !+ *-/!9) 0)r r!/-/(!'c-a, *)'*! +a/ car6a/ /! m+(-0+-ca' 0)r 1ac()r!/ *! car6a a0r)0-a*)/8 E/ )75-) <! 'a car6a "+(-ma ') 0!*! *-5-*-r/! !'(r! 'a 0r!/-.' *! /!+) 0!rm-/-7+! 0ara *!(!rm-'ar !+ :r!a *! a0)2) r!<!r-*a8
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E+ c)m! c)m!'( '(ar ar-) -) %8 %8# # *!+ *!+ ACI ACI *! %% %% 0r)5 0r)5!! !! ' m;() m;()*) *) a+(! a+(!r' r'a( a(-5 -5) ) 0ara 0ara *!(!rm-'ar !+ :r!a *! 4a0a(a r!<!r-*a <! *ar: !?ac(am!'(! !+ m-/m) r!/+(a*) <! !+ 0r)c!*-m-!'() *!/cr-() a'(!r-)rm!'(!8 S!6"' !/(! m;()*) a+(!r'a(-5), +a 0r!/-.' 0!rm-/-7+! *!+ /!+) /! -'cr!m!'(a a ' 5a+)r "+(-m) m+(-0+-c:'*)+) 0)r 'a r!+ac-.' -6a+ a +a /a*a 0ara -'cr!m!'(ar +a ma6'-(* *! +a/ car6a/ *! /!r5-c-)8 P)r !j!m0+), +a r!+ac-.' 0ara +a/ car6a/ D 2 L /!r>a8
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CAPÍTULO II
DISEO DE APATAS COMBINADAS
La/ 4a0a(a/ c)m7-'a*a/ /)0)r(a' m:/ *! 'a c)+m'a8 U' ca/) !' <! 0!*!' /ar/! !/ ca'*) +a/ c)+m'a/ !/(:' (a' c!rca 'a *! )(ra <! +a/ 4a0a(a/ -'*-5-'*-5-*a *a+!/ +!/ /! -'(!r1 -'(!r1!r!r-r>a r>a' ' F-6r F-6ra a $a8 $a8 O(r) O(r) /) 1r!c 1r!c!'( !'(! ! *! +a/ 4a0a(a 4a0a(a// c)m7-'a*a/ !/ ca'*) 'a c)+m'a !/(: m2 c!rca *! ' +-'*!r), *! ma'!ra <! 'a 4a0a(a a-/+a*a /! !?(!'*!r>a m:/ a++: *!+ +-'*!r) *! +a 0r)0-!*a*8 E' !/(! ca/), +a 4a0a(a *! +a c)+m'a !?(!r-)r 0!*! c)m7-'ar/! c)' +a *! 'a c)+m'a -'(!r-)r F-6ra $78
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F-6ra $&8 Za0a(a c)m7-'a*a c)m7-'a*a *)/ c)+m'a/ *!/0;/ *!/0;/ *! =a7!r c)+a*) !+ c)'cr!() *! +a 4a0a(a <! m! m!/(r /(ra a !+ r!1 r!1!r !r4) 4) *! +a c)+ c)+m'a m'a +-/() 0ara !+ !m0a !m0a+m! +m!,, a'! a'!?) ?) *! R)* R)*a/3 a/3 C+! C+!m/) m/)' ' U'-5!r/-(2,, #$$&8 U'-5!r/-(2
P!/() <! !/ c)'5!'-!'(! <! +a/ 0r!/-)'!/ *! a0)2) /!a' '-1)rm!/ /)7r! ()*a +a 4a0a(a, !+ c!'(r)-*! *! ;/(a *!7! =ac!r/! c)-'c-*-r c)' !+ c!'(r)-*! *! +a/
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La/ 4a0a(a/ c)m7-'a*a/ (ra0!4)-*a+!/ 2 !' T 0!rm-(!' a+ 0r)2!c(-/(a =ac!r <! +)/ c!'(r)-*!/ c)-'c-*a'8 La/ 4a0a(a/ c)' !/a/ 1)rma/ /)' !c)'.m-ca/ ca'*) =a2 6ra'*!/ *-1!r!'c-a/ !'(r! +a/ ma6'-(*!/ *! +a/ car6a/ *! +a/ c)+m'a/ ) ca'*) +)/ !/0ac-)/ *-/0)'-7+!/ ') /! 0r!/(a' a 4a0a(a/ r!c(a'6+ar!/ +ar6a/8 Ca'*) /! /a' 4a0a(a/ (ra0!4)-*a+!/, +a/ 5ar-++a/ +)'6-(*-'a+!/ /! *-/0)'!' /a+m!'(! !' 1)rma *! a7a'-c) c)' +a/ 5ar-++a/ a+(!r'a*a/ 2 c)r(a*a/ a c-!r(a *-/(a'c-a *!+ !?(r! !?(r!m) m) !/(r !/(r!c !c=) =)88 Pr)7 Pr)7a7 a7+! +!m! m!'( '(! ! /! a*5! a*5!r(r(-r: r: <! <! /r6 /r6! ! ' 0r)7 0r)7+! +!ma ma a+ !/(a7+!c!r +)/ c!'(r)-*!/ *! +a/ car6a/ 2 *! +a/ 4a0a(a/ 2 (-!'! <! *!c-*-r/! /- /! /a' car6a/ *! /!r5-c-) ) car6a/ 1ac()r-4a*a/8
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!.1 SECCIONES CRITICAS PARA APATAS E+ 0r)c!*-m-!'() 0ara 0r)2!c(ar 4a0a(a/, c)m) !+ <! /! !m0+!a 0ara )(r)/ !+!m!'()/ *! c)'cr!() r!1)r4a*), /! 1'*am!'(a !' +a ma'!ra !' +a <! ;/(! 0!* 0!*! ! 1a++ 1a++ar ar88 L)/ L)/ !?0! !?0!rr-m! m!'( '()/ )/ =a' =a' *!m) *!m)/( /(ra ra*) *) <! <! /! 0!* 0!*!' !' 0r!/ 0r!/!' !'(a (ar r *-1!r!'(!/ (-0)/ *! c)m0)r(am-!'() !/(rc(ra+, a'(!/ *! a+ca'4ar +a r!/-/(!'c-a m:?m:?-ma ma !' 'a 'a 4a0a 4a0a(a (a88 E' a+6 a+6'a 'a r!/r!/-/( /(!' !'cc-a, a, m!') m!')rr <! <! +a m:?m:?-ma ma,, +a/ +a/ *!1)rmac-)'!/ 2 6r-!(a/ *! +a 4a0a(a 0r)7a7+!m!'(! /!a' (a' 6ra'*!/ <! +a 4a0a(a <!*! -'/!r5-7+!8 A !/(a !(a0a /! +! ++ama *! 1a++a 0r-mar-a8 La 'a(ra+!4a *! +a 1a++a 0r-mar-a !/ a 5!c!/ *-1>c-+ *! *!(!rm-'ar, *!7-*) a +a -'(!r*!0!'*!'c-a !'(r! 5ar-)/ 1ac()r!/8
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!.! DISEO DE CIMENTACIONES CIMENTACIONES POR EL METODO CONVENCIONAL D!(! D! (!rm rm-' -'ac ac-. -.' ' *! +a +a// r! r!/ /+(+(a' a'(! (!// *! +a +a// ca car6 r6a/ a/ ac ac( (a' a'(! (!// R R 2 +a 7-cac-.' *! +a r!/+(a'(!8
S- ca+<-!r c)+m'a !/(: /j!() a m)m!'() 1+!?-)'a'(!, !+ !1!c() *!+ m)m!'() *!7!r: /!r ()ma*) !' c)'/-*!rac-.'8
D!(!rm-'a D!(!rm -'ac-. c-.' ' *! *! +a +a *-/( *-/(r-7 r-7cc-.' .' *! 0r! 0r!/-) /-)'!/ '!/88 D!(! D! (!rmrm-'! '! !+ a' a'c= c=) ) *! *! +a +a c-m c-m!' !'(a (acc-.' .'88 D!(! D! (!rmrm-'a 'ar! r! *-a *-a6r 6ram ama a *! 1! 1!r4 r4a a c)r( c)r(a' a'(! (!88 D!(!rm D!( !rm-'a -'arr !+ !+ *-a6 *-a6ram rama a *! *! m)m m)m!' !'()/ ()/ 1+! 1+!c() c()r!/ r!/88 D-/!9a D-/ !9arr +a c-m c-m!'( !'(ac ac-.' -.' c)m c)m) ) 'a 'a 5-6 5-6a a c)'( c)'(-' -'a8 a8 D-/!9ar D-/!9 ar +a c-m!' c-m!'(ac-. (ac-.' ' !' !' *-r!cc*-r!cc-.' .' (ra'/5 (ra'/5!r/a !r/a++ !' 1)rma !<-5 !<-5a+!'( a+!'(! ! a+ a+ *! 4a0a(a/ a-/+a*a8
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@8 Ha++am)/ !+ c!'(r) *! 6ra5!*a*
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A/m-m)/ 4a0a(a *! #8$ #8$ m ? %$8$$ m #88 REACCION NETA POR UNIDAD DE LONGITUD
#88 REACCIQN NETA POR UNIDAD DE ÁREA
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@%8$ ('8m $8 $8#
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@8@8 DIMENSIONAMIENTO DEL PERALTE =4 DE LA ZAPATA8
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C)m)3
3. DISEO POR
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U/ar 3
CHEUEO DE CUANTIA
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