Análisis y Diseño Estructural de Edificación

8/16/2019 Análisis y Diseño Estructural de Edificación

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ANÁLISIS Y DISEÑO ESTRUCTURAL DE EDIFICACIÓNMATERIA: ARMADO II

1 INTRODUCCIÓN................................................................................................4

2 OBJETIVOS........................................................................................................4

3 ESPECIFICACIONES.........................................................................................53.1 Ubicación......................................................................................................5

3.2 Est!ct!a"#s.................................................................................................5

3.3 Es$#ci%icaci&n#s (# "&s )at#ia"#s..............................................................5

3.4 *&(#"a)i#nt& (# "a #st!ct!a.....................................................................5

4 DI*ENSIONA*IENTO.......................................................................................+

4.1 Di)#nsi&na)i#nt& (# "a $"aca a"i,#a(a.....................................................+

4.1.1 A"t!a (# "a $"aca a"i,#a(a...................................................................+4.1.2 Anc-& (# "as i,!#tas............................................................................+

4.1.3 S#$aación )/0i)a #nt# n#i&s.........................................................

4.1.4 Es$#s& (# "a t&ta s!$#i&...................................................................

4.2 S#cción (# "a $"aca a"i,#a(a......................................................................

4.3 S#cción (# "a i,!#ta...................................................................................

4.4 Di)#nsi&na)i#nt& (# "as c&"!)nas............................................................

4.5 Di)#nsi&na)i#nt& (# "as i,as....................................................................

4.+ Di)#nsi&na)i#nt& (# "as i,as a!0i"ia#s.......................................................

5 EVAUACIÓN DE CARAS...............................................................................

5.1 Ca,as )!#tas............................................................................................

5.1.1 P&$ias 67D18.......................................................................................

5.1.2 S&b#i)$!#stas 67D28.........................................................................

5.2 P#s& t&ta" (#" #(i%ici&..................................................................................19

P#s& (#" #(i%ici& $& #" ):t&(& si)$"i%ica(&.....................................................19

5.2.1 P#s& (#" #(i%ici& $& #" ):t&(& "a,&...................................................115.3 P#s& (# ca(a #nt#$is&..............................................................................12

5.4 Ca,a ia...................................................................................................12

+ AN;ISIS DIN;*ICO DE FUER


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+.2


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..1 Dis#& a %"#0ión...................................................................................45

..2 Dis#& a c&tant#.................................................................................4+

1 INTRODUCCIÓN

3


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E" c&nc#t& #%&?a(& #s !na c&)binación #nt# c&nc#t& ac#& (# #%!#?&H !#"& c&ni#t# #n !n #%ici#nt# )at#ia" (# c&nst!cción "a n&tab"# #sist#ncia a "ac&)$#sión (#" c&nc#t& a "a tacción (#" ac#& -ac#n $&sib"# s! c&)binación #n"a s#cción (# !na #st!ct!a. Estas &tas $&$i#(a(#s "# (an #" $a$#" )/s

i)$&tant# #n #" (is#& (# #st!ct!as (# -&)i,ón a)a(&. Act!a")#nt# a "a -&a(# (is#a s# #)$"#an S&%ta# !# a!(an a #a"i?a & c&)$&ba c/"c!"&s $aa"a &$ti)i?ación (# #stas.

E" $&#ct& a tabaKaH #s !na #(i%icación (# c!at& ni#"#s (# a$ata)#nt&s !n$i)# ni#" (# $a!#a(#&. Est/ !bica(& #n "a ci!(a( (# CLc!ta s! sist#)a#st!ct!a" #s (# $ótic&s s# #nc!#nta #n !na ?&na (# a)#na?a s@s)ica a"taH "&c!a" n&s c&n""#a a t#n# #s$#ci%icaci&n#s #0$"icitas a "a -&a (# s! (is#& basan&s #n #" R#,"a)#nt& C&"&)bian& (# C&nst!cción Sis)& #sist#nt# NSRG19.

En #st# tabaK& s# ana"i?a (is#a !na #st!ct!a (# c&nc#t& #%&?a(& (# cinc&ni#"#s c&n !n /#a a$&0i)a(a (# 495. )M2 !bica(& #n "a ci!(a( (# CLc!ta. E"#(i%ici& s# (is$&n(/ $aa !s& #si(#ncia" baK& s# $#s#ntan "as )#)&ias (#c/"c!"& $"an& #st!ct!a"

2 OBJETIVOS

General:

Dis#a #st!ct!a" s@s)ica)#nt# !n #(i%ici& (# cinc& $is&sH "&ca"i?a(&#n "a ci!(a( (# CLc!taH N&t# (# Santan(#.

E!e"#$%"&:

R#a"i?a #" (i)#nsi&na)i#nt& (# "a $"aca a"i,#a(aH "as i,as "asc&"!)nas (# "a #(i%icaciónH t#ni#n(& #n c!#nta #" R#,"a)#nt& C&"&)bian&(# Dis#& C&nst!cción Sis)& R#sist#nt# 6NSRG198.

V#i%ica "as (#ias )/0i)as (# "a #st!ct!a $aa ca(a $is& (# ac!#(& a"a NSRG19.

R#a"i?a #" (is#& a %"#0iónH c&tant# t&sión (# "as i,asH i,!#tas c&"!)nas s#,Ln c&#s$&n(a.

R#a"i?a #" (is#& (# "a ci)#ntación.

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' ES(ECIFICACIONES

'.1 U)%"a"%*n

E(i%ici& (# cinc& $is&sH c&n $a!#a(#&s inc"!i(&s !bica(& #n "a ci!(a( (#CLc!ta 6N&t# (# Santan(#8H Bai& "&s *&ti"&n#s.

'.2 E+r,"+,rale

Sist#)a #st!ct!a" Ti$& $ótic&. Us& R#si(#ncia". a #st!ct!a s# c"asi%ica (# ac!#(& a" ti$& (# !s& (#nt& (#" ,!$& I

Est!ct!as (# &c!$ación n&)a"Q.


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/ DI0ENSIONA0IENTO

/.1 D%en%&na%en+& -e la !la"a al%era-a

4.1.1 A"t!a (# "a $"aca a"i,#a(aEn #" a$ata(& C..3.24 Eleen+& re$&r5a-& en ,na -%re""%*n 6n&!ree$&r5a-&7 (# "a NSRG19 #s$#ci%ica "as a"t!as & #s$#s&#s )@ni)&s (# i,asn& $##s%&?a(as & "&sas #%&?a(as #n !na (i#cción.

Si)$"#)#nt# a$&a(a

e1=

L

20

!? )/s "a,a.

e1=5.6

20=0.28m≊0.3m

En &"a(i?&

e2=

L

8

!? (#" &"a(i?&.

e2=1.1

8=0.14≊0.15

a a"t!a !# s# t&)a (#" #nt#$is& #s 9.3 ) !# #s "a )a& (# "as (&s.

D#s$!:s (# #a"i?a #" an/"isis #s$#cta" c&n "a a"t!a (# "a $"aca (# 9.3 ) s#

(#t#)inó !# "as (#ias n& c!)$"@an $& "& c!a" %!# n#c#sai& #a"i?a !na)&(i%icación #n "a a"t!a (# "a $"aca a"i,#a(a.

h=0 .4m

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4.1.2 Anc-& (# "as i,!#tas

En #" a$ata(& C.8.1'.2 (# "a NSRG19 s# #s$#ci%ica !# #" anc-& (# "asn#a(!as n& (#b# s# )#n& (# 199 )) #n s! $at# s!$#i& s! anc-&

$&)#(i& n& $!#(# s# )#n& a 9 ))H (#b# t#n# !na a"t!a )a& (# 5 #c#ss! anc-& $&)#(i&.

bw=100mm

4.1.3 S#$aación )/0i)a #nt# n#i&s

En #" a$ata(& C.8.1'.' (# "a NSRG19 $aa "&sas n#a(as #n !na (i#cción "as#$aación )/0i)a #nt# n#i&sH )#(i(a c#nt& a c#nt&H n& $!#(# s# )a& a2.5 #c#s #" #s$#s& t&ta" (# "a "&sa sin #0c#(# 1.2 ). Paa "&sas n#a(as #n

(&s (i#cci&n#sH "a s#$aación )/0i)a #nt# n#i&sH )#(i(a c#nt& a c#nt&H n&$!#(# s# )a& !# 3.5 #c#s #" #s$#s& t&ta" (# "a "&saH sin #0c#(# 1.5 ).

Separació n má ximaentrenervios=2.5∗0.4 [ m ] :1m


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0,7 [m

0,4[m

0,![m

0,31[m

0,4 [m

0,1 [m

0,6 [m

0,6 [m

0,6 [m

0,6 [m

0,4 [m

0,3 [m


/.2 Se""%*n -e la !la"a al%era-a

/.' Se""%*n -e la %,e+a

/./ D%en%&na%en+& -e la "&l,na

/.3 D%en%&na%en+& -e la %a

/.9 D%en%&na%en+& -e la %a a,;%l%are

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3 EVALUACIÓN DE CARGAS

3.1 Cara ,er+a

5.1.1 P&$ias 67D18

Cas#tón 0.5[

KN

m2 ]

P"acas (0.06+0.03 ) [ m ]∗24 [ KN m3 ]=2.16 [ KN m2 ]

Vi,!#tas:(0.31∗0.1 ) [m2 ]

0.8[m ] ∗24 [ KN m3 ]=0.93[ KN m2 ]

T&ta" 7D1 Caset ó n+ Placas+Viuetas

T&ta" 7D1 0.5

KN

m2 +2.16[ KN m2 ]+0.93 [ KN m2 ]

T&ta" 7D1 3.59

KN

m2

5.1.2 S&b#i)$!#stas 67D28.

a #(i%icación (# !s& #si(#ncia" ti#n# !na a"t!a (# #nt# $is&s (# 2.99


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*!&s 3[ KN m2 ]

Acaba(&s 1.6[ KN m2 ]

T&ta" 7D2 !uros+ "cabados

T&ta" 7D2 3[ KN m2 ]+1.6 [ KN m2 ]

T&ta" 7D2 4 .6 [ KN m2 ]

T&ta" ca,as )!#tas #$=#$1+#$2

T&ta" ca,as )!#tas

#$=3.59[ KN m2 ]+4.6 [ KN m2 ]

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T&ta" ca,as )!#tas #$=8 .19 [ KN m2 ]

3.2 (e& +&+al -el e-%$%"%&

P#s& (#" #(i%ici& Pesodelasplacas+ Pesodelascolumnas %

o muros

P#s& (#" #(i%ici& $& #" ):t&(& si)$"i%ica(&.

4 P#s& $"acas # $[ KN m2 ]∗ " &otal ( Placa) [m2 ]

P#s& $"acas 8.19[ KN

m2

]∗374.72 [m

2

]

P#s& $"acas 3068 .96[ KN ]

4 P#s& c&"!)nas 6P"aca 18 (bw∗h∗lon.libre )∗' ∗¿decolumnas

P#s& c&"!)nas 6P"aca 18 (0.6∗0.6∗2.57 ) [ m3 ]∗24 [ KN m3 ]∗27

P#s& c&"!)nas 6P"aca 18 599 .53 [ KN ]

4 P#s& c&"!)nas 6P"aca 2G48 (bw∗h∗lon.libre )∗' ∗¿decolumnas

P#s& c&"!)nas 6P"aca 2G48 (0.6∗0.6∗2.48 ) [m3 ]∗24 [ KN m3 ]∗27

P#s& c&"!)nas 6P"aca 2G48 578 .54 [ KN ]

4 P#s& c&"!)nas 6P"aca 58 (bw∗h∗lon.libre )∗' ∗¿decolumnas

P#s& c&"!)nas 6P"aca 58 (0.6∗0.6∗1.24 ) [ m3 ]∗24 [

KN

m3 ]∗27

P#s& c&"!)nas 6P"aca 58 289 .27 [ KN ]

P#s& (#" #(i%ici& ¿ placas∗ pesoplacas+ pesodecolumnas

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P#s& (#" #(i%ici&

5∗3068.96 [ KN ]+599.53 [ KN ]+3∗578.54 [ KN ]+289.27[ KN ]

P#s& (#" #(i%ici& 17969 .22[ KN ]

5.2.1 P#s& (#" #(i%ici& $& #" ):t&(& "a,&.

Á#$% &'&%( )(%*% +AT: 374 .72[m2]

4 ;#a (# "as i,as 6AV8 ( Lvias∗¿devias )∗bvias

;#a (# "as i,as 6AV8 (208.71 )∗0.6 [m]

;#a (# "as i,as 6AV8 125 .226 [m2

]

4 A"a)a-& G " t ∗ $2 374.72 [ m2 ]∗4.6[ KN m2 ]

" t ∗ $2 1723 .71[ KN ]

$onde $2= $ivisorios+acabados

4 V%,e+a 4

"

(¿¿ t − "vias)∗ $1¿

(374.72−125.226 ) [m2 ]∗3.59[ KN m2 ] "

(¿¿ t − "vias)∗ $ 1¿

895 .68[ KN ]

$onde $1= Peso Placa

4 P#s& i,as " v∗h∗' concreto

P#s& i,as122.226[m2]∗0.4 [m ]∗24 [ KN m3 ]

P#s& i,as 1202.17 [ KN ]

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4 P#s& $"aca ( "& )#$2+( " & − " V ) #$1+ Pesovias

P#s& $"aca 1723.71[ KN ]+895.68[ KN ]+1202.17 [ KN ]

P#s& $"aca 3821.56 [ KN ]

4 P#s& (#" #(i%ici&¿ placas∗ pesoplaca+ pesodecolumnas∗distanciaaferente

P#s& (#" #(i%ici&

5∗3821.49 [ KN ]+559.53 [ KN ]+578.54 [ KN ]∗3+289.27[ KN ]

P#s& (#" #(i%ici& 21732.22[ KN ]

3.' (e& -e "a-a en+re!%&

P"aca $i)# #nt#$is&.

(e&: pesoplaca+ pesodecolumnas

(e&: 3821.56 [ KN ]+599.53 [ KN ]

(e&: 4421.09 [ KN ]

P"aca s#,!n(&H t#c# c!at& #nt#$is&.


(e&: 3821.56 [ KN ]+578.53 [ KN ]

(e&: 4400.01 [ KN ]

P"aca !int& #nt#$is&.


(e&: 3821.56 [ KN ]+289.27 [ KN ]

(e&: 4110.83 [ KN ]

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3./ Cara %a

En #" a$ata(& B./.2.1 Cargas vivas requeridas, "as ca,as ias !# s# !ti"ic#n #n#" (is#& (# "a #st!ct!a (#b#n s# "as )/0i)as ca,as !# s# #s$#an &c!an

#n "a #(i%icación (#bi(& a" !s& !# #sta a a t#n#. En nin,Ln cas& #stas ca,asias $!#(#n s# )#n&#s a "as ca,as ias )@ni)as !# s# (an #n "as tab"asB.4.2.1G1 B.4.2.1G2.

T#ni#n(& #n c!#nta "a &c!$ación (# "a #(i%icación "a ca,a ia #s (#

Cara viva :1.8 KN

m2

9 ANÁLISIS DINÁ0ICO DE FUER>A ?ORI>ONTAL E@UIVALENTE

D# ac!#(& a "a NSRG19 #s n#c#sai& ca"c!"a "as %!#?as s@s)icas a !# #stas

s&n "as !# ca!san )/s (a& a "as #st!ct!as. Estas %!#?as s# $!#(#n ca"c!"a t#ni#n(& #n c!#nta "a ?&na (&n(# a a #sta !bica(a "a #(i%icación.

9.1 T%!& -e !er$%l -e ,el&

En #" a$ata(& A.2././ (# "a NSRG19 Definición del tipo de perfil de suelo#s$#ci%ica !# #" $#%i" (#" s!#"& s# basa #n "&s a"&#s (# "&s $a/)#t&s (#"s!#"&. a c"asi%icación s# #s$#c@%ica #n "a tab"a A.2.4G1.

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9.2 >&na -e aena5a #%"a

E" $&#ct& a #a"i?a s# #nc!#nta !bica(& #n "a ci!(a( (# CLc!taH 6?&na (#a)#na?a s@s)ica a"ta8H #n !na ?&na %&)a(a $& s!#"&s ti$& c. S# (is#aa c&n #"%in (# (a"# !n !s& #si(#ncia" c&n ,!$& (# !s& I.

T#ni#n(& #n c!#nta "a ?&na (# a)#na?a s@s)ica #n (&n(# #st/ !bica(a "a ci!(a((# CLc!ta s# ca"c!"a "&s a"&#s (# " a " v !# s# $!#(#n &bt#n# #n "a

tab"a A.2.'42..

&s a"&#s (# Fa F s# ca"c!"an c&n a!(a (# Aa A #s$#ctia)#nt#. En "atab"a A.2./4' s# (an "&s a"&#s (# Fa !# a)$"i%ica "as &(#na(as (#" #s$#ct& #n&ca $aa t#n# #n c!#nta "&s #%#ct&s (# siti&. Paa a"&#s int#)#(i&s (# A a As# $#)it# int#$&"a "in#a")#nt# #nt# "&s a"&#s (#" )is)& $#%i".

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9.' C&e$%"%en+e -e %!&r+an"%a

En "a s#cción A.2.3 s# #s$#c@%ica #" c%ici#nt# (# i)$&tancia !# (#$#n(# (# "&s,!$&s ti$& (# !s&. E" ,!$& (# !s& (# "a #(i%icación #s I estructuras de ocupaciónnormal.

P& "& tant& #" c%ici#nt# (# i)$&tancia #s (# 1.

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C&n&ci#n(& "&s a"&#s s# $!#(# #a"i?a #" #s$#ct& (# ac#"#aci&n#s $aa #"(is#&. Est# #s$#ct& s# ana"i?aa basa(& #n #" #s$#ct& (# (is#& !# s# (#%in#

#n "a NSRG19 #n A.2.9 #" c!a" #st/ (#%ini(& #n "&s si,!i#nt#s "@)it#s ¿ (&c(&l.

a #(i%icación s# #nc!#nta #n "a ?&na (# a)#na?a s@s)ica 5 6?&na (# a)#na?a A"ta8H(# ac!#(& a "a tab"a A.2.3G2 "&s a"&#s (# Aa A s&n

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Ta)la '. Val&re -e Aa A.

Aa .'3

A 9.3

Paa (#%ini "&s a"&#s (# Fa F s# c&nsi(#ó !n s!#"& ti$& cH &bt#ni#n(& "&si,!i#nt# (# ac!#(& a "as %i,!as A.2./41 A./.242.

Ta)la /. Val&re -e Fa F.

Fa 1.3F 1.45

C%ici#nt# (# i)$&tancia $aa !na #st!ct!a (# &c!$ación n&)a" I1H s#,Ln "&(#scit& #n A.2.3.1./.

• P#i&(& (# ibación inicia"

& o=0.1 " v∗ ) v " a∗ ) a

& 0=0.1

0.3∗1.450.35∗1.05

=0.11837 s

• P#i&(& (# ibación

& c

=0.48 "v∗ ) v

"a∗ ) a

& c=0.48 0.3∗1.450.35∗1.05

=0.56816 s

• P#i&(& (# ibación inicia"& L=2.4 ) v

& c=2.4∗1.45=3.48 s

• Es$#ct& (# Ac#"#aci&n#sE" a"& (# Sa s# $!#(# "i)ita a" &bt#ni(& $& "as si,!i#nt#s #c!aci&n#s A.2.+.1.1 Paa $#i&(&s (# ibación )#n&#s a Tc.

Sa=2.5 " a ) a *

Sa=2.5∗0.35∗1.05∗1=0.91875+

1!


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A.2.+.1.2 Paa $#i&(&s (# ibación )a&#s !# & L .

Sa=1.2 " v∗ ) v *

&

Se lleva a cabo unatabla en excel dondese calcula el espectro se,nel periodo de vibración .

F-./#% 1 E)$*' E(&-*' $ %*$($#%*-'$ $ -$'

0 1 2 3 4 5 6 70

02

04

06

0!

1

Espectro de Diseño.

Periodo, T[s]

Aceleración Espectral, Sa/g

9./ Cal",l& -el !er%&-& $,n-aen+al -e la e+r,"+,ra 60+&-& -e la F,er5a&r%5&n+al E,%alen+e7.E" a"& (#" $#i&(& %!n(a)#nta" (# "a #(i%icaciónH TH (#b# &bt#n#s# a $ati (# "as$&$i#(a(#s (# s! sist#)a (# #sist#ncia s@s)ica.

& a=C t h-

D&n(# Ct 9H94 9H s#,Ln "a tab"a A.4.2G1 (# "a NSRG19 Pótic&s #sist#nt#sa )&)#nt&s (# c&nc#t& #%&?a(& !# #sist#n "a t&ta"i(a( (# "as %!#?ass@s)icas !# n& #st/n "i)ita(&s & a(-#i(&s a c&)$&n#nt#s )/s @,i(&sH

#st!ct!a"#s & n& #st!ct!a"#sH !# "i)it#n "&s (#s$"a?a)i#nt&s -&i?&nta"#s a"#s# s&)#ti(&s a "as %!#?as s@s)icas.

D$ (' %('#$ $ C t , - $ '8&-$$ $ (% tabla A.4.2-.

Tabla . !alores deC t , - .

1"


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"t #.#4$

% 0"

& total

'()

132

& a=0.047 ¿15.580.9=0.5564 s=&

9.3. De+er%na"%*n -e Sa el "&r+an+e )aal VS

C&tant# s@s)ic& (# "a bas#H VsH #!ia"#nt# a "a t&ta"i(a( (# "&s #%#ct&sin#cia"#s -&i?&nta"#s $&(!ci(&s $& "&s )&i)i#nt&s s@s)ic&s (# (is#&H #n "a(i#cción #n #st!(i&H s# &bti#n# $& )#(i& (# "a si,!i#nt# #c!ación

E" a"& (# Sa #n "a #c!ación ant#i& c&#s$&n(# a" a"& (# "a ac#"#aciónHc&)& %acción (# "a ,a#(a(.

a %!#?a s@s)ica -&i?&nta"H F0H #n c!a"!i# ni#" (# 0H $aa "a (i#cción #n#st!(i&H (#b# (#t#)inas# !san(& "as si,!i#nt#s #c!aci&n#s

D&n(# #s !n #0$&n#nt# #"aci&na(& c&n #" $#i&(& %!n(a)#nta"H TH (# "a#(i%icación (# "a si,!i#nt# )an#a

4 Paa T )#n& & i,!a" a 9H5 s#,!n(&s 1H94 Paa T #nt# 9.5 2H5 s#,!n(&s 9.5 9.5T4 Paa T )a& a 2.5 s#,!n(&s T2

E" $#i&(& &bt#ni(& #sta #nt# "&s a"&#s (# Tc TH c&n #st& s# ca"c!"a Sa c&)&

si,!#Sa=2.5∗ "a∗ )a∗ *

Sa=2.5∗0.35∗1.15∗1

Sa=0.719

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a s#cción A./.'.1 (# "a NSRG19 (#%in# #" c&tant# basa"

Vs=Sa∗ Pesototaldelaestructura

Vs=0.719∗21732.23

Vs=15620.04 [ KN ]

9.9F,er5a #%"a &r%5&n+al

)x=Cvx∗VsCvx= ! ∗h

∑i=1

n

!i∗hi

. 0ODELO EN SA(2

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D#s$!:s (# #s$#ci%ica "as (i)#nsi&n#s (# "as c&"!)nasH i,as "as $&$i#(a(#s(# "&s )at#ia"#s s# $&c#(# a #s$#ci%ica #" c#nt& (# ca(a !n& (# "&s $is&sHi,i(i?an(& ca(a !n& (# "&s $is&s $& )#(i& (# (ia%a,)as

´ x :5.478m

´ % :18.288m

S# #s$#ci%ica ca(a !n& (# "as %!#?as s@s)icas #n "as (i#cci&n#s .

.1 F,er5a #%"a en H Y.

22


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s# c&# #" SAP $aa F0 F.

.2 Ver%$%"a"%*n -e -er%a

Paa #st# cas&H #" $#s& (# "as $"acas #st/ c&nc#nta(& #n "&s c#nt&i(#sH $& "&tant& s&"& s# ana"i?an "&s (#s$"a?a)i#nt&s (# #st&s n&(&sH si,!i#n(& "asin(icaci&n#s (# "a NSRG19

D#s$!:s (# #a"i?a #" )&(#"& #n SAP2999 c&n "as caact#@sticas (# "&s)at#ia"#s "as (i)#nsi&n#s (# "&s #"#)#nt&s #st!ct!a"#s s# ca"c!"a&n "as(#ias $aa ca(a !na (# "as %!#?as s@s)icas (# (is#& a$"ica(as #n "&s

c#nt&i(#s (# ca(a !na (# "as $"acas

23


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.1F,er5a #%"a enY

.2F,er5a #%"a en H

8 DISEÑO AR@UITECTÓNICO Fac-a(a $inci$a" 9-&% ('.-&/-%(

(%&% &-)'

24


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DISEÑO DE (LACAS

.1Cara a!l%"a-a

• Ca,a ia

# L=1.8 [ KN m2 ]• Ca,a )!#ta 6P&$ia s&b#i)$!#sta8

# $=8.19[ KN

m2

]• Ca,a L"ti)a

# / =1.6∗# L+1.2∗# $

# / =1.6∗1.8 [ KN m2 ]+1.2∗8.19[ KN m2 ]# / =12.71

[ KN

m2

]

25


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.2Cara !&r %,e+a

Paa "in#a"i?a "a ca,a L"ti)a $aa "a a$"icación (# #stas #n "as i,as #s n#c#sai&)!"ti$"ica "a ca,a L"ti)a $& "a (istancia !# s#$aa "as i,!#tas )#(i(as (#s(#

s! c#nt&.

# /

m =12.71[ KN m2 ]∗0.8 [ m ]=10.17[ KN m ]

.2.1 Ti$&s (# i,!#tas

S# (#b# ca"c!"a ca(a !na (# "as #acci&n#s #n "&s a$&&s (# "as i,!#tasH $aaca(a ti$& (# ca,a "in#a"i?a(a 6ia )!#ta8.

• Ca,a ia "in#a"i?a(a

# L

m =1.8[ KN m2 ]∗0.8 [m ]=1.44 [ KN m ]

• Ca,a )!#ta "in#a"i?a(a

# L

m =8.19[ KN m2 ]∗0.8 [m ]=6.55 [ KN m ]

.2.2 R#acci&n#s (# "as i,!#tas

Paa ca"c!"a "a ca,a ia "a ca,a )!#ta !# s&$&tan "as i,as #s n#c#sai&-a""a "as #acci&n#s (# ca(a !na (# "as i,!#tas ti$& !# ti#n# #" $&#ct& (ii(i #sa #acción #n 9..

V%,e+a +%!& 1

Rea""%&ne "&n "ara ,er+a

26


28/53


Rea""%&ne "&n "ara %a

V%,e+a +%!& 2



V%,e+a +%!& '



27


29/53


.'D%e& -e %,e+a

.3.1 Dis#& a %"#0ión

Ee!l& %,e+a +%!& IPaa #" (is#& a %"#0ión (# "as i,!#tas %!# n#c#sai& #" !s& (# "&s )&)#nt&sca"c!"a(&s #n #" #K# !# a&Ka SAP2999.

as $&$i#(a(#s "as c&n(ici&n#s n#c#saias $aa #" (is#& (# "a i,!#ta s&n

C&n&ci#n(& #" )&)#nt& L"ti)& ca"c!"a(& c&n SAP2999 s# -a""a #" )&)#nt&

n&)ina" c&n "a si,!i#nt# %ó)!"a !n= !u/∅

P&st#i&)#nt# s# ca"c!"a #" As #!#i(& $& an/"isis !san(& "a si,!i#nt# %ó)!"a

" sre0=

f % . d−√ f %2 . d2−4.( f %

2

2 ' . f c1

. bw ). ! u

∅

f %2

' . f c

1 . b

w

E" As #!#i(& $& an/"isis s# c&)$aa c&n #" As )in !# s# #stab"#c# #n "aNSRG19 #n #" a$ata(& C.19.5.1

"smin=0.25∗√ f c

1

f %bw . d

2!


30/53


P#& n& )#n& a 1.4bw . d / f %

Fina")#nt# s# ca"c!"a c&n baas c&)#cia"#s !n As $aa s!)inista.

Es n#c#sai& #i%ica si "a i,!#ta #s si)$"#)#nt# #%&?a(a c&)$aan(& #")&)#nt& L"ti)& ca"c!"a(& c&n SAP2999 #n "a caa (#" a$&& c&n #" )&)#nt&)/0i)& !# s# ca"c!"a c&)&

cmax=0.375d

amax= 21. cmax

" Smax

=' . f c

1 . bw .a max

f %

! nmax= " smax . f % (d−amax2 )

! umax=∅ ! nmax∅=0.9

Fina")#nt# s# ca"c!"a #" )&)#nt& L"ti)& #sist#nt# (#" As s!)inista(&

"s∑ ¿ . f %

2 ' . f c1

.bwd−¿

∑ ¿ . f % .¿ ! nresist = " s¿

! uresist =∅ ! nresist

V%,e+a +%!& 1

2"


31/53


V%,e+a +%!& 2

As@ s!c#sia)#nt#H s# ca"c!"an (is#an "as i,!#tas ti$& !# ti#n# #" #(i%ici& #n-&Kas (#bi(a)#nt# $&,a)a(as #n E0c#".

.3.2 Dis#& a c&tant# (# i,!#tas

Paa #" (is#& a c&tant# (# !na i,!#ta #s n#c#sai& $ati (# a",!n&s$a/)#t&s n#c#sai&s $aa #" an/"isis

Pi)#& s# (#b# ca"c!"a #" c&tant# !"ti)& 6V!8 (# "a i,!#ta a !na (istancia d (#"a caa (#" a$&& c&n a!(a (# SAP.

30


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P&st#i&)#nt# s# ca"c!"a Vcϕ $& )#(i& (# "a si,!i#nt# #c!ación

Vcϕ =0.75∗0.17 3√ f c1

bw . d

C&n Vcϕ s# $!#(# ca"c!"a #" V sre0uerido

V sre0uerido=Vu∗ Vcϕ

ϕ

S#,!i(a)#nt# s# (#b# c&)$&ba si "a i,!#ta n#c#sita (is#& si #" Vu #s

)a& !# #" V sre0uerido s# n#c#sita (is#& a c&tant#.

S# (#b# c&)$aa #" V sre0uerido c&n 0.33√ f c1

bw . d si #" V sre0uerido #s )a&

!# #st# a"& s# (#b# #(!ci #" Smin (#" a$ata(& C.11.5.4.1 a "a )ita(

Smin=d

2Smin=

d

4

Smin=600mm Smin=300mm

Si s# n#c#sita (is#& a c&tant# s# $!#(# ca"c!"a S# c&n "a si,!i#nt# #c!ación

Sre0= "v . f %t . d

V sre0uerido

P#& #st# a"& s# (#b# c&)$aa c&n C.11.5.4.1 C.11.4.+.3 (# "a NSRG19

Smin=d

2Smin=600mm(C .11.5.4.1)

Smin 4 "v . f %t

0.062√ f c1

bwSmin 4

"v . f %t

0.35bw(C .11.4 .6.3)

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V%,e+a +%!& 1

V%,e+a

+%!& 2

As@ s!c#sia)#nt#H s# ca"c!"an (is#an "as i,!#tas ti$& !# ti#n# #" #(i%ici& #n-&Kas (#bi(a)#nt# $&,a)a(as #n E0c#".

./Cara !ara la %a n& "ar,era

Paa "as i,as !# n& s&$&tan ca,as (# "as i,!#tas s# (#b#n (is#a $aa !#s&$&t#n (&s #c#s "a ca,a (# "as i,!#tas

Cara ,er+a

# $=Cara muerta viueta∗2

# $=6.55

[ KN

m

]∗2=13.1

[ KN

m

] Cara %a# L=Cara viva viueta∗2

32


34/53


# L=1.44 [ KN m ]∗2=2.88[ KN m ]

.3D%e& -e %a.5.1 Dis#& a %"#0ión

Ee!l& -%e& -e %a ee 9.

Paa #a"i?a #" (is#& a %"#0ión (# i,as #s n#c#sai& t#n# #n c!#nta "&s )is)&s$a/)#t&s !# s# c&nsi(#a&n $aa "as i,!#tas $#& -a !# t#n# #n c!#nta!# "as i,as s# a$&an s&b# "as c&"!)nas.

E" As #!#i(& $aa #" (is#& s# &bt!& (# SAP2999 sin #)ba,& "a )a&@a (##c#s #st# n& c!)$"@a c&n "a c!ant@a )@ni)a $& #sta a?ón %!# n#c#sai& ca"c!"a !n As )@ni)& $aa s!)inista #st# #n #" (is#&.

5max=0.75∗0.51∗ 21∗( f c1

f % )

5min 4

0.25√ f c1

f % 5min 4

1.4

f %

A(#)/s (# "a c!ant@a )@ni)a ta)bi:n (#b@a c&)$aas# c&n "a c!ant@a )/0i)a $& "& tant& c&n #" As )/0i)&.

" smin= 5min . bw . d=0.00333∗600mm∗540mm=1080m m2

33


35/53


si n& c!)$"# s# t&)a #" As !# (a c!ant@a )/0i)a & "a c!ant@a )@ni)a.

Fina")#nt# s# ca"c!"a c&n baas c&)#cia"#s !n As $aa s!)inista.

Es n#c#sai& #i%ica si "a i,a #s si)$"#)#nt# #%&?a(a c&)$aan(& #")&)#nt& L"ti)& ca"c!"a(& c&n SAP2999 #n "a caa (#" a$&& c&n #" )&)#nt&)/0i)& !# s# ca"c!"a c&)&

cmax=0.375d

amax= 21. cmax

" S max=' . f c

1 . bw .a max

f %

! nmax= " smax . f % (d−amax2 )

! umax=∅ ! nmax∅=0.9

Fina")#nt# s# ca"c!"a #" )&)#nt& L"ti)& #sist#nt# (#" As s!)inista(&

"s∑ ¿ . f

%

2 ' . f c1

.bwd−¿

∑ ¿ . f % .¿ ! nresist = " s¿

! uresist =∅ ! nresist

34


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V%a ee A

35


37/53


V%a a,;%l%ar 1

36


38/53


.5.2 Dis#& a c&tant#

Paa #" (is#& a c&tant# (# !na i,a #s n#c#sai& $ati (# a",!n&s $a/)#t&s

Pi)#& s# (#b# ca"c!"a #" c&tant# !"ti)& 6V!8 (# "a i,!#ta a !na (istancia d (#

"a caa (#" a$&& c&n a!(a (# SAP.

P&st#i&)#nt# s# ca"c!"a Vcϕ $& )#(i& (# "a si,!i#nt# #c!ación

Vcϕ =0.75∗0.17 3√ f c1

bw . d

C&n Vcϕ s# $!#(# ca"c!"a #" V sre0uerido

V sre0uerido=Vu∗ Vcϕ

ϕ

S#,!i(a)#nt# s# (#b# c&)$&ba si "a i,!#ta n#c#sita (is#& si #" Vu #s

)a& !# #" V sre0uerido s# n#c#sita (is#& a c&tant#.

S# (#b# c&)$aa #" V sre0uerido c&n 0.33√ f c1

bw . d si #" V sre0uerido #s )a&

!# #st# a"& s# (#b# #(!ci #" Smin (#" a$ata(& C.11.5.4.1 a "a )ita(

Smin=d

2Smin=

d

4

Smin=600mm Smin=300mm

37


39/53


Es n#c#sai& c&)$&ba !# "a s#cción (# "a i,a #s a$ta $& )#(i& (# "asi,!i#nt# c&)$aación

Vs 60.66 √ f c1

bw . d

Si #sta (#si,!a"(a( s# c!)$"# "a s#cción #s a$ta (# "& c&ntai& s# (#b# ca)bia "a s#cción.

Si s# n#c#sita (is#& a c&tant# s# $!#(# ca"c!"a S# c&n "a si,!i#nt# #c!ación

Sre0= "v . f %t . d

V sre0uerido

P#& #st# a"& s# (#b# c&)$aa c&n C.11.5.4.1H C.11.4.+.3H C.21.5.3.2 (# "aNSRG19

Smin=d

2Smin=600mm(C .11.5.4.1)

Smin 4 "v . f %t

0.062√ f c1

bwSmin 4

"v . f %t

0.35bw(C .11.4 .6.3)

Smin 4

d

4 Smin 4

6veces el diametro delas barras

lonitudinalesmas pe0ue7as Smin 4150

mm (C .21.5.3.2

)

Fina")#nt# s# (#b# #sc&,# #" )#n& (# "&s S inc"!#n(& #" #!#i(& $& an/"isis.

V%a ee 2

3!


40/53


V%a ee A

V%a a,;%l%ar 1

3"


41/53


.9D%e& -e "&l,na

.+.1 Dis#& a %"#0ión

Paa #a"i?a #" (is#& (# c&"!)nas (#bi(& a" #!#i)i#nt& a c&tant# s# t&)ó#stib&s NW4 (# (&s a)as.

Paa #a"i?a #" (is#& "&n,it!(ina" (# "as c&"!)nas #s n#c#sai& -a""a "a ca,aa0ia" !# s&$&ta "a c&"!)na 6P!8 "&s )&)#nt&s !# s# ,#n#an #n "&s #0t#)&s(# "&s n&(&s #n "a (i#cción x y .

Paa c&)$&ba si "a c&"!)na s# c&)$&ta c&)& c&"!)na & i,a c&"!)na

Pu40.1∗ " ∗f c1

Si s# c!)$"# s# c&)$&ta c&)& c&"!)na (# "& c&ntai& s# c&)$&ta c&)& i,a

c&"!)na.

S#,!i(a)#nt# s# (#b# #a"i?a #" an/"isis (# #sb#"t#? tant& #n #" #K# c&)& #n #"#K# 0H $aa #st& #s n#c#sai& -a""a "a in#cia (# "a i,a #s$#ct& a" #K# (# an/"isis.

Es n#c#sai& $aa "a in#cia (# "a i,a )!"ti$"ica"& $& !n %act& (# a,i#ta)i#nt&H#n #" cas& (# i,as c&)& "& (ic# #" C.19.19.4.1 #st# %act& (# a,i#ta)i#nt& #s (#9.35.

I,!a")#nt# !# c&n "as i,as "as c&"!)nas ta)bi:n -a !# -a""a"# "a in#cia c&n#s$#ct& a" #K# (# an/"isis )!"ti$"ica"& $& !n %act& (# a,i#ta)i#nt& (a(& #n #"a$ata(& C.19.19.4.1 !# #s (# 9..

Paa -a""a "&s %act&#s (# "&n,it!( #%#ctia X #s n#c#sai& -a""a "&s a"&#s (#

8 " % 8 9

40


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8 "=2∗( *nercia ) . " columnas3000 )

( *nercia ) . " vias5500 + *nercia ) . " vias5000 )

8 9=2∗( *nercia ) . " columnas3000 )

( *nercia ) . " vias5500 + *nercia ) . " vias5000 )

C&n #st&s (&s a"&#s s# $!#(# #nta a" /bac& (# "a %i,!a CR19.19.1 (# "a NRSG19 $aa -a""a #" a"& (# "&n,it!( #%#ctia (#" #K# !# s# #st/ ana"i?an(&.

Paa (#t#)ina si "&s #%#ct&s (# "a #sb#"t#? s&n c&nsi(#a(&s s# (#b# -a""a "a

#"ación K lu

r (&n(# #s #" a(i& (# ,i& !# s# $!#(# t&)a c&)& 9.3 #c#s "a

(i)#nsión t&ta" (# "a s#cción #n "a (i#cción #n "a c!a" s# #st/ c&nsi(#an(& "a#stabi"i(a( 6C.19.19.1.28.

lu #s "a "&n,it!( n& a$&a(a "at#a")#nt# (# !n #"#)#nt& #n c&)$#sión #s

(#ci (#b# t&)as# c&)& "a (istancia "ib# #nt# "&sas (# $is&.

C&)& s# #stab"#c# #s #" a$ata(& C.19.19.1 (# "a NSRG19 s# $#)it# i,n&a "&s#%#ct&s (# #sb#"t#? $aa #"#)#nt&s a c&)$#sión n& ai&sta(&s c&nta(#s$"a?a)i#nt&s "at#a"#s c!an(&

K lu

r 634−12( ! 1 !

2)640

D&n(# *1*2 #s $&siti& si "a c&"!)na #sta %"#cta(a #n c!at!a si)$"# n#,ati&si ti#n# c!at!a (&b"#.

Paa #" (is#& (# c&"!)nas bia0ia")#nt# #s n#c#sai& c&nsi(#a "a ca,a P!H #")&)#nt& *!0 #" )&)#nt& *!.

C&)& s# a a (is#a c&n #stib&s s# t&)a !n ∅=0.65 s# (#b# c&)$&ba si

#s c&"!)na $& )#(i& (# "a si,!i#nt# (#si,!a"(a(

41


43/53


Pu40.1∗f c1 ∗ "

Si s# c!)$"# s# c&)$&ta c&)& i,a (# "& c&ntai& s# c&)$&ta c&)& i,a

c&"!)na.S# (#b# ca"c!"a PnH *n0 *n (ii(i#n(& *!0H *! P! #n 9.+5 !# #s #" a"&

(# ∅ .

Paa -a""a "a #0c#ntici(a( #s n#c#sai& ca"c!"a !n )&)#nt& c&n "a si,!i#nt#%&)!"a

! =( ! n x+ ! n % )∗( bh )

s# ca"c!"a "a #0c#ntici(a( c&n "a %ó)!"a

e= !

Pn

s# ca"c!"a n!#a)#nt# !n a"& (# "&n,it!( #%#ctia n c&n "a si,!i#nt##c!ación

Kn= Pu

"∗f c1

s# (#b# ca"c!"a #" a"& (# Rn

Kn=¿( eb )

Paa -a""a !n a"& a$&0i)a(& (# ' #s n#c#sai& c&nsi(#a #" nL)#& (# "a

baa "&n,it!(ina" #" nL)#& (#" #stib& !# s# an a tabaKa s# a$"ica "a

si,!i#nt# #c!ación

' =(b−(2∗(r+de+db)))

b

D&n(# b #s "a bas# (# "a c&"!)naH #s #" #c!bi)i#nt& (# "a c&"!)naH ( # #s #"(i/)#t& (#" #stib&H (b #s #" (i/)#t& (# "a baa "&n,it!(ina".

42


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C&n "&s a"&#s (# f c1

( f % (' (Kn( :n s# $!#(# in,#sa a "as (ia,a)as (#

int#acción $aa ca"c!"a "a c!ant@a.

Fina")#nt# $aa ca"c!"a #" As #!#i(& $& an/"isis s# (#b# )!"ti$"ica "a c!ant@a$& #" /#a (# "a s#cción tans#sa" (# "a c&"!)na s# $!#(# $&c#(# as!)inista #" ac#& #!#i(& $& an/"isis c&n baas c&)#cia"#s.

Un $as& %!n(a)#nta" #s #" c-#!#& !# s# (#b# -ac# a"#(#(& (# ca(a #K# "&

$i)#& #s &"# a -a""a ' c&n "a %&)!"a )#nci&na(a ant#i&)#nt# -a""a

!na #0c#ntici(a( $aa ca(a !na (# "as (i#cci&n#s #n "as !# s# #a"i?ó #"an/"isis.

e %=

! u %

Pu e

x=

! u x

Pu

P&st#i&)#nt# s# a$"icae

h s# $&n# !n Rn (# #nsa& s# ca"c!"a !n n (#

#nsa&

K nensa%o= :nensa%o∗e

h

c&n n#nsa& "a c!ant@a !# -ab@a #stab"#ci(& s# ca"c!"a $& )#(i& (# "&s(ia,a)as (# int#acción $& "& tant& !n Pn #sist#nt# $aa ca(a #K# #n #" !# s# -i?&#" an/"isis.

S# c&)$!#ba c&n "a #c!ación

Po=(0.85∗f c1 ∗b∗h )+ f %∗ "s

D&n(# As #s #" ac#& !# s# #!i## $& an/"isis.

S# ca"c!"a Pi c&n "a si,!i#nt# #c!ación

P ni= 1

( 1 P n x )+( 1

P n % )−( 1

Po )

43


45/53


Fina")#nt# s# c&)$aa Pni c&n Pn -a""a(& c&n SAP si Pni #s )a& c!)$"# c&n"&s #!isit&s.

A c&ntin!ación #" (is#& ti$& (# !na (# "as c&"!)nas (#" #(i%ici&.

44


46/53


.+.2 Dis#& a c&tant#

Paa #" (is#& a c&tant# #s n#c#sai& t#n# #n c!#nta "as s#$aaci&n#s )/0i)as(a(a $& "a NSRG19 (a(as #n #" a$ata(& C..19.5.1 C..19.5.2

Smax=6db Smax=48db Smax=150mm

Smax= La menor dimensiónde lacolumna

C&n "a )#n& (istancia (# "a s#cción tans#sa" (# "a c&"!)na "a (istacia (

d=b−r−de−db

S# ca"c!"a 0.5∅Vc=0.5∗0.75∗

(0.17∗(

1+ Pu14 " )

3 √ f c1 ∗b w∗d )

c&n V! ca"c!"a(& $& (is#& s# (#t#)ina si s# n#c#sita & n& (is#& $&

c&tant#H si V u40.5 Vcϕ si #st& s# c!)$"# s# #!i## (is#& (# "& c&ntai& n&.

S# ca"c!"a #" As)in c&)& "& #stab"#c# #n #" a$ata(& C.11.4.+.3 (# "a NSRG19

" vmin

=0.062 √ f c

1 ∗bw∗s

f %t

" vmin=0.35bw S

f %t

D&n(# S c&#s$&n(# a "a )#n& (# "as S)a0.

D# "&s (&s " vmin ant#i&#s s# #sc&,# #" )/0i)& s# c&)$aa c&n #" /#a (#"

nL)#& (# a)as (# "a s#cción tans#sa"H si #" As (# "as a)as #s )a& #" As)in c!)$"#.

Fina")#nt# s# t&)a "a )#n& (# "as s#$aaci&n#s S)a0 #sta #s "a s#$aación!# a #n "a ?&na !# n& #s (# c&n%ina)i#nt&.

a (istancia & s# ca"c!"a t&)an(& #" )a& a"& #nt#

45


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Lo=1

6 Lu; libre Lo=450mm Lo=h dela columna

a s#$aación #nt# #stib&s s# t&)a c&)& "a )#n& (istancia #nt#

S=6 db S=1

4delamenor dimensión

S=100+350−hx

3

2∗(r+de

2)

¿b−¿¿

hx= Es lamenor separación entre300mm % ¿

.D%e& C%en+a"%*n4>a!a+a

Paa #" (is#& (# "as ?a$atas s# ti#n#n #n c!#nta "&s cit#i&s (# (is#&a$#n(i(&s #n c"as#.

S# -i?& !n $i)# (i)#nsi&na)i#nt& $#& n& #a $&sib"# (is#a !na ?a$ata $&

c&"!)na 6


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1. E+%a"%*n -e L&n%+,- -e >a!a+a %n+erna.

2. C&!r&)a"%*n -e l&n%+,- -e >a!a+a %n+erna.

'. E+%a"%*n -e l&n%+,- -e 5a!a+a e;+erna.

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/. C&!r&)a"%*n -e l&n%+,- -e 5a!a+a e;+erna.

!#,& (# t#n# "&s a"&#s inicia"#s (# "as "&n,it!(#s (# "as ?a$atas ais"a(asH s#(is$!s& a (i)#nsi&na "as ?a$ata c&)bina(as. Paa s! $&st#i& (is#& asi,nación (# #%!#?&.

3. Área +&+al !ara -%e& 5a!a+a "&)%na-a.

9. L&n%+,- 5a!a+a "&)%na-a "Kl",l& -el e$,er5&.

4!


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. Cal",l& -e !r&$,n-%-a- -el "%%en+& , er%$%"a"%*n.

8. Cal",l& -el a"er& -e re$,er5& !ara la )arra al+a.

. Cal",l& -el re$,er5& !ara )arra )aa.

1. Cal",l& -el re$,er5& !ara )arra +ranerale.

4"


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.8D%e& -e %a -e aarre

..1 Dis#& a %"#0ión

Paa #" (is#& (# "a i,a (# a)a#H s# t&)ó "a )a& ca,a a0ia" (# "as (&sc&"!)nas (# ca(a ta)&.

D# ac!#(& c&n #" at@c!"& A.3.+.4.2 (# "a NSRG19H #stab"#c# !# "as i,as (#%!n(ación (#b#n #sisti !na %!#?a a s#a (# tacción & (# c&)$#sión 6 8H (a(a$& "a #0$#sión

C o & =0.5< "a < Pu

C&n #sta %!#?a s# (is#ó t&(&s "&s ta)&sH c&n "a si,!i#nt# #0$#sión -a""a)&s

AstH !# #s #" /#a (#" #%!#?&.C =0.75∅ [0.85 f = c ( "− "st )+ f% < "st ]

S# &bti#n# !# n& #!i## #%!#?&H $#& "a NSRG19 #n "&s at@c!"&s C.19..1 C.19..2 (# "a NSRG19H c&nt#)$"a

"smin=0.01< "

D&n(# A, #s #" /#a b!ta (# "a i,a !# #n n!#st& cas& #s (# 999 mm2

H a

!# "as (i)#nsi&n#s (# "a i,a (# a)a# s&n (# 39039 c)H As)in99 mm2

H

%ina")#nt# s# s!)inistó 4 baas nL)#& s#is (an(& c&)& #s!"ta(& !n ac#&

s!)inista(& (# 113+ mm2

.

Paa #" (is#& a c&tant# #n "a ?&na (# c&n%ina)i#nt&H s# c&)$aó +(b11.4 c) H9.25(+ c)H 15 c) (an(& 2 a)as (# #stib&s n!)#& 3 a !na s#$aación (# +

c) #n "a ?&na (# c&n%ina)i#nt&H #n "a ?&na (# tas"a$& s# c&)$aó 9.25( + c) 19 c)H $& "& c!a" s# (#Kó !na s#$aación #n "a #s$#ctia ?&na (# +c). Paa #"#st& (# "a i,a (# a)a# "a NSRG19 #n #" at@c!"& C.15.13.4H #stab"#c# !#(#b#)&s c&"&ca "a )#n& s#$aación (#" "a(& )/s "a,& (# "a i,a (ii(ió #n (&s 399 ))H c&)& "a i,a #a (# 39039 c) s# (is$!s& !na s#$aación (# 15 c).

50


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.VIGAS DE CONTRA(ESO

..1 Dis#& a %"#0ión

Paa #" (is#& (# "as i,as (# c&nta$#s&H s# )&(#"& ca(a ta)& #n Sa$ 2999H&bt#ni#n(& (# a-@ "&s a"&#s (# c&tant# a !na (istancia (+3 c) (# "a caa (#"a$&&H c&n #st# s# (is#óH (# i,!a" %&)a c&n #" )&)#nt& )a& (#" (ia,a)a(is#a)&s "a i,a.

Paa "as i,as (# c&nta$#s& s# t&)ó !na s#cción (# +9c)9 c) t#s a)as(# #stib&s nL)#& 4 $aa #" (is#& a c&tant#.

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..2 Dis#& a c&tant#

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