Memoria de Calculo Estructural _ cálculos con Etabs 9

1

MEMORIA DE CÁLCULO

2

MEMORIA DE CÁLCULO

El proye!o o"pre#$e l% o#&!r'()# $e '#% e$(*(%()# $e + p(&o& ",& 1 &)!%#o 'e &er.(r, o"o lo%l "'#((p%l/

3

MEMORIA DE CÁLCULO

4

MEMORIA DE CÁLCULO

El $(&e3o e&!r'!'r%l $el proye!o &e or(e#!% % propor(o#%r %$e'%$% e&!%4(l($%$ r(5($e6 y $'!(l($%$ *re#!e % &ol((!%(o#e& pro.e#(e#!e& $e %r5%& "'er!%& .(.%& %&e#!%"(e#!o& $(*ere#(%le& y e.e#!o& &7&"(o&/ El $(&e3o &7&"(o o4e$ee % lo& Pr(#(p(o& $e l% Nor"% E0+0-2018 DISE9O SISMORESISTENTE $el Re5l%"e#!o N%(o#%l $e E$(*(%(o#e& o#*or"e % lo& '%le&: 



L% e&!r'!'r% #o $e4er7% ol%p&%r #( %'&%r $%3o& 5r%.e& % l%& per&o#%& $e4($o % "o.("(e#!o& &7&"(o& &e.ero& 'e p'e$%# o'rr(r e# el &(!(o/ L% e&!r'!'r% $e4er7% &opor!%r "o.("(e#!o& &7&"(o& "o$er%$o& 'e p'e$%# o'rr(r e# el &(!(o $'r%#!e &' .($% $e &er.((o e;per("e#!%#$o $%3o& $e#!ro $e l7"(!e& %ep!%4le&/

E&!o& pr(#(p(o& 5'%r$%# e&!re<% rel%()# o# l% *(lo&o*7% $e D(&e3o S(&"orre&(&!e#!e $e l% Nor"%:   

E.(!%r p=r$($% $e .($%& <'"%#%&/ A&e5'r%r l% o#!(#'($%$ $e lo& &er.((o& 4,&(o&/ M(#("(6%r lo& $%3o& % l% prop(e$%$/

L% ("e#!%()# o#&(&!e $e pl%!e%& $e C("e#!%()#/ L% ("e#!%()# &e o#&!(!'ye %&7 e# el pr("er $(%*r%5"% r75($o e# l% 4%&e $e l% o#&!r'()# o# l% r(5($e6 #ee&%r(% p%r% o#!rol%r lo& %&e#!%"(e#!o& $(*ere#(%le&/ Lo& !e
El &(&!e"% E&!r'!'r%l pre$o"(#%#!e e# l% $(re()# ? e Y e& el S(&!e"% $e "'ro& e&!r'!'r%le& $e e&!% "%#er% l% #or"% pr(#(p%l 'e r(5e &' $(&e3o e& l% E080 $e $(&e3o e# o#re!o %r"%$o $el RNE/ Se <%# (#l'($o ol'"#%& re!%#5'l%re& $e 2@;80 y ol'"#%& e# L $e 80;80;2@ % "%#er% 'e !e#5% 4'e# o"por!%"(e#!o e&!r'!'r%l/ A$e",& &e 'e#!% o# .(5%& per%l!%$%& $e V-2@;@0 e# el ee &e'#$%r(o V-2@;@0 e# el ee Pr(#(p%l y V(5%& Me!,l(%& %$e",& &e <%# o#&($er%$o "'ro& $e or!e $e e&pe&or e2@"/ L%& lo&%& Col%4or%#!e& &e <%# $("e#&(o#%$o o# 10" $e e&pe&or &o4re pl%#<%& $e %ero $e e&pe&or $e / To$o el o#re!o $e l%& e&!r'!'r% e& $e 2105"2/ L% o#*(5'r%()# 4'&% &%!(&*%er lo& &(5'(e#!e& re'(&(!o&:

5

MEMORIA DE CÁLCULO

  

 

Pl%#!% S("ple S("e!r7% e# $(&!r(4'()# $e "%&%& y $(&po&(()# $e "'ro&/ Re5'l%r($%$ e# pl%#!% y ele.%()# &(# %"4(o& 4r'&o& $e r(5($e6 "%&% o $(&o#!(#'($%$e& e# l% !r%#&"(&()# $e l%& *'er6%& $e 5r%.e$%$ y
E.%l'%()# $e l% o#*(5'r%()#: Irre5'l%r($%$ $e r(5($e6-P(&o Bl%#$o/ No pre&e#!%  Irre5'l%r($%$ $e M%&%/ No pre&e#!%  Irre5'l%r($%$ eo"=!r(% Ver!(%l / No pre&e#!%  D(&o#!(#'($%$ e# el &(&!e"% re&(&!e#!e/ No pre&e#!%  Irre5'l%r($%$ Tor&(o#%l/ No pre&e#!% E&'(#%& e#!r%#!e&/ No pre&e#!%  D(&o#!(#'($%$ e# el $(%*r%5"%/ No pre&e#!%  L% e&!r'!'r% &e l%&(*(% o"o: L% e&!r'!'r% &e l%&(*(% o"o:

1.00

1.00

1.00

1.00

Se e"ple) el pro5r%"% $e %#,l(&(& e&!r'!'r%l E!%4& F/G/H 'e e"ple% el "=!o$o "%!r((%l $e r(5($e6 y $e ele"e#!o& *(#(!o&/ Se "o$el) l% 5eo"e!r7% $e l% e&!r'!'r% y l%& %r5%& %!'%#!e&/

A o#!(#'%()# &e $e!%ll%# l%& %r5%& o#&($er%$% e# el %#,l(&(& por 5r%.e$%$/ Co#re!o 2H00 5"+ P(&o %%4%$o 1005"2 SC &o4re !e
6

MEMORIA DE CÁLCULO

El "o$elo e"ple%$o p%r% .(5%& y ol'"#%& o#&(&!() e# 4%rr%& $e ee re!o 'e (#l'ye# $e*or"%(o#e& por *le;()# %r5% %;(%l *'er6% or!%#!e y !or&()#/ E&!e "o$elo o#&($er% el e*e!o !r($("e#&(o#%l $el %por!e $e r(5($e6 $e %$% ele"e#!o e&!r'!'r%l/ P%r% "o$el%r lo& "'ro& $e or!e &e e"ple%ro# ele"e#!o& !(po S
7

MEMORIA DE CÁLCULO

L%& "%&%& pro.e#(e#!e& $e l%& lo&%& p(&o !er"(#%$o y $e l% &o4re%r5% &e o#e#!r%# % #(.el $el e#!ro $e "%&%& $e %$% lo&% y l%& "%&%& pro.e#(e#!e& $el pe&o prop(o $e l%& .(5%& y ol'"#%& &e o#&($er%# $(&!r(4'($%& e# !o$% &' lo#5(!'$/ L'e5o el pro5r%"% lle.% l% "%&% $e lo& ele"e#!o& e&!r'!'r%le& <%(% lo& #'$o& e;!re"o&/ E# el ,l'lo l% "%&% $e l% e&!r'!'r% &e o#&($er) el 100 $e l% %r5% "'er!% ",& el @0 $e l% %r5% .(.% C%p(!'lo H/+ NTE-E0+0-2018/

MASA SÍSMICA 100%CM+50%CV

Se re%l(6) '# %#,l(&(& &7&"(o D(#,"(o por S'perpo&(()# Mo$%l E&pe!r%l/ Lo& p%r,"e!ro& e"ple%$o& p%r% el ,l'lo $el E&pe!ro $e re&p'e&!% *'ero#: Q0/+@ Qo#% + U1/@0 C%!e5or7% A S1/20 Se5# E/M/S TP1/0 TL1/8 Ro;8 Roy8 I%;1Ip;1 RI%IpRo1188 I%y1Ipy1 RI%IpRo1188 P%r% l% &'perpo&(()# $e lo& "o$o& &e e"ple) l% *)r"'l% $e l% o"4(#%()# '%$r,!(% o"ple!% o#!e"pl%#$o '# @ $e %"or!(5'%"(e#!o r7!(o/

8

MEMORIA DE CÁLCULO

S+ Q+ A 0/+@ 1/00

1/80

1/20 1/@0 8 8 0.35*1.50*1.20*9.81/6=1.03 0.35*1.50*1.20*9.81/6=1.03

T (s)

C

0

2.500

 

0.1

2.500

0.2

2.500

0.3

 

2.500

0.4

2.500

0.5

2.500

0.6 0.7

 

2.500

 

2.500

0.8

2.500

0.9

2.500

9

MEMORIA DE CÁLCULO 1

 

2.500

1.1

2.273

1.2

2.083

1.3 1.4

 

1.923

 

1.786

1.5

1.667

1.6

1.563

1.7

 

1.384

1.8

1.235

1.9

1.108

2   2.1  

1.000 0.907

2.2

0.826

2.3

0.756

2.4

 

0.694

2.5

0.640

2.6

0.592

2.7 2.8

 

0.549

 

0.510

2.9

0.476

3

0.444

3.1

 

0.416

3.2

0.391

3.3

0.367

3.4 3.5

 

0.346

 

0.327

3.6

0.309

3.7

0.292

3.8

 

0.277

3.9

0.263

4

0.250

4.1

 

0.238

10

MEMORIA DE CÁLCULO

ESSPECTRO DE PSEUDOACELERACIONES NORMA E030-2016 3.000

2.500

2.000

      C

1.500

1.000

0.500

0.000 0

1

2

3

4

5

6

T

ESPECTRO E030- 2016

Tp=   TL=   Z=   U=   S=   Cxx=   Cyy   = Rx=   Ry=  

1.000 1.600 0.350 1.500 1.200 2.500 2.500

PESO Tx=

0.093708 Vxx=(Z*U*C*S)/Rx

   

0.31317

Ty= Vyy=(Z*U*C*S)/Ry 6.000 CX/RX>0!"#   0.41666667 CUMPLE 6.000 C$/R$>0!"#   0.41666667 CUMPLE

0.2625 1137.66

CORTANTE CORTANTE ESTATICA DINAMICA

FACTOR

298.64

130.13   1.84

298.64

148.43   1.61

0.262 5

1137.66

11

MEMORIA DE CÁLCULO

M%&' 1

P'%&

UX

U$

RZ

S+R$

S+RZ

12.6495 7.16E+01

3.885

12.6495

0.31317

2.4119

41.0639

2 0.150531

14.5003

1.0229

14.8714

76.8921

29.0776

27.5208

3 0.093708

3.0948

2.8018

0.172

78.4162

33.7608

27.6928

4 0.088872

7.3826

26.3571

0.0022

92.7511

46.3626

27.695

5 0.061401

34.915

0.2806

1.2469

92.785

76.8142

28.9419

6 0.052766

13.573

6.156

51.6216 9.91E+01

99.3217

80.5635

7 0.034343

0.0877

10.1626

0.5428

99.6708

99.3388

81.1063

8

0.03246

0.5304

0.0106

0.0012

99.6713

99.3392

81.1075

9 0.032401

0.0077

0.019

0.0024 9.97E+01

99.3573

81.1099

10 0.027145

0.2244

0.001

0.9684

99.6733

99.3627

82.0783

11 0.022915

11.191

0.7642

0.8135 9.97E+01

99.6438

82.8918

12 0.022592

0.0679

6.1397

1.2792

99.6548

84.171

P

VX

S,%y

L%-&

L%.

T!

SDXX

T%p

0

T!

SDXX

%%+

0

T!

SD$$

T%p

0

T!

S+RX

SD$$

%%+

0

129.65 130.13 65.22 65.2

99.8963

V$

T

  1865.36 5   1867.18 60.69 4   1940.65 148.1 5   1942.18 148.43 9 60.54

MX

M$

238.653

452.562

455.219

1008.078

649.301

324.857

1268.89   4

614.792

P%r% %$% '#% $e l%& $(re(o#e& o#&($er%$%& e# el %#,l(&(& l% *'er6% or!%#!e e# el pr("er e#!rep(&o $el e$(*((o #o po$r, &er "e#or 'e el 0 $el .%lor %l'l%$o &e5# el #'"er%l H/@ p%r% e&!r'!'r%& re5'l%re& #( "e#or 'e el F0  p%r% e&!r'!'r%& (rre5'l%re&/ S( *'er% #ee&%r(o (#re"e#!%r el or!%#!e p%r% '"pl(r lo& "7#("o& &e3%l%$o& &e $e4er,# e&%l%r propor(o#%l"e#!e !o$o& lo& o!ro& re&'l!%$o& o4!e#($o& e;ep!o lo& $e&pl%6%"(e#!o&/

298.64

130.13

298.64

148.43

12

MEMORIA DE CÁLCULO

T+ T2 T1 SOTANO

M%; Dr(*! ? M%; Dr(*! ? M%; Dr(*! ? M%; Dr(*! ?

T+ T2 T1 SOTANO

DERIVA?? DERIVA?? DERIVA?? DERIVA??

M%; Dr(*! Y M%; Dr(*! Y M%; Dr(*! Y M%; Dr(*! Y

DERIVAYY DERIVAYY DERIVAYY DERIVAYY

8G 8 @G @G

2+ 28/@ G/@@ G/@@

21 21 21 @+

0 0 0 0

0 0 0 0

1H/1 11/1 G/2@ 2/GH

CUMPLE111 CUMPLE111 CUMPLE111 CUMPLE111

@/@ 1H/1 @/@ 11/1 @/@ G/2@ 12/@+ 2/GH

Se o#&($er%# l%& o"4(#%(o#e& e;(5($%& por l% Nor"% E080 C1: 1/HCMX1/GCV C2: 1/2@ CMXCVX-SIS?? C+: 1/2@ CMXCVX-SISYY CH: 0/F0 CMX-SIS?? C@: 0/F0 CMX-SISYY P%r% el $(&e3o $e .(5%& &e !r%6%ro# l%& e#.ol.e#!e& $e *'er6%&/ P%r% el $(&e3o $e .(5%& y ol'"#%& el pro5r%"% &(5'e lo& l(#e%"(e#!o& $el ACI-FF 'y%& *or"'l%& y *%!ore& $e %r5% e'(.%le# % #'e&!r% #or"% E080/ P%r% el !r%6o $e lo& pl%#o& &e .er(*(% 'e l%& '%#!7%& $e $(&e3o &e%# "%yore& % l% "7#("% y "e#ore& % l% ",;("% e&!(p'l%$%& e# l% Nor"% E080/

13

MEMORIA DE CÁLCULO

Del %#,l(&(& e&!r'!'r%l !e#e"o&:

Se proe$er, o# el $(&e3o $el p)r!(o $el ee 2/ L% .(5% $e e&!e p)r!(o e&: VS-2@?@0 P%r% ello &ele(o#%"o& lo& "o"e#!o& ",& r7!(o& $e l%& .(5%& p%r% el $(&e3o por *le;()#/

14

MEMORIA DE CÁLCULO

w 1= 0.8475 −

 ρ 1=

√

0.7182 −

  1.695∗ Mu

φ∗f ´ c ∗b∗d

w∗f ´ c = 0.00984 fy

 As 1 = ρ 1∗b∗d =10.34 cm 2

2

=0.1969

15

MEMORIA DE CÁLCULO

Lo& or!%#!e& e# l% $ere<% y e# l% (6'(er$% re&pe!(.%"e#!e "e$($o& % l% $(&!%#(% $Z $el %poyo &o# lo& &(5'(e#!e&: V'$1+/+F !o# (6'(er$% V'$ 12/F+ !o# $ere<%

16

MEMORIA DE CÁLCULO

Co"o po$e"o& %pre(%r lo& or!%#!e& %!'%#!e& e# l% .(5% #o &'per% el or!%#!e re&(&!e#!e prop'e&!o "7#("o &e5# el $e l% #or"% Arre5lo:

Co#l'ye#$o 'e el e&!r(4%e prop'e&!o e& el orre!o/

17

MEMORIA DE CÁLCULO

DIARAMA DE ITERACCIN M++

2F1/H@H 2F1/H@H 28H/81@ 22@/1@+ 1H/H@ 1H+/082 108/G@+ G/1+H1 @G/0G@ ++/@F0@ 1@/F11@ -/0H2 -+H/HH+ -8+/222F -F0/G1F

0/21H+ 11/118 1G/+2FF 22/081G 2@/H0G+ 2G/+F2 2/+2GF 2F/0022 2G/@+8 2@/FH28 28/GFFG 2+/FH0F 1G/@HFH /G8F -0/2GG

2F1/H@H 2F1/H@H 2F1/H@H 2F1/H@H 2GF/F@+ 2@F/G@ 2+G/+H1 212/211 1@/F+ 1HG/@+ 110/1+2 8G/+HG@ ++/12G1 -11/@+88 -F0/G1F

DIARAMA DE ITERACCIN M22

0/21H+ -/2++ -12/FG2 -1G/1H+ -20/@@H -2H/00FF -28/HG+ -2F/H+82 -+0/18+ -+0/21G1 -2/+22 -2@/10G -21/0F+ -18/+H -0/2GG

MEMORIA DE CÁLCULO

18

2F1/H@+F 2F1/H@+F 28H/H28 22@/HG1H 1H/8+ 1H+/@F2H 10G/128 G/8F+G @8/GF2+ ++/22F 1@/HG+ -/H211 -+2/81G1 -@F/88+ -F0/G1F

L%-& S,-4%5 C-2'/C%+3% D'-& 0 L7' 0 SISXX M-x 0 SIS$$ M-x 0

   

SISXX

SIS$$

0/+2 11/1FGG 1G/2281 21/F+HG 2@/2@ 2G/21+ 2/11GF 2/GH1H 2G/HG+ 2@/F@@1 28/0+ 2H/2+11 1/1HF2 F/211 -0/HH0H

2F1/H@+F 2F1/H@+F 2F1/H@+F 2F1/H@+F 20/F8F2 281/12F@ 2+F/0F8 21H/@2@2 1F/GHH 1@1/08H8 112/8@1 8F/H121 +2/1+G@ -1@/2G -F0/G1F

0/+2 -/1+H -12/G@HG -18/FGH8 -20/8G1 -2+/2@2 -28/88H2 -2F/2@2 -2F/FG -+0/0G22 -2/++01 -2@/1228 -20/+8 -1@/F++G -0/HH0H

P

V"

V6

T

M"

M6

-20.06 -9.21 15.09 25.93

0.65 0.68 2.45 2.89

0.37 0.39 4.87 5.62

0.041 0.043 0.388 0.395

0.572 0.576 6.398 5.385

0.776 0.839 3.585 6.289

COMOS !8CM9!:CV !"#*(CM9CV)9SISXX !"#*(CM9CV)
P

M"

M6

86:8! 1.78 2.5127 #!;::# 7.833 5.60375 "!8:# -4.963 -1.56625 66!88   6.9128 4.2834 ";8   -5.8832 -2.8866 62.5175 10.6575 43.984 -7.876

6.82 8.30775 -3.95 -4.27025 5.8998 6.9874 -4.8702 -5.5906

SISMO ??-M++

19

MEMORIA DE CÁLCULO

COMBOS

M33-0°

M33-180°

350 300 250 200 150

   &     %    $    "    T    #    "    !    

100 50 -40

-30

-20

0

-10

0

10

20

30

40

-50 -100 -150 !"# T"$&

SISMO ??-M22 COMBOS

M22-90°

M22-270°

350 300 250 200 150

   &     %    $    "

   T    #    "    !    

100 50

-40

-30

-20

-10

0

0

-50 -100 -150 !"# T"$&

10

20

30

40

20

MEMORIA DE CÁLCULO

SISMO YY-M++ COMBOS

M33-0°

M33-180°

350 300 250 200 150

   &     %    $    "    T    #    "    !    

100 50 -40

-30

-20

-10

0

0

10

20

30

40

-50 -100 -150 !"# T"$&

SISMO YY-M22 COMBOS

M22-90°

M22-270°

350 300 250 200 150

   &     %    $    "    T    #    "    !    

100 50 -40

-30

-20

-10

0

0

10

20

30

40

-50 -100 -150 !"# T"$&

Se "'e&!r% lo& re&pe!(.o& $(%5r%"%& $e (#!er%()# $e l% ol'"#% y &e p'e$e %pre(%r 'e l%& o"4(#%(o#e& P-M %e# $e#!ro $el $(%5r%"% por lo 'e &e o#&($er% 'e el $(&e3o e& orre!o/

21

MEMORIA DE CÁLCULO

DIARAMA DE ITERACCIN M++

1 2 + H @ 8 G  F 10 11 12 1+ 1H 1@

F/HGF@ 1H@F 8++/+H@F 11G 1F/FF2+ F@@/HF@ GF/G212 88/0@ F+2/+1G G8F/20 F1/121 88+/GF21 102/F+2@ @HH/H281 10G/H2@ H08/21G 10G2/1+8+ +0G/181H 1028/082 2+2/@021 F8F/08@ 1@F/@0H1 100+/H1+ FH/G+2 F+/+0GG -1/@GF+ 8F8/10G8 -1G/2F12 -12/G2F -@8F/81H

F/HGF@ -H21/+0G -@1/012F -88/1@0F -G@/28@ -0/10@F -FGH/++8 -10G2 -111G -11+1 -1128 -1101 -10H1 -G2/@101 -12/G2F

DIARAMA DE ITERACCIN M22

1H@F 1H@F 1H@F 1H01 1+2+ 12+F 11HG 10H@ F82/G80@ /H+ 12/F2@ G+H/G28 8+H/88 +28/@@2 -@8F/81H

22

MEMORIA DE CÁLCULO

1 2 + H @ 8 G  F 10 11 12 1+ 1H 1@

H+/+G1 2@@/H@F +@0/F82+ +G0/+0@F +0/F1+ +8/21+8 +F0/02@2 +F2/+@ H20/F1 H+/+001 +H/@H@8 +1H/+G 21@/+@0F 122/@GH -@/2+F

1H@F 118@ GF1/8@+ 88F/121 @+F/@1FF H2H/11 +0F/G8+H 1G+/G+2H G8/+G -22/00+@ -10+/2H8 -1F@/H101 -+1+/GF+@ -H0/@882 -@8F/81H

Bo!!o" Bo!!o" Bo!!o" Bo!!o"

+10/1G@ 2@/FF 2@+/@1 18/2F@ 1@+/1@ +G2/0 18G/H2 2G2/+@ 8G/G2@

H+/+G1 1H@F -GF/F11F 1H@F -1++/FGF 1H@F -1@/118 1H@F -2++/2FG 1H@F -20/FF1 1H@ -+2/1G 1++ -+G/@08 12F -H11/H+H 121 -H++/H 11+F -HH0/18 10H -H+@/FFF F0F/802@ -H18/F@G G2H/F+GG -+00/08 282/G2+8 -@/2+F -@8F/81H

-1/F@ -28/@ 18/2H 102/++

-@/H8GF 10/1F8@ -11G/8@1@ 110/0+F@ -11@/0@ 2+/2G0@ -2HG/G2@@ 2H0/11+@ -2H@/2@

SISMO ??-M++

-1 -0/1H G0/+H 18/F8

-H/2 -0/F2 1/GG @0/8@

-10/+28 @+1/@H+G@ -@HF/HH82@ @+H/F@1F -@H8/0+1 20G/H+G@ -22@/+82@ 210/F1F -221/FG1

-2/+F+ -+/20@ -8/1@F -0/H@+ -0/@GG -1/002 H0/022 112/F2H @H0/HF@ H1/1H 2H2/FF 218/H+@

23

MEMORIA DE CÁLCULO

COMBOS

M33-0°

M33-180°

2000

1500

1000    &     %    $    "    T    #    "    !    

500

-1500

-1000

0

-500

0

500

1000

1500

-500

-1000 !"# T"$&

SISMO ??-M22 COMBOS

M22-90°

M22-270°

2000

1500

1000    &     %    $    "    T    #    "    !    

500

-500

-400

-300

-200

-100

0

0

-500

-1000 !"# T"$&

100

200

300

400

500

24

MEMORIA DE CÁLCULO

SISMO YY-M++ COMBOS

M33-0°

M33-180°

2000

1500

1000    &     %    $    "    T    #    "    !    

500

-1500

-1000

0

-500

0

500

1000

1500

-500

-1000 !"# T"$&

SISMO YY-M22 COMBOS

M22-90°

M22-270°

2000

1500

1000    &     %    $    "    T    #    "    !    

500

-500

-400

-300

-200

-100

0

0

100

200

300

400

500

-500

-1000 !"# T"$&

Se "'e&!r% lo& re&pe!(.o& $(%5r%"%& $e (#!er%()# $e l% pl%% y &e p'e$e %pre(%r 'e l%& o"4(#%(o#e& P-M %e# $e#!ro $el $(%5r%"% por lo 'e &e o#&($er% 'e el $(&e3o e& orre!o/ Ver(*(%()# $e E&*'er6o& e# el !erre#o

25

MEMORIA DE CÁLCULO

P%r% e&!% p%r!e &e <% !o"%$o el $(&e3o $e l% ("e#!%()# por "e$(o $e Pl%!e%& $e C("e#!%()#

 C%r5% %;(%l &(# %"pl(*(%r p%r% %r5% "'er!% y .(.% re&pe!(.%"e#!e/  Mo"e#!o& %lre$e$or $l ee ;Z e yZ $e4($o % %r5% "'er!% y .(.% re&pe!(.%"e#!e/  C%r5% A;(%l "o"e#!o %lre$e$or $el ee ;Z e yZ y Mo"e#!o %lre$e$or $el ee ;Z e yZ Pro$'($o por el S(&"o e# &e#!($o ;Z S(&;; y e# &e#!($o yZ S(&yy/

26

MEMORIA DE CÁLCULO

1/ 2/ +/ H/ 5.

Nor"% T=#(% $e E$(*(%()# E/020 Nor"% T=#(% $e E$(*(%()# E/0+0-2018 D(&e3o S(&"orre&(&!e#!e Nor"% T=#(% $e E$(*(%()# E/0@0 S'elo& y C("e#!%(o#e& Nor"% T=#(% $e E$(*(%()# E/080 Co#re!o Ar"%$o Nor"% T=#(% $e E$(*(%()# E/0G0 Al4%3(ler7%