Sismica Analisis Estatico y Dinamico

Condensación - Rigidez Lateral Rigideces en el Eje "X"  ,1

VP1

 ,11

VP1

###  ,7

VP1

 ,"

VP1

###  ,$

###

VP1

 ,%

VP1

Condensación - Rigidez Lateral

R'O! 'E L)ER& L) ER&' ' *1=1 ,11 

,111 

,121 

,31 

k11 k21

,71 

,"1 

,1 

,21 

k31 k41 k51


R'O! 'E L)ER& L) ER&' ' *1=1 ,11 

,111 

,121 

,31 

k11 k21

,71 

,"1 

,1 

,21 

k31 k41 k51


,/3=10

*+=1  ,13

 ,113

 ,123

,33 

k13 k23

 ,73

 ,"3

 ,3

,23 

k33 k43 k53

 ,$3

 ,%3

 ,63

,13 

k63

=

k73 k83 k93 k103 k113 k123

,$=1  ,1$

 ,11$

 ,12$

Condensación - Rigidez Lateral k85 k95 k105 k115 k125

,6=1  ,16

 ,116

 ,126

,36 

k16 k26

,76 

,"6 

,6 

,26 

k36 k46 k56

 ,$6

 ,%6

 ,66

,16 

k66 k76 k86 k96 k106 k116 k126

=

Condensación - Rigidez Lateral ,

,

,

,1" 

k68

=

k78 k88 k98 k108 k118 k128

,/=1  ,1

 ,11

 ,12

,3 

k19 k29

,7 

," 

, 

,2 

k39 k49 k59

 ,$

 ,%

 ,6

,1 

k69 k79 k89 k99 k109 k119

=

Condensación - Rigidez Lateral ,

k411 k511

,$11 

,%11 

,611 

,111 

k611

=

k711 k811 k911 k1011 k1111 k1211

,12=1  ,112

 ,1112

 ,1212

,312 

k112 k212

,712 

,"12 

,12 

,212 

k312 k412 k512

 ,$12

 ,%12

 ,612

,112 

k612 k712 k812 k912

=


 ,12

,3

 ,

,2

 ,6

,1


71.%6 -3%.7" . . .


=

. -3%.7" 3%.7" . . . 21$6."7 21$6."7 21$6."7 21$6."7 21$6."7 21$6."7

Condensación - Rigidez Lateral 2%762$.$" . . . .

=

. 21$6."7 . . $631$.32 1%1126.%$ . . 2%762$.$" . . .

Condensación - Rigidez Lateral =

=

. $631$.32 2"717%%.1" $631$.32 . 2%762$.$" .

-21$6."7 . 21$6."7 . . 2%762$.$" . $631$.32 1%1126.%$ . .


=

=

. . . . 2%762$.$" . $631$.32 23%6%6.23 $631$.32

. -21$6."7 21$6."7 . . . . . 2%762$.$"

Condensación atricial - Rigidez Lateral Condensación Matricial - Rigid

k11 k21

k12 k22

k13 k23

k14 k24

k15 k25

k16 k26

k17 k27

k18 k28

k19 k29

k110 k210

k111 k211

k31

k32

k33

k34

k35

k36

k37

k38

k39

k310

k311

k41

k42

k43

k44

k45

k46

k47

k48

k49

k410

k411

k51

k52

k53

k54

k55

k56

k57

k58

k59

k510

k511

k61 k71

k62 k72

k63 k73

k64 k74

k65 k75

k66 k76

k67 k77

k68 k78

k69 k79

k610 k710

k611 k711

k81

k82

k83

k84

k85

k86

k87

k88

k89

k810

k811

k91

k92

k93

k94

k95

k96

k97

k98

k99

k910

k911

k101

k102

k103

k104

k105

k106

k107

k108

k109

k1010

k1011

k111 k121

k112 k122

k113 k123

k114 k124

k115 k125

k116 k126

k117 k127

k118 k128

k119 k129

k1110 k1210

k1111 k1211

71.56

-35.78

0.00

0.00

0.00

0.00

-2146.87

-2146.87

-2146.87

0.00

0.00

-35.78

71.56

-35.78

2146.87

2146.87

2146.87

0.00

0.00

0.00

-2146.87

-2146.87

0.00

-35.78

35.78

0.00

0.00

0.00

2146.87

2146.87

2146.87

2146.87

2146.87

0.00

2146.87

0.00

1951126.54

460314.32

0.00

257624.48

0.00

0.00

0.00

0.00

0.00

2146.87

0.00

460314.32

2871755.18

460314.32

0.00

257624.48

0.00

0.00

0.00

0.00

2146.87

0.00

0.00

460314.32

1951126.54

0.00

0.00

257624.48

0.00

0.00

-2146.87 -2146.87

0.00 0.00

2146.87 2146.87

257624.48 0.00

0.00 257624.48

0.00 0.00

1951126.54 460314.32

460314.32 2871755.18

0.00 460314.32

257624.48 0.00

0.00 257624.48

-2146.87

0.00

2146.87

0.00

0.00

257624.48

0.00

460314.32

1951126.54

0.00

0.00

0.00 0.00

-2146.87 -2146.87

2146.87 2146.87

0.00 0.00

0.00 0.00

0.00 0.00

257624.48 0.00

0.00 257624.48

0.00 0.00

1435877.59 460314.32

460314.32 2356506.23

0.00

-2146.87

2146.87

0.00

0.00

0.00

0.00

0.00

257624.48

0.00

460314.32

Página 13

Condensación atricial - Rigidez Lateral

ktt

=

kt1

=

71.56 -35.78 0.00

-35.78 71.56 -35.78

0.00 -35.78 35.78

0.00 0.00 0.00 -2146.87 -2146.87 -2146.87 0.00 0.00 0.00

2146.87 2146.87 2146.87 0.00 0.00 0.00 -2146.87 -2146.87 -2146.87

0.00 0.00 0.00 2146.87 2146.87 2146.87 2146.87 2146.87 2146.87

kt2

=

k00

=

0.00 2146.87 0.00 1951126.54 460314.32 0.00 257624.48 0.00 0.00 0.00 0.00 0.00

Página 1$


k00

-1 =

/410 5 , 2 5=

5 ,/410 5 , 2 5=

5.5E-07 -9.3E-08 2.3E-08 -8.0E-08 2.3E-08 -9.0E-09 1.6E-08 -6.4E-09 3.7E-09

-9.3E-08 3.8E-07 -9.3E-08 2.3E-08 -4.2E-08 2.3E-08 -6.4E-09 7.1E-09 -6.4E-09

2.3E-08 -9.3E-08 5.5E-07 -9.0E-09 2.3E-08 -8.0E-08 3.7E-09 -6.4E-09 1.6E-08

-8.0E-08 2.3E-08 -9.0E-09 5.6E-07 -1.0E-07 2.7E-08 -1.1E-07 3.6E-08 -1.6E-08

2.3E-08 -4.2E-08 2.3E-08 -1.0E-07 3.9E-07 -1.0E-07 3.6E-08 -5.7E-08 3.6E-08

-9.0E-09 2.3E-08 -8.0E-08 2.7E-08 -1.0E-07 5.6E-07 -1.6E-08 3.6E-08 -1.1E-07

1.6E-08 -6.4E-09 3.7E-09 -1.1E-07 3.6E-08 -1.6E-08 7.7E-07 -1.7E-07 5.6E-08

-6.4E-09 7.1E-09 -6.4E-09 3.6E-08 -5.7E-08 3.6E-08 -1.7E-07 5.0E-07 -1.7E-07

1.4E-04 9.9E-04 -1.1E-04

-8.5E-06 4.3E-04 -3.8E-06

1.4E-04 9.9E-04 -1.1E-04

-1.0E-03 5.8E-05 8.5E-04

-4.1E-04 -2.5E-05 4.4E-04

-1.0E-03 5.8E-05 8.5E-04

2.0E-04 -1.4E-03 1.2E-03

-3.3E-05 -3.7E-04 3.9E-04

5.4E+00 -2.0E-01 -4.6E+00

-2.0E-01 1.2E+01 -6.5E+00

-4.6E+00 -6.5E+00 1.1E+01

Ennces l m3i4 cndensd es5

  5=

66.18

-35.58

4.60

-35.58

59.63

-29.23

4.60

-29.23

25.12

l se3 3es P3ics 1/8.-7106.1+./ 7106.18./0 78.0 1+./ 78.0 -.+

Página 1%

Condensación atricial - Rigidez Lateral ez Lateral Eje "X"

k112 k212 k312 k412 k512 k612 k712 k812 k912 k1012 k1112 k1212

12



Matriz ensamblada de = 12

 5= ,  54 , 1 5  ,/410 5 , 2 5

0.00 -2146.87 2146.87 0.00 0.00 0.00 0.00 0.00 257624.48 0.00 460314.32 1435877.59

Página 16


0.00 2146.87 0.00

0.00 2146.87 0.00

-2146.87 0.00 2146.87

-2146.87 0.00 2146.87

-2146.87 0.00 2146.87

0.00 -2146.87 2146.87

0.00 -2146.87 2146.87

0.00 -2146.87 2146.87

460314.32 2871755.18 460314.32 0.00 257624.48 0.00 0.00 0.00 0.00

0.00 460314.32 1951126.54 0.00 0.00 257624.48 0.00 0.00 0.00

257624.48 0.00 0.00 1951126.54 460314.32 0.00 257624.48 0.00 0.00

0.00 257624.48 0.00 460314.32 2871755.18 460314.32 0.00 257624.48 0.00

0.00 0.00 257624.48 0.00 460314.32 1951126.54 0.00 0.00 257624.48

0.00 0.00 0.00 257624.48 0.00 0.00 1435877.59 460314.32 0.00

0.00 0.00 0.00 0.00 257624.48 0.00 460314.32 2356506.23 460314.32

0.00 0.00 0.00 0.00 0.00 257624.48 0.00 460314.32 1435877.59

Página 17

Condensación atricial - Rigidez Lateral 3.7E-09 -6.4E-09 1.6E-08 -1.6E-08 3.6E-08 -1.1E-07 5.6E-08 -1.7E-07 7.7E-07 2.0E-04 -1.4E-03 1.2E-03

Página 1"

alas ( 3 - 8ise9o :is!oresistente Tabla "&' #actores de Zona Zona 3 2 1

Tipo S1

Z 0.4 0.3 0.15 Tabla "() ar*metros del S+elo Descripción Roca o suelos muy rí!"os

Tp ,s0.4

S 1

S2

Suelos !#terme"!os

0.6

1.2

S3

Suelos $le%!&les

0.9

1.4

S4

'o#"!c!o#es e%ce(c!o#ales

)

)

) os alores "e ( y S (ara este caso ser# esta&lec!"os (or el es(ec!al!sta (ero e# #!## caso ser ue los es(ec!$!ca"os (ara el (er$!l t!(o S3.

CATEGORÍA *

Tabla "& . Cate/or0a de edi1icaciones DESCRICI!" E"!$!cac!o#es ese#c!al

#AC$ % 1.5

alas ( 3 - 8ise9o :is!oresistente

# me#ores

alas ( 3 - 8ise9o :is!oresistente Tabla "& 2 Sistemas Estr+ct+rales

Sistema Estr+ct+ral *ceroD Brt!cos "ct!les co# u#!o#es res!ste#tes a mome#tos. *ceroD *rr!ostres E%cF#tr!cos. *ceroD *rr!ostres e# 'ru. 'o#creto *rma"oD Brt!cos 'o#creto *rma"oD ual 'o#creto *rma"oD e muros estructurales 'o#creto *rma"oD uros "e "uct!l!"a" l!m!ta"a *l&aC!lería *rma"a o 'o#$!#a"a a"era or es$ueros a"m!s!&les

Tabla "& 3 40mites para dezplazamiento lateral de entrepiso Material redominante 'o#creto *rma"o *cero

alas ( 3 - 8ise9o :is!oresistente

Coe1iciente de Red+cción5 R ara estr+ct+ras re/+lares

Coe1iciente de Red+cción5 R ara estr+ct+ras Irre/+lares

9.5 6.5 6 8 7 6

7.125 4.875 4.5 6 5.25 4.5

4

3

3

2.25

7

5.25

,*i 6 7,i0.007 0.010

Cortante 8asal '$9

Zoni1icación$ /o#a D

)$9

.

Z=

S)

Descripción <

Tp ,S- <

:$2:

S<

'$):

%<

'$:

S+elos intermedios

Cate/or0a del Edi1icio 'ateoría D Importancia <

;$9

/

ar*metros de Sitio er$!l !(o D

.$9

:$;

A Edi1icaciones esenciales

Coe1iciente 8*sico de Red+cción de #+erzas S0smicas

*nálisis (stático - >todo atricial

N9L!! E!&9&CO 7 En l di3eccin "


'$9 Establecemos el modelo din*mico A3

!e#e D

E3  m3

<

E#to#ces la matr! "e r!!"e later 

O3  u3 A2

.

E2  m2

..

O2  u2 A1

E1  m1 O1  u1

9ucs

I&= R E

'$9 Metrado de car/as "iel :'

"iel :)


)$9 Cortante basal5 #i  ?ni ?b =

"iel 3 2 1

.$3@ Tn

>;$::

eso ,m103.41 109.63 109.63 S+matoria

Tn

Alt+ra ,m10.80 7.20 3.60

7

Fi

1116.83 789.34 394.67 2300.84

0.485 0.343 0.172 1.000

:$': Tn6cm

.$3@ Tn )$.3 Tn

:$'') Tn6cm

#i = Fi  ?b 35.89 25.38 12.73 74.00


@1 @2 @3

0./6 =

2.01

cm

2.6$

;$9 Modelo Din*mico #inal .$3@ Tn

O= P# = # =

13.59 #Ncm 11.4 ra"Nse 0.55 se

)$.3 Tn

O= P# = # =

12.63 #Ncm 10.62 ra"Nse 0.59 se

m= :$': Tn6cm .= ':.$;' Tn +=

)$2; cm .$3@ Tn

m= :$'') Tn6cm )= ':@$2. Tn +=

)$:' cm 2'$)> Tn


"


l es "eD

"iel :.


?ni 35.89 61.27 74.00


*nálisis 8iná!ico - >todo atricial 8el análisis !odal =

G  5−2   5G ,   = 1.7 M3i4 de 3igide4 1".%% -16.7% 13.7

  5=

-16.7% 17". -"7.7

13.7 -"7.7 7%.37

n'c!

2.7 M3i4 de mss

  5=D"/ ,1EEFE ,2 EFEE ,3 05

  5 =

.112  

 .112 

=

0

  .1%

n

+.7 Clc3ec
G  5−2   5= 1".%% -16.7% 13.7

-16.7% 17". -"7.7

13.7 -"7.7 7%.37

7

?2

.112  

 .112 

  .1%

AHace!os @n ca!io de 1".%% -16.7% 13.7

-16.7% 17". -"7.7

13.7 -"7.7 7%.37

1".%% -16.7%

-16.7% 17".

13.7 -"7.7



7

7

.112  

 .112 

  .1%

=

0

.112 .

. .112

. .

=

0

@=!



Página 33

*nálisis 8iná!ico - >todo atricial 13.7

-"7.7

7%.37

1".%% - /I20A .112 -16.7%

.

-16.7% 17". -

13.7"27%7"2

.

.1%

13.7

/I20A .

-"7.7

=

7%.37 - /I20A .1%

-"7.7

I2 = 

26776.67

-3$17.22

-372.71 

-1%266$."

70.001+ @+

A -.+8 @2

-167%.% 

J 2.33$ 2

"61.3$ 

7$8-.8 

-1%1.11 

-"%""%.%%

A -1-$1./2

J 2.1 2

J .$%$ 2

-.13 3

12.%

12.%

116.%6 

=0

Clc
% 3

1 = 2 = + =

?21 = ?22 = ?2+ =

5.38

% #

-485.8

% #

!

51541.#

?1 = ?2 = ? +=

122.1$ 112/.0 28+6.0$

$

11.0++.61 -+.2-

$.7 Mds de i:3cin Md 01

Para K1 =

11.%

Para K 1 =

122.1

13.6"

.

2

1".%%

-16.7%

13.7

11

rad's

.

11

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*nálisis 8iná!ico - >todo atricial -16.7%

17".

-"7.7

13.7

-"7.7

7%.37

7

.

.

13.6"

.

.

.

12."2

1"$."7

-16.7%

13.7

-16.7%

16%.22

-"7.7

13.7

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62.%%

.

21 31

1. 21 31 11 21 31

Md 02

Para K2 =

33.61

=

=

 

   1. 2." 2.7

=

12

rad's

Para K = 112.63 2 2

1".%%

-16.7%

13.7

-16.7%

17".

-"7.7

13.7

-"7.7

7%.37

7

126.%2

.

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.

126.%2

.

.

.

11".61

72.3

-16.7%

13.7

-16.7%

%2.3"

-"7.7

13.7

-"7.7

-$3.2$

.

12 22 32

.

1. 22 32

=

  

=

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*nálisis 8iná!ico - >todo atricial

12 22 32

Md 0+

Para K3 =

%3.2%

1. .%6 -."2

=

13

rad's

Para K = 2"3%.%6 2 3

1".%%

-16.7%

13.7

-16.7%

17".

-"7.7

13.7

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7%.37

7

317.%"

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.

317.%"

.

.

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27.73

-11.3

-16.7%

13.7

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13.7

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-222.36

.

13 23 33

.

1. 23 33 13 23 33

=

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=

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=

1. -1.6 .$"

M3i4 de Eigen Vec3es



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1. .%6 -."2

1. -1.6 .$"

Página 36


-.7 M3i4 de %3ec


2

=

122.1

.

.

112.63

.

.

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2"3%.%6

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6.7 M3i4 de cele3cines " , =#$" ' %&

 =2.%/' 02.%

M= N= O= C= := R= g=

0.$ 1.0.6 2.1.2 8 1

Para Para Para

&1= &2= &+=

(ntonces

C C C

= = =

2.-0 2.-0 2.-0

!1 !2 !+

= = =

0.220.220.22-

(ntonces (ntonces (ntonces (ntonces (ntonces

0.- 0.1/ 0.12

g g g

Página 37


*

22.73 . .

=

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. . 22.73

."$2 1.7%2 2.27

2.123 1.11 -1.737

.7 M3i4 de Mdl N3mli4d  , 'Q/S 〖 , ; 〖 ,  〗 2 〗 0

⧲

MO'O 01

=

/S 〖T , ; 〖T ,  〗 2 〗 0=

1.1""

MO'O 02  〗 2 〗 0= /S 〖T , ; 〖T ,

.$71

MO'O 0+ /S 〖T , ; 〖T ,  〗 2 〗 0=

.$6

8.7 M3i4 de P3iciDcin  5=T5 ;  5;G1

P

 =

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1.7%2 1.11

2.27 -1.737

.

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.

1. 1.

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*nálisis 8iná!ico - >todo atricial 2.16

-2.13

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P

=

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.16 .133 -.23

.23" -.1"2 .11

P

=

.%2 .1" ."

P

=

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A

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A

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/.7 M3i4 de 'e4Dl4miens $ 5=U5 5 '5 2 5/410

N N N

=

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2.12 1.1 -1.7$

2.2 -2.13 .7

=

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.1" -.1 .

=

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"".$7 $.63 -72.3"

3.$1 -$1.6$ 1"."6

."%

.7"

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A

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N

1.67% 2.17

=

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-.1% .7

'E!PL(MEN&O! M9XMO! RE!UL&N&E! U1 U2 U+

= = =

0.81 1.68 2.1

cm cm cm

=

1".%% -16.7% 13.7

-16.7% 17". -"7.7

13.7 -"7.7 7%.37

=

1.% 23.$" 27.772

.76 %.11 -7.62

$.$1 -$.6$ 1."1

1-.$6 2$.$2 28.86

&n &n &n

10.7M3i4 de %
Vs Vs

A

."% 1.67% 2.17

.7" .$$ -.6$

.1$ -.1% .7

%
= = =

11.7C3ne )sl 

 Página $


W

=

1.% ." $.$2

W

=

62.1+ .$/ 1.1

23.$1 %.12 -$.6

27.77 -7.6 1."

.

1. 1. 1.

P3 l n5

( ) $

&#.&0

'n

12.7Mdel 'inmic %inl )3$32 Tn O = 13.30 #Ncm P# = 53.25 ra"Nse # = 0.12 se

+=

:$': Tn6cm ':.$;' Tn )$'> cm

1.1 &n );$;) Tn

O = 14.54 #Ncm P# = 33.61 ra"Nse # = 0.19 se

m= .=

m= )=

:$'') Tn6cm ':@$2. Tn

+=

'$23 cm

.$/ &n m=

:$'') Tn6cm

Página $1

*nálisis 8iná!ico - >todo atricial '$;2 Tn O = 19.09 #Ncm P# = 11.05 ra"Nse # = 0.57 se

'=

':@$2. Tn

+=

:$3' cm

62.1+ &n

V:=

62.60 &n

Página $2


)arialeB

Página $3


0

3dBs 3dBs 3dBs

=

&1= &2= &+=

0.- 0.1/ 0.12

seg seg seg

1

Página $$


=

1

Página

%$ *nálisis 8iná!ico - >todo atricial

=

1

Página $6


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2.16 -2.13 .6%

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RaXces CYicas

Raíces "e u#a ecuac!B# c&!ca a% + &% +

@#a ecuac!B# c&!ca e#eral co# a Q 0 t!e#e la $ormaD

a -0.00131712

& 5.38

c -4857.87

" 515417.92

0131712% + 5.38422738014296% -

as raíces "e u#a ecuac!B# so# los alores "e la ar!a&le % ue sat!s$ace# la ecuac!B# (ara ue ala 0. 'lculo "e las raíces "e u#a ecuac!B# c&!ca s!e#"o #meros reales los coe$!c!e#tes a & c ". 'a"a ecuac!B# c&!ca co# coe$!c!e#tes reales t!e#e al me#os u#a soluc!B# % e#tre los #meros reales. Se (ue"e# "!st!#u!r tres casos usa#"o el "!scr!m!#a#teD T = 18a&c" - 4&" + &c - 4ac - 27a" = S! T U 0 e#to#ces la ecuac!B# t!e#e tres raíces reales "!st! #tas. S! T = 0 e#to#ces la ecuac!B# t!e#e u#a raí mlt!(le y to"as sus raíces so# reales. S! T V 0 e#to#ces la ecuac!B# t!e#e u#a raí real y "os raíces !ma!#ar!as.

ABrmula (ara las raíces s! T V 0D x 1 realW x 2 y x 3 !ma!#ar!as =

2b3 X 9abc + 27a2d =

:=

b2 X

=

M 2-4N 3 =

x ' =

-&-E:',*+R'@*N2W1N3-E:',*-R'@*N2W1N3N3)a =

3ac = 2b3 X 9abc + 27a2d 2 X 4b2 X 3ac 3 =

ABrmula (ara las raíces s! T U 0 x ' =

Seu#"a y tercera raí x ) =

-&-%1)a+R'@*&Y2-4)a)c-2)a)&)%1-3)aY2)%1Y2N2)a

X 27a2T U 0

RaXces CYicas x . =

-&-%1)a-R'@*&Y2-4)a)c-2)a)&)%1-3)aY2)%1Y2N2)a

RaXces CYicas

c% + " = 0 857.8703731045% + 515417.917310167

65517944.1229312

26.2646366355 9.7947098036 -3068.843307455 'om(ro&ac!B# "e las raíces

)3.2$:.>;:@;.''3

-3.2130628824234E-08

'))$';:'>>:''

5.66360540688038E-08

Sismica Analisis Estatico y Dinamico

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