Metodo Especial -y Metrado

70

k2=4 k2= 3

70

k1= 4 k1= 7

a). MATRIZ DE RIGIDEZ

10 -3K= -3 3 ton/cm M=

c). ECUACIONES DE EIGENVALORES

0.0710= 10 -3 - Wn* 0.0000

-3 3

21 - 0.923 Wn

Wn= -5.16Wn= 5.155Wn= -12.57Wn= 12.571

d). CALCULO DE FRECUENCIA NATURALWn1 = 5.155wn2 = 12.571

*ANALISIS DEL ESPECTRO (T)A1 = 0.230A2 = 0.830

e). DETERMINACION DE MODOS DE VIBRACION

((K)-Wn*(M))*(

*FRECUENCIA NATURAL Wn1= 5.155

8.113 -3 * 110= -3 1.113 11

*FRECUENCIA NATURAL Wn2= 12.571

-1.220 -3 * 120= -3 -8.220 22

= 1.00 1.002.704 -0.4070

f). DETERMINACION DE MODOS

M1= 0.7682 =M2= 0.2877

g). VECTOR DE FACTORES DE PARTICIPACION (P)=

P = 1.302 3.520 * 0.07103.476 -1.415 0.0000

P = 0.3424 0.34200.1463 0.1460

h). MATRIZ DE DESPLAZAMIENTO U= ()*(P)*(A)/(^2)

U= 1.302 3.476 * 0.3423.520 -1.415 0

U= 3.781 2.61510.221 -1.064

Uc= 4.59710.277

i). MATRIZ DE FUERZAS LATERALES Fs= K

10 -3 * 3.781Fs= -3 3 10.221

7.143 29.341Fs= 19.322 -11.038

j). FUERZA LATERAL EN CADA NUDO

Fsc= 30.19822.252

k). VECTOR CORTANTE BASAL

V= 7.143 19.322 * 129.341 -11.038 1

26.4648548521 = 26.465 18.30318.3033909251V(TRANSP)=

w2= 70 Tn

Tn/cm

w1= 70 Tn

Tn/cm

b). MATRIZ DE MASA

0.0710 0.00000.0000 0.0710 ton.s/cm

0.0000 110.071 * 21

+ 0.0050 Wn^4 = 0

*PERIODO NATURAL CORRESPONDIENTET1 = 1.219 seg.T2 = 0.500 seg.

*ACELERACION ESPECTRALT1= 225.630T2= 814.230

((K)-Wn*(M))*(1n)=0

11= 1.0021= 2.704

12= 1.0022= -0.407

*MATRIZ NORMALIZADA

1.302 3.4763.520 -1.415

()^T*(M)*(1)

0.0000 * 10.0710 1

()*(P)*(A)/(^2)

0 * 225.63 0

26.574 26.5740.146 0 814.23 158.03 158.03

* U

2.615-1.064

W3= 35

k3= 3 Tn/cm

W2= 55

k2= 3 Tn/cm

W1= 55

k1= 7 Tn/cm

a). MATRIZ DE MASA

0.056065 0 0M = 0 0.0560652396 0

0 0 0.0356779

b). MATRIZ DE RIGIDEZ

10 -3 0K= -3 6 -3 Tn/cm

0 -3 3

c). ECUACION EIGENVALORES

10 -3 00= -3 6 -3 -

0 -3 3

0.000112147 Wn^6 - 0.04143456 Wn^4

Wn= -4.41 FRECUENCIA NATURALWn= 4.41 Wn1= 4.41Wn= -11.56 Wn2= 11.56Wn= 11.56 Wn3= 14.71

Wn= -14.71Wn= 14.71

d). PERIODO NATURAL

T1= 1.42476T2= 0.54348T3= 0.42714

e). ANALISIS ESPECTRAL (POR TABLA)

A1= 55.88 cm/S convertir en unidadesA2= 91.44 cm/s chi = 0.5A3= 63.5 cm/s

F). CALCULO DE ()*PARA FRECUENCIA Wn1= 4.41

8.90964 -3 00= -3 4.909638 -3 *

0 -3 2.3061330275

11 = 121 = 2.9698831 = 3.86034

*PARA FRECUENCIA Wn2= 11.56

2.5065 -3 00= -3 -1.4935 -3 *

0 -3 -1.7685884149

12= 122= 0.835532= -1.41594


-2.13163 -30= -3 -6.131626 -3 *

-3 -4.7201258919

13= 123= -0.7105433= 0.45226

F). CALCULO DE MODOS DE VIBRACION

*MATRIZ MODAL

1 1 1= 2.970 0.836 -0.7105421

3.860 -1.4159393088 0.4522596

*MATRIZ MODAL NORMALIZADA

0.96125 2.449008 3.3028598177= 2.85479 2.046149 -2.3468210627

3.71075 -3.467646 1.4937501784

g). VECTRO CORTANTE BASAL

*PRIMER MODO v= 55.88

A1= 246.431

NIVEL Wi i Wi*i Wi*i1 55 0.961249 52.8686914262 50.8199732 55 2.854793 157.0136272565 448.241443 35 3.710751 129.8762894794 481.93859

339.7586081622 981

W^E= 117.672V= 29.5596

*SEGUNDO MODO v= 91.44

A2= 1057.14

NIVEL Wi i Wi*i Wi*i1 55 2.449008 134.695420253 329.870112 55 2.046149 112.5381995996 230.269933 35 -3.467646 -121.3676165271 420.85995

125.8660033254 981

W^E= 16.1491V= 17.4025

*TERCER MODO v= 63.5

A3= 934.085

NIVEL Wi i Wi*i Wi*i1 55 3.30286 181.6572899713 599.988562 55 -2.346821 -129.0751584505 302.91633 35 1.49375 52.281256244 78.095136

104.8633877648 981

W^E= 11.2093V= 10.6732

J). CORTANTE BASAL

(V) = 29.5596 17.40245 10.6732369614

10.67324

17.4025

29.55955624

Tn

Tn

Tn

981

Tn*s/cm

0.05606524 0 0Wn 0 0.0560652 0

0 0 0.0356779

+ 4.006116208 Wn - 63 .= 0

FRECUENCIA NATURAL

112131

122232

132333

MODO1= 1.040313MODO2= 0.408329MODO3= 0.302768

Fi4.5996628813.660443111.2994502

Fi18.623224415.5597283-16.780499

Fi18.4894971-13.1375675.32130659

w4= 5 Tn

K4= 5 Tn/cmW3= 6 Tn

K3= 7 Tn/cmW2= 8 Tn

K2= 9 Tn/cm

W1= 8 Tn

K1= 12 Tn/cm

a). MATRIZ DE MASA

0.00815494 0 0M = 0 0.00815494 0

0 0 0.006116210 0


21 -9 0 0K= -9 16 -7 0

0 -7 12 -50 0 -5 5


21 -9 0 00= -9 16 -7 0

0 -7 12 -50 0 -5 5

0.= 2.0731*10^-9 Wn^8 - 1.5507*10^-5

Wn= -13.53 FRECUENCIA NATURALWn= 13.53 Wn1= 13.53Wn= -32.61 Wn2= 32.61Wn= 32.61 Wn3= 50.23Wn= -50.23 Wn4= 60.91

Wn= 50.23Wn= -60.91Wn= 60.91

d). PERIODO NATURAL

T1= 0.4643902439T2= 0.1926770929T3= 0.1250885925T4= 0.103155814

e). ANALISIS ESPECTRAL (POR TABLA)

A1= 60.96 cm/SA2= 20.32 cm/sA3= 12.7 cm/sA4= 6.2 cm/s

F). CALCULO DE ()*PARA FRECUENCIA Wn1= 13.53

19.507148624 -9 0 00= -9 14.5071486 -7 0

0 -7 10.8803615 -50 0 -5 4.06696789

11 = 121 =2.167460958231 = 3.20623975141 =3.9425641473


12.327933945 -9 0 00= -9 7.32793394 -7 0

0 -7 5.49595046 -50 0 -5 -0.42004128

12= 122= 1.369770438332= 0.14822675642= -1.754749232


0.4246450561 -9 0 00= -9 -4.57535494 -7 0

0 -7 -3.43151621 -50 0 -5 -7.85959684

13= 123= 0.04718278433= -1.31655399843= 0.8374993788


-9.254872465 -9 0 00= -9 -14.2548725 -7 0

0 -7 -10.6911543 -50 0 -5 -13.9092953

13= 123= -1.02831916333= 0.808365502743= -0.288825244

F). CALCULO DE MODOS DE VIBRACION

*MATRIZ MODAL

1 1 1= 2.16746096 1.36977044 0.04718278

3.20623975 0.14822676 -1.3165543.94256415 -1.75474923 0.83749938


2.3028718583 5.04535229 6.68909637 6.86800323= 4.9913848446 6.91097442 0.31561019 -7.06249933

7.3835592936 0.7478562 -8.80655656 5.551856889.0792200243 -8.85332806 5.60211405 -1.98365271

g). VECTOR CORTANTE BASAL

*PRIMER MODO v= 60.96

A1= 824.7888

NIVEL Wi i Wi*i Wi*i1 8 2.30287186 18.4229749 42.42575042 8 4.99138484 39.9310788 199.3113813 6 7.38355929 44.3013558 327.1016874 5 9.07922002 45.3961001 412.161181

148.05151 981

WÊ=22.343781312V= 18.785831372

*SEGUNDO MODO v= 20.32

A2= 662.6352

NIVEL Wi i Wi*i Wi*i1 8 5.04535229 40.3628183 203.6446382 8 6.91097442 55.2877954 382.092543 6 0.7478562 4.48713722 3.35573344 5 -8.85332806 -44.2666403 391.907089

55.8711106 981

WÊ= 3.182039758V= 2.1493695733

*TERCER MODO v= 12.7

A3= 637.921

NIVEL Wi i Wi*i Wi*i1 8 6.68909637 53.5127709 357.9520822 8 0.31561019 2.52488151 0.796878333 6 -8.80655656 -52.8393394 465.3326314 5 5.60211405 28.0105703 156.918409

31.2088833 981

WÊ= 0.992858714V= 0.64563244

*CUARTO MODO v= 6.2

A3= 377.64076

NIVEL Wi i Wi*i Wi*i1 8 6.86800323 54.9440258 377.355747

2 8 -7.06249933 -56.4999946 399.0311743 6 5.55185688 33.3111413 184.9386894 5 -1.98365271 -9.91826354 19.6743903

21.8369089 981

W^E=0.4860862302V= 0.1871212777

J). CORTANTE BASAL

00 Tn*s/cm0

0.00509684

Tn/cm

0.0081549439 0 0 0- Wn 0 0.00815494 0 0

0 0 0.00611621 00 0 0 0.00509684

Wn^6 + 3.59221*10^-2 Wn^4 - 26.7125

FRECUENCIA NATURAL

11* 21

3141

12* 22

3242

13* 23

3343

13* 23

3343

1 MODO1= 0.4342404-1.02831916 MODO2= 0.1982022

0.8083655 MODO3= 0.149497-0.28882524 MODO4= 0.1456027

Fi2.337638445.066740055.621271965.76018093

Fi1.552763362.126929350.17262081-1.70294395

Fi1.107043160.05223338-1.093111580.57946748

Fi0.47081738

-0.484150540.2854444

-0.08498997

Wn^2 + 3780

m3= 5.31

k3= 5

m2= 7.92

k2= 7

m1= 7.92

k1= 10

a). MATRIZ DE MASA

0.00807339 0 0M = 0 0.00807339 0

0 0 0.00541284


17 -7 0K= -7 12 -5 Tn/cm

0 -5 5


17 -7 00= -7 12 -5 -

0 -5 5

3.52808E-007 Wn^6 - 0.0015932 Wn^4

Wn= -15.64 FRECUENCIA NATURALWn= 15.64 Wn1= 15.64Wn= -38.44 Wn2= 38.44Wn= 38.44 Wn3= 53.55

Wn= -53.55Wn= 53.55

d). PERIODO NATURAL

T1= 0.4017391304T2= 0.1634547347T3= 0.1173333333

e). ANALISIS ESPECTRAL (POR TABLA) ACELERACION ESPECTRAL

A1= 1.058 g T1=A2= 1.04 g T2=A3= 0.65 g T2=

f). DETERMINACION DE MODOS DE VIBRACION*PARA FRECUENCIA Wn1= 15.64

15.025170202 -70= -7 10.0251702 -5 *

-5 3.67596639

11= 121= 2.14645288631= 2.9037111024


5.0704810275 -7 00= -7 0.07048103 -5 *

0 -5 -2.99820022

12= 122= 0.724354432532= -1.3897893511


-6.1512862385 -7 00= -7 -11.1512862 -5 *

0 -5 -10.5218851

12= 122= -0.878755176932= 0.5598501023


1 1 1= 2.146452886 0.72435443 -0.87875518

2.9037111024 -1.38978935 0.5598501

*MATRIZ NORMALIZADA

3.3166406217 6.62783745 7.90462832= 7.1190128343 4.80090343 -6.94623305

9.6305661961 -9.2112979 4.42540697

g). VECTOR DE FACTORES DE PARTICIPACION

(P)= ()^T*(M)*(1)

3.3166406217 7.11901283 9.6305662(P)= 6.6278374472 4.80090343 -9.2112979 *

7.9046283155 -6.94623305 4.42540697

0.1363799(P)= 0.0424094148

0.0316915408

h). MATRIZ DE DESPLAZAMIENTO

U= ()*(P)*(A)/(^2)

3.3166406217 6.62783745 7.90462832U= 7.1190128343 4.80090343 -6.94623305 *

9.6305661961 -9.2112979 4.42540697

1.9192429802 0.19407505 0.05570424U= 4.1195646338 0.14057913 -0.04895039

5.5729271499 -0.26972344 0.03118602

1.9298346317Uc= 4.1222531949

5.5795376442


17 -7 0Fs= -7 12 -5 *

0 -5 5

3.7901782273 2.31522204 1.28962471Fs= 8.1354389943 1.67704135 -1.13326439

7.2668125807 -2.05151285 0.40068204

*FUERZA LATERAL EN CADA NUDO SRSS

4.6248065906Fsc= 8.3834434153

7.5614691794

j). VECTOR CORTANTE BASAL V= F^T

3.7901782273 8.13543899 7.26681258V= 2.3152220441 1.67704135 -2.05151285 *

1.2896247102 -1.13326439 0.40068204

19.192429802V= 1.9407505444 VTRANSP= 19.1924298

0.5570423591

Tn

Tn

Tn

Tn*s/cm

0.00807339 0 0Wn 0 0.00807339 0

0 0 0.00541284

+ 1.80779817 Wn - 350 .= 0

FRECUENCIA NATURAL

ACELERACION ESPECTRAL

1037.8981020.24

637.65

112131

122232

132333

*DETERMINACION DE MODOS

M1= 0.30150991M2= 0.15087878M3= 0.12650816

0.0080733945 0 0 10 0.00807339 0 * 10 0 0.00541284 1

0.1363799 0 0 1037.898 00 0.04240941 0 * 0 1020.240 0 0.03169154 0 0

4.2430795800

* U

1.9192429802 0.19407505 0.055704244.1195646338 0.14057913 -0.04895039

5.5729271499 -0.26972344 0.03118602

* 1

111

1.9407505444 0.55704236

0 244.6096 244.6096 244.60960 1477.6336 1477.6336 1477.6336

637.65 2867.6025 2867.6025 2867.6025

0 00.69045533 0

0 0.22236346

W4=

k4= 8 Tn/cm

W3=

k3= 6 Tn/cm

W2=

k2= 5 Tn/cm

W1=

k1= 4 Tn/cm

a). MATRIZ DE MASA

0.016309888 0 0 0M= 0 0.01223242 0 0

0 0 0.00815494 00 0 0 0.00611621


9 -5 0 0K= -5 11 -6 0

0 -6 14 -80 0 -8 8


9 -5 0 00= -5 11 -6 0

0 -6 14 -80 0 -8 8

2.3564 Wn^8 - 25.3014 Wn^6

Wn= -15.64 FRECUENCIA NATURALWn= 15.64 Wn1= 15.64Wn= -38.44 Wn2= 38.44Wn= 38.44 Wn3= 40Wn= -53.55 Wn4= 50.2Wn= 53.55Wn= -25.36Wn= 25.36

d). PERIODO NATURAL

T1= 0.40173913T2= 0.163454735T3= 0.15708T4= 0.125163347

e). ANALISIS ESPECTRAL (POR TABLA) ACELERACION ESPECTRAL

A1= 1.058 g T1=A2= 1.04 g T2=A3= 0.65 g T3=A4= 0.68 g T4=

f). DETERMINACION DE MODOS DE VIBRACION*PARA FRECUENCIA Wn1= 15.64

5.010444852 -5 0 00= -5 8.00783364 -6 0

0 -6 12.0052224 -80 0 -8 6.50391682

11= 121= 1.0020889731= 0.50409362841= 0.004902788


-15.10003833 -5 0 0

0= -5 -7.07502875 -6 00 -6 1.94998084 -80 0 -8 -1.03751437

12= 122= -3.02000766632= 2.72777350842= 2.929894007

*PARA FRECUENCIA Wn3= 40

-17.09582059 -5 0 00= -5 -8.57186544 -6 0

0 -6 0.9520897 -80 0 -8 -1.78593272

13= 123= -3.41916411833= 4.05143579243= 25.53185339


-32.10156983 -5 0 00= -5 -19.8261774 -6 0

0 -6 -6.55078491 -80 0 -8 -7.41308869

14= 124= -6.42031396534= 20.3817139144= -11.87429252


1 1 1 1= 1.00208897 -3.02000767 -3.41916412 -6.42031397

0.504093628 2.72777351 4.05143579 20.38171390.004902788 2.92989401 25.5318534 -11.8742925

*MATRIZ NORMALIZADA

5.710476914 2.03676084 0.4833582 0.45784007= 5.722405932 -6.15103334 -1.65268102 -2.93947696

2.878615024 5.55582226 1.95829472 9.33156522

0.027997257 5.96749337 12.3410307 -5.43652686

g). VECTOR DE FACTORES DE PARTICIPACION

(P)= ()^T*(M)*(1)

5.710476914 5.72240593 2.87861502 0.02799726(P)= 2.036760838 -6.15103334 5.55582226 5.96749337

0.483358201 -1.65268102 1.95829472 12.34103070.457840065 -2.93947696 9.33156522 -5.43652686

0.186782269(P)= 0.039783192

0.079117330.014357878

h). MATRIZ DE DESPLAZAMIENTO

U= ()*(P)*(A)/(^2)

5.710476914 2.03676084 0.4833582 0.45784007U= 5.722405932 -6.15103334 -1.65268102 -2.93947696

2.878615024 5.55582226 1.95829472 9.331565220.027997257 5.96749337 12.3410307 -5.43652686

4.525735867 0.0559468 0.01524064 0.0017401U= 4.535189995 -0.16895977 -0.05211024 -0.011172

2.281394612 0.1526102 0.06174646 0.035466250.022188723 0.16391819 0.38912169 -0.02066247

4.526107653Uc= 4.538649136

2.2876017410.423325102


9 -5 0 0Fs= -5 11 -6 0

0 -6 14 -80 0 -8 8

40.73496887 -22.6932457 0 0Fs= -22.63053826 49.9251405 -13.7256104 0

0 -27.2318948 32.0264244 -3.38660081

0 0 -18.3008139 3.38660081

*FUERZA LATERAL EN CADA NUDO SRSS

46.62961601Fsc= 56.50710839

42.175075818.6115248

j). VECTOR CORTANTE BASAL V= F^T

40.73496887 -22.6305383 0 0V= -22.69324568 49.9251405 -27.2318948 0

0 -13.7256104 32.0264244 -18.30081390 0 -18.3008139 3.38660081

18.10443061V= 0 VTRANSP= 18.1044306

0-14.91421312

6 Tn

8 Tn

12 Tn

16 tn

Tn*s/cm

Tn/cm

0.01630989 0 0 0- Wn 0 0.01223242 0 0

0 0 0.00815494 00 0 0 0.00611621

+ 12354 Wn4 - 124.354 Wn

FRECUENCIA NATURAL

ACELERACION ESPECTRAL

1037.8981020.24

637.65667.08

11* 21

3141

12

* 223242

13* 23

3343

14* 24

3444

*DETERMINACION DE MODOS

M1= 0.17511672M2= 0.49097566M3= 2.06885907M4= 2.18416883

0.01630989 0 0 0* 0 0.01223242 0 0 *

0 0 0.00815494 00 0 0 0.00611621

0.18678227 0 0 0* 0 0.03978319 0 0 *

0 0 0.07911733 00 0 0 0.01435788

4.24307958000

* U

4.52610765 0 0 0* 0 4.53864914 0 0

0 0 2.28760174 00 0 0 0.4233251

* 1

1* 1

11

0 0 -14.9142131

+ 4000 .= 0

1111

1037.898 0 0 0 244.60960 1020.24 0 0 1477.63360 0 637.65 0 16000 0 0 667.08 2520.04

0 0 00.69045533 0 0

0 0.39853125 00 0 0.26471008

244.6096 244.6096 244.60961477.6336 1477.6336 1477.6336

1600 1600 16002520.04 2520.04 2520.04

970 k/m2

75

L= m 3.5

50

L= m 3.5

6

6 m

a). DETERM. CARGA MUERTA TRIBUTARIA

Piso 1:Losa = 34.92 ton

4 muros = 4.2 ton4 columnas = 1.05 ton

peso total = w1 40.17 ton

piso 2:Losa = 34.92 ton

4 muros = 2.1 ton4 columnas = 0.525 ton

peso total = w2 37.545 ton

b). DETRMINACION DE LA RIGIDEZ DE CADA PISO

K1 = K2 = 15 ton/cm

c). MODELO DINAMICO DEL PORTICO

ESTRUCTURA

k2=

k1=

d). DETRMN. DE LA FORMA MODAL Y EL PERIODEO FUNDAMENTAL DE VIBRACION POR ITERACION

u2 = 1u1 = 0.66

Piso

2 37.545 /g 15 1 37.5451 40.170 /g 15 0.66 26.512

2 37.545 /g 15 1 37.5451 40.170 /g 15 0.63 25.307

2 37.545 /g 15 1 37.5451 40.170 /g 15 0.64 25.709

e). DETERMINACION DE LA FRECUENCIA CIRCULAR NATURAL

6.720 w/g = 1w = 12.082 rad/seg

f). DETERM. DEL PERIODO

T = 0.52 seg

g). DETERMINACION DE LAS FUERZAS LATERALES

A = 0.18 *g

h). DETERMINACION DEL FACTOR DE PARTICIPACION

NIVEL Wi 1 Wi*1 Wi*1 Fi2 37.545 1 37.545 37.545 7.9231 40.17 0.64 25.60939 16.326636 5.404

BASESUMATORIA 63.154 53.872

masa de piso m

Rigidez del piso k

Modo inicial u

Fuerza de inercia m*w*u

P = 1.172

i). DTERMINACION DE LA ACELERACION PICO t=0 seg

A = 0.2 *g

k/m2

k/m2

m

DATOS DEL PROBLEMARazon de amortiguamiento= 7 %

Desplazamiento = 0.3 cmEsfuerzo cortante= 4.5 ton

DATO ASUMIDO T1= 0.5 seg2= 11= 0.66

MODELO DINAMICO FORMA MODAL

w2= 37.545

15 Tn/cm

w1= 40.17

15 Tn/cm

d). DETRMN. DE LA FORMA MODAL Y EL PERIODEO FUNDAMENTAL DE VIBRACION POR ITERACION

w/g 37.545 w/g 2.503 w/g 6.773 w/gw/g 64.057 w/g 4.270 w/g 4.270 w/g



Vi Fi=Fuerzas laterales 7.923 Vi=cortante basal

13.327

Fuerza de inercia m*w*u

Fuerza de corte k*

Derivada del piso

Despl. Del pison

FORMA MODAL1

0.64

Modo del piso

10.63

10.64

10.64

DATOS PROPORCIONADOS DE LA PREGUNTA

0.939 3.159EIGENVECTORES: = 2.181 2.871

3.491 -3.129

^T * M *

w3

4.0 mw2

4.0 mw1

4.0 m

PROCEDIMIENTO:* EMPEZAMOS DE LA MATRIZ DE PARTICIPACION (dato matriz modal normalizada)se cumple:

P = ^T * M

*matriz de masa

55 0 0M= 0 35 0 *Tn/g

0 0 35

0.939 2.181 3.491P= 3.159 2.871 -3.129 *

3.135 -4.084 1.226

250.165P= 164.715 *1/g

72.395

a). VERIFICACION DE LOS FACTORES DE PARTICIPACION SI SON CORRECTOS O NOSe cumple:Pn*m =1

250.165 * 0.939 + 164.715

POR LO TANTO: 1.00 = 1

b). CALCULO DE DESPLAZAMIENTOS UTILIZANDO EL ESPECTRO DE ACELERACION

T1= 0.73240841 seg A1=T2= 0.32402418 seg A2=T3= 0.21562729 seg A3=

* MATRIZ DE DESPLAZAMIENTO

U = * P

0.939 3.159 3.135U = 2.181 2.871 -4.084

3.491 -3.129 1.226

0.478773731 0.830288714 0.205818579U = 1.112039943 0.754592877 -0.268122193

1.779977736 -0.822403731 0.080489179

* SRSS PPARA CADA NUDO DE DESPLAZAMIENTO

0.980288183Uc = 1.370376866

1.962433985

c). CALCULO DE LA DERIVA ENTRE CADA PISO O DESPLAZAMIENTOS ENTRE PISOS

-0.633266213 0.075695837 0.473940772A = -0.667937793 1.576996608 -0.348611373

1.779977736 -0.822403731 0.080489179

0.7945916A = 1.747738278

1.962433985

3.135 8.5788-4.084 FRECUENCIAS: w= 19.39111.226 29.1391

= Iw3= 35

k3= 3 Tn/cmw2= 35

k2= 3 Tn/cm

w1= 55

k1= 7 Tn/cm

* EMPEZAMOS DE LA MATRIZ DE PARTICIPACION (dato matriz modal normalizada)

* 1

55 0 0 10 35 0 * 10 0 35 1

a). VERIFICACION DE LOS FACTORES DE PARTICIPACION SI SON CORRECTOS O NO

* 3.159 + 72.395 * 3.135

b). CALCULO DE DESPLAZAMIENTOS UTILIZANDO EL ESPECTRO DE ACELERACION

0.15 *g0.6 *g

0.77 *g

* A

250.165 0 0 0.15* 0 164.715 0 * 0

0 0 72.395 0

c). CALCULO DE LA DERIVA ENTRE CADA PISO O DESPLAZAMIENTOS ENTRE PISOS

Tn

Tn

Tn

*1/g = 1

0 0 73.59580944 73.5958094 73.59580940.6 0 376.0147592 376.014759 376.014759

0 0.77 849.0871488 849.087149 849.087149

METRADOS:V4

w= 1.5 tn/m3 m

c2 c2V3

w= 1.5 tn/m3 m

c2 c2V2

w= 2 tn/m3 m

c1 c2V1

w= 2 tn/m4 m

c1 c1

6.5

a) C1 = 2520 b) C1 =V = 3276 C2 =M = 2275 V =W = 13000 M =

21071 kg W =

f'C = 210 KG/cm2S/C muro = 100 Kg/m2

LARGO ANCHOVIGA 1 : 0.3 0.7VIGA 2 : 0.3 0.6VIGA 3 : 0.3 0.4VIGA 4 : 0.3 0.4

COLUMNA 1 : 0.3 0.5COLUMNA 2 : 0.3 0.3

1080 c) C2 = 1296648 V = 1872

2808 M = 19501950 W = 9750

13000 14868 kg19486 kg

m= 13245

m= 14868

m= 19486

m= 21071

d) C2 = 648V = 1872M = 975W = 9750

13245 kg

2 GRADOS3 GRADOS4 GRADOS3 GRADOS 14 GRADOS 13 GRADOS 2CLASE 1METRADO

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