70 w2= 70 Tn

k2=4 k2= 3 Tn/cm

70 w1= 70 Tn

k1= 4 k1= 7 Tn/cm

a). MATRIZ DE RIGIDEZ b). MATRIZ DE MASA

10 -3 0.0710 0.0000K= -3 3 ton/cm M= 0.0000 0.0710 ton.s²/cm

c). ECUACIONES DE EIGENVALORES

0= 10 -3 - Wn² 0.071 0.0000 ф11-3 3 0.0000 0.071 * ф21

0.005041 0.923 w2 21

d). CALCULO DE FRECUENCIA NATURAL *PERIODO NATURAL CORRESPONDIENTEWn1 = 5.150 5.160 T1 = 1.220 seg.wn2 = 12.570 12.509 T2 = 0.500 seg.

*ANALISIS DEL ESPECTRO (T) *ACELERACION ESPECTRAL - CON RESPECTO A TA1 = 0.230 * gravedad T1= 225.630A2 = 0.830 * gravedad T2= 814.230

e). DETERMINACION DE MODOS DE VIBRACION*FRECUENCIA NATURAL Wn1= 5.15

8.117 -3 * ф11 ф11= 1.000= -3 1.117 ф21 ф21= 2.706

*FRECUENCIA NATURAL Wn2= 12.57

-1.218 -3 * ф12 ф12= 1.000= -3 -8.218 ф22 ф22= -0.406

MATRIZ MODAL

ф= 1.00 1.002.706 -0.4060

f). DETERMINACION DE MODOS *MATRIZ NORMALIZADA

M1= 0.7687 ф= 1.301 3.477M2= 0.2876 3.520 -1.412

((K)-Wn²*(M))*(ф1n)=0

w4 ±

g). VECTOR DE FACTORES DE PARTICIPACION (P)= (ф)^T*(M)*(1)

P = 1.301 3.520 * 0.0710 0.0000 * 13.477 -1.412 0.0000 0.0710 1

P = 0.3423 0.34200.1466 0.1470

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

U= 1.301 3.477 * 0.342 0 * 225.63 0÷3.520 -1.412 0 0.147 0 814.23

U= 3.785 2.63410.241 -1.070

DESPLAMIENTO MAXIMO -- SRSS

Uc= 4.61110.297

i). MATRIZ DE FUERZAS LATERALES [Fs] = [K] * [u]

10 -3 * 3.785 2.634Fs= -3 3 10.241 -1.070

7.128 29.548Fs= 19.368 -11.111

FUERZA LATERAL EN CADA NUDO - SRSS

Fsc= 30.395 SEGUNDO NIVEL

22.328 PRIMER NIVEL

J). VECTOR CORTANTE BASAL [v] = ([F])^T * 1])^T^T

V = 7.128 19.368 * 129.548 -11.111 1

26.496V = 18.437

V = 26.496 18.437

K) VB

Vb= 32.279420456 Ton

.

26.523 26.523158.005 158.005

W3= 47.88 Tn6

k3= 5

W2= 67.104 Tn

k2= 6

W1= 107.748 Tn

k1= 11

a). MATRIZ DE MASA

0.10983 0 0M = 0 0.06840 0 Tn*s²/cm

0 0 0.04881

b). MATRIZ DE RIGIDEZ

17 -6 0K= -6 11 -5 Tn/cm

0 -5 5

c). ECUACION EIGENVALORES

17 -6 00= -6 11 -5 - Wn²

0 -5 5

0.0003667 Wn^6 - 0.1533 Wn^4 +

Wn= -15.64 FRECUENCIA NATURALWn= 15.64 Wn1= 5.15Wn= -38.44 Wn2= 12.52Wn= 38.44 Wn3= 16.76

Wn= -53.55Wn= 53.55

d). PERIODO NATURAL

T1= 1.2200T2= 0.5019T3= 0.3749

e). ANALISIS ESPECTRAL (POR TABLA) ACELERACION ESPECTRAL

A1= 0.23 g T1= 225.63A2= 0.83 T2= 814.23A3= 0.25 g T2= 245.25

f). DETERMINACION DE MODOS DE VIBRACION*PARA FRECUENCIA Wn1= 5.15

14.0869 -6 0 ф110= -6 9.1858 -5 * ф21

0 -5 3.7055 ф31

ф11= 1ф21= 2.348ф31= 3.168

*PARA FRECUENCIA Wn2= 12.52

-0.21665861284 -6 0 ф120= -6 0.2776974092 -5 * ф22

0 -5 -2.650569982 ф32

ф12= 1ф22= -0.03610976881ф32= -1.20200551785

*PARA FRECUENCIA Wn3= 16.76

-13.8523492404 -6 0 ф130= -6 -8.2144266569 -5 * ф23

0 -5 -8.709864514 ф33

ф12= 1ф22= -2.309ф32= 2.593

*MATRIZ MODAL NORMALIZADA *DETERMINACION DE MODOS

1 1 1 M1=ф= 2.348 -0.036 -2.309 M2=

3.168 -1.202 2.593 M3=

*MATRIZ NORMALIZADA

0.742 2.445 1.253ф= 1.742 -0.088 -2.893

2.35 -2.939 3.25

g). VECTOR DE FACTORES DE PARTICIPACION

(P)= (ф)^T*(M)*(1)

0.742 1.742 2.35 0.1098348624(P)= 2.445 -0.088 -2.939 * 0

1.253 -2.893 3.25 0

0.315353908257(P)= 0.119081944954

0.098355119266

h). MATRIZ DE DESPLAZAMIENTO

U= (ф)*(P)*(A)/(Ω^2)

0.742 2.445 1.253 0.3153539083

U= 1.742 -0.088 -2.893 * 02.35 -2.939 3.25 0

1.99 1.51 0.11U= 4.67 -0.05 -0.25

6.30 -1.82 0.28

DESPLAMIENTO MAXIMO -- SRSS

2.502277504656Uc= 4.680269887693

6.567281289547

i). MATRIZ DE FUERZAS LATERALES Fs= K *

17 -6 0 1.9906023309Fs= -6 11 -5 * 4.6733547984

0 -5 5 6.3044682987

5.800 26.037 3.320Fs= 7.941 -0.583 -4.774

8.156 -8.818 2.638

*FUERZA LATERAL EN CADA NUDO SRSS

26.88118025399Fsc= 9.283742204594

12.29718243974

j). VECTOR CORTANTE BASAL V= F^T *

5.800110834795 7.9409473039 8.155567501 1V= 26.03719769927 -0.5833054767 -8.817624147 * 1

3.319774408137 -4.7737804683 2.63759722 1

21.89662563996V= 16.63626807597 VTRANSP= 21.8966256 16.636268076

1.183591160334

k) vb 27.52505255121

l) deriva de cada piso

A= -2.68275246753 1.5668216039 0.356030541-1.63111350026 1.7635248293 -0.5275194446.30446829869 -1.8179584263 0.279088099

3.127115042137AC= 2.459436487948

6.567281289547

0.10983486 0 00 0.06840367 00 0 0.04880734

16.479 Wn² - 330 .= 0

#NAME?

cm/s^2cm/s^2cm/s^2

*DETERMINACION DE MODOS

1.3480.4090.798

0 0 10.06840367 0 * 1

0 0.04880734 1

0 0 225.63 0 0 26.5225

0.11908194 0 * 0 814.23 0 ÷ 156.75040 0.09835512 0 0 245.25 280.8976

8.5071166 0 00 5.1944365054 00 0 0.87309397

U

1.51238801 0.1075992-0.0544336 -0.24843134

-1.81795843 0.2790881

1

1.18359116

26.5225 26.5225

156.7504 156.7504280.8976 280.8976

W4= 6 Tn

k4= 8 Tn/cm

W3= 8 Tn

k3= 6 Tn/cm

W2= 12 Tn

k2= 5 Tn/cm

W1= 16 tn

k1= 4 Tn/cm

a). MATRIZ DE MASA

0.016309888 0 0 0M= 0 0.01223242 0 0 Tn*s²/cm

0 0 0.00815494 00 0 0 0.00611621

b). MATRIZ DE RIGIDEZ

9 -5 0 0K= -5 11 -6 0 Tn/cm

0 -6 14 -80 0 -8 8

c). ECUACION EIGENVALORES

9 -5 0 00= -5 11 -6 0 - Wn²

0 -6 14 -80 0 -8 8

2.3564 Wn^8 - 25.3014 Wn^6 + 12354

Wn= -15.64 FRECUENCIA NATURALWn= 20.625 Wn1= 20.625Wn= -38.44 Wn2= 42.97Wn= 42.97 Wn3= 42.97Wn= -53.55 Wn4= 42.97Wn= 42.97Wn= -25.36Wn= 42.97

d). PERIODO NATURAL

T1= 0.30464T2= 0.146222946T3= 0.146222946T4= 0.146222946

e). ANALISIS ESPECTRAL (POR TABLA) ACELERACION ESPECTRAL

A1= 2.4 g T1= 2354.4A2= 1.04 g T2= 1020.24A3= 0.65 g T3= 637.65A4= 0.68 g T4= 667.08

f). DETERMINACION DE MODOS DE VIBRACION*PARA FRECUENCIA Wn1= 20.625

2.061926606 -5 0 0 ф110= -5 5.79644495 -6 0 * ф21

0 -6 10.5309633 -8 ф310 0 -8 5.39822248 ф41

ф11= 1ф21= 0.412385321ф31= -0.43493853ф41= -0.8818292

*PARA FRECUENCIA Wn2= 42.97

-21.1149178 -5 0 0 ф12

0= -5 -11.5861884 -6 0 * ф220 -6 -1.05745892 -8 ф320 0 -8 -3.29309419 ф42

ф12= 1ф22= -4.22298357ф32= 7.321380523ф42= 2.199480284

*PARA FRECUENCIA Wn3= 42.97

-21.1149178 -5 0 0 ф130= -5 -11.5861884 -6 0 * ф23

0 -6 -1.05745892 -8 ф330 0 -8 -3.29309419 ф43

ф13= 1ф23= -4.22298357ф33= 7.321380523ф43= -41.5413614

*PARA FRECUENCIA Wn4= 42.97

-21.1149178 -5 0 0 ф140= -5 -11.5861884 -6 0 * ф24

0 -6 -1.05745892 -8 ф340 0 -8 -3.29309419 ф44

ф14= 1ф24= -4.22298357ф34= 7.321380523ф44= 2.199480284

*MATRIZ MODAL NORMALIZADA

1 1 1 1ф= 0.412385321 -4.22298357 -4.22298357 -4.22298357

-0.43493853 7.32138052 7.32138052 7.32138052-0.8818292 2.19948028 -41.5413614 2.19948028

*MATRIZ NORMALIZADA

5.35657132 1.02855476 0.26114401 1.45459609ф= 2.208971384 -4.34356985 -1.10280685 -6.14273539

-2.32977926 7.53044079 1.91193465 10.6496515

-4.72358103 2.26228592 -10.8482776 3.19935542

g). VECTOR DE FACTORES DE PARTICIPACION

(P)= (ф)^T*(M)*(1)

5.35657132 2.20897138 -2.32977926 -4.72358103 0.01630989(P)= 1.02855476 -4.34356985 7.53044079 2.26228592 * 0

0.261144008 -1.10280685 1.91193465 -10.8482776 01.454596092 -6.14273539 10.6496515 3.19935542 0

0.066496511(P)= 0.038890193

-0.059989360.054999039

h). MATRIZ DE DESPLAZAMIENTO

U= (ф)*(P)*(A)/(Ω^2)

5.35657132 1.02855476 0.26114401 1.45459609 0.06649651U= 2.208971384 -4.34356985 -1.10280685 -6.14273539 * 0

-2.32977926 7.53044079 1.91193465 10.6496515 0-4.72358103 2.26228592 -10.8482776 3.19935542 0

1.971415136 0.02210239 -0.00541011 0.02890312U= 0.812982664 -0.09333801 0.0228468 -0.1220574

-0.8574444 0.16181998 -0.03960946 0.21161074-1.73845144 0.04861376 0.22474328 0.06357184

1.971758305Uc= 0.827691236

0.8987461411.75474432

i). MATRIZ DE FUERZAS LATERALES Fs= K * U

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

0 -6 14 -80 0 -8 8

17.74582474 -4.13845618 0 0Fs= -9.85879152 9.10460359 -5.39247685 0

0 -4.96614742 12.582446 -14.0379546

0 0 -7.18996913 14.0379546

*FUERZA LATERAL EN CADA NUDO SRSS

18.22199537Fsc= 14.46265479

19.4947360915.77212174

j). VECTOR CORTANTE BASAL V= F^T * 1

17.74582474 -9.85879152 0 0 1V= -4.13845618 9.10460359 -4.96614742 0 * 1

0 -5.39247685 12.582446 -7.18996913 10 0 -7.18996913 14.0379546 1

7.887033219V= 0 VTRANSP= 7.88703322 0 0

06.847985434

0.01630989 0 0 00 0.01223242 0 00 0 0.00815494 00 0 0 0.00611621

Wn4 - 124.354 Wn² + 960 .= 0

*DETERMINACION DE MODOS

M1= 0.18668658M2= 0.97223798M3= 3.82930479M4= 0.68747607

0 0 0 10.01223242 0 0 * 1

0 0.00815494 0 10 0 0.00611621 1

0 0 0 2354.4 0 0 00.03889019 0 0 * 0 1020.24 0 0

0 -0.05998936 0 0 0 637.65 00 0 0.05499904 0 0 0 667.08

5.53467769 0 0 00 0.55255007 0 00 0 0.34534379 00 0 0 0.36128274

1.9717583 0 0 00 0.82769124 0 00 0 0.89874614 00 0 0 1.75474432

NJ

6.84798543

J

425.390625 425.390625 425.390625 425.390625÷ 1846.4209 1846.4209 1846.4209 1846.4209

1846.4209 1846.4209 1846.4209 1846.42091846.4209 1846.4209 1846.4209 1846.4209

70 w2= 70 Tn

k2=4 k2= 3 Tn/cm

70 w1= 70 Tn

k1= 4 k1= 7 Tn/cm

a). MATRIZ DE RIGIDEZ b). MATRIZ DE MASA

10 -3 0.0710 0.0000K= -3 3 ton/cm M= 0.0000 0.0710 ton.s²/cm

c). ECUACIONES DE EIGENVALORES

0= 10 -3 - Wn² 0.071 0.0000 ф11-3 3 0.0000 0.071 * ф21

0.005041 0.923 w2 21

d). CALCULO DE FRECUENCIA NATURAL *PERIODO NATURAL CORRESPONDIENTEWn1 = 5.150 T1 = 1.220 seg.wn2 = 12.570 T2 = 0.500 seg.

*ANALISIS DEL ESPECTRO (T) GRAFICO SEUDOA1 = 12.70 cm/S 5A2 = 5.08 cm/S 2

e). DETERMINACION DE MODOS DE VIBRACION*FRECUENCIA NATURAL Wn1= 5.15

8.117 -3 * ф11 ф11= 1.000= -3 1.117 ф21 ф21= 2.706

*FRECUENCIA NATURAL Wn2= 12.57

-1.218 -3 * ф12 ф12= 1.000= -3 -8.218 ф22 ф22= -0.406

MATRIZ MODAL

ф= 1.00 1.002.706 -0.4060

f). DETERMINACION DE MODOS *MATRIZ NORMALIZADA

M1= 0.7687 ф= 1.301 3.477M2= 0.2876 3.520 -1.412

g). CORTANTE BASAL*PRIMER MODO v = 12.70

A1= 65.405.

NIVEL Wi фi Wi*фi Wi*фi² Fi1 70 1.301 91.07 118.4821 2.07854392 70 3.520 246.4 867.328 5.62373137

337.47 985.8101

W^E = 115.52529677V = 7.7022752656

*SEGUNDO MOD v = 5.08

A1= 63.8556

NIVEL Wi фi Wi*фi Wi*фi² Fi1 70 3.477 243.39 846.267 2.322999792 70 -1.412 -98.84 139.5621 -0.9433637

144.55 985.8291

W^E = 21.195055297V = 1.3796360581

DIAGRAMA DE CORTANTE BASAL1.3796360581

7.7022752656

((K)-Wn²*(M))*(ф1n)=0

w4 ±

W3= 35 Tn

k3= 3 Tn/cm

W2= 55 Tn

k2= 3 Tn/cm

W1= 55 Tn

k1= 7 Tn/cm

a). MATRIZ DE MASA

0.056065 0 0M = 0 0.056065 0 Tn*s²/cm

0 0 0.03568

b). MATRIZ DE RIGIDEZ

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

0 -3 3

c). ECUACION EIGENVALORES

10 -3 0 0.05606524-3 6 -3 - Wn² 00 -3 3 0

1.1215E-04 Wn^6 ± 0.04143456 Wn^4 + 4.006116208

Wn= -15.58 FRECUENCIA NATURALWn= 15.58 Wn1= 4.40600Wn= -38.02 Wn2= 11.56200

Wn= 38.02 Wn3= 14.70900Wn= -53.18Wn= 53.18

d). PERIODO NATURAL

T1= 1.426T2= 0.543T3= 0.427

e). ANALISIS ESPECTRAL (POR TABLA)

A1= 66.04 cm/S 26A2= 101.6 cm/s 40A3= 73.66 cm/s 29

F). CALCULO DE (ф)*PARA FRECUENCIA Wn1= 4.406

8.91161 -3 0 ф110= -3 4.911615 -3 * ф21

0 -3 2.3074 ф31

ф11 = 1ф21 = 2.971ф31 = 3.864

*PARA FRECUENCIA Wn2= 11.562

2.50521 -3 0 ф120= -3 -1.49479 -3 * ф22

0 -3 -1.7694133944954 ф32

ф12= 1ф22= 0.835ф32= -1.416

*PARA FRECUENCIA Wn3= 14.709

-2.13 -3 ф130= -3 -6.12998 -3 * ф23

-3 -4.7190762844037 ф33

ф13= 1ф23= -0.71

ф33= 0.451

F). CALCULO DE MODOS DE VIBRACION

*MATRIZ MODAL

1 1 1ф= 2.971 0.835 -0.71

3.864 -1.416 0.451

*MATRIZ MODAL NORMALIZADA

0.849 2.193 4.05ф= 2.522 1.831 -2.8744939271255

3.28 -3.105 1.82591093117409y

g). VECTRO CORTANTE BASAL

*PRIMER MODO v= 66.04

A1= 290.972

NIVEL Wi фi Wi*фi Wi*фi² Fi1 55 0.849 46.695 39.644 5.428 tn2 55 2.522 138.71 349.827 16.124 tn3 35 3.28 114.8 376.544 13.345 tn

300.205 766.015

W^E= 117.652V= 34.8964

*SEGUNDO MODO v= 101.6

A2= 1174.7

NIVEL Wi фi Wi*фi Wi*фi² Fi1 55 2.193 120.615 264.509 20.692 55 1.831 100.705 184.391 17.2753 35 -3.105 -108.675 337.436 -18.642

112.645 786.336

W^E= 16.1367V= 19.3229

*TERCER MODO v= 73.66

A3= 1083.46

NIVEL Wi фi Wi*фi Wi*фi² Fi1 55 4.048583 222.672064777328 901.50634 21.4563272 55 -2.87449 -158.0971659919 454.44934 -15.2339923 35 1.825911 63.9068825910931 116.68828 6.1579659

128.481781376518 1472.644

W^E= 11.2095V= 12.3803

J). CORTANTE BASAL

(V) = 34.8964 19.32295 12.3803007542654

12.3803

19.3229

34.89643955

0 00.0560652 0 .= 0

0 0.035678

Wn² - 63 .= 0

valores para sacar la frecuencia natural

15 10 unidades intervalo menor = 07.5 x = 5

MODO1= 1.178MODO2= 0.456MODO3= 0.247

GRAFICA DE MODO E BIBRAR PAR 1ER MODO

tn 13.35 3

tn 16.12 3

tn 5.43 1

GRAFICA DE MODO E BIBRAR PAR 2DO MODO

-18.64 -3

17.282

20.69 2

GRAFICA DE MODO E BIBRAR PARA 3ER MODO

6.16 2

-15.23 -3

21.46 4

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 0 0M = 0 0.00815494 0 0 Tn*s²/cm

0 0 0.00611621 00 0 0.00509684

b). MATRIZ DE RIGIDEZ

21 -9 0 0K= -9 16 -7 0 Tn/cm

0 -7 12 -50 0 -5 5

c). ECUACION EIGENVALORES

21 -9 0 00= -9 16 -7 0 - Wn²

0 -7 12 -50 0 -5 5

0.= 2.073124E-09 Wn^8 - 1.5507*10^-5 Wn^6 +

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

Wn= -50.23 Wn4= 60.91Wn= 50.23Wn= -60.91Wn= 60.91

d). PERIODO NATURAL

T1= 0.464390244T2= 0.192677093T3= 0.125088592T4= 0.103155814

e). ANALISIS ESPECTRAL (POR TABLA)

A1= 60.96 cm/S 24A2= 20.32 cm/s 8A3= 12.7 cm/s 5A4= 15.24 cm/s 6

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

19.50714862 -9 0 0 ф110= -9 14.5071486 -7 0 * ф21

0 -7 10.8803615 -5 ф310 0 -5 4.06696789 ф41

ф11 = 1ф21 = 2.167460958ф31 = 3.206239751ф41 = 3.942564147

*PARA FRECUENCIA Wn2= 32.61

12.32793394 -9 0 0 ф120= -9 7.32793394 -7 0 * ф22

0 -7 5.49595046 -5 ф320 0 -5 -0.42004128 ф42

ф12= 1ф22= 1.369770438ф32= 0.148226756ф42= -1.754749232

*PARA FRECUENCIA Wn3= 50.23

0.424645056 -9 0 0 ф130= -9 -4.57535494 -7 0 * ф23

0 -7 -3.43151621 -5 ф330 0 -5 -7.85959684 ф43

ф13= 1ф23= 0.047182784ф33= -1.316553998ф43= 0.837499379

*PARA FRECUENCIA Wn3= 0.00

-9.254872465 -9 0 0 ф130= -9 -14.2548725 -7 0 * ф23

0 -7 -10.6911543 -5 ф330 0 -5 -13.9092953 ф43

ф13= 1ф23= -1.028319163ф33= 0.808365503ф43= -0.288825244

F). CALCULO DE MODOS DE VIBRACION

*MATRIZ MODAL

1 1 1 1ф= 2.16746096 1.36977044 0.04718278 -1.02831916

3.20623975 0.14822676 -1.316554 0.80836553.94256415 -1.75474923 0.83749938 -0.28882524

*MATRIZ MODAL NORMALIZADA

1.972354088 4.52932849 6.89719546 8.37937858ф= 4.275000482 6.20414028 0.32542888 -8.61667556

6.32384008 0.67136767 -9.08053025 6.773600587.776132514 -7.9478357 5.77639691 -2.42017606

g). VECTOR CORTANTE BASAL

*PRIMER MODO v= 60.96

A1= 824.7888

NIVEL Wi фi Wi*фi Wi*фi² Fi1 8 1.97235409 15.7788327 31.1214452 2.337638442 8 4.27500048 34.2000039 146.205033 5.066740053 6 6.32384008 37.9430405 239.94572 5.621271964 5 7.77613251 38.8806626 302.341184 5.76018093

126.80254 719.613383

W^E= 22.34378131V= 18.78583137

*SEGUNDO MODO v= 20.32

A2= 662.6352

NIVEL Wi фi Wi*фi Wi*фi² Fi1 8 4.52932849 36.234628 164.118533 1.552763362 8 6.20414028 49.6331222 307.930853 2.126929353 6 0.67136767 4.02820602 2.70440729 0.172620814 5 -7.9478357 -39.7391785 315.840461 -1.70294395

50.1567777 790.594254

W^E= 3.182039758V= 2.149369573

*TERCER MODO v= 12.7

A3= 637.921

NIVEL Wi фi Wi*фi Wi*фi² Fi1 8 6.89719546 55.1775636 380.570441 1.107043162 8 0.32542888 2.60343107 0.84723167 0.052233383 6 -9.08053025 -54.4831815 494.736178 -1.093111584 5 5.77639691 28.8819845 166.833806 0.57946748

32.1797978 1042.98766

W^E= 0.992858714V= 0.64563244

*CUARTO MODO v= 15.24

A3= 928.265352

NIVEL Wi фi Wi*фi Wi*фi² Fi

1 8 8.37937858 67.0350286 561.711883 1.15729952 8 -8.61667556 -68.9334045 593.976782 -1.190073253 6 6.77360058 40.6416035 275.289989 0.701640754 5 -2.42017606 -12.1008803 29.2862609 -0.20891082

26.6423473 1460.26491

W^E= 0.48608623V= 0.459956173

J). CORTANTE BASAL

0.0081549439 0 0 00 0.00815494 0 00 0 0.00611621 00 0 0 0.00509684

3.59221*10^-2 Wn^4 - 26.7125 Wn^2 + 3780

MODO1= 0.50700835MODO2= 0.22078328MODO3= 0.14498647MODO4= 0.11934059

970 k/m2

75 k/m2

L= m 3.5

50 k/m2

L= m 3.5

6 m

6 m

a). DETERM. CARGA MUERTA TRIBUTARIA DATOS DEL PROBLEMARazon de amortiguamiento=

Piso 1: Desplazamiento =

Losa = 34.92 ton Esfuerzo cortante=

4 muros = 4.2 ton4 columnas = 1.05 ton DATO ASUMIDO

T1= 0.5peso total = w1 40.17 ton ф2= 1

ф1= 0.66piso 2:

Losa = 34.92 ton4 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 MODELO DINAMICO

k2= 15 Tn/cm

k1= 15 Tn/cm

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 37.545 w²/g 37.545

1 40.170 /g 15 0.66 26.512 w²/g 64.057

2 37.545 /g 15 1 37.545 w²/g 37.5451 40.170 /g 15 0.63 25.307 w²/g 62.852

2 37.545 /g 15 1 37.545 w²/g 37.5451 40.170 /g 15 0.64 25.709 w²/g 63.254

e). DETERMINACION DE LA FRECUENCIA CIRCULAR NATURAL

6.720 w²/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 ф1 Wi*ф1 Wi*ф1² Fi Vi2 37.545 1 37.545 37.545 7.923 7.9231 40.17 0.64 25.6094 16.326636 5.404 13.327

BASESUMATORIA 63.154 53.872

masa de piso m

Rigidez del piso k

Modo inicial u

Fuerza de inercia m*w²*u

Fuerza de corte k*∆

P = 1.172

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

A = 0.2 *g

DATOS DEL PROBLEMA7 %

0.3 cm4.5 ton

DATO ASUMIDO seg

MODELO DINAMICO FORMA MODAL1

w2= 37.545

w1= 40.17 0.64

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

Modo del piso

w²/g 2.503 w²/g 6.773 w²/g 1

w²/g 4.270 w²/g 4.270 w²/g 0.63

w²/g 2.503 w²/g 6.693 w²/g 1w²/g 4.190 w²/g 4.190 w²/g 0.64

w²/g 2.503 w²/g 6.720 w²/g 1w²/g 4.217 w²/g 4.217 w²/g 0.64

Fi=Fuerzas laterales Vi=cortante basal

Fuerza de corte k*∆

Derivada del piso ∆

Despl. Del pison ∑∆

DATOS PROPORCIONADOS DE LA PREGUNTA

0.939 3.159 3.135EIGENVECTORES: ф= 2.181 2.871 -4.084

3.491 -3.129 1.226

ф^T * M * ф = I

w3k3=

4.0 mw2

k2=4.0 m

w1

4.0 m k1=

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

P = ф^T * M * 1

*matriz de masa

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

0 0 35

0.939 2.181 3.491 55 0P= 3.159 2.871 -3.129 * 0 35

3.135 -4.084 1.226 0 0

250.165P= 164.715 *1/g

72.395

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

250.165 * 0.939 + 164.715 * 3.159

POR LO TANTO: 1.00 = 1

b). CALCULO DE DESPLAZAMIENTOS UTILIZANDO EL ESPECTRO DE ACELERACION

T1= 0.73240841 seg A1= 0.15 *gT2= 0.32402418 seg A2= 0.6 *gT3= 0.21562729 seg A3= 0.77 *g

* MATRIZ DE DESPLAZAMIENTO

U = ф * P * A

0.939 3.159 3.135 250.165U = 2.181 2.871 -4.084 * 0

3.491 -3.129 1.226 0

0.478773731 0.830288714 0.205818579U = 1.112039943 0.754592877 -0.26812219

1.779977736 -0.82240373 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

-0.63326621 0.075695837 0.473940772A = -0.66793779 1.576996608 -0.34861137

1.779977736 -0.82240373 0.080489179

0.7945916A = 1.747738278

1.962433985

8.5788FRECUENCIAS: w= 19.3911

29.1391

w3= 35 Tn

3 Tn/cmw2= 35 Tn

3 Tn/cm

w1= 55 Tn

7 Tn/cm

0 10 * 1

35 1

+ 72.395 * 3.135 *1/g = 1

÷ Ω²

0 0 0.15 0 0164.715 0 * 0 0.6 0 ÷

0 72.395 0 0 0.77

73.59580944 73.5958094 73.5958094376.0147592 376.014759 376.014759849.0871488 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/m COLUMNA 1 :3 m COLUMNA 2 :

c1 c2V1

w= 2 tn/m4 m

c1 c1

6.5

a) C1 = 2520 b) C1 = 1080V = 3276 C2 = 648

M = 2275 V = 2808W = 13000 M = 1950

21071 kg W = 1300019486 kg

PARA TRES PISOS

a) C1 = b) C1 =V = C2 =

M = V =W = M =

0 kg W =0 kg

f'C = 210 KG/cm2S/C muro = 100 Kg/m2 m= 13245

LARGO ANCHOVIGA 1 : 0.3 0.7 m= 14868VIGA 2 : 0.3 0.6VIGA 3 : 0.3 0.4VIGA 4 : 0.3 0.4

COLUMNA 1 : 0.3 0.5 m= 19486COLUMNA 2 : 0.3 0.3

m= 21071

c) C2 = 1296 d) C2 = 648V = 1872 V = 1872

M = 1950 M = 975W = 9750 W = 9750

14868 kg 13245 kg

c) C2 = d) C2 =V = V =

M = M =W = W =

0 kg 0 kg

0.1

DATOS3

210 Kg/cm2 1.2 1.2Colum= 30 30 m

41.4 1.2

5

5 5

DETERMINACION DE I Y E

Inercia = 67500 cm4E = 217371 kg/cm2

W3= 0.5 Tn

k3= 3 Tn/cm

W2= 12 Tn

k2= 3 Tn/cm

W1= 13 Tn

k1= 7 Tn/cm

f‛c =

0.1 tn/mDatosfc= 210

3 u= 0.171.2 tn/m 1.2 tn/m column= 30

viga= 30

41.4 tn/m 1.2 tn/m

5

5 m 5 m

determinacion de I y Ec

Ic= 30 X 27000 = 67500 cm412

Ic= 0.000675 m4

E= 2173706.51 tn/m2E= 21737.0651 Tn/cm2

Calculoela rigides de empotramiento de cada piso

1ER PISO ke1= ke2= (12*Ei)/l al3= 1.408562 tn/cmKROTUL= 3EI= 0.35214 tn/cm2

L32DO PISO ke1= Ke2 =ke3 (12*Ei)/l al3= 2.751097 tn/cm

3ER PISO ke1= Ke2 =ke3 (12*Ei)/l al3= 6.52112 tn/cm

* Keq(1er P)= 2 X 1.408562 + 0.35214 3.169Keq(2do P)= 3 X 2.751097 8.253Keq(3er P)= 2 X 6.52112 13.04224

m3= 0.00051k3= 13.04224

m2= 0.012232k2= 8.253

m1= 0.013252

k1= 3.169

kg/cm2

3060