sismorresistente n° g.d.l varios - modificado

70 w2=

k2=4 k2= 3 Tn/cm

70 w1=

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

c). ECUACIONES DE EIGENVALORES

0.071 0.0000 ф110= 10 -3 - Wn²* 0.0000 0.071 * ф21

-3 3

21 - 0.923 W²n + 0.0050

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

d). CALCULO DE FRECUENCIA NATURAL *PERIODO NATURAL CORRESPONDIENTEWn1 = 5.155 T1 = 1.219wn2 = 12.571 T2 = 0.500

*ANALISIS DEL ESPECTRO (T) *ACELERACION ESPECTRALA1 = 0.230 T1= 225.630A2 = 0.830 T2= 814.230

e). DETERMINACION DE MODOS DE VIBRACION

((K)-Wn²*(M))*(ф1n)=0

D42

TABLA INSERTAR INGRESAR DATOS POR EL GRAFICO ESPECTRAL

*FRECUENCIA NATURAL Wn1= 5.155

8.113 -3 * ф110= -3 1.113 ф11

*FRECUENCIA NATURAL Wn2= 12.571

-1.220 -3 * ф120= -3 -8.220 ф22

ф= 1.00 1.002.704 -0.4070

f). DETERMINACION DE MODOS *MATRIZ NORMALIZADA

M1= 0.7682 ф= 1.302 3.476M2= 0.2877 3.520 -1.415

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

P = 1.302 3.520 * 0.0710 0.0000 *3.476 -1.415 0.0000 0.0710

P = 0.3424 0.34200.1463 0.1460

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

U= 1.302 3.476 * 0.342 0 *3.520 -1.415 0 0.146

U= 3.781 2.61510.221 -1.064

Uc= 4.59710.277

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

10 -3 * 3.781 2.615Fs= -3 3 10.221 -1.064

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

26.464854852 = 26.465 18.30318.303390925

luego el srss aplicado a la cortante basal 32.17

V(TRANSP)=

70 Tn

70 Tn

ton.s²/cm

Wn^4 = 0

*PERIODO NATURAL CORRESPONDIENTEseg.seg.

*ACELERACION ESPECTRAL

ф11= 1.00ф21= 2.704

ф12= 1.00ф22= -0.407

*MATRIZ NORMALIZADA

11

hoja225.63 0

÷26.574 26.574

0 814.23 158.03 158.03

W3= 7.5 Tn

k3= 18.52 Tn/cm

W2= 8.75 Tn

k2= 58.54 Tn/cm

W1= 10.5 Tn

k1= 47.60 Tn/cm

a). MATRIZ DE MASA

0.010703 0 0M = 0 0.00891946992864 0 Tn*s²/cm

0 0 0.0076453

b). MATRIZ DE RIGIDEZ

106.138 -58.5418 0K= -58.542 77.0648 -18.522994392108 Tn/cm

0 -18.523 18.5229943921083

c). ECUACION EIGENVALORES

106.138 -58.5418 0 0.0107033640= -58.542 77.0648 -18.522994392108 - Wn² 0

0 -18.523 18.5229943921083 0

7.298802E-07 Wn^6 - 0.01531233 Wn^4 + 65.47540959

Wn= -32.02 FRECUENCIA NATURALWn= 32.02 Wn1= 32.02Wn= -67.16 Wn2= 67.16Wn= 67.16 Wn3= 125.07

Wn= -125.07Wn= 125.07

d). PERIODO NATURAL

T1= 0.19623T2= 0.09356T3= 0.05024

e). ANALISIS ESPECTRAL (POR TABLA)

A1= 25.654 cm/SA2= 12.7 cm/sA3= 7.62 cm/s

F). CALCULO DE (ф)*PARA FRECUENCIA Wn1= 32.02

95.1645 -58.5418 0 ф110= -58.542 67.91985 -18.522994392108 * ф21

0 -18.523 10.6844592239126 ф31

ф11 = 1ф21 = 1.62558ф31 = 2.80017

*PARA FRECUENCIA Wn2= 67.16

57.8613 -58.5418 0 ф120= -58.542 36.83384 -18.522994392108 * ф22

0 -18.523 -15.960687565078 ф32

ф12= 1ф22= 0.98838ф32= -1.1951


-61.289 -58.5418 ф130= -58.542 -62.458 -18.522994392108 * ф23

-18.523 -101.06802166294 ф33

ф13= 1ф23= -1.0469ф33= 0.36966

C57

USER: INGRESAR DATOS del grafico espectral por tabla

F). CALCULO DE MODOS DE VIBRACION

*MATRIZ MODAL

1 1 1ф= 1.625582 0.9883759067351 -1.0469262

2.800167 -1.1950620635148 0.3696571

*MATRIZ MODAL NORMALIZADA

3.25784 5.741494 6.81609481710324ф= 5.29589 5.674754 -7.1359482059165

9.12251 -6.86144 2.51961817706278

g). VECTRO CORTANTE BASAL

*PRIMER MODO v= 25.654

A1= 821.441

NIVEL Wi фi Wi*фi Wi*фi² Fi1 10.5 3.257844 34.2073612262354 111.44224 4.34953552 8.75 5.295893 46.3390627055783 245.40671 5.89210613 7.5 9.122507 68.4188046363823 624.15104 8.6995901

148.965228568196 981

W^E= 22.6204V= 18.9412

*SEGUNDO MODO v= 12.7

A2= 852.932

NIVEL Wi фi Wi*фi Wi*фi² Fi1 10.5 5.741494 60.2856840703289 346.12988 3.12457042 8.75 5.674754 49.6540980467975 281.77479 2.57354183 7.5 -6.86144 -51.46081000392 353.09533 -2.6671826

58.4789721132068 981

W^E= 3.48602V= 3.03093

*TERCER MODO v= 7.62

A3= 953.033

NIVEL Wi фi Wi*фi Wi*фi² Fi1 10.5 6.816095 71.568995579584 487.82106 1.98639322 8.75 -7.13595 -62.439546801769 445.56537 -1.73300593 7.5 2.519618 18.8971363279708 47.613568 0.5244889

28.0265851057856 981

W^E= 0.8007V= 0.77788

J). CORTANTE BASAL

(V) = 18.9412 3.03093 0.77787618453336

0.777876

3.03093

18.94123175

Alturasf´c= 280 Kg/cm2 C1 300 Altura Losa Ali. Peso PropioEconcreto 250998.008 C1 280 h=0.20 300 Kg/m2C1 40X40 C2 280 h=0.25 350 Kg/m2

40 40 213333.333 h=0.30 420 Kg/m2C2 30X30 L 5 A

30 30 67500.000 Area Losa 25w1 10.5 Tn

K1= 47.60 w2 8.75 TnK2= 58.54 w3 7.5 TnK3= 18.52

981

0 00.0089195 0

0 0.00764526

Wn² - 51612.37077 .= 0

MODO1= 0.306951475MODO2= 0.174170703MODO3= 0.146711574

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

0.00815 0 0 0M = 0 0.00815 0 0 Tn*s²/cm

0 0 0.00612 00 0 0.00510


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

0 -7 12 -50 0 -5 5


21 -9 0 00= -9 16 -7 0 - Wn²

0 -7 12 -50 0 -5 5

0.= 2.0731*10^-9 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= 50.23Wn= -50.23 Wn4= 60.91

E41

USER: OBTENER VALORES DE LOS Wn CON HP

Wn= 50.23Wn= -60.91Wn= 60.91

d). PERIODO NATURAL

T1= 0.46439T2= 0.19268T3= 0.12509T4= 0.10316

e). ANALISIS ESPECTRAL (POR TABLA)

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


19.50715 -9 0 0 ф110= -9 14.50715 -7 0 * ф21

0 -7 10.88036 -5 ф310 0 -5 4.06697 ф41

ф11 = 1ф21 = 2.16746ф31 = 3.20624ф41 = 3.94256


12.32793 -9 0 0 ф120= -9 7.32793 -7 0 * ф22

0 -7 5.49595 -5 ф320 0 -5 -0.42004 ф42

ф12= 1ф22= 1.36977ф32= 0.14823

ф42= -1.75475


D59

USER: INGRESAR DATOS CARAJOS¡

0.4246450561 -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= 0.8374993788


-9.25487 -9.00000 0 0 ф130= -9.00000 -14.25487 -7.00000 0 * ф23

0 -7.00000 -10.69115 -5.00000 ф330 0 -5.00000 -13.90930 ф43

ф13= 1ф23= -1.028319163ф33= 0.8083655027ф43= -0.288825244


*MATRIZ MODAL

1 1 1 1ф= 2.16746 1.36977 0.04718 -1.02832

3.20624 0.14823 -1.31655 0.808373.94256 -1.75475 0.83750 -0.28883


2.30287 5.04535 6.68910 6.86800ф= 4.99138 6.91097 0.31561 -7.06250

7.38356 0.74786 -8.80656 5.551869.07922 -8.85333 5.60211 -1.98365

g). VECTOR CORTANTE BASAL

*PRIMER MODO v= 60.96

A1= 824.7888

NIVEL Wi фi Wi*фi Wi*фi² Fi1 8 2.30287 18.42297 42.42575 2.337642 8 4.99138 39.93108 199.31138 5.066743 6 7.38356 44.30136 327.10169 5.621274 5 9.07922 45.39610 412.16118 5.76018

148.05151 981

WÊ= 22.343781312V= 18.785831372

*SEGUNDO MODO v= 20.32

A2= 662.6352

NIVEL Wi фi Wi*фi Wi*фi² Fi1 8 5.04535 40.36282 203.64464 1.552762 8 6.91097 55.28780 382.09254 2.126933 6 0.74786 4.48714 3.35573 0.172624 5 -8.85333 -44.26664 391.90709 -1.70294

55.87111 981

WÊ= 3.182039758V= 2.1493695733

*TERCER MODO v= 12.7

A3= 637.921

NIVEL Wi фi Wi*фi Wi*фi² Fi1 8 6.68910 53.51277 357.95208 1.107042 8 0.31561 2.52488 0.79688 0.052233 6 -8.80656 -52.83934 465.33263 -1.093114 5 5.60211 28.01057 156.91841 0.57947

31.20888 981

WÊ= 0.992858714V= 0.64563244

*CUARTO MODO v= 6.2

A3= 377.64076

NIVEL Wi фi Wi*фi Wi*фi² Fi1 8 6.86800 54.94403 377.35575 0.47082

2 8 -7.06250 -56.49999 399.03117 -0.484153 6 5.55186 33.31114 184.93869 0.285444 5 -1.98365 -9.91826 19.67439 -0.08499

21.83691 981

W^E= 0.48609V= 0.18712

J). CORTANTE BASAL (V) = 2.14937 2.14937 0.64563

CORTANTE BASAL MAS PROBABLE* COMO : T4/T3 = 0.8247 < 0.75 NO CUMPLE

T3/T2 = 0.6492 < 0.75 CUMPLE T2/T1 = 0.4149 < 0.75 CUMPLE

solo si todas las proposiciones cumplenVc = 18.92034

0.00815 0 0 00 0.00815 0 00 0 0.00612 00 0 0 0.00510

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

P38

USER: SACR LA ECUACION CON HP

MODO1= 0.43424MODO2= 0.19820MODO3= 0.14950MODO4= 0.14560

0.18712

w3= 7.5 Tn

k3= 18.523

w2= 8.75 Tn

k2= 58.543

w1= 10.5 Tn

k1= 47.6

a). MATRIZ DE MASA

0.01070336 0 0M = 0 0.00891947 0 Tn*s²/cm

0 0 0.00764526


106.143 -58.543 0K= -58.543 77.066 -18.523 Tn/cm

0 -18.523 18.523


106.143 -58.543 00= -58.543 77.066 -18.523 - Wn²

0 -18.523 18.523

7.298802E-07 Wn^6 - 0.01531274 Wn^4 +

Wn= -15.64 FRECUENCIA NATURALWn= 32.02 Wn1= 32.02Wn= -38.44 Wn2= 67.16Wn= 67.16 Wn3= 125.07Wn= -53.55Wn= 125.07

D42

USER: ESTOS VALORES SE OBTIENEN DE LA ECUACION POLINOMICA EN HP

d). PERIODO NATURAL

T1= 0.20T2= 0.09T3= 0.05

e). ANALISIS ESPECTRAL (POR TABLA) ACELERACION ESPECTRAL

A1= 1.756 g T1= 1722.636A2= 0.869 g T2= 852.489A3= 0.971 g T2= 952.551

f). DETERMINACION DE MODOS DE VIBRACION*PARA FRECUENCIA Wn1= 32.02

95.169050765 -58.543 ф110= -58.543 67.9210423 -18.523 * ф21

-18.523 10.6844648 ф31

ф11= 1ф21= 1.6256264757ф31= 2.8003695202


57.86584526 -58.543 0 ф120= -58.543 36.8350377 -18.523 * ф22

0 -18.523 -15.960682 ф32

ф12= 1ф22= 0.9884332074ф32= -1.194948201


-61.28442248 -58.543 0 ф130= -58.543 -62.4568521 -18.523 * ф23

0 -18.523 -101.068016 ф33

ф12= 1ф22= -1.046827502ф32= 0.3691923802

*MATRIZ MODAL NORMALIZADA *DETERMINACION DE MODOS

1 1 1 M1=ф= 1.6256264757 0.98843321 -1.0468275 M2=

2.8003695202 -1.1949482 0.36919238 M3=

D57

USER: INGRESAR DATO DEL GRAFICO ESPECTRAL

*MATRIZ NORMALIZADA

3.2576718443 5.741595 6.81680243ф= 5.2957575991 5.67518316 -7.13601627

9.1226849397 -6.86090862 2.51671152

g). VECTOR DE FACTORES DE PARTICIPACION

(P)= (ф)^T*(M)*(1)

3.2576718443 5.2957576 9.12268494 0.0107033639(P)= 5.741595 5.67518316 -6.86090862 * 0

6.8168024348 -7.13601627 2.51671152 0

0.1518486956(P)= 0.0596205765

0.0285541484

h). MATRIZ DE DESPLAZAMIENTO

U= (ф)*(P)*(A)/(Ω^2)

3.2576718443 5.741595 6.81680243 0.1518486956

U= 5.2957575991 5.67518316 -7.13601627 * 09.1226849397 -6.86090862 2.51671152 0

0.831130584 0.06469879 0.0118531U= 1.351107882 0.06395043 -0.01240815

2.3274727546 -0.0773117 0.00437607

0.8337292585Uc= 1.3526773926

2.3287605442

i). MATRIZ DE FUERZAS LATERALES Fs= K *

106.143 -58.543 0 0.83113Fs= -58.543 77.066 -18.523 * 1.35111

0 -18.523 18.523 2.32747

9.12078 3.12347 1.98453Fs= 12.35582 2.57279 -1.73122

18.08521 -2.61660 0.31089

*FUERZA LATERAL EN CADA NUDO SRSS

9.8429251308

Fsc= 12.73902489518.276157631

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

9.12078 12.35582 18.08521 1V= 3.12347 2.57279 -2.61660 * 1

1.98453 -1.73122 0.31089 1

39.56182V= 3.07966 VTRANSP= 39.5618158 3.0796622372

0.56421SRSS = 39.68551

0.01070336 0 00 0.00891947 00 0 0.00764526

65.4789778 Wn² - 51617.0587 .= 0

*DETERMINACION DE MODOS

0.306967690.174167630.14669634

0 0 10.00891947 0 * 1

0 0.00764526 1

0 0 1722.636 0 0 1025.2804

0.05962058 0 * 0 852.489 0 ÷ 4510.46560 0.02855415 0 0 952.551 15642.5049

1.68016086 0 00 0.18900244 00 0 0.06089504

U

0.06470 0.011850.06395 -0.01241-0.07731 0.00438

N125

USER: NO COPIAR ESTA MATRIZ EN TU HOJA DE CALCULO

1

0.56420744

1025.2804 1025.2804

4510.4656 4510.465615642.5049 15642.5049

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


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

0 -6 14 -80 0 -8 8


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


-21.1149178 -5 0 0 ф12

B47

calcular con hp

C50

operar en hp polinomios

C70

USER:ingresar los valores por el grafico espectral

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


-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


-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


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

6.364272878 1.19422882 0.29845786 1.19422882ф= 2.624532714 -5.0432087 -1.26038264 -5.0432087

-2.7680675 8.74340365 2.18512356 8.74340365

-5.61220169 2.62668275 -12.3983458 2.62668275


(P)= (ф)^T*(M)*(1)

6.364272878 2.62453271 -2.7680675 -5.61220169 0.01630989(P)= 1.194228824 -5.0432087 8.74340365 2.62668275 * 0

0.29845786 -1.26038264 2.18512356 -12.3983458 01.194228824 -5.0432087 8.74340365 2.62668275 0

0.079006125(P)= 0.045154416

-0.068561010.045154416


U= (ф)*(P)*(A)/(Ω^2)

6.364272878 1.19422882 0.29845786 1.19422882 0.07900612U= 2.624532714 -5.0432087 -1.26038264 -5.0432087 * 0

-2.7680675 8.74340365 2.18512356 8.74340365 0-5.61220169 2.62668275 -12.3983458 2.62668275 0

2.782927472 0.0297961 -0.00706662 0.01948207U= 1.147638439 -0.12582844 0.02984223 -0.08227244

-1.21040239 0.21814859 -0.05173743 0.14263561-2.45406672 0.06553593 0.29355712 0.04285042

2.783164136Uc= 1.157828181

1.2392273492.472802127


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

0 -6 14 -80 0 -8 8

25.04847723 -5.7891409 0 0Fs= -13.9158207 12.73611 -7.4353641 0

0 -6.94696909 17.3491829 -19.782417

0 0 -9.91381879 19.782417


25.70876045Fsc= 20.27666645

27.2139403522.12753547

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

25.04847723 -13.9158207 0 0 1V= -5.7891409 12.73611 -6.94696909 0 * 1

0 -7.4353641 17.3491829 -9.91381879 10 0 -9.91381879 19.782417 1

11.13265654V= 0 VTRANSP= 11.1326565 0 0

09.868598222

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

L41

USER: ingresas la matriz al HP para calcular la ecuacion polynomica

Wn4 - 124.354 Wn² + 960 .= 0

*DETERMINACION DE MODOS

M1= 0.15712714M2= 0.83736046M3= 3.35055676M4= 0.83736046

0 0 0 10.01223242 0 0 * 1

0 0.00815494 0 10 0 0.00611621 1

0 0 0 2354.4 0 0 00.04515442 0 0 * 0 1020.24 0 0

0 -0.06856101 0 0 0 637.65 00 0 0.04515442 0 0 0 667.08

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

2.78316414 0 0 00 1.15782818 0 00 0 1.23922735 00 0 0 2.47280213

9.86859822

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

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*∆

D81

SE OBTIENE UTILIZANDO EL GRAFICO ESPECTRAL

P = 1.172

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

A = 0.2 *g

D95

SE OBTIENE DEL GRAFICO ESPECTRAL

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 ∑∆

O67

RESULTADO DE LA FORMA MODAL POR ITERACION

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

F48

SI CUMPLE CON LA CONDICIEN EN LA IGUALDAD SON CORRECTOS

H52

se obtienen por tabla espectral

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

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

Q3 = 1000 kg/m RESUMEN

NIVEL 3 k3= 13.042m3

Q2 = 1200 Q2 = 1200 kg/mNIVEL 2 k2= 8.253

4 Q1 = 1400 Q1 = 1200 kg/m

NIVEL 1 k1= 3.169

5

5 m 5 m

ANALISIS DE LA RIGIDEZ DE ELEMENTOS

NIVEL 1 - EMPOTRAMIENTO NIVEL 1 - EMPOTRAMIENTO

fc = 210 kg/cm2 fc = 210 0E = 217370.65119 ton/m2 E = 217370.6512 ton/m2

b = 0.3 m b = 0.3 m 6.521h = 0.3 m h = 0.3 mI = 0.000675 m^4 I = 0.000675 m^4A = 0.09 m^2 A = 0.09 m^2

2.751L= 5 m L= 5 mK= 1.4085618197 ton/cm K= 0.352140455 ton/cm

1.409NIVEL 2 - EMPOTRAMIENTO NIVEL 3 - EMPOTRAMIENTO

fc = 210 0 fc = 210 0E = 217370.65119 ton/m2 E = 217370.6512 ton/m2

b = 0.3 m b = 0.3 mh = 0.3 m h = 0.3 mI = 0.000675 m^4 I = 0.000675 m^4A = 0.09 m^2 A = 0.09 m^2

L= 4 m L= 3 mK= 2.7510973042 ton/cm K= 6.521119536 ton/cm

a). MATRIZ DE MASA

0.01325 0.00000 0.00000M= 0.00000 0.01223 0.00000 Tn*s²/cm

0.00000 0.00000 0.00510


11.423 -8.253 0.000 K1 +K2 -K2K= -8.253 21.296 -13.042 Tn/cm K= -K2 K2+K3

0.000 -13.042 13.042 0 -K3


11.42256 -8.25329 0.00000 0.01325 0.000000= -8.25329 21.29553 -13.04224 - Wn² 0.00000 0.01223

0.00000 -13.04224 13.04224 0.00000 0.00000

11.42256 - 0.01325 Wn² -8.25330= -8.2533 21.2955 - 0.01223

0.0000 -13.0422

8.264E-07 Wn^6 - 14.690643797 Wn^4 + 4.141398 Wn²

resolver en HP50g SOLUCION DE LA ECUACIONx1 = -9.523x2 = 9.523 Wn1= 9.523x3 = -34.143 Wn2= 34.143x4 = 34.143 Wn3= 62.483x5 = -62.483

x6 = 62.483 =ᵹ 5%

ANALISIS DEL ESPECTRO EN FUNCION DE T (diagrama)ANALISIS DEL ESPECTRO (CONVERSION)

V1= 25 pulg/s V1= 63.5 cmV2= 6 pulg/s V2= 15.24 cmV3= 4 pulg/s V3= 10.16 cm

ACELERACION ESPECTRAL - FUNCION DE TA1 = 604.740 cm/s2A2 = 520.339 cm/s2A3 = 634.832 cm/s2


10.220827811 -8.2533 0 ф110= -8.2533 20.1863132 -13.0422 * ф21

0 -13.0422 12.579687087 ф31

ф11 = 1ф21 = 1.2383940759

ф31 = 1.28392975

*PARA FRECUENCIA Wn2= Wn1=

-4.023548531 -8.2533 0 ф120= -8.2533 20.1863132 -13.0422 * ф22

0 -13.0422 7.0969460042 ф32

ф12= 1ф22= -0.487508327ф32= -1.387360527

*PARA FRECUENCIA Wn3= Wn2=

-40.30789436 -8.2533 0 ф130= -8.2533 7.03848506 -13.0422 * ф23

0 -13.0422 -6.869104089 ф33

ф13= 1ф23= -4.883856622ф33= -3.268475877


*MATRIZ MODAL

1 1 1 MODO1=ф= 1.238 -0.488 -4.884 MODO2=

1.284 -1.387 -3.268 MODO3=


4.974 6.205 1.668ф= 6.160 -3.025 -8.146

6.387 -8.609 -5.451


(P)= (ф)^T*(M)*(1)

4.974 6.160 6.387 0.01325 0 0(P)= 6.205 -3.025 -8.609 * 0 0.01223 0

1.668 -8.146 -5.451 0 0 0.00510

0.1738(P)= 0.0013

-0.1053


U= (ф)*(P)*(A)/(Ω^2)

4.974 6.205 1.668 0.1738 0.0000 0.0000

U= 6.160 -3.025 -8.146 * 0.0000 0.0013 0.00006.387 -8.609 -5.451 0.0000 0.0000 -0.1053

5.765 0.004 -0.029U= 7.140 -0.002 0.140

7.402 -0.005 0.093

5.765Uc= 7.141

7.403


11.423 -8.253 0.000 5.765 0.004 -0.029Fs= -8.253 21.296 -13.042 * 7.140 -0.002 0.140

0.000 -13.042 13.042 7.402 -0.005 0.093

6.9284 0.0577 -1.4777Fs= 7.9196 -0.0020 1.9889

3.4240 -0.0438 -0.6018


7.0845Fsc= 8.1655

3.4767

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

6.9284 7.9196 3.4240 1V= 0.0577 -0.0020 -0.0438 * 1

-1.4777 1.9889 -0.6018 1

18.2720V= 0.0118 VTRANSP= 18.2720 0.0118 -0.0905

-0.0905CORTANTE BASAL - SRSS

18.2722 ton[Vb] =

W3= 5 Tn 1. MATERIALCONCRETO EN VIGAS 210

Tn/cm CONCRETO EN COLUMNAS 210CONCRETO EN PLACAS 210

W2= 12 Tn MODULO DE POISSON µ = 0.172. DIMENSIONES:

Tn/cm COLUMNAS : b x h = 30VIGAS PRINCPALES : b x h = 30

W1= 13 tn 3. ANALISIS :NO CONSIDERAR PESO DE VIGAS

Tn/cm NO CONSIDERAR PESO DE COLUMNAS

6.521 6.521

2.751 2.751 2.751

1.409 0.352 1.409

E : 15000*fc^0.5 kg/cm2

0-K3 Tn/cmK3

0.00000 Ø1n0.00000 * Ø2n0.00510

0.0000Wn² -13.0422

13.0422 - 0.00510 Wn²

- 341.144 .= 0

PERIODO NATURAL CORRESPONDIENTE

T1 = 0.6598 sT2 = 0.1840 sT3 = 0.1006 s

ANALISIS DEL ESPECTRO (CONVERSION)

0.2010 0.01325 0.00000 0.000000.1611 M= 0.00000 0.01223 0.00000 Tn*s²/cm0.5996 0.00000 0.00000 0.00510

1* 1

1

604.740 0 0 90.696 90.696 90.696

* 0 520.339 0 ÷ 1165.744 1165.744 1165.7440 0 634.832 3904.185 3904.185 3904.185

6.667738 0 00 0.44636 00 0 0.162603

M155

USER: NO COPIAR ESTA MATRIZ EN TU HOJA DE CALCULO

kg/cm2kg/cm2kg/cm2

* 30 cm* 60 cm

sismorresistente n° g.d.l varios - modificado

Documents