Espectros Frecuencias y Modales Elias

PROYECTO "B" TIPO "1"

PISO (i) Ko (cm3) H (cm) Kxi (Tn/cm)

1 23.11 210 1000 320 568.722 7.70 210 1000 320 189.493 7.70 210 1000 320 189.494 7.70 210 1000 320 189.495 7.70 210 1000 320 189.496 7.70 210 1000 320 189.497 7.70 210 1000 320 189.49

0.425 (Tn*seg2/cm)

K7= 189.492 (Tn/cm)

0.459 (Tn*seg2/cm)

K6= 189.492 (Tn/cm)

0.459 (Tn*seg2/cm)

K5= 189.492 (Tn/cm)

0.459 (Tn*seg2/cm)

K4= 189.492 (Tn/cm)

0.459 (Tn*seg2/cm)

K3= 189.492 (Tn/cm)

0.459 (Tn*seg2/cm)

K2= 189.492 (Tn/cm)

0.459 (Tn*seg2/cm)

CALCULO DE RIGIDECES Ki EN LA DIRECCION "X" EN (Tn/cm) EN BASE A RESULTADOS DE LOS VALORES Dji CALCULADOS POR EL METODO MUTUO

SUMA DE LOS Dx

Ec (C°A°) (Tn/cm2)

m7

m600000

m5

m1

m2

m4

m3

K1= 568.723 (Tn/cm)

CALCULO DEL PRIMER PERIODO Y MODO POR STODOLA

Piso "i"

7 7 0.425 2.975 2.975 189.492 0.0166 6 0.459 2.754 5.729 189.492 0.0305 5 0.459 2.295 8.023 189.492 0.0424 4 0.459 1.836 9.859 189.492 0.0523 3 0.459 1.377 11.236 189.492 0.0592 2 0.459 0.918 12.154 189.492 0.0641 1 0.459 0.459 12.613 568.723 0.022

Piso "i"

7 12.892 0.425 5.479 5.479 189.492 0.0296 12.184 0.459 5.592 11.071 189.492 0.0585 10.821 0.459 4.966 16.037 189.492 0.0854 8.912 0.459 4.090 20.128 189.492 0.1063 6.566 0.459 3.013 23.141 189.492 0.1222 3.892 0.459 1.786 24.927 189.492 0.1321 1.000 0.459 0.459 25.386 568.723 0.045

Piso "i"

7 12.915 0.425 5.489 5.489 189.492 0.0296 12.267 0.459 5.630 11.119 189.492 0.0595 10.959 0.459 5.029 16.149 189.492 0.0854 9.063 0.459 4.159 20.308 189.492 0.1073 6.683 0.459 3.067 23.375 189.492 0.1232 3.947 0.459 1.811 25.186 189.492 0.1331 1.000 0.459 0.459 25.645 568.723 0.045

Piso "i"

7 12.893 0.425 5.480 5.480 189.492 0.0296 12.251 0.459 5.623 11.102 189.492 0.059

𝜙_𝑖 𝑚_𝑖 𝜙_𝑖∗𝑚_𝑖 ∑▒〖𝑚 _𝑖_∗𝜙 𝑖 〗 𝑘_𝑖 (∑▒〖𝑚 _𝑖∗

_ 𝜙 𝑖 〗 )/ _𝑘 𝑖


_ 𝜙 𝑖 〗 )/ _𝑘 𝑖


_ 𝜙 𝑖 〗 )/ _𝑘 𝑖


_ 𝜙 𝑖 〗 )/ _𝑘 𝑖

5 10.950 0.459 5.025 16.128 189.492 0.0854 9.060 0.459 4.158 20.286 189.492 0.1073 6.683 0.459 3.067 23.353 189.492 0.1232 3.948 0.459 1.812 25.165 189.492 0.1331 1.000 0.459 0.459 25.624 568.723 0.045

Piso "i"

7 12.890 0.425 5.479 5.479 189.492 0.0296 12.248 0.459 5.621 11.100 189.492 0.0595 10.948 0.459 5.025 16.124 189.492 0.0854 9.059 0.459 4.158 20.282 189.492 0.1073 6.683 0.459 3.067 23.349 189.492 0.1232 3.948 0.459 1.812 25.161 189.492 0.1331 1.000 0.459 0.459 25.620 568.723 0.045

PRIMERA FRECUENCIA PRIMER PERIODO PRIMER MODO

22.199 1.334

4.712

ACELERACIÓN ESPECTRAL

LOS RESULTADOS OBTENIDOS SON: C

0.4 0.0 2.501.5 0.1 2.501.27 0.2 2.50980 0.3 2.507 0.4 2.5022.4 0.5 2.50

DATOS DE NUESTRO TRABAJO

ESCALONADO


_ 𝜙 𝑖 〗 )/ _𝑘 𝑖

〖𝜔 _1〗^2=𝜔_1=

𝑇_1=

𝜙_1=

𝑆_𝑎=(𝑍∗𝑈∗𝐶∗𝑆)/𝑅∗𝑔

𝑍= 𝑇_𝐸=𝐻_𝐸/𝐶_𝑇 𝑈=𝑆=𝑔= 𝐶=2.5 (𝑇_𝑆/𝑇_𝐸 )≤2.5𝑅=𝐻_𝐸=𝐶_𝑇=

( _𝑇 𝐸 )



(𝑇_𝐸 )



35 0.6 2.500.7 0.7 2.50

0.8 2.190.9 1.941.0 1.751.1 1.591.2 1.461.3 1.351.4 1.251.5 1.171.6 1.091.7 1.031.8 0.971.9 0.922.0 0.882.1 0.832.2 0.802.3 0.762.4 0.732.5 0.702.6 0.672.7 0.652.8 0.63

DATOS DE NUESTRO TRABAJO

ESCALONADO 𝑆_𝑎=(𝑍∗𝑈∗𝐶∗𝑆)/𝑅∗𝑔𝐶_𝑇=𝑇_𝑆=

0.0 0.5 1.0 1.5 2.0 2.5 3.00.00

0.05

0.10

0.15

0.20

0.25

0.30

ACELERACIÓN ESPECTRAL E-030

PERIODO DE LA ESTRUCTURA (Te) (seg)

ACEL

ERAC

IÓN

ESPE

CTRA

L (Sa

) (m

/seg

2)

𝑆_𝑎=(𝑍∗𝑈∗𝐶∗𝑆)/𝑅∗𝑔𝐶_𝑇=𝑇_𝑆=

0.0 0.5 1.0 1.5 2.0 2.5 3.00.00

0.05

0.10

0.15

0.20

0.25

0.30 7; 0.27

ACELERACION ESPECTRAL E-030


ACEL

ERAC

IÓN

ESPE

CTRA

L (Sa

) (m

/seg

2)

𝑆_𝑎=(𝑍∗𝑈∗𝐶∗𝑆)/𝑅∗𝑔𝐶_𝑇=𝑇_𝑆=

0.5 1.0 1.5 2.0 2.5 3.00.00

0.05

0.10

0.15

0.20

0.25

0.301; 0.27

f(x) = 0.1905 x^-1

ECUACION DE ACELERACION ESPECTRAL


ACEL

ERAC

IÓN

ESPE

CTRA

L (Sa

) (m

/seg

2)


PISO (i) Ko (cm3) H (cm) Kyi (Tn/cm)

1 7.30 210 1000 320 179.652 5.82 210 1000 320 143.233 5.82 210 1000 320 143.234 5.82 210 1000 320 143.235 5.82 210 1000 320 143.236 5.82 210 1000 320 143.237 5.82 210 1000 320 143.23

0.425 (Tn*seg2/cm)

K7= 143.227 (Tn/cm)

0.459 (Tn*seg2/cm)

K6= 143.227 (Tn/cm)

0.459 (Tn*seg2/cm)

K5= 143.227 (Tn/cm)

0.459 (Tn*seg2/cm)

K4= 143.227 (Tn/cm)

0.459 (Tn*seg2/cm)

K3= 143.227 (Tn/cm)

0.459 (Tn*seg2/cm)

K2= 143.227 (Tn/cm)

0.459 (Tn*seg2/cm)

CALCULO DE RIGIDECES Ki EN LA DIRECCION "Y" EN (Tn/cm) EN BASE A RESULTADOS DE LOS VALORES Dji CALCULADOS POR EL METODO MUTUO

SUMA DE LOS Dy


m7

m600000

m5

m1

m2

m4

m3

K1= 179.648 (Tn/cm)

CALCULO DEL SEGUNDO PERIODO Y MODO POR EL METODO HOLSER

133.196CALCULO DEL PRIMER PERIODO Y MODO POR STODOLA

Piso "i"

0.286 24.483 12.892 7 0.425 1.0000.270 22.204 12.184 6 0.459 0.7010.240 20.835 10.821 5 0.459 0.1760.198 20.239 8.912 4 0.459 -0.4060.146 20.603 6.566 3 0.459 -0.8570.086 23.170 3.892 2 0.459 -1.0310.022 45.090 1.000 1 0.459 -0.873

-0.727218

Piso "i"0.576 22.363 12.9150.548 22.251 12.267 7 0.425 1.0000.489 22.122 10.959 6 0.459 0.5110.405 22.030 9.063 5 0.459 -0.2480.298 22.010 6.683 4 0.459 -0.8760.176 22.091 3.947 3 0.459 -1.0410.045 22.403 1.000 2 0.459 -0.657

1 0.459 0.0740.305

INTERPOLANDO:0.581 22.214 12.8930.552 22.206 12.2510.494 22.194 10.9500.409 22.183 9.060 133.1960.301 22.176 6.6830.178 22.173 3.948 -0.7270.045 22.177 1.000

Piso "i"

0.581 22.201 12.890 7 0.425 1.0000.552 22.200 12.248 6 0.459 0.567

(∑▒〖𝑚 _𝑖∗_ 𝜙 𝑖 〗 )/ _𝑘 𝑖 𝛿_𝑖 �̂�2 𝐷_𝑖/𝐷_1

(∑▒〖𝑚 _𝑖∗_ 𝜙 𝑖 〗 )/ _𝑘 𝑖 𝛿_𝑖 �̂�2 𝐷_𝑖/𝐷_1

(∑▒〖𝑚 _𝑖∗_ 𝜙 𝑖 〗 )/ _𝑘 𝑖 𝛿_𝑖 �̂�2 𝐷_𝑖/𝐷_1

(∑▒〖𝑚 _𝑖∗_ 𝜙 𝑖 〗 )/ _𝑘 𝑖 𝛿_𝑖 �̂�2 𝐷_𝑖/𝐷_1

〖𝜔 _2〗 ^2=〖〖 6𝜔〗_1〗 ^2=𝑚_𝑖 〖𝐹 _𝑖=𝜙〗 _𝑖∗𝑚_𝑖* ^2𝜔2𝜙_0

2𝜙_0=

〖𝜔 _2〗 ^2= 𝑚_𝑖 〖𝐹 _𝑖=𝜙〗 _𝑖∗𝑚_𝑖* ^2𝜔𝜙_0

𝜙_0=

〖𝜔 _2〗 ^2

𝑚_𝑖 〖𝐹 _𝑖=𝜙〗 _𝑖∗𝑚_𝑖* ^2𝜔𝜙_0

0.493 22.199 10.948 5 0.459 -0.1310.408 22.197 9.059 4 0.459 -0.7670.301 22.196 6.683 3 0.459 -1.0460.178 22.196 3.948 2 0.459 -0.8350.045 22.195 1.000 1 0.459 -0.234

0.002

SEGUNDA FRECUENCIA

192.9530.581 22.199 12.8900.552 22.199 12.248

13.8910.493 22.199 10.9480.408 22.199 9.0590.301 22.199 6.6830.178 22.199 3.9480.045 22.199 1.000

PRIMER MODO12.89012.24810.9489.0596.6833.9481.000


0.27 #DIV/0! #DIV/0! #DIV/0!0.27 62.83 0.0043 0.00010.27 31.42 0.0087 0.00030.27 20.94 0.0130 0.00060.27 15.71 0.0173 0.00110.27 12.57 0.0217 0.0017

(∑▒〖𝑚 _𝑖∗_ 𝜙 𝑖 〗 )/ _𝑘 𝑖 𝛿_𝑖 �̂�2 𝐷_𝑖/𝐷_1

𝜙_0=

〖𝜔 _2〗^2=𝜔_2=

𝑆_𝑎𝑆_𝑎 𝑤_𝑖 𝑆_𝑣 𝑆_𝐷

0.0 0.5 1.0 1.5 2.0 2.5 3.00.0000

0.0050

0.0100

0.0150

0.0200

0.0250

0.0300

0.0350

VELOCIDAD ESPECTRAL

Te (PERIODO DE LA ESTRUCTURA) (seg)

Sv (V

ELO

CIDA

D ES

PECT

RAL)

(m/s

eg.)

0.27 10.47 0.0260 0.00250.27 8.98 0.0303 0.00340.24 7.85 0.0303 0.00390.21 6.98 0.0303 0.00430.19 6.28 0.0303 0.00480.17 5.71 0.0303 0.00530.16 5.24 0.0303 0.00580.15 4.83 0.0303 0.00630.14 4.49 0.0303 0.00680.13 4.19 0.0303 0.00720.12 3.93 0.0303 0.00770.11 3.70 0.0303 0.00820.11 3.49 0.0303 0.00870.10 3.31 0.0303 0.00920.10 3.14 0.0303 0.00970.09 2.99 0.0303 0.01010.09 2.86 0.0303 0.01060.08 2.73 0.0303 0.01110.08 2.62 0.0303 0.01160.08 2.51 0.0303 0.01210.07 2.42 0.0303 0.01250.07 2.33 0.0303 0.01300.07 2.24 0.0303 0.0135

0.0 0.5 1.0 1.5 2.0 2.5 3.00.0000

0.0050

0.0100

0.0150

0.0200

0.0250

0.0300

0.0350

VELOCIDAD ESPECTRAL


Sv (V

ELO

CIDA

D ES

PECT

RAL)

(m/s

eg.)

0.0 0.5 1.0 1.5 2.0 2.5 3.00.0000

0.0020

0.0040

0.0060

0.0080

0.0100

0.0120

0.0140

0.0160

DESPLAZAMIENTO ESPECTRAL

Te (PERIODO DE LA ESTRUCTURA) (seg)Sd

(DES

PLAZ

AMIE

NTO

ESP

ECTR

AL) (

m)


56.610 56.610 189.492 0.29942.867 99.477 189.492 0.52510.776 110.254 189.492 0.582-24.791 85.462 189.492 0.451-52.361 33.101 189.492 0.175-63.039 -29.938 189.492 -0.158-53.381 -83.320 568.723 -0.147

92.653 92.653 189.492 0.48951.130 143.783 189.492 0.759-24.786 118.997 189.492 0.628-87.615 31.382 189.492 0.166

-104.184 -72.802 189.492 -0.384-65.746 -138.548 189.492 -0.7317.406 -131.142 568.723 -0.231

0.305 192.953

218

82.008 82.008 189.492 0.43350.230 132.238 189.492 0.698

〖𝐹 _𝑖=𝜙〗 _𝑖∗𝑚_𝑖* ^2𝜔 𝑘_𝑖𝑄_𝑖=∑▒〖〖〗𝜙 _𝑖_ "*" ^2∗𝑚 𝑖 𝜔 〗 𝛿_𝑖= _𝑄 𝑖/

_𝑘 𝑖


_𝑘 𝑖

〖𝜔 _2〗 ^2=


_𝑘 𝑖

-11.568 120.670 189.492 0.637-67.960 52.710 189.492 0.278-92.593 -39.883 189.492 -0.210-73.954 -113.838 189.492 -0.601-20.755 -134.593 568.723 -0.237

SEGUNDO PERIODO SEGUNDO MODO

0.452 -4.267-2.4200.5573.2744.4613.5631.000

1° MODO 2° MODO 3° MODO

DATO

m7 0.425 0.425 0.425m6 0.459 0.459 0.459m5 0.459 0.459 0.459m4 0.459 0.459 0.459m3 0.459 0.459 0.459m2 0.459 0.459 0.459m1 0.459 0.459 0.459

4.712 13.891 22.30412.890 -4.267 2.39912.248 -2.420 -0.27810.948 0.557 -2.6209.059 3.274 -1.8056.683 4.461 1.1843.948 3.563 2.7471.000 1.000 1.000

T1 1.334 0.452 0.282

0.098 0.096 0.096198.417 584.973 939.27542.112 42.112 42.1128.938 3.032 1.888

X7 11.342 -1.246 0.436X6 10.777 -0.706 -0.050X5 9.633 0.163 -0.476X4 7.971 0.956 -0.328X3 5.880 1.302 0.215X2 3.473 1.040 0.499

𝑇_2=

𝜙_2=

0.0 0.5 1.0 1.5 2.0 2.5 3.00.0000

0.0050

0.0100

0.0150

0.0200

0.0250

0.0300

0.0350

VELOCIDAD ESPECTRAL


Sv (V

ELO

CIDA

D ES

PECT

RAL)

(m/s

eg.)

𝜔_𝑖=

𝜙_𝑖=

𝛽_𝑖=𝑆_𝐴=𝑆_𝑉=𝑆_𝐷=

X1 0.880 0.292 0.182251.779 -240.328 216.677239.243 -136.319 -25.087213.844 31.395 -236.625176.947 184.437 -163.066130.536 251.287 106.96477.107 200.705 248.11819.533 56.327 90.327

F7 107.010 -102.143 92.091F6 109.799 -62.563 -11.513F5 98.142 14.408 -108.598F4 81.208 84.646 -74.838F3 59.909 115.327 49.090F2 35.388 92.112 113.872F1 8.965 25.851 41.455

11.81910.9849.8028.3406.3693.9981.047

F7 206.003F6 141.141F5 165.598F4 164.530F3 160.272F2 173.351F1 56.321

7448.628 -371.087 449.0647670.725

0.0 0.5 1.0 1.5 2.0 2.5 3.00.0000

0.0050

0.0100

0.0150

0.0200

0.0250

0.0300

0.0350

VELOCIDAD ESPECTRAL


Sv (V

ELO

CIDA

D ES

PECT

RAL)

(m/s

eg.)

0.0 0.5 1.0 1.5 2.0 2.5 3.00.0000

0.0020

0.0040

0.0060

0.0080

0.0100

0.0120

0.0140

0.0160

DESPLAZAMIENTO ESPECTRAL


Sd (D

ESPL

AZAM

IENT

O E

SPEC

TRAL

) (m

)

𝑋 ̈,7𝑋 ̈,6𝑋 ̈,5𝑋 ̈,4𝑋 ̈,3𝑋 ̈,2𝑋 ̈,1

𝑟_𝑚𝑎𝑥

𝑀_𝑉𝑂𝐿𝑇𝐸𝑂𝑀_(𝑉𝑂𝐿𝑇𝐸𝑂 𝑀Á𝑋.)

CALCULO DEL TERCER PERIODO Y MODO POR EL METODO HOLSER

332.990

Piso "i"

7 0.425 1.000 141.526 141.526 189.492 0.7476 0.459 0.253 38.684 180.210 189.492 0.9515 0.459 -0.698 -106.653 73.557 189.492 0.3884 0.459 -1.086 -165.976 -92.419 189.492 -0.4883 0.459 -0.598 -91.441 -183.860 189.492 -0.9702 0.459 0.372 56.840 -127.020 189.492 -0.6701 0.459 1.042 159.281 32.261 568.723 0.057

0.986500

Piso "i"

7 0.425 1.000 212.508 212.508 189.492 1.1216 0.459 -0.121 -27.871 184.636 189.492 0.9745 0.459 -1.096 -251.463 -66.826 189.492 -0.3534 0.459 -0.743 -170.537 -237.364 189.492 -1.2533 0.459 0.509 116.906 -120.458 189.492 -0.6362 0.459 1.145 262.778 142.320 189.492 0.7511 0.459 0.394 90.430 232.751 568.723 0.409

-0.015

INTERPOLANDO:

-0.015 497.47332.990

5000.986

Piso "i"

7 0.425 1.000 211.432 211.432 189.492 1.1166 0.459 -0.116 -26.434 184.998 189.492 0.976

〖𝜔 _3〗 ^2=〖〖 15𝜔〗 _1〗 ^2=𝑚_𝑖 〖𝐹 _𝑖=𝜙〗 _𝑖∗𝑚_𝑖* ^2𝜔 𝑘_𝑖𝑄_𝑖=∑▒〖〖〗𝜙 _𝑖

_ "*" ^2∗𝑚 𝑖 𝜔 〗 𝛿_𝑖= _𝑄 𝑖/_𝑘 𝑖 3𝜙_0

3𝜙_0=

〖𝜔 _3〗 ^2= 𝑚_𝑖 〖𝐹 _𝑖=𝜙〗 _𝑖∗𝑚_𝑖* ^2𝜔 𝑘_𝑖𝑄_𝑖=∑▒〖〖〗𝜙 _𝑖

_ "*" ^2∗𝑚 𝑖 𝜔 〗 𝛿_𝑖= _𝑄 𝑖/_𝑘 𝑖 〖3𝜙

〗_0

〖3𝜙〗 _0=

〖𝜔 _3〗 ^2

〖𝜔 _3〗 ^2=

𝑚_𝑖 〖𝐹 _𝑖=𝜙〗 _𝑖∗𝑚_𝑖* ^2𝜔 𝑘_𝑖𝑄_𝑖=∑▒〖〖〗𝜙 _𝑖_ "*" ^2∗𝑚 𝑖 𝜔 〗 𝛿_𝑖= _𝑄 𝑖/

_𝑘 𝑖 𝜙_0

5 0.459 -1.092 -249.328 -64.330 189.492 -0.3394 0.459 -0.753 -171.820 -236.150 189.492 -1.2463 0.459 0.494 112.706 -123.444 189.492 -0.6512 0.459 1.145 261.438 137.994 189.492 0.7281 0.459 0.417 95.176 233.170 568.723 0.410

0.007

TERCERA FRECUENCIA TERCER PERIODO TERCER MODO

497.468 0.282

22.304

〖3𝜙〗 _0=

〖𝜔 _3〗^2=𝜔_3=

𝑇_3=

𝜙_3=

𝑟_𝑚𝑎𝑥=0.25∑_(𝑖=1)^𝑛▒|𝑟_𝑖 | +0.75√(∑_(𝑖=1)^𝑛▒〖𝑟 _𝑖〗^2 ) ; 𝑟_𝑖=𝑋_𝑖


Piso "i"

7 7 0.425 2.975 2.9756 6 0.459 2.754 5.7295 5 0.459 2.295 8.0234 4 0.459 1.836 9.8593 3 0.459 1.377 11.2362 2 0.459 0.918 12.1541 1 0.459 0.459 12.613

Piso "i"

7 5.970 0.425 2.537 2.5376 5.674 0.459 2.604 5.1415 5.104 0.459 2.343 7.4844 4.306 0.459 1.976 9.4603 3.326 0.459 1.526 10.9872 2.209 0.459 1.014 12.0011 1.000 0.459 0.459 12.460

Piso "i"

7 5.793 0.425 2.462 2.4626 5.538 0.459 2.541 5.0045 5.020 0.459 2.304 7.3074 4.267 0.459 1.958 9.2653 3.314 0.459 1.521 10.7862 2.208 0.459 1.013 11.8001 1.000 0.459 0.459 12.259

Piso "i"

7 5.771 0.425 2.453 2.4536 5.519 0.459 2.533 4.985

𝜙_𝑖 𝑚_𝑖 𝜙_𝑖∗𝑚_𝑖 ∑▒〖𝑚 _𝑖∗𝜙_𝑖 〗

𝜙_𝑖 𝑚_𝑖 𝜙_𝑖∗𝑚_𝑖 ∑▒〖𝑚 _𝑖∗𝜙_𝑖 〗

𝜙_𝑖 𝑚_𝑖 𝜙_𝑖∗𝑚_𝑖 ∑▒〖𝑚 _𝑖_∗𝜙 𝑖 〗

𝜙_𝑖 𝑚_𝑖 𝜙_𝑖∗𝑚_𝑖 ∑▒〖𝑚 _𝑖_∗𝜙 𝑖 〗𝜙_𝑖

5 5.007 0.459 2.298 7.2834 4.259 0.459 1.955 9.2383 3.311 0.459 1.520 10.7572 2.207 0.459 1.013 11.7701 1.000 0.459 0.459 12.229

TERCER MODOPiso "i"

2.399-0.278 7 5.768 0.425 2.451 2.451-2.620 6 5.516 0.459 2.532 4.983-1.805 5 5.005 0.459 2.297 7.2801.184 4 4.258 0.459 1.954 9.2342.747 3 3.311 0.459 1.519 10.7541.000 2 2.207 0.459 1.013 11.767

1 1.000 0.459 0.459 12.226

PRIMERA FRECUENCIA PRIMER PERIODO

14.695 1.639

3.833

𝜙_𝑖 𝑚_𝑖 𝜙_𝑖∗𝑚_𝑖 ∑▒〖𝑚 _𝑖_∗𝜙 𝑖 〗

〖𝜔 _1〗^2=𝜔_1=

𝑇_1=



Piso "i"

143.227 0.021 0.419 16.701 5.970 7143.227 0.040 0.398 15.061 5.674 6143.227 0.056 0.358 13.952 5.104 5143.227 0.069 0.302 13.230 4.306 4143.227 0.078 0.234 12.847 3.326 3143.227 0.085 0.155 12.898 2.209 2179.648 0.070 0.070 14.243 1.000 1

Piso "i"143.227 0.018 0.402 14.859 5.793143.227 0.036 0.384 14.774 5.538 7143.227 0.052 0.348 14.661 5.020 6143.227 0.066 0.296 14.554 4.267 5143.227 0.077 0.230 14.470 3.314 4143.227 0.084 0.153 14.422 2.208 3179.648 0.069 0.069 14.419 1.000 2

1

143.227 0.017 0.394 14.712 5.771143.227 0.035 0.377 14.705 5.519143.227 0.051 0.342 14.693 5.007143.227 0.065 0.291 14.681 4.259 88.171143.227 0.075 0.226 14.669 3.311143.227 0.082 0.151 14.660 2.207 -0.735179.648 0.068 0.068 14.655 1.000

Piso "i"

143.227 0.017 0.393 14.697 5.768 7143.227 0.035 0.376 14.696 5.516 6

𝑘_𝑖 (∑▒〖𝑚 _𝑖∗𝜙_𝑖 〗 )/𝑘_𝑖 𝛿_𝑖 �̂�2 𝐷_𝑖/𝐷_1

𝑘_𝑖 (∑▒〖𝑚 _𝑖∗𝜙_𝑖 〗 )/𝑘_𝑖 𝛿_𝑖 �̂�2 𝐷_𝑖/𝐷_1

𝑘_𝑖 (∑▒〖𝑚 _𝑖∗𝜙_𝑖 〗 )/𝑘_𝑖 𝛿_𝑖 �̂�2 𝐷_𝑖/𝐷_1

𝑘_𝑖 (∑▒〖𝑚 _𝑖∗_ 𝜙 𝑖 〗 )/ _𝑘 𝑖 𝛿_𝑖 �̂�2 𝐷_𝑖/𝐷_1

〖𝜔 _2〗 ^2=

143.227 0.051 0.341 14.695 5.005 5143.227 0.064 0.290 14.693 4.258 4143.227 0.075 0.225 14.692 3.311 3143.227 0.082 0.150 14.691 2.207 2179.648 0.068 0.068 14.690 1.000 1

SEGUNDA FRECUENCIA

143.227 0.017 0.392 14.695 5.768143.227 0.035 0.375 14.695 5.516143.227 0.051 0.341 14.695 5.005143.227 0.064 0.290 14.695 4.258143.227 0.075 0.225 14.695 3.310143.227 0.082 0.150 14.695 2.207179.648 0.068 0.068 14.694 1.000

PRIMER MODO5.7685.5165.0054.2583.3102.2071.000

𝑘_𝑖 (∑▒〖𝑚 _𝑖∗_ 𝜙 𝑖 〗 )/ _𝑘 𝑖 𝛿_𝑖 �̂�2 𝐷_𝑖/𝐷_1

𝜙_1=

〖𝜔 _2〗^2=𝜔_2=


88.171

0.425 1.000 37.474 37.474 143.227 0.2620.459 0.738 29.878 67.352 143.227 0.4700.459 0.268 10.849 78.201 143.227 0.5460.459 -0.278 -11.245 66.956 143.227 0.4670.459 -0.745 -30.162 36.794 143.227 0.2570.459 -1.002 -40.558 -3.764 143.227 -0.0260.459 -0.976 -39.494 -43.258 179.648 -0.241

-0.735145.000

0.425 1.000 61.627 61.627 143.227 0.4300.459 0.570 37.913 99.540 143.227 0.6950.459 -0.125 -8.336 91.205 143.227 0.6370.459 -0.762 -50.712 40.493 143.227 0.2830.459 -1.045 -69.526 -29.033 143.227 -0.2030.459 -0.842 -56.036 -85.069 143.227 -0.5940.459 -0.248 -16.511 -101.580 179.648 -0.565

0.317

INTERPOLANDO:

0.317 127.867

145

0.425 1.000 54.345 54.345 143.227 0.3790.459 0.621 36.417 90.762 143.227 0.634

〖𝜔 _2〗 ^2=〖〖 6𝜔〗_1〗 ^2=𝑚_𝑖 〖𝐹 _𝑖=𝜙〗 _𝑖∗𝑚_𝑖*𝜔^2 𝑘_𝑖𝑄_𝑖=∑▒ 〖〖〗𝜙 _𝑖∗𝑚_𝑖 "∗" 𝜔^2 〗

𝛿_𝑖=𝑄_𝑖/𝑘_𝑖 2𝜙_0

2𝜙_0=

〖𝜔 _2〗 ^2= 𝑚_𝑖 〖𝐹 _𝑖=𝜙〗 _𝑖∗𝑚_𝑖*𝜔^2 𝑘_𝑖𝑄_𝑖=∑▒ 〖〖〗𝜙 _𝑖∗𝑚_𝑖 "∗" 𝜔^2 〗

𝛿_𝑖=𝑄_𝑖/𝑘_𝑖 𝜙_0

𝜙_0=

〖𝜔 _2〗 ^2

〖𝜔 _2〗 ^2=


_𝑘 𝑖 𝜙_0

0.459 -0.013 -0.771 89.992 143.227 0.6280.459 -0.641 -37.642 52.349 143.227 0.3650.459 -1.007 -59.091 -6.742 143.227 -0.0470.459 -0.960 -56.329 -63.071 143.227 -0.4400.459 -0.520 -30.487 -93.558 179.648 -0.521

0.001

SEGUNDA FRECUENCIA SEGUNDO PERIODO SEGUNDO MODO

127.867 0.556 -1.925-1.195

11.308 0.0251.2351.9381.8481.000

𝜙_0=

𝑇_2=

𝜙_2=


220.429

Piso "i"

7 0.425 1.000 93.686 93.686 143.2276 0.459 0.346 34.992 128.678 143.2275 0.459 -0.553 -55.896 72.782 143.2274 0.459 -1.061 -107.303 -34.522 143.2273 0.459 -0.820 -82.920 -117.442 143.2272 0.459 0.000 0.032 -117.410 143.2271 0.459 0.820 82.961 -34.449 179.648

1.012332

Piso "i"

7 0.425 1.000 141.105 141.105 143.2276 0.459 0.015 2.257 143.362 143.2275 0.459 -0.986 -150.256 -6.894 143.2274 0.459 -0.938 -142.922 -149.816 143.2273 0.459 0.108 16.458 -133.359 143.2272 0.459 1.039 158.329 24.971 143.2271 0.459 0.865 131.765 156.735 179.648

-0.008

INTERPOLANDO:

-0.008220.429

3321.012

Piso "i"

7 0.425 1.000 140.748 140.748 143.2276 0.459 0.017 2.630 143.378 143.227

〖𝜔 _3〗 ^2=〖〖 15𝜔〗 _1〗 ^2=𝑚_𝑖 〖𝐹 _𝑖=𝜙〗 _𝑖∗𝑚_𝑖*𝜔^2 𝑘_𝑖𝑄_𝑖=∑▒ 〖〖〗𝜙 _𝑖∗𝑚_𝑖 "∗" 𝜔^2 〗


3𝜙_0=


𝛿_𝑖=𝑄_𝑖/𝑘_𝑖 〖3𝜙〗_0

〖3𝜙〗 _0=

〖𝜔 _3〗 ^2

〖𝜔 _3〗 ^2=


_𝑘 𝑖 𝜙_0

5 0.459 -0.984 -149.514 -6.136 143.2274 0.459 -0.941 -143.003 -149.139 143.2273 0.459 0.100 15.254 -133.885 143.2272 0.459 1.035 157.324 23.440 143.2271 0.459 0.871 132.452 155.891 179.648

0.004

TERCERA FRECUENCIA TERCER PERIODO

331.159 0.345

18.198

〖3𝜙〗 _0=

〖𝜔 _3〗^2=𝜔_3=

𝑇_3=


0.6540.8980.508-0.241-0.820-0.820-0.192

0.9851.001-0.048-1.046-0.9310.1740.872

331.159

0.9831.001

𝛿_𝑖=𝑄_𝑖/𝑘_𝑖


〖𝜔 _3〗 ^2=

𝛿_𝑖= _𝑄 𝑖/_𝑘 𝑖

-0.043-1.041-0.9350.1640.868

TERCER MODO1.1470.020-1.129-1.0800.1151.1881.000

𝜙_3=


PISO (i) Ko (cm3) H (cm) Kxi (Tn/cm)

1 23.11 210 1000 320 300.002 7.70 210 1000 320 280.003 7.70 210 1000 320 250.004 7.70 210 1000 320 200.005 7.70 210 1000 320 200.006 7.70 210 1000 320 190.007 7.70 210 1000 320 170.00

1.327 (Tn*seg2/cm)

K7= 170.000 (Tn/cm)

1.480 (Tn*seg2/cm)

K6= 190.000 (Tn/cm)

1.480 (Tn*seg2/cm)

K5= 200.000 (Tn/cm)

1.531 (Tn*seg2/cm)

K4= 200.000 (Tn/cm)

1.633 (Tn*seg2/cm)

K3= 250.000 (Tn/cm)

1.735 (Tn*seg2/cm)

K2= 280.000 (Tn/cm)

1.837 (Tn*seg2/cm)

K1= 300.000 (Tn/cm)

CALCULO DE RIGIDECES Ki EN LA DIRECCION "X" EN (Tn/cm) EN BASE A RESULTADOS DE LOS VALORES Dji CALCULADOS POR EL METODO MUTUO

SUMA DE LOS Dx


m7

m600000

m5

m1

m2

m4

m3

1periodo

Piso "i"

7 7 1.330 9.310 9.310 170.000 0.0556 6 1.480 8.880 18.190 190.000 0.0965 5 1.480 7.400 25.590 200.000 0.1284 4 1.530 6.120 31.710 200.000 0.1593 3 1.630 4.890 36.600 250.000 0.1462 2 1.730 3.460 40.060 280.000 0.1431 1 1.840 1.840 41.900 300.000 0.140

Piso "i"

7 6.201 1.330 8.248 8.248 170.000 0.0496 5.809 1.480 8.598 16.846 190.000 0.0895 5.124 1.480 7.583 24.429 200.000 0.1224 4.208 1.530 6.438 30.867 200.000 0.1543 3.073 1.630 5.008 35.875 250.000 0.1442 2.024 1.730 3.502 39.378 280.000 0.1411 1.000 1.840 1.840 41.218 300.000 0.137

Piso "i"

7 6.079 1.330 8.085 8.085 170.000 0.0486 5.726 1.480 8.474 16.559 190.000 0.0875 5.080 1.480 7.519 24.078 200.000 0.1204 4.191 1.530 6.413 30.491 200.000 0.1523 3.068 1.630 5.001 35.492 250.000 0.1422 2.024 1.730 3.501 38.993 280.000 0.1391 1.000 1.840 1.840 40.833 300.000 0.136

Piso "i"

7 6.061 1.330 8.060 8.060 170.000 0.0476 5.711 1.480 8.452 16.513 190.000 0.0875 5.071 1.480 7.505 24.018 200.000 0.1204 4.186 1.530 6.405 30.423 200.000 0.1523 3.066 1.630 4.998 35.421 250.000 0.1422 2.023 1.730 3.500 38.921 280.000 0.1391 1.000 1.840 1.840 40.761 300.000 0.136

𝜙_𝑖 𝑚_𝑖 𝜙_𝑖∗𝑚_𝑖 ∑▒〖𝑚 _𝑖∗𝜙_𝑖 〗 𝑘_𝑖 (∑▒〖𝑚 _𝑖∗𝜙_𝑖 〗 )/𝑘_𝑖




Piso "i"

7 6.058 1.330 8.057 8.057 170.000 0.0476 5.709 1.480 8.449 16.506 190.000 0.0875 5.069 1.480 7.503 24.009 200.000 0.1204 4.185 1.530 6.404 30.412 200.000 0.1523 3.066 1.630 4.997 35.410 250.000 0.1422 2.023 1.730 3.500 38.910 280.000 0.1391 1.000 1.840 1.840 40.750 300.000 0.136

PRIMERA FRECUENCIA PRIMER PERIODO PRIMER MODO

7.360 2.316

2.713


LOS RESULTADOS OBTENIDOS SON: C

0.4 0.0 2.501.5 0.1 2.501.27 0.2 2.509.806 0.3 2.507 0.4 2.5022.4 0.5 2.5035 0.6 2.500.7 0.7 2.50

0.8 2.190.9 1.941.0 1.751.1 1.591.2 1.461.3 1.351.4 1.25


〖𝜔 _1〗^2=𝜔_1=

𝑇_1=

𝜙_1=



(𝑇_𝐸 )

𝑇_𝑆=

0.0 0.5 1.0 1.5 2.0 2.5 3.00.00

0.05

0.10

0.15

0.20

0.25

0.30



ACEL

ERAC

IÓN

ESPE

CTRA

L (Sa

) (m

/seg

2)

1.5 1.171.6 1.091.7 1.031.8 0.971.9 0.922.0 0.882.1 0.832.2 0.802.3 0.762.4 0.732.5 0.702.6 0.672.7 0.652.8 0.63

0.0 0.5 1.0 1.5 2.0 2.5 3.00.00

0.05

0.10

0.15

0.20

0.25

0.30



ACEL

ERAC

IÓN

ESPE

CTRA

L (Sa

) (m

/seg

2)


PISO (i) Ko (cm3) H (cm)

1 7.30 210 1000 3202 5.82 210 1000 3203 5.82 210 1000 3204 5.82 210 1000 3205 5.82 210 1000 3206 5.82 210 1000 3207 5.82 210 1000 320

1.327 (Tn*seg2/cm)

K7= 143.227 (Tn/cm)

1.837 (Tn*seg2/cm)

K6= 143.227 (Tn/cm)

1.837 (Tn*seg2/cm)

K5= 143.227 (Tn/cm)

1.837 (Tn*seg2/cm)

K4= 143.227 (Tn/cm)

1.837 (Tn*seg2/cm)

K3= 143.227 (Tn/cm)

1.837 (Tn*seg2/cm)

K2= 143.227 (Tn/cm)

1.837 (Tn*seg2/cm)

K1= 179.648 (Tn/cm)

CALCULO DE RIGIDECES Ki EN LA DIRECCION "Y" EN (Tn/cm) EN BASE A RESULTADOS DE LOS VALORES Dji CALCULADOS POR EL METODO MUTUO

SUMA DE LOS Dy


m7

m600000

m5

m1

m2

m4

m3


1periodo

Piso "i"

0.866 8.080 6.201 70.811 7.390 5.809 60.716 6.990 5.124 50.588 6.810 4.208 40.429 6.990 3.073 30.283 7.070 2.024 20.140 7.160 1.000 1

Piso "i"0.835 7.430 6.0790.787 7.380 5.726 70.698 7.340 5.080 60.576 7.310 4.191 50.422 7.290 3.068 40.278 7.280 2.024 30.137 7.280 1.000 2

1

0.825 7.370 6.0610.777 7.370 5.7110.690 7.360 5.0710.570 7.360 4.186 44.1600.417 7.350 3.0660.275 7.350 2.023 -0.3750.136 7.350 1.000

Piso "i"

0.823 7.360 6.058 70.776 7.360 5.709 60.689 7.360 5.069 50.569 7.360 4.185 40.417 7.360 3.066 30.275 7.360 2.023 20.136 7.360 1.000 1

(∑▒〖𝑚 _𝑖∗𝜙_𝑖 〗 )/𝑘_𝑖 𝛿_𝑖 �̂�2 𝐷_𝑖/𝐷_1

(∑▒〖𝑚 _𝑖∗𝜙_𝑖 〗 )/𝑘_𝑖 𝛿_𝑖 �̂�2 𝐷_𝑖/𝐷_1

(∑▒〖𝑚 _𝑖∗𝜙_𝑖 〗 )/𝑘_𝑖 𝛿_𝑖 �̂�2 𝐷_𝑖/𝐷_1

(∑▒〖𝑚 _𝑖∗𝜙_𝑖 〗 )/𝑘_𝑖 𝛿_𝑖 �̂�2 𝐷_𝑖/𝐷_1

〖𝜔 _2〗 ^2=

SEGUNDA FRECUENCIA

0.823 7.362 6.0580.775 7.362 5.7090.689 7.362 5.0690.568 7.362 4.1850.416 7.362 3.0660.275 7.362 2.0230.136 7.362 1.000

PRIMER MODO6.0585.7095.0694.1853.0662.0231.000


2.672.672.672.672.672.672.672.672.342.081.871.701.561.441.33

(∑▒〖𝑚 _𝑖∗𝜙_𝑖 〗 )/𝑘_𝑖 𝛿_𝑖 �̂�2 𝐷_𝑖/𝐷_1 〖𝜔 _2〗^2=𝜔_2=

𝑆_𝑎

1.251.171.101.040.980.930.890.850.810.780.750.720.690.67


Kyi (Tn/cm)

179.65143.23143.23143.23143.23143.23143.23

CALCULO DE RIGIDECES Ki EN LA DIRECCION "Y" EN (Tn/cm) EN BASE A RESULTADOS DE LOS VALORES Dji


44.160

1.330 1.000 58.733 58.733 170.000 0.3451.480 0.655 42.777 101.510 190.000 0.5341.480 0.120 7.859 109.369 200.000 0.5471.530 -0.427 -28.823 80.546 200.000 0.4031.630 -0.829 -59.695 20.851 250.000 0.0831.730 -0.913 -69.729 -48.879 280.000 -0.1751.840 -0.738 -59.979 -108.857 300.000 -0.363

-0.37560

1.330 1.000 79.800 79.800 170.000 0.4691.480 0.531 47.116 126.916 190.000 0.6681.480 -0.137 -12.200 114.716 200.000 0.5741.530 -0.711 -65.267 49.449 200.000 0.2471.630 -0.958 -93.713 -44.265 250.000 -0.1771.730 -0.781 -81.084 -125.349 280.000 -0.4481.840 -0.333 -36.816 -162.165 300.000 -0.541

0.207

INTERPOLANDO:

0.207 54.368

60

1.330 1.000 72.309 72.309 170.000 0.4251.480 0.575 46.239 118.548 190.000 0.6241.480 -0.049 -3.966 114.582 200.000 0.5731.530 -0.622 -51.756 62.826 200.000 0.3141.630 -0.936 -82.977 -20.151 250.000 -0.0811.730 -0.856 -80.487 -100.638 280.000 -0.3591.840 -0.496 -49.649 -150.287 300.000 -0.501

0.005



2𝜙_0=



𝜙_0=

〖𝜔 _2〗 ^2

〖𝜔 _2〗 ^2=

𝑚_𝑖 〖𝐹 _𝑖=𝜙〗 _𝑖∗𝑚_𝑖*𝜔^2 𝑘_𝑖𝑄_𝑖=∑▒ 〖〖〗𝜙 _𝑖∗𝑚_𝑖 "∗" 𝜔^2 〗𝛿_𝑖=𝑄_𝑖/𝑘_𝑖 𝜙_0

𝜙_0=

SEGUNDA FRECUENCIA SEGUNDO PERIODO SEGUNDO MODO

54.368 0.852

7.373

𝜙_0=

𝑇_2=

𝜙_2=


110.400

Piso "i"

7 1.330 1.000 146.832 146.8326 1.480 0.136 22.267 169.0995 1.480 -0.754 -123.151 45.9484 1.530 -0.983 -166.118 -120.1693 1.630 -0.383 -68.852 -189.0212 1.730 0.373 71.330 -117.6911 1.840 0.794 161.249 43.558

0.649137.3

Piso "i"

7 1.330 1.000 182.609 182.6096 1.480 -0.074 -15.072 167.5375 1.480 -0.956 -194.252 -26.7154 1.530 -0.822 -172.755 -199.4703 1.630 0.175 39.159 -160.3102 1.730 0.816 193.875 33.5651 1.840 0.696 175.918 209.483

-0.002

INTERPOLANDO:

-0.002110.400

137.30.649

Piso "i"

7 1.330 1.000 182.503 182.5036 1.480 -0.074 -14.936 167.5675 1.480 -0.955 -194.043 -26.4764 1.530 -0.823 -172.806 -199.2823 1.630 0.173 38.765 -160.5162 1.730 0.815 193.564 33.0481 1.840 0.697 176.072 209.119

0.000

〖𝜔 _3〗 ^2=〖〖 15𝜔〗 _1〗 ^2=𝑚_𝑖 〖𝐹 _𝑖=𝜙〗 _𝑖∗𝑚_𝑖*𝜔^2 𝑄_𝑖=∑▒ 〖〖〗𝜙 _𝑖∗𝑚_𝑖 "∗" 𝜔^2 〗3𝜙_0

3𝜙_0=

〖𝜔 _3〗 ^2= 𝑚_𝑖 〖𝐹 _𝑖=𝜙〗 _𝑖∗𝑚_𝑖*𝜔^2 𝑄_𝑖=∑▒ 〖〖〗𝜙 _𝑖∗𝑚_𝑖 "∗" 𝜔^2 〗〖3𝜙

〗_0

〖3𝜙〗 _0=

〖𝜔 _3〗 ^2

𝑚_𝑖 〖𝐹 _𝑖=𝜙〗 _𝑖∗𝑚_𝑖*𝜔^2 𝑄_𝑖=∑▒ 〖〖〗𝜙 _𝑖∗𝑚_𝑖 "∗" 𝜔^2 〗𝜙_0

〖3𝜙〗 _0=

SEGUNDO MODO TERCERA FRECUENCIA TERCER PERIODO-2.015 137.220 0.536-1.1580.099 11.7141.2541.8871.7241.000

〖3𝜙〗 _0=

〖𝜔 _3〗^2=𝜔_3=

𝑇_3=



Piso "i"

170.000 0.864 7 7 1.330190.000 0.890 6 6 1.480200.000 0.230 5 5 1.480200.000 -0.601 4 4 1.530250.000 -0.756 3 3 1.630280.000 -0.420 2 2 1.730300.000 0.145 1 1 1.840

Piso "i"

7 5.833 1.330170.000 1.074 6 5.555 1.480190.000 0.882 5 5.010 1.480200.000 -0.134 4 4.244 1.530200.000 -0.997 3 3.295 1.630250.000 -0.641 2 2.199 1.730280.000 0.120 1 1.000 1.840300.000 0.698

Piso "i"

7 5.641 1.3306 5.403 1.480

137.22 5 4.913 1.4804 4.196 1.5303 3.279 1.6302 2.198 1.7301 1.000 1.840

Piso "i"

170.000 1.074 7 5.615 1.330190.000 0.882 6 5.381 1.480200.000 -0.132 5 4.897 1.480200.000 -0.996 4 4.186 1.530250.000 -0.642 3 3.275 1.630280.000 0.118 2 2.197 1.730300.000 0.697 1 1.000 1.840

𝑘_𝑖 𝛿_𝑖=𝑄_𝑖/𝑘_𝑖


〖𝜔 _3〗 ^2=


𝜙_𝑖 𝑚_𝑖

𝜙_𝑖 𝑚_𝑖

𝜙_𝑖 𝑚_𝑖

𝜙_𝑖 𝑚_𝑖𝜙_𝑖

TERCER MODOPiso "i"

1.434-0.105 7 5.612 1.330-1.370 6 5.378 1.480-1.180 5 4.895 1.4800.249 4 4.185 1.5301.169 3 3.274 1.6301.000 2 2.197 1.730

1 1.000 1.840

PRIMERA FRECUENCIA

4.486

2.118

𝜙_3=

𝜙_𝑖 𝑚_𝑖

〖𝜔 _1〗^2=𝜔_1=


9.310 9.310 143.227 0.065 1.361 5.145 5.8338.880 18.190 143.227 0.127 1.296 4.631 5.5557.400 25.590 143.227 0.179 1.169 4.279 5.0106.120 31.710 143.227 0.221 0.990 4.041 4.2444.890 36.600 143.227 0.256 0.768 3.904 3.2953.460 40.060 143.227 0.280 0.513 3.899 2.1991.840 41.900 179.648 0.233 0.233 4.288 1.000

7.758 7.758 143.227 0.054 1.284 4.542 5.6418.221 15.979 143.227 0.112 1.230 4.515 5.4037.415 23.394 143.227 0.163 1.119 4.479 4.9136.493 29.888 143.227 0.209 0.955 4.443 4.1965.371 35.258 143.227 0.246 0.747 4.413 3.2793.805 39.063 143.227 0.273 0.500 4.395 2.1981.840 40.903 179.648 0.228 0.228 4.392 1.000

7.502 7.502 143.227 0.052 1.256 4.492 5.6157.996 15.499 143.227 0.108 1.203 4.490 5.3817.271 22.770 143.227 0.159 1.095 4.486 4.8976.419 29.189 143.227 0.204 0.936 4.481 4.1865.345 34.534 143.227 0.241 0.732 4.477 3.2753.802 38.336 143.227 0.268 0.491 4.474 2.1971.840 40.176 179.648 0.224 0.224 4.471 1.000

7.468 7.468 143.227 0.052 1.252 4.487 5.6127.964 15.432 143.227 0.108 1.199 4.486 5.3787.248 22.680 143.227 0.158 1.092 4.486 4.8956.405 29.085 143.227 0.203 0.933 4.485 4.1855.338 34.423 143.227 0.240 0.730 4.485 3.2743.801 38.224 143.227 0.267 0.490 4.484 2.1971.840 40.064 179.648 0.223 0.223 4.484 1.000

𝜙_𝑖∗𝑚_𝑖 ∑▒〖𝑚 _𝑖∗𝜙_𝑖 〗 𝑘_𝑖 (∑▒〖𝑚 _𝑖∗𝜙_𝑖 〗 )/𝑘_𝑖 𝛿_𝑖 �̂�2 𝐷_𝑖/𝐷_1




7.464 7.464 143.227 0.052 1.251 4.486 5.6127.960 15.424 143.227 0.108 1.199 4.486 5.3787.245 22.668 143.227 0.158 1.091 4.486 4.8956.403 29.071 143.227 0.203 0.933 4.486 4.1855.337 34.409 143.227 0.240 0.730 4.486 3.2743.800 38.209 143.227 0.267 0.490 4.486 2.1971.840 40.049 179.648 0.223 0.223 4.486 1.000

PRIMER PERIODO PRIMER MODO

2.967 5.6125.3784.8954.1853.2742.1971.000


𝑇_1=

𝜙_1=


26.916

Piso "i"

7 1.330 1.000 35.799 35.799 143.2276 1.480 0.750 29.879 65.678 143.2275 1.480 0.291 11.612 77.290 143.2274 1.530 -0.248 -10.219 67.071 143.2273 1.630 -0.716 -31.432 35.639 143.2272 1.730 -0.965 -44.948 -9.309 143.2271 1.840 -0.900 -44.587 -53.895 179.648

-0.600145.000

Piso "i"

7 1.330 1.000 192.850 192.850 143.2276 1.480 -0.346 -74.352 118.498 143.2275 1.480 -1.174 -251.901 -133.403 143.2274 1.530 -0.242 -53.777 -187.180 143.2273 1.630 1.064 251.589 64.409 143.2272 1.730 0.615 154.217 218.626 143.2271 1.840 -0.912 -243.230 -24.604 179.648

-0.775

INTERPOLANDO:

-0.77526.916

145-0.600

Piso "i"

7 1.330 1.000 104.362 104.362 143.2276 1.480 0.271 31.513 135.874 143.2275 1.480 -0.677 -78.658 57.216 143.2274 1.530 -1.077 -129.275 -72.059 143.2273 1.630 -0.574 -73.375 -145.435 143.2272 1.730 0.442 59.965 -85.470 143.2271 1.840 1.038 149.936 64.466 179.648

0.680



2𝜙_0=



𝜙_0=

〖𝜔 _2〗 ^2

〖𝜔 _2〗 ^2=

𝑚_𝑖 〖𝐹 _𝑖=𝜙〗 _𝑖∗𝑚_𝑖*𝜔^2 𝑘_𝑖𝑄_𝑖=∑▒ 〖〖〗𝜙 _𝑖∗𝑚_𝑖 "∗" 𝜔^2 〗𝛿_𝑖=𝑄_𝑖/𝑘_𝑖 𝜙_0

𝜙_0=

SEGUNDA FRECUENCIA SEGUNDO PERIODO

78.468 0.709

8.858

𝜙_0=

〖𝜔 _2〗^2=𝜔_2=

𝑇_2=

CALCULO DEL SEGUNDO PERIODO Y MODO POR EL METODO HOLSER CALCULO DEL TERCER PERIODO Y MODO POR EL METODO HOLSER

67.291

Piso "i"

0.250 7 1.330 1.000 89.4970.459 6 1.480 0.375 37.3600.540 5 1.480 -0.511 -50.8480.468 4 1.530 -1.041 -107.2030.249 3 1.630 -0.823 -90.321-0.065 2 1.730 0.025 2.904-0.300 1 1.840 0.853 105.625

0.925332

Piso "i"

1.346 7 1.330 1.000 441.5600.827 6 1.480 -2.083 -1023.477-0.931 5 1.480 1.980 972.876-1.307 4 1.530 -0.750 -380.8110.450 3 1.630 -0.821 -444.0421.526 2 1.730 2.209 1268.698-0.137 1 1.840 -3.620 -2211.179

4.042

INTERPOLANDO:

78.46867.291

0.925

Piso "i"

0.729 7 1.330 1.000 155.0850.949 6 1.480 -0.083 -14.2880.399 5 1.480 -1.066 -183.936-0.503 4 1.530 -0.765 -136.415-1.015 3 1.630 0.489 92.944-0.597 2 1.730 1.094 220.6320.359 1 1.840 0.158 33.896

-0.777



〖𝜔 _2〗 ^2=

〖𝜔 _3〗 ^2=〖〖 15𝜔〗 _1〗 ^2=𝑚_𝑖 〖𝐹 _𝑖=𝜙〗 _𝑖∗𝑚_𝑖*𝜔^23𝜙_0

3𝜙_0=

〖𝜔 _3〗 ^2= 𝑚_𝑖 〖𝐹 _𝑖=𝜙〗 _𝑖∗𝑚_𝑖*𝜔^2〖3𝜙

〗_0

〖3𝜙〗 _0=


〖𝜔 _3〗 ^2

𝑚_𝑖 〖𝐹 _𝑖=𝜙〗 _𝑖∗𝑚_𝑖*𝜔^2𝜙_0

〖3𝜙〗 _0=

SEGUNDO MODO TERCERA FRECUENCIA TERCER PERIODO2.031 116.6052.6441.113 10.798-1.402-2.830-1.6631.000

〖3𝜙〗 _0=

𝜙_2=

〖𝜔 _3〗^2=𝜔_3=

𝑇_3=


89.497 143.227 0.625126.857 143.227 0.88676.009 143.227 0.531-31.194 143.227 -0.218

-121.515 143.227 -0.848-118.611 143.227 -0.828-12.986 179.648 -0.072

441.560 143.227 3.083-581.917 143.227 -4.063390.959 143.227 2.73010.147 143.227 0.071

-433.894 143.227 -3.029834.803 143.227 5.829

-1376.376 179.648 -7.661

4.042 116.605

332

155.085 143.227 1.083140.797 143.227 0.983-43.139 143.227 -0.301

-179.554 143.227 -1.254-86.610 143.227 -0.605134.022 143.227 0.936167.918 179.648 0.935

𝑘_𝑖𝑄_𝑖=∑▒ 〖〖〗𝜙 _𝑖∗𝑚_𝑖 "∗" 𝜔^2 〗𝛿_𝑖=𝑄_𝑖/𝑘_𝑖


〖𝜔 _3〗 ^2=


TERCER PERIODO TERCER MODO

0.582 1.1581.052-0.322-1.341-0.6471.0011.000

𝜙_3=

Espectros Frecuencias y Modales Elias

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