Calculo Modal Espectral. - X

RIGIDECES MASAS

(tn/cm) en X (tn-S2/cm)

1 376.147 0.154

2 376.147 0.164

3 376.147 0.164

4 376.147 0.164

5 376.147 0.164

6 376.147 0.164

7 376.147 0.164

8 376.147 0.091

0.154 0 0 0 0 0 0 0

0 0.164 0 0 0 0 0 0

0 0 0.164 0 0 0 0 0

0 0 0 0.164 0 0 0 0

0 0 0 0 0.164 0 0 0

0 0 0 0 0 0.164 0 0

0 0 0 0 0 0 0.164 0

0 0 0 0 0 0 0 0.091

8X8

K

752.294 -376.147 0.000 0.000 0.000 0.000 0.000 0.000

-376.147 752.294 -376.147 0.000 0.000 0.000 0.000 0.000

0.000 -376.147 752.294 -376.147 0.000 0.000 0.000 0.000

0.000 0.000 -376.147 752.294 -376.147 0.000 0.000 0.000

0.000 0.000 0.000 -376.147 752.294 -376.147 0.000 0.000

0.000 0.000 0.000 0.000 -376.147 752.294 -376.147 0.000

0.000 0.000 0.000 0.000 0.000 -376.147 752.294 -376.147

0.000 0.000 0.000 0.000 0.000 0.000 -376.147 376.147

8X8

1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

1.964 1.686 1.168 0.487 -0.247 -0.916 -1.416 -1.688

2.854 1.809 0.302 -0.810 -0.903 0.013 1.318 2.252

3.636 1.328 -0.832 -0.803 0.603 0.902 -0.743 -2.653

4.280 0.403 -1.229 0.498 0.666 -1.010 -0.102 2.860

4.761 -0.657 -0.537 0.996 -0.864 0.215 0.909 -2.859

5.062 -1.497 0.630 -0.111 -0.325 0.773 -1.388 2.650

5.170 -1.837 1.239 -1.039 0.992 -1.069 1.363 -2.247

8X8

transpuesta :

1.000 1.964 2.854 3.636 4.280 4.761 5.062 5.170

1.000 1.686 1.809 1.328 0.403 -0.657 -1.497 -1.837

1.000 1.168 0.302 -0.832 -1.229 -0.537 0.630 1.239

1.000 0.487 -0.810 -0.803 0.498 0.996 -0.111 -1.039

1.000 -0.247 -0.903 0.603 0.666 -0.864 -0.325 0.992

1.000 -0.916 0.013 0.902 -1.010 0.215 0.773 -1.069

1.000 -1.416 1.318 -0.743 -0.102 0.909 -1.388 1.363

1.000 -1.688 2.252 -2.653 2.860 -2.859 2.650 -2.247

8X8

CALCULO MODAL ESPECTRAL EN "X"

=

T =

ENTREPISO

MATRIZ DE MASAS

M =

MATRIZ DE RIGIDECES

K =

MATRIZ DE MODOS DE VIBRACION

17.646 -0.001 0.000 0.000 0.000 0.000 0.000 0.000

-0.001 2.218 0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.000 1.006 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.710 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.659 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.802 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000 1.480 0.000

0.000 0.000 0.000 0.000 0.000 0.000 0.000 6.901

8X8

1535.077 -0.047 -0.036 0.018 -0.029 0.030 -0.039 0.072

-0.047 1699.387 0.317 -0.165 0.186 -0.191 0.241 -0.419

-0.036 0.317 2044.201 -0.140 -0.005 0.000 -0.004 0.058

0.018 -0.165 -0.140 2623.704 0.294 -0.204 0.235 -0.467

-0.029 0.186 -0.005 0.294 3619.871 -0.032 0.005 0.211

0.030 -0.191 0.000 -0.204 -0.032 5711.229 0.075 -0.654

-0.039 0.241 -0.004 0.235 0.005 0.075 12349.737 2.404

0.072 -0.419 0.058 -0.467 0.211 -0.654 2.404 62158.741

8X8

L = TxMxI

1 4.324

1 0.491

1 0.185

I = 1 0.102

1 0.069

1 0.053

1 0.045

1 0.0428X1 8X1

Le = (Li)2/Mei

Mtotal = 1.2291.059

0.109

0.034

0.015

0.007

0.003

0.001

0.000

8X1

FACTOR DE PARTICIPACION MODAL (FPMi) r = Li/Mei

0.245 TOTAL= 1.000.221

0.184

0.143

0.104

0.066

0.030

0.006

8X1

P

EN %

86.213 Total: 100.008.833

2.773

1.187

0.580

0.283

0.112

0.021 8X1

>=90%

P =

MATRIZ DE MASAS PARTICIPANTES

L =

MATRIZ DE MASAS EFECTIVAS

Le =

r =

FACTOR DE PARTICIPACION DE MASAS

MATRIZ DE Me

Me =

MATRIZ DE Ke

Ke =

T C = 2.5 (Tp/T) C Sa = (ZUCS)g/R

Z = 0.4 0.03047 49.23 2.5 147

U = 1 0.03212 46.70 2.5 147

S = 1.2 0.03522 42.59 2.5 147

g = 980 0.04052 37.02 2.5 147

R = 8 0.0497 30.18 2.5 147

Tp = 0.6 0.06719 22.32 2.5 147

0.10943 13.71 2.5 147

0.32458 4.62 2.5 147

T C = 2.5 (Tp/T) C Sa = (ZUCS)g/R0.1 15.00 2.5 147.000.2 7.50 2.5 147.000.3 5.00 2.5 147.00

0.4 3.75 2.5 147.000.5 3.00 2.5 147.000.6 2.50 2.5 147.000.7 2.14 2.1 126.000.8 1.88 1.9 110.250.9 1.67 1.7 98.001 1.50 1.5 88.201.1 1.36 1.4 80.181.2 1.25 1.3 73.501.3 1.15 1.2 67.851.4 1.07 1.1 63.001.5 1.00 1.0 58.801.6 0.94 0.9 55.131.7 0.88 0.9 51.881.8 0.83 0.8 49.001.9 0.79 0.8 46.422 0.75 0.8 44.102.1 0.71 0.7 42.002.2 0.68 0.7 40.092.3 0.65 0.7 38.352.4 0.63 0.6 36.752.5 0.60 0.6 35.282.6 0.58 0.6 33.922.7 0.56 0.6 32.672.8 0.54 0.5 31.502.9 0.52 0.5 30.413 0.50 0.5 29.40

ESPECTRO DE DISEO

ANALISIS MODAL ESPECTRAL

Parametros sismicos

0.00

20.00

40.00

60.00

80.00

100.00

120.00

140.00

160.00

0 0.5 1 1.5 2 2.5 3 3.5

Sa

(cm

/s2

)

Periodos (s)

Espectro de diseo Eje X

(W1) T1 1 Sa1 Sd187.011584 0.32458 0.245 147 1.6894

1.000 0.41396

1.964 0.81317

2.854 1.18154

3.636 1.50509

4.280 1.77155

4.761 1.97080

5.062 2.09530

5.170 2.14031

8x1

(W2) T2 2 Sa2 Sd2766.237761 0.10943 0.221 147 0.1918

1.000 0.04244

1.686 0.07156

1.809 0.07678

1.328 0.05635

0.403 0.01709

-0.657 -0.02787

-1.497 -0.06353

-1.837 -0.07796

8x1

(W3) T3 3 Sa3 Sd32031.575329 0.06719 0.184 147 0.0724

1.000 0.01331

1.168 0.01555

0.302 0.00402

-0.832 -0.01108

-1.229 -0.01636

-0.537 -0.00715

0.630 0.00839

1.239 0.01650

8x1

(W4) T4 4 Sa4 Sd43694.937796 0.0497 0.143 147 0.0398

1.000 0.00570

0.487 0.00278

-0.810 -0.00462

-0.803 -0.00458

0.498 0.00284

0.996 0.00568

-0.111 -0.00063

-1.039 -0.00593

8x1

(W5) T5 5 Sa5 Sd55489.476281 0.04052 0.104 147 0.0268

1.000 0.00278

-0.247 -0.00069

-0.903 -0.00251

0.603 0.00168

0.666 0.00185

-0.864 -0.00241

-0.325 -0.00091

0.992 0.00276

Quinto

modo de

vibracion

= Umax 5 = cm

Tercer modo

de vibracion

= Umax 3 = cm

Cuarto

modo de

vibracion

= Umax 4 = cm

Primer

modo de

vibracion

= Umax 1 = cm

Segundo

modo de

vibracion

= Umax 2 = cm

DESPLAZAMIENTOS MAXIMOS : Sd = Sa / 2 y Umax = .Sd.

(W6) T6 6 Sa6 Sd67122.684816 0.03522 0.066 147 0.0206

1.000 0.00136

-0.916 -0.00125

0.013 0.00002

0.902 0.00123

-1.010 -0.00137

0.215 0.00029

0.773 0.00105

-1.069 -0.00145

8x1

(W7) T7 r7 Sa7 Sd78342.9956 0.03212 0.030 147 0.0176

1.000 0.00054

-1.416 -0.00076

1.318 0.00071

-0.743 -0.00040

-0.102 -0.00005

0.909 0.00049

-1.388 -0.00074

1.363 0.00073

8x1

(W8) T8 8 Sa8 Sd89007.148836 0.03047 0.006 147 0.0163

1.000 0.00010

-1.688 -0.00017

2.252 0.00022

-2.653 -0.00026

2.860 0.00028

-2.859 -0.00028

2.650 0.00026

-2.247 -0.00022

0.48019

0.90593

1.27042

1.58066

1.81140

2.01497

2.17081

2.24587

0.41639

0.81647

1.18405

1.50619

1.77171

1.97102

2.09628

2.14181

0.43234

0.83884

1.20564

1.52481

1.78163

1.98201

Norma NTE - 030: 0.25abs + 0.75rss

Umax = cm

COMBINACION POR SUPERPOSICION MODAL

Sumatoria de valores absolutos (abs)

U1 = cm

Raiz de la suma de los cuadrados(rss)

U2 = cm

Septimo

modo de

vibracion

= Umax 7 = cm

Octavo

modo de

vibracion

= Umax 8 = cm

Sexto

modo de

vibracion

= Umax 6 = cm

2.11491

2.16782

0.00432

0.00839

0.01206

0.01525

0.01782

0.01982

0.02115

0.02168

R Entrepiso MATERIALRestriccion

mximaObservacion

6 8 0.0010 Concreto 0.007 S cumple

7 0.0025 Concreto 0.007 S cumple





2 0.0076 Concreto 0.007 Redisear

1 0.0081 Concreto 0.007 Redisear

CORTANTE DE ENTREPISO

162.624

152.901

137.974

120.053

96.603

75.372

49.991

19.902

9.723

14.927

17.921

23.450

21.231

25.381

30.088

19.902

V = 162.62 Tn

F8 = 19.90

F7= 30.09

F6 = 25.38

F5 = 21.23

F4 = 23.45

F3 = 17.92

F2 = 14.93

F1 = 9.72

V=

FUERZAS SISMICAS :

F = Tn

CORTANTE BASAL: V = fi

= m

DISTORSION DE ENTREPISO: = (Ui - Ui-1)/h * 0.75 * R

Documents

Calculo Modal Espectral. - X