2 PISOS (modelo1)SISTEMAS DE VARIOS GRADOS DE
LIBERTAD2.59tonMATRIZ DE RIGIDEZ Y DE
MASA:90.9857614622-29.8148949051-29.814894905114.30959992675ton/cm[K]=90.9857614622-29.8148949051ton/cm-29.814894905114.30959992675.184ton[M]=0.0050ton.s/cm8ton/cm00.0031.-
ECUACION DE
EINGENVALORES:([K]-[M])*{1}=00=90.9857614622-29.8148949051-0.00501-29.814894905114.309599926700.00320=0.0000-0.3445+413.0419Frecuencias
naturales ()Periodos naturales correspondientes
(T)1=34.626rad/sT1=0.18segV1=61lb/s=154.94cm/s2=34.626rad/sT2=0.18segV2=61lb/s=154.94cm/sV3=22lb/s=55.88cm/sAnalisis
del espectro (T)Aceleracion espectral - funcion de
TA1=5.4689gT1=5364.95244cm/sA2=5.4689gT2=5364.95244cm/s2.- CALCULO
DE LOS MODOS DE VIBRACIONObtencion del primer
modo0=90.9857614622373 -
0.005(34.626)-29.814894905110-29.814894905114.3095999266842 -
0.003(34.626)20 =55.18 1-19.10 21=1.00002=2.8885Obtencion del
segundo modo0=90.9857614622373 -
0.005(34.626)-29.814894905110-29.814894905114.3095999266842 -
0.003(34.626)20 =-29.81 110.71 21=1.00002=2.78313.- NORMALIZACION
DE MODOS[]=11[M]=0.00500.00002.88852.78310.00000.0030Calculo del
escalar1=0.04672=0.0437Forma modal
normalizada{}1=11=4.62664036772.88850.046713.3639140565{}2=11=4.78205859032.78310.043713.3090914656{}=4.64.813.413.33.-
VECTOR DE FACTORES DE PARTICIPACION[K]=[]T * [M] * {1}[]T * [M] *
{}[P] = []T * [M] *
{1}[P]=4.626640367713.3639140565*0.0050*1.000=0.0632249444.782058590313.309091465600.0031.0000.06383756734.-
MATRIZ DE DESPLAZAMIENTO[U] = [] * [P] * [D] =[] * [P] *
[A][]4.634.78*0.0632249440*5364.95244013.3613.3100.063837567305364.952441.30892699051.3660055027[U]
==1,198.96003.78079695373.801771106401198.959876Desplazamiento
maximo - SRSS[Uc] =1.89189346955.3617058065.- MATRIZ DE FUERZAS
LATERALES[Fs] = [K] *
[U][Fs]=90.9857614622-29.8148949051*1.30892699051.3660055027=6.36965510210.9376448336-29.814894905114.30959992673.78079695373.801771106415.076171149713.6745130428Fuerza
lateral en cada nudo -SRSS[Fsc]=12.65720.3546.- VECTOR CORTANTE
BASAL[V] = ([Fs]T * {1})TT[V]
=6.36965510215.0761711497*1=21.44624.61210.937644833613.674513042817.-
SRSS [V]Vb=21.446 + 24.612=32.6447769176
USER:dato obtenido d acuerdo a tabla
3 PISOS (modelo1)SISTEMAS DE VARIOS GRADOS DE
LIBERTAD35tonMATRIZ DE
RIGIDEZ:3ton/cm[K]=10-30ton/cm-36-355ton0-333ton/cmMATRIZ DE
MASA:55ton[M]=0.0560700ton.s/cm00.0560707ton/cm000.035681.-
ECUACION DE
EINGENVALORES:([K]-[M])*{1}=00=10-30-0.056070010-36-300.056070200-33000.0356830=10
- 0.05607()-3010-36 - 0.05607()-3200-33 -
0.03568()30=-0.0001121723860 +0.04144078 +-4.00641 +63Frecuencias
naturales ()Periodos naturales correspondientes
(T)1=4.407rad/sT1=2/4.407
=1.42573segV1=18lb/s=45.72cm/s2=11.561rad/sT2=2/11.561
=0.54348segV2=25lb/s=63.5cm/s3=14.709rad/sT2=2/14.709
=0.42717segV3=22lb/s=55.88cm/sAnalisis del espectro (T)Aceleracion
espectral - funcion de TA1=0.2054gT1=0.205390458715596 * 981
=201.48804cm/sA2=0.7483gT2=0.748341997961264 * 981
=734.1235cm/sA3=0.8379gT2=0.837858226299694 * 981 =821.93892cm/s2.-
CALCULO DE LOS MODOS DE VIBRACIONObtencion del primer modo0=10 -
0.05607(4.407)-3010-36 - 0.05607(4.407)-3200-33 - 0.03568(4.407)30
= (10 - 0.05607 * 4.407) * 1 + ( -3) * 2 + 0Para 1 =1.0000 = -31+
(6 - 0.05607 * 4.407)2 + (-3)3=> 2 =2.9700 = 0 + (-3)2 + (3 -
0.03568 * 4.407)3=> 3 =3.862Obtencion del segundo modo0=10 -
0.05607(11.561)-3010-36 - 0.05607(11.561)-3200-33 -
0.03568(11.561)30 = (10 - 0.05607 * 11.561) * 1 + ( -3) * 2 + 0Para
1 =1.0000 = -31+ (6 - 0.05607 * 11.561)2 + (-3)3=> 2 =0.8350 = 0
+ (-3)2 + (3 - 0.03568 * 11.561)3=> 3 =-1.416Obtencion del
tercer modo0=10 - 0.05607(14.709)-3010-36 - 0.05607(14.709)-3200-33
- 0.03568(14.709)30 = (10 - 0.05607 * 11.561) * 1 + ( -3) * 2 +
0Para 1 =1.0000 = -31+ (6 - 0.05607 * 11.561)2 + (-3)3=> 2
=-0.7100 = 0 + (-3)2 + (3 - 0.03568 * 11.561)3=> 3 =0.452Modos
de vibracion
obtenidos1.0001.0001.000=2.9700.835-0.7103.862-1.4160.4523.-
NORMALIZACION DE
MODOS[]=1.00001.00001.0000[M]=0.05607002.97030.8353-0.71000.0560703.8624-1.41600.452000.03568Calculo
del escalar1 = (1 *0.05607) + (2.9703 * 0.05607) + (3.8624
*0.03568) =1.0412 = (1 *0.05607) + (0.8353 * 0.05607) + (-1.416
*0.03568) =0.4083 = (1 *0.05607) + (-0.7103 * 0.05607) + (0.4516
*0.03568) =0.303Forma modal
normalizada{}=1/1.0411/0.4081/0.3030.96062.45103.30032.9703/1.0410.8353/0.408-0.7103/0.303=2.85332.0473-2.34423.8624/1.041-1.416/0.4080.4516/0.3033.7103-3.47061.49043.-
VECTOR DE FACTORES DE PARTICIPACION[K]=[]T * [M] * {1}[]T * [M] *
{}Como el sistema esta normalizado, se tiene:[P] = []T * [M] *
{1}[P]=0.9612.8533.710*0.0560700*1.0002.4512.047-3.47100.0560701.0003.300-2.3441.490000.035681.0000.3462339.6505=0.1284=125.9493*10.1068104.7571981.00Comprobacion:P
* 1 = 1339.6505 * 0.9606+ 125.9493 * 2.451 + 104.7571 *
3.3003=19811.00= 1 OK4.- MATRIZ DE DESPLAZAMIENTO[U] = [] * [P] *
[D] =[] * [P] * [A][][U]
=0.962.453.3003*0.346200*201.48804002.852.05-2.344200.128400734.123503.71-3.471.4904000.106800821.9389219.42000133.656721000216.43.45011.72861.3391[U]
=10.2481.4439-0.951113.326-2.44760.6047SRSS para cada
desplazamiento[Uc] =(3.4501) + (1.7286) +
(1.3391)=4.0846587103(10.248) + (1.4439) +
(-0.9511)10.3928312995(13.326) + (-2.4476) +
(0.6047)13.5623996347Desplazamiento entre pisos[]
=3.4501-10.2481.7286-1.44391.3391--0.9511=-6.79790.28472.290210.248-13.3261.4439--2.4476-0.9511-0.6047-3.0783.8915-1.555813.326-
0-2.4476- 00.6047- 013.326-2.44760.60475.- MATRIZ DE FUERZAS
LATERALES[Fs] = [K] *
[U][Fs]=10-30*3.45011.72861.3391=3.75712.954316.2443-36-310.2481.4439-0.951111.159710.8204-11.5380-3313.326-2.44760.60479.234-11.67454.6674Fuerza
lateral en cada nudo -SRSS[Fsc]=(3.757) + (12.9543) +
(16.2443)=21.114(11.1597) + (10.8204) + (-11.538)19.358(9.234) +
(-11.6745) + (4.6674)15.6006.- VECTOR CORTANTE BASAL[V] = ([Fs]T *
{1})TT[V]
=3.75711.15979.234*112.954310.8204-11.67451=24.15112.19.37416.2443-11.5384.667417.-
SRSS [V]Vb=(24.151) + (12.1) + (9.374)=28.5928780818
USER:dato obtenido d acuerdo a tabla
4 PISOS (modelo1)SISTEMAS DE VARIOS GRADOS DE
LIBERTAD11.938tonMATRIZ DE
RIGIDEZ:30.914ton/cm[K]=85.9-60.40.00.0ton/cm19.844ton-60.491.3-30.90.00.0-30.961.8-30.930.91ton/cm0.00.0-30.930.98.468tonMATRIZ
DE
MASA:60.38ton/cm[M]=0.02200gton.s/cm00.0090021.994ton000.0200000.01225.473ton/cm1.-
ECUACION DE EINGENVALORES:([K]-[M])*{1}=0!NO
BORRAR!0=85.853-60.380.0000.000-0.02200g1-738.42839795514954034.07428094-60.3891.294-30.9140.000.009002-2591.9035715033484148.223184780.000-30.91461.828-30.9000.02032125.713088530100.0000.000-30.930.90000.01241269.480969030600=0.0000000475+-3.12E-04+4.7260+-6725.526+1469885.85Frecuencias
naturales ()Periodos naturales correspondientes
(T)1=18.977rad/sT1=0.33seg2=42.220rad/sT2=0.15seg3=57.790rad/sT2=0.11seg4=87.050rad/sT2=0.07segAnalisis
del espectro (T)Aceleracion espectral - funcion de
TA1=12.7500gT1=12507.75cm/sA2=0.8750gT2=858.375cm/sA3=0.7250gT2=711.225cm/sA4=0.7100gT2=696.51cm/s2.-
CALCULO DE LOS MODOS DE VIBRACIONObtencion del primer modo0=85.853
- 0.022(18.977)-60.3800.00010-60.3891.294 -
0.009(18.977)-30.9140.0200-30.91461.828 -
0.02(18.977)-30.9300.0000.000-30.930.914 -
0.012(18.977)41=1.0002=85.7223=242.2104=281.571Obtencion del
segundo modo0=85.853 - 0.022(42.22)-60.3800.00010-60.3891.294 -
0.009(42.22)-30.9140.0200-30.91461.828 -
0.02(42.22)-30.930.0000.000-30.9-30.914 -
0.012(42.22)41=1.0002=85.2043=205.4514=666.898Obtencion del tercer
modo0=85.853 - 0.022(57.79)-60.3800.00010-60.3891.294 -
0.009(57.79)-30.9140.0200-30.91461.828 -
0.02(57.79)-30.930.0000.000-30.9-30.914 -
0.012(57.79)41=1.0002=84.6363=165.7004=-559.085Obtencion del cuarto
modo0=85.853 - 0.022(87.05)-60.380.0000.00010-60.3891.294 -
0.009(87.05)-30.9140.000200.000-30.91461.828 -
0.02(87.05)-30.91430.0000-30.9-30.914 -
0.012(87.05)41=1.0002=83.0923=60.1224=-30.967Modos de vibracion
obtenidos1.0001.0001.0001.000=85.72285.20484.63683.092242.210205.451165.70060.122281.571666.898-559.085-30.9673.-
NORMALIZACION DE
MODOS[]=1.0001.0001.0001.000[M]=0.022000g85.72285.20484.63683.09200.009000242.210205.451165.70060.122000.02000281.571666.898-559.085-30.9670000.0120Calculo
del escalar1=46.8072=79.0353=66.0654=12.081Forma modal
normalizada{}=1/46.8071/79.0351/66.0651/12.0810.02140.01270.01510.082885.722/46.80785.204/79.03584.636/66.06583.092/12.081=1.83141.07811.28116.8779242.21/46.807205.451/79.035165.7/66.06560.122/12.0815.17472.59952.50814.9766281.571/46.807666.898/79.035-559.085/66.065-30.967/12.0816.01568.4380-46.2780-2.56333.-
VECTOR DE FACTORES DE PARTICIPACION[K]=[]T * [M] * {1}[]T * [M] *
{}[P] = []T * [M] *
{1}[P]=0.0211.8315.1756.02*0.022000g*1.000=0.19263251220.0131.0782.5998.43800.0090001.0000.16322682360.0151.2812.508-46.278000.020001.000-0.49331083740.0836.8784.977-2.5630000.01201.0000.13249432994.-
MATRIZ DE DESPLAZAMIENTO[U] = [] * [P] * [D] =[] * [P] * [A][][U]
=0.020.010.01510.0828*0.1926325122000*12507.750001.831.081.28116.877900.1632268236000858.375005.172.602.5084.976600-0.4933108374000711.22506.028.44-46.278-2.56330000.1324943299000696.51360.130001782.52840003,3407,5780.14293640620.0009945181-0.00159019670.001008055[U]
=12.25279461610.0847369168-0.13458788610.083761303334.62062695650.2043247299-0.26349558970.060606280740.24674684270.66324210514.8618016602-0.0312164382Desplazamiento
maximo - SRSS[Uc]
=0.142952265412.254113028134.622285633740.54477292285.- MATRIZ DE
FUERZAS LATERALES[Fs] = [K] *
[U][Fs]=85.853-60.3800.0*0.14293640620.0009945181-0.00159019670.001008055=-727.552219635-5.03103267557.9898934082-4.9709629529-60.3891.294-30.9140.012.25279461610.0847369168-0.13458788610.083761303339.71406973981.3594283787-4.04534773985.71245550580-30.91461.828-30.934.62062695650.2043247299-0.26349558970.0606062807517.5532988096-10.4900340799-162.4284919322.12279316400-30.91430.940.24674684270.66324210514.8618016602-0.0312164382173.925870161814.1869717353158.4434391835-2.8386075327Fuerza
lateral en cada nudo -SRSS[Fsc]=727.63040.349542.549235.7206.-
VECTOR CORTANTE BASAL[V] = ([Fs]T * {1})TT[V]
=-727.55221963539.7140697398517.5532988096173.9258701618*1-5.03103267551.3594283787-10.490034079914.18697173531=3.6410.025-0.0410.0267.9898934082-4.0453477398-162.428491932158.44343918351-4.97096295295.71245550582.122793164-2.838607532717.-
SRSS [V]Vb=3.641 + 0.025+ -0.041+0.026=3.6414094799
3 PISOS (modelo2)SISTEMAS DE VARIOS GRADOS DE
LIBERTAD35tonMATRIZ DE
RIGIDEZ:3ton/cm[K]=10-30ton/cm-36-355ton0-333ton/cmMATRIZ DE
MASA:55ton[M]=0.0560700ton.s/cm00.0560707ton/cm000.035681.-
ECUACION DE
EINGENVALORES:([K]-[M])*{1}=00=10-30-0.056070010-36-300.056070200-33000.0356830=10
- 0.05607()-3010-36 - 0.05607()-3200-33 -
0.03568()30=-0.0001121723860 +0.04144078 +-4.00641 +63Frecuencias
naturales ()Periodos naturales correspondientes
(T)1=4.407rad/sT1=2/4.407 =1.42573seg2=11.561rad/sT2=2/11.561
=0.54348seg3=14.709rad/sT2=2/14.709 =0.42717seg2.- CALCULO DE LOS
MODOS DE VIBRACIONObtencion del primer modo0=10 -
0.05607(4.407)-3010-36 - 0.05607(4.407)-3200-33 - 0.03568(4.407)30
= (10 - 0.05607 * 4.407) * 1 + ( -3) * 2 + 0Para 1 =1.0000 = -31+
(6 - 0.05607 * 4.407)2 + (-3)3=> 2 =2.9700 = 0 + (-3)2 + (3 -
0.03568 * 4.407)3=> 3 =3.862Obtencion del segundo modo0=10 -
0.05607(11.561)-3010-36 - 0.05607(11.561)-3200-33 -
0.03568(11.561)30 = (10 - 0.05607 * 11.561) * 1 + ( -3) * 2 + 0Para
1 =1.0000 = -31+ (6 - 0.05607 * 11.561)2 + (-3)3=> 2 =0.8350 = 0
+ (-3)2 + (3 - 0.03568 * 11.561)3=> 3 =-1.416Obtencion del
tercer modo0=10 - 0.05607(14.709)-3010-36 - 0.05607(14.709)-3200-33
- 0.03568(14.709)30 = (10 - 0.05607 * 14.709) * 1 + ( -3) * 2 +
0Para 1 =1.0000 = -31+ (6 - 0.05607 * 14.709)2 + (-3)3=> 2
=-0.7100 = 0 + (-3)2 + (3 - 0.03568 * 14.709)3=> 3 =0.452Modos
de vibracion
obtenidos1.0001.0001.000=2.9700.835-0.7103.862-1.4160.4523.-
NORMALIZACION DE
MODOS[]=1.00001.00001.0000[M]=0.05607002.97030.8353-0.71000.0560703.8624-1.41600.452000.03568Calculo
del escalar1 = (1 *0.05607) + (2.9703 * 0.05607) + (3.8624
*0.03568) =1.0412 = (1 *0.05607) + (0.8353 * 0.05607) + (-1.416
*0.03568) =0.4083 = (1 *0.05607) + (-0.7103 * 0.05607) + (0.4516
*0.03568) =0.303Forma modal
normalizada{}=1/1.0411/0.4081/0.3030.96062.45103.30032.9703/1.0410.8353/0.408-0.7103/0.303=2.85332.0473-2.34423.8624/1.041-1.416/0.4080.4516/0.3033.7103-3.47061.49043.-
FUERZAS LATERALES3.1. Primer modoPara
T1=1.42573SegV1=18.00000Pulg/Seg45.720cm/segA1=4.407 *
45.72=201.48804cm/seg2Peso
efectivo:W=(Wii)(Wii)NIVELWiiWiiWiiFi1550.960652.83350.75137983.75932552.8533156.9315447.7726489511.16633353.7103129.8605481.821413159.2401339.625980.3454419W=339.625=117.6576980.3454419Cortante
Basal:V=WA= 117.6576*201.48804*(1/981) =24.1657gFuerza lateral en
cada nudo:Fi=VWiiF1 = 24.1657*(52.833/339.625) =3.7593Ton(Wii)F2 =
24.1657*(156.9315/339.625) =11.1663TonF3 =
24.1657*(129.8605/339.625) =9.2401Ton3.2. Segundo modoPara
T2=0.54348SegV2=26.50000Pulg/s =67.310cm/segA2=11.561 *
67.31=778.17091cm/s2Peso
efectivo:W=(Wii)(Wii)NIVELWiiWiiWiiFi1552.4510134.805330.40705513.70632552.0473112.6015230.5290509511.4488335-3.4706-121.471421.5772526-12.3506125.9355982.51335855W=125.9355=16.142982.51335855Cortante
Basal:V=WA= 16.142*778.17091*(1/981) =12.8045gFuerza lateral en
cada nudo:Fi=VWiiF1 = 12.8045*(134.805/125.9355) =13.7063Ton(Wii)F2
= 12.8045*(112.6015/125.9355) =11.4488F3 =
12.8045*(-121.471/125.9355) =-12.35063.3. Tercer modoPara
T3=0.42717SegV3=23.00000Pulg/Seg58.420cm/segA3=14.709 *
58.42=859.2998cm/seg2Peso
efectivo:W=(Wii)(Wii)NIVELWiiWiiWiiFi1553.3003181.5165599.0589049517.0115255-2.3442-128.931302.2400502-12.08333351.490452.16477.74522564.8887104.7495979.0442W=104.7495=11.2073979.0442Cortante
Basal:V=WA= 11.2073*859.2998*(1/981) =9.817gFuerza lateral en cada
nudo:Fi=VWiiF1 = 9.817*(181.5165/104.7495) =17.0115Ton(Wii)F2 =
9.817*(-128.931/104.7495) =-12.0833F3 = 9.817*(52.164/104.7495)
=4.8887
Datos obtenidos de tabla, segun T1Datos obtenidos de tabla,
segun T2Datos obtenidos de tabla, segun T3
TRABAJOSISTEMAS DE VARIOS GRADOS DE LIBERTADAMORTIGUAMIENTO
=1%10.000tonMATRIZ DE
RIGIDEZ:30.000ton/cm[K]=85.0-60.00.00.0ton/cm15.000ton-60.090.0-30.00.00.0-30.060.0-30.030.00ton/cm0.00.0-30.030.020.000tonMATRIZ
DE
MASA:60.00ton/cm[M]=0.0200gton.s/cm00.0200020.000ton000.01500000.0125.000ton/cm1.-
ECUACION DE EINGENVALORES:([K]-[M])*{1}=0!NO
BORRAR!0=85-600.0000.000-0.0200001-15304590000-6090-300.000.020002-1822.532400000.000-3060-30.0000.01503166500.0000.000-30.030.00000.014108000=0.00000006+-4.40E-04+4.4625+-6097.500+1350000.00Frecuencias
naturales ()Periodos naturales correspondientes
(T)1=16.598rad/sT1=0.38seg2=35.405rad/sT2=0.18seg3=74.074rad/sT2=0.08seg4=50.841rad/sT2=0.12seg2.-
CALCULO DE LOS MODOS DE VIBRACIONObtencion del primer modo0=85 -
0.02(16.598)-6000.00010-6090 - 0.02(16.598)-300.0200-3060 -
0.015(16.598)-30.0300.0000.000-30.030 -
0.01(16.598)41=1.0002=1.3253=1.7324=1.907Obtencion del segundo
modo0=85 - 0.02(35.405)-6000.00010-6090 -
0.02(35.405)-300.0200-3060 - 0.015(35.405)-30.030.0000.000-30.0-30
- 0.01(35.405)41=1.0002=0.9993=0.1624=0.278Obtencion del tercer
modo0=85 - 0.02(74.0744)-6000.00010-6090 -
0.02(74.0744)-300.0200-3060 -
0.015(74.0744)-30.030.0000.000-30.0-30 -
0.01(74.0744)41=1.0002=-0.4123=-1.7294=2.086Obtencion del cuarto
modo0=85 - 0.02(50.841)-600.0000.00010-6090 -
0.02(50.841)-30.0000.000200.000-3060 -
0.015(50.841)-30.00030.0000-30.0-30 -
0.01(50.841)41=1.0002=0.5553=-1.2914=-9.328Modos de vibracion
obtenidos1.0001.0001.0001.000=1.3250.999-0.4120.5551.7320.162-1.73-1.291.9070.2782.086-9.333.-
NORMALIZACION DE
MODOS[]=1.0001.0001.0001.000[M]=0.020000g1.3250.999-0.4120.55500.0200001.7320.162-1.73-1.29000.015001.9070.2782.086-9.330000.0100Calculo
del escalar1=0.3692=0.2033=0.3344=0.960Forma modal
normalizada{}=1/0.3691/0.2031/0.3341/0.962.71004.92612.99401.04171.325/0.3690.999/0.203-0.412/0.3340.555/0.96=3.59084.9212-1.23350.57811.732/0.3690.162/0.203-1.729/0.334-1.291/0.964.69380.7980-5.1766-1.34481.907/0.3690.278/0.2032.086/0.334-9.328/0.965.16801.36952.1729-9.71673.-
FUERZAS LATERALES3.1. Primer modoPara
T1=0.37855SegV1=18.00000Pulg/s =45.720cm/segA1=16.598 *
45.72=758.86056cm/seg2Peso
efectivo:W=(Wii)(Wii)NIVELWiiWiiWiiFi120.0002.710054.2005146.884937684110.3782220.0003.590871.8157257.874868721613.7512315.0004.693870.4065330.471720977413.481310.0005.168051.6802267.08448087199.8957248.10291002.3160082549W=248.1029=61.41281002.3160082549Cortante
Basal:V=WA= 61.4128*758.86056*(1/981) =47.5064gFuerza lateral en
cada nudo:Fi=VWiiF1 = 47.5064*(54.2005/248.1029) =10.3782Ton(Wii)F2
= 47.5064*(71.8157/248.1029) =13.7512TonF3 =
47.5064*(70.4065/248.1029) =13.4813TonF4 =
47.5064*(51.6802/248.1029) =9.8957Ton3.2. Segundo modoPara
T2=0.17747SegV2=7.00000Pulg/s =17.780cm/segA2=35.405 *
17.78=629.5009cm/s2Peso
efectivo:W=(Wii)(Wii)NIVELWiiWiiWiiFi120.0004.926198.5222485.330874323614.1019220.0004.921298.4236484.360697905814.0878315.0000.798011.97049.55276759931.7134410.0001.369513.694618.75415564561.9602222.6108997.9984954743W=222.6108=49.655997.9984954743Cortante
Basal:V=WA= 49.655*629.5009*(1/981) =31.8633gFuerza lateral en cada
nudo:Fi=VWiiF1 = 31.8633*(98.5222/222.6108) =14.1019Ton(Wii)F2 =
31.8633*(98.4236/222.6108) =14.0878TonF3 =
31.8633*(11.9704/222.6108) =1.7134TonF4 =
31.8633*(13.6946/222.6108) =1.9602Ton3.3. Tercer modoPara
T3=0.08482SegV3=2.50000Pulg/s =6.350cm/segA3=74.0744 *
6.35=470.3724cm/seg2Peso
efectivo:W=(Wii)(Wii)NIVELWiiWiiWiiFi120.0002.994059.8802179.2821542544-1.9921220.000-1.2335-24.670730.43206999180.8207315.000-5.1766-77.6497401.96506687222.5832410.0002.172921.729247.2156684028-0.7229-42.4402611.6793W=-42.4402=2.9446611.6793Cortante
Basal:V=WA= 2.9446*470.3724*(1/981) =1.4119gFuerza lateral en cada
nudo:Fi=VWiiF1 = 1.4119*(59.8802/-42.4402) =-1.9921Ton(Wii)F2 =
1.4119*(-24.6707/-42.4402) =0.8207TonF3 =
1.4119*(-77.6497/-42.4402) =2.5832TonF4 = 1.4119*(21.7292/-42.4402)
=-0.7229Ton3.3. Cuarto modoPara T3=0.12359SegV3=4.00000Pulg/s
=10.160cm/segA3=50.841 * 10.16=516.5446cm/seg2Peso
efectivo:W=(Wii)(Wii)NIVELWiiWiiWiiFi120.0001.041720.833321.70138888892.4155220.0000.578111.56256.68457031251.3406315.000-1.3448-20.171927.126969401-2.3388410.000-9.7167-97.1667944.1361111111-11.26612.223955.5129W=12.2239=2.691755.5129Cortante
Basal:V=WA= 2.6917*516.5446*(1/981) =1.4173gFuerza lateral en cada
nudo:Fi=VWiiF1 = 1.4173*(20.8333/12.2239) =2.4155Ton(Wii)F2 =
1.4173*(11.5625/12.2239) =1.3406TonF3 = 1.4173*(-20.1719/12.2239)
=-2.3388TonF4 = 1.4173*(-97.1667/12.2239) =-11.266Ton
Datos obtenidos de tabla, segun T1Datos obtenidos de tabla,
segun T2Datos obtenidos de tabla, segun T3Datos obtenidos de tabla,
segun T3
Hoja1Datos:Desplazamiento:0.3cmRazon de
amortiguamiento:1%Esfuerzo cortante:4.5TnK1=K2==Kn=15Tn/cm1.-
Metrado de cargas1er
pisoLosa=34.92TnMuros=4.2TnColumnas=1.05TnW1=40.17Tn2do
pisoLosa=34.92TnMuros=2.1TnColumnas=0.525TnW2=37.545TnPrimera forma
modal aproximada por iteracionesIteracionNivel de pisomasa
inicialrigidez inicialModo inicialFuerza de inerciaFuerza de
corteDeriva del pisoDesplazam. de pisomodo
revisado1ra237.54515137.545 w2/g37.545 w2/g2.503 w2/g6.773
w2/g1.00140.17150.6626.512 w2/g64.057 w2/g4.270 w2/g4.270
w2/g0.632da237.54515137.545 w2/g37.545 w2/g2.503 w2/g6.693
w2/g1.00140.17150.6325.307 w2/g62.852 w2/g4.190 w2/g4.190
w2/g0.633ra237.54515137.545 w2/g37.545 w2/g2.503 w2/g6.720
w2/g1.00140.17150.6425.709 w2/g63.254 w2/g4.217 w2/g4.217
w2/g0.63Modos de vibracion obtenidos1=1.002=0.63Frecuencia natural
del primer modo1=6.72 w2/gw=12.0823789363rad/sPerido
natural=0.5200288238sFuerzas laterales en c/nudoT1=0.5200288238
=1%A=0.18gFactor de participacionW=(Mii)(Mii)Nivel de
pisoWiiWiiWiiFiVi237.5451.0037.54537.5457.947140.170.6325.20815.8185.3367.947Base13.28362.75269241353.3634654416P=62.752692413=1.175948598853.3634654416Fi=Wi*i*P*A/gF2=7.9471782255TonF1=5.335731103TonCortante
basalV1=7.9471782255V2=13.2829093285
