2 GRADOS70w2=70Tnk2=4k2=3Tn/cm70w1=70Tnk1=4k1=7Tn/cma). MATRIZ DE RIGIDEZb). MATRIZ DE MASA10-30.07100.0000K=-33ton/cmM=0.00000.0710ton.s/cmc). ECUACIONES DE EIGENVALORES((K)-Wn*(M))*(1n)=00.0710.0000110=10-3-Wn*0.00000.071* 21-3321-0.923Wn+0.0050Wn^4 = 0Wn=-5.16Wn=5.155Wn=-12.57Wn=12.571d). CALCULO DE FRECUENCIA NATURAL*PERIODO NATURAL CORRESPONDIENTEWn1 =5.155T1 =1.219seg.wn2 =12.571T2 =0.500seg.*ANALISIS DEL ESPECTRO (T)*ACELERACION ESPECTRALA1 =0.230T1=225.630A2 =0.830T2=814.230e). DETERMINACION DE MODOS DE VIBRACION*FRECUENCIA NATURAL Wn1=5.1558.113-3*1111=1.000=-31.1131121=2.704*FRECUENCIA NATURAL Wn2=12.571-1.220-3*1212=1.000=-3-8.2202222=-0.407=1.001.002.704-0.4070f). DETERMINACION DE MODOS*MATRIZ NORMALIZADAM1=0.7682=1.3023.476M2=0.28773.520-1.415g). VECTOR DE FACTORES DE PARTICIPACION(P)=()^T*(M)*(1)la anterior transpuestaP=1.3023.520*0.07100.0000*13.476-1.4150.00000.07101P=0.34240.34200.14630.1460h). MATRIZ DE DESPLAZAMIENTOU=()*(P)*(A)/(^2)hojaU=1.3023.476*0.3420*225.63026.57426.5743.520-1.41500.1460814.23158.03158.03U=3.7812.61510.221-1.064Uc=4.59710.277i). MATRIZ DE FUERZAS LATERALESFs=K*U10-3*3.7812.615Fs=-3310.221-1.0647.14329.341Fs=19.322-11.038j). FUERZA LATERAL EN CADA NUDOFsc=30.19822.252k). VECTOR CORTANTE BASALV=7.14319.322*129.341-11.038126.4648548521=26.46518.303V(TRANSP)=18.3033909251luego el srss aplicado a la cortante basal32.17

TABLA INSERTARINGRESAR DATOS POR EL GRAFICO ESPECTRAL

3 GRADOSW3=5.31Tnk3=5Tn/cmW2=7.92Tnk2=7Tn/cmW1=7.92Tnk1=10Tn/cm981a). MATRIZ DE MASA0.008073394500M=00.00807339450Tn*s/cm000.005412844b). MATRIZ DE RIGIDEZ17-70K=-712-5Tn/cm0-55c). ECUACION EIGENVALORES17-700.0080733945000=-712-5-Wn00.008073394500-55000.0054128440.0000003528Wn^6-0.00159320Wn^4+1.8077981651Wn-350.= 0Wn=-15.58FRECUENCIA NATURALWn=15.58Wn1=15.58Wn=-38.02Wn2=38.02Wn=38.02Wn3=53.18Wn=-53.18Wn=53.18d). PERIODO NATURALT1=0.4032862644T2=0.1652777778T3=0.1181519021e). ANALISIS ESPECTRAL (POR TABLA)A1=60.96cm/SA2=20.32cm/sA3=12.7cm/sF). CALCULO DE ()*PARA FRECUENCIA Wn1=15.5815.0402932844-70110=-710.0402932844-5*210-53.68610572483111 =121 =2.148613326331 =2.9145415903*PARA FRECUENCIA Wn2=38.025.3321990341-70120=-70.3321990341-5*220-5-2.8227301933212=122=0.761742719232=-1.3493899609*PARA FRECUENCIA Wn3=53.18-5.8316084044-7130=-7-10.8316084044-5*23-5-10.30755563483313=123=-0.833086914933=0.4047342458F). CALCULO DE MODOS DE VIBRACION*MATRIZ MODAL111MODO1=0.3021989836=2.14861332630.7617427192-0.8330869149MODO2=0.15037949432.9145415903-1.34938996090.4047342458MODO3=0.1206784163*MATRIZ MODAL NORMALIZADA3.30907797256.64984281758.2864859377=7.10992902975.0654693498-6.90336300539.6444453764-8.97323113943.3538246366g). VECTRO CORTANTE BASAL*PRIMER MODOv=60.96A1=949.7568NIVELWiiWi*iWi*iFi17.923.309077972526.207897542586.72397646463.458893408827.927.109929029756.3106379153400.36463919577.431824472535.319.644445376451.2120049485493.91138433976.7589117394133.7305404063981W^E=18.2302318424V=17.6496296207*SEGUNDO MODOv=20.32A2=772.48512NIVELWiiWi*iWi*iFi17.926.649842817552.6667551142350.22564321511.908206422127.925.065469349840.1185172501203.21911948841.453562348735.31-8.9732311394-47.64785735427.5552372965-1.726363190545.1374150144981W^E=2.0768463141V=1.6354055802*TERCER MODOv=12.7A3=675.3733NIVELWiiWi*iWi*iFi17.928.286485937765.6289686264543.83352562711.324761761527.92-6.9033630053-54.674635002377.4388526015-1.103641688935.313.353824636617.808808820559.72762177140.359481939728.7631424449981W^E=0.8433418586V=0.5806020123J). CORTANTE BASAL(V) =17.64962962071.63540558020.58060201230.58060201231.635405580217.6496296207

USER:INGRESAR DATOS del grafico espectral por tabla

4 GRADOSw4=5TnK4=5Tn/cmW3=6TnK3=7Tn/cmW2=8TnK2=9Tn/cmW1=8TnK1=12Tn/cma). MATRIZ DE MASA0.0081549439000M=00.008154943900Tn*s/cm000.0061162080000.00509684b). MATRIZ DE RIGIDEZ21-900K=-916-70Tn/cm0-712-500-55c). ECUACION EIGENVALORES21-9000.00815494390000=-916-70-Wn00.0081549439000-712-5000.006116208000-550000.005096840.=2.0731*10^-9Wn^8-1.5507*10^-5Wn^6+3.59221*10^-2Wn^4-26.7125Wn^2+3780Wn=-13.53FRECUENCIA NATURALWn=13.53Wn1=13.53Wn=-32.61Wn2=32.61Wn=32.61Wn3=50.23Wn=-50.23Wn4=60.91Wn=50.23Wn=-60.91Wn=60.91d). PERIODO NATURALT1=0.4643902439T2=0.1926770929T3=0.1250885925T4=0.103155814e). ANALISIS ESPECTRAL (POR TABLA)A1=60.96cm/SA2=20.32cm/sA3=12.7cm/sA4=6.2cm/sF). CALCULO DE ()*PARA FRECUENCIA Wn1=13.5319.5071486239-900110=-914.5071486239-70*210-710.8803614679-53100-54.06696788994111 =121 =2.167460958231 =3.20623975141 =3.9425641473*PARA FRECUENCIA Wn2=32.6112.327933945-900120=-97.327933945-70*220-75.4959504587-53200-5-0.42004128444212=122=1.369770438332=0.14822675642=-1.7547492322*PARA FRECUENCIA Wn3=50.230.4246450561-900130=-9-4.5753549439-70*230-7-3.431516208-53300-5-7.859596844313=123=0.04718278433=-1.316553997743=0.8374993788*PARA FRECUENCIA Wn3=0.00-9.2548724652-900130=-9-14.2548724652-70*230-7-10.6911543489-53300-5-13.90929529074313=123=-1.028319162833=0.808365502743=-0.2888252441F). CALCULO DE MODOS DE VIBRACION*MATRIZ MODAL1111MODO1=0.4342404013=2.16746095821.36977043830.047182784-1.0283191628MODO2=0.1982022153.2062397510.148226756-1.31655399770.8083655027MODO3=0.1494970243.9425641473-1.75474923220.8374993788-0.2888252441MODO4=0.1456027272*MATRIZ MODAL NORMALIZADA2.30287185835.04535229296.68909636626.8680032268=4.99138484466.91097442170.3156101891-7.06249932837.38355929360.7478562031-8.80655656215.55185688129.0792200243-8.85332806195.6021140511-1.9836527084g). VECTOR CORTANTE BASAL*PRIMER MODOv=60.96A1=824.7888NIVELWiiWi*iWi*iFi182.302871858318.422974866442.42575036612.3376384365284.991384844639.931078757199.3113813375.0667400456367.383559293644.3013557615327.10168705085.621271959459.079220024345.3961001214412.16118124625.7601809307148.0515095063981W^E=22.343781312V=18.7858313719*SEGUNDO MODOv=20.32A2=662.6352NIVELWiiWi*iWi*iFi185.045352292940.362818343203.64463807411.5527633632286.910974421755.2877953739382.09253966332.1269293526360.74785620314.48713721873.35573340330.172620807145-8.8533280619-44.2666403096391.9070888593-1.702943949655.8711106261981W^E=3.182039758V=2.1493695733*TERCER MODOv=12.7A3=637.921NIVELWiiWi*iWi*iFi186.689096366253.5127709296357.95208157071.1070431617280.31561018912.52488151240.79687833150.052233378436-8.8065565621-52.8393393726465.3326308879-1.0931115751455.602114051128.0105702557156.918409210.579467475131.2088833252981W^E=0.992858714V=0.64563244*CUARTO MODOv=6.2A3=377.64076NIVELWiiWi*iWi*iFi186.868003226854.9440258146377.35574658930.470817382728-7.0624993283-56.4999946263399.031174096-0.4841505368365.551856881233.3111412873184.93868897720.285444397745-1.9836527084-9.918263541919.6743903375-0.084989965921.8369089337981W^E=0.4860862302V=0.1871212777J). CORTANTE BASAL

USER:INGRESAR DATOS CARAJOSUSER:SACR LA ECUACION CON HPUSER:OBTENER VALORES DE LOS Wn CON HP

3 GRADOS 1m3=5.31Tnk3=5m2=7.92Tnk2=7m1=7.92Tnk1=10a). MATRIZ DE MASA0.008073394500M=00.00807339450Tn*s/cm000.005412844b). MATRIZ DE RIGIDEZ17-70K=-712-5Tn/cm0-55c). ECUACION EIGENVALORES17-700.0080733945000=-712-5-Wn00.008073394500-55000.0054128440.0000003528Wn^6-0.0015931992Wn^4+1.8077981651Wn-350.= 0Wn=-15.64FRECUENCIA NATURALWn=15.64Wn1=15.64Wn=-38.44Wn2=38.44Wn=38.44Wn3=53.55Wn=-53.55Wn=53.55d). PERIODO NATURALT1=0.4017391304T2=0.1634547347T3=0.1173333333e). ANALISIS ESPECTRAL (POR TABLA)ACELERACION ESPECTRALA1=1.058gT1=1037.898A2=1.04gT2=1020.24A3=0.65gT2=637.65f). DETERMINACION DE MODOS DE VIBRACION*PARA FRECUENCIA Wn1=15.6415.0251702018-7110=-710.0251702018-5*21-53.67596638533111=121=2.14645288631=2.9037111024*PARA FRECUENCIA Wn2=38.445.0704810275-70120=-70.0704810275-5*220-5-2.99820022023212=122=0.724354432532=-1.3897893511*PARA FRECUENCIA Wn3=53.55-6.1512862385-70130=-7-11.1512862385-5*230-5-10.52188509173312=122=-0.878755176932=0.5598501023*MATRIZ MODAL NORMALIZADA*DETERMINACION DE MODOS111M1=0.3015099054=2.1464528860.7243544325-0.8787551769M2=0.15087877582.9037111024-1.38978935110.5598501023M3=0.1265081621*MATRIZ NORMALIZADA3.31664062176.62783744727.9046283155=7.11901283434.8009034328-6.9462330549.6305661961-9.21129790474.4254069712g). VECTOR DE FACTORES DE PARTICIPACION(P)=()^T*(M)*(1)3.31664062177.11901283439.63056619610.0080733945001(P)=6.62783744724.8009034328-9.2112979047*00.00807339450*17.9046283155-6.9462330544.4254069712000.00541284410.1363799(P)=0.04240941480.0316915408h). MATRIZ DE DESPLAZAMIENTOU=()*(P)*(A)/(^2)3.31664062176.62783744727.90462831550.1363799001037.89800244.6096244.6096244.6096U=7.11901283434.8009034328-6.946233054*00.04240941480*01020.2401477.63361477.63361477.63369.6305661961-9.21129790474.4254069712000.031691540800637.652867.60252867.60252867.60251.91924298020.19407505440.0557042359U=4.11956463380.1405791259-0.04895038574.2430795848005.5729271499-0.2697234440.031186022200.69045533340000.22236345521.9298346317Uc=4.12225319495.5795376442i). MATRIZ DE FUERZAS LATERALESFs=K*U17-701.91924298020.19407505440.0557042359Fs=-712-5*4.11956463380.1405791259-0.04895038570-555.5729271499-0.2697234440.03118602223.79017822732.31522204411.2896247102Fs=8.13543899431.6770413498-1.13326439047.2668125807-2.05151284950.4006820393*FUERZA LATERAL EN CADA NUDO SRSS4.6248065906Fsc=8.38344341537.5614691794j). VECTOR CORTANTE BASALV=F^T*13.79017822738.13543899437.26681258071V=2.31522204411.6770413498-2.0515128495*11.2896247102-1.13326439040.4006820393119.1924298022V=1.9407505444VTRANSP=19.19242980221.94075054440.55704235910.5570423591

USER: INGRESAR DATO DEL GRAFICO ESPECTRALUSER: ESTOS VALORES SE OBTIENEN DE LA ECUACION POLINOMICA EN HPUSER:NO COPIAR ESTA MATRIZ EN TU HOJA DE CALCULO

4 GRADOS 1W4=6Tnk4=8Tn/cmW3=8Tnk3=6Tn/cmW2=12Tnk2=5Tn/cmW1=16tnk1=4Tn/cma). MATRIZ DE MASA0.0163098879000M=00.012232415900Tn*s/cm000.008154943900000.006116208b). MATRIZ DE RIGIDEZ9-500K=-511-60Tn/cm0-614-800-88c). ECUACION EIGENVALORES9-5000.01630988790000=-511-60-Wn00.0122324159000-614-8000.0081549439000-880000.0061162082.3564Wn^8-25.3014Wn^6+12354Wn4-124.354Wn+960.= 0Wn=-15.64FRECUENCIA NATURALWn=20.625Wn1=20.625Wn=-38.44Wn2=42.97Wn=42.97Wn3=42.97Wn=-53.55Wn4=42.97Wn=42.97Wn=-25.36Wn=42.97d). PERIODO NATURALT1=0.30464T2=0.1462229462T3=0.1462229462T4=0.1462229462e). ANALISIS ESPECTRAL (POR TABLA)ACELERACION ESPECTRALA1=2.4gT1=2354.4A2=1.04gT2=1020.24A3=0.65gT3=637.65A4=0.68gT4=667.08f). DETERMINACION DE MODOS DE VIBRACION*PARA FRECUENCIA Wn1=20.6252.0619266055-500110=-55.7964449541-60*210-610.5309633028-83100-85.39822247714111=121=0.412385321131=-0.434938531141=-0.8818292045*PARA FRECUENCIA Wn2=42.97-21.1149178389-500120=-5-11.5861883792-60*220-6-1.0574589195-83200-8-3.29309418964212=122=-4.222983567832=7.321380523142=2.1994802837*PARA FRECUENCIA Wn3=42.97-21.1149178389-500130=-5-11.5861883792-60*230-6-1.0574589195-83300-8-3.29309418964313=123=-4.222983567833=7.321380523143=-41.5413613994*PARA FRECUENCIA Wn4=42.97-21.1149178389-500140=-5-11.5861883792-60*240-6-1.0574589195-83400-8-3.29309418964414=124=-4.222983567834=7.321380523144=2.1994802837*MATRIZ MODAL NORMALIZADA*DETERMINACION DE MODOS1111M1=0.1571271407=0.4123853211-4.2229835678-4.2229835678-4.2229835678M2=0.8373604625-0.43493853117.32138052317.32138052317.3213805231M3=3.3505567609-0.88182920452.1994802837-41.54136139942.1994802837M4=0.8373604625*MATRIZ NORMALIZADA6.36427287791.19422882360.29845785981.1942288236=2.6245327143-5.043208698-1.2603826376-5.043208698-2.76806749688.74340364892.18512356178.7434036489-5.61220168932.6266827517-12.39834581662.6266827517g). VECTOR DE FACTORES DE PARTICIPACION(P)=()^T*(M)*(1)6.36427287792.6245327143-2.7680674968-5.61220168930.01630988790001(P)=1.1942288236-5.0432086988.74340364892.6266827517*00.012232415900*10.2984578598-1.26038263762.1851235617-12.3983458166000.0081549439011.1942288236-5.0432086988.74340364892.62668275170000.00611620810.0790061249(P)=0.0451544164-0.06856101150.0451544164h). MATRIZ DE DESPLAZAMIENTOU=()*(P)*(A)/(^2)6.36427287791.19422882360.29845785981.19422882360.07900612490002354.4000425.390625425.390625425.390625425.390625U=2.6245327143-5.043208698-1.2603826376-5.043208698*00.045154416400*01020.24001846.42091846.42091846.42091846.4209-2.76806749688.74340364892.18512356178.743403648900-0.0685610115000637.6501846.42091846.42091846.42091846.4209-5.61220168932.6266827517-12.39834581662.62668275170000.0451544164000667.081846.42091846.42091846.42091846.42092.78292747180.0297960999-0.00706662250.0194820653U=1.147638439-0.12582844040.0298422308-0.08227244185.534677686000-1.21040238660.2181485856-0.05173743250.142635613700.552550071300-2.45406671860.06553593430.29355712020.0428504186000.345343794600000.36128273892.7831641361Uc=1.15782818091.23922734922.472802127i). MATRIZ DE FUERZAS LATERALESFs=K*U9-5002.7831641361000Fs=-511-60*01.1578281809000-614-8001.2392273492000-880002.47280212725.0484772252-5.789140904700Fs=-13.915820680712.7361099903-7.435364095500-6.946969085617.3491828895-19.782417016200-9.91381879419.7824170162*FUERZA LATERAL EN CADA NUDO SRSS25.7087604469Fsc=20.276666445327.213940350722.1275354724j). VECTOR CORTANTE BASALV=F^T*125.0484772252-13.9158206807001V=-5.789140904712.7361099903-6.94696908560*10-7.435364095517.3491828895-9.913818794100-9.91381879419.7824170162111.1326565445V=-0VTRANSP=11.1326565445-009.868598222209.8685982222

calcular con hpoperar en hp polinomiosUSER:ingresas la matriz al HP para calcular la ecuacion polynomicaUSER:ingresar los valores por el grafico espectral

3 GRADOS 2970k/m275k/m2L= m3.550k/m2L= m3.56m6ma). DETERM. CARGA MUERTA TRIBUTARIADATOS DEL PROBLEMARazon de amortiguamiento=7%Piso 1:Desplazamiento =0.3cmLosa =34.92tonEsfuerzo cortante=4.5ton4muros =4.2ton4columnas =1.05tonDATO ASUMIDOT1=0.5segpeso total = w140.17ton2=11=0.66piso 2:Losa =34.92ton4muros =2.1ton4columnas =0.525tonpeso total = w237.545tonb). DETRMINACION DE LA RIGIDEZ DE CADA PISOK1 = K2 =15ton/cmc). MODELO DINAMICO DEL PORTICOESTRUCTURAMODELO DINAMICOFORMA MODAL1w2=37.545k2=15Tn/cmw1=40.170.64k1=15Tn/cmd). DETRMN. DE LA FORMA MODAL Y EL PERIODEO FUNDAMENTAL DE VIBRACION POR ITERACIONu2 =1u1 =0.66Pisomasa de piso mRigidez del piso kModo inicial uFuerza de inercia m*w*uFuerza de corte k*Derivada del piso Despl. Del pison Modo del piso237.545/g15137.545w/g37.545w/g2.503w/g6.773w/g1140.170/g150.6626.512w/g64.057w/g4.270w/g4.270w/g0.63237.545/g15137.545w/g37.545w/g2.503w/g6.693w/g1140.170/g150.6325.307w/g62.852w/g4.190w/g4.190w/g0.64237.545/g15137.545w/g37.545w/g2.503w/g6.720w/g1140.170/g150.6425.709w/g63.254w/g4.217w/g4.217w/g0.64e). DETERMINACION DE LA FRECUENCIA CIRCULAR NATURAL6.720w/g =1w =12.082rad/segf). DETERM. DEL PERIODOT =0.52segg). DETERMINACION DE LAS FUERZAS LATERALESA =0.18*gh). DETERMINACION DEL FACTOR DE PARTICIPACIONNIVELWi1Wi*1Wi*1FiViFi=Fuerzas laterales237.545137.54537.5457.9237.923Vi=cortante basal140.170.6425.60939241316.32663628985.40413.327BASESUMATORIA63.15453.872P =1.172i). DTERMINACION DE LA ACELERACION PICOt=0 segA =0.2*g

RESULTADO DE LA FORMA MODAL POR ITERACIONSE OBTIENE UTILIZANDO EL GRAFICO ESPECTRALSE OBTIENE DEL GRAFICO ESPECTRAL

G.L.2DATOS PROPORCIONADOS DE LA PREGUNTA0.9393.1593.1358.5788EIGENVECTORES:=2.1812.871-4.084FRECUENCIAS:w=19.39113.491-3.1291.22629.1391^T*M*=Iw3=35Tnw3k3=3Tn/cm4.0 mw2=35Tnw2k2=3Tn/cm4.0 mw1w1=55Tn4.0 mk1=7Tn/cmPROCEDIMIENTO:* EMPEZAMOS DE LA MATRIZ DE PARTICIPACION (dato matriz modal normalizada)se cumple:P=^T*M*1*matriz de masa5500M=0350*Tn/g00350.9392.1813.49155001P=3.1592.871-3.129*0350*13.135-4.0841.22600351250.165P=164.715*1/g72.395a). VERIFICACION DE LOS FACTORES DE PARTICIPACION SI SON CORRECTOS O NOSe cumple:Pn*m =1250.165*0.939+164.715*3.159+72.395*3.135*1/g =1POR LO TANTO:1.00=1b). CALCULO DE DESPLAZAMIENTOS UTILIZANDO EL ESPECTRO DE ACELERACIONT1=0.7324084147segA1=0.15*gT2=0.3240241816segA2=0.6*gT3=0.2156272949segA3=0.77*g* MATRIZ DE DESPLAZAMIENTOU=*P*A0.9393.1593.135250.165000.150073.5958094473.5958094473.59580944U=2.1812.871-4.084*0164.7150*00.60376.01475921376.01475921376.014759213.491-3.1291.2260072.395000.77849.08714881849.08714881849.087148810.47877373070.83028871430.2058185788U=1.11203994320.7545928771-0.26812219331.7799777358-0.82240373130.0804891795* SRSS PPARA CADA NUDO DE DESPLAZAMIENTO0.980288183Uc=1.37037686641.9624339849c). CALCULO DE LA DERIVA ENTRE CADA PISO O DESPLAZAMIENTOS ENTRE PISOS-0.63326621250.07569583720.4739407721A=-0.66793779261.5769966084-0.34861137271.7799777358-0.82240373130.08048917950.7945916002A=1.74773827761.9624339849

SI CUMPLE CON LA CONDICIEN EN LA IGUALDAD SON CORRECTOSse obtienen por tabla espectral

METRADOMETRADOS:V4f'C =210KG/cm2w=1.5tn/mS/C muro =100Kg/m2m=132453mc2c2V3LARGOANCHOw=1.5tn/mVIGA 1 :0.30.7m=148683mVIGA 2 :0.30.6c2c2VIGA 3 :0.30.4V2VIGA 4 :0.30.4w=2tn/mCOLUMNA 1 :0.30.5m=194863mCOLUMNA 2 :0.30.3c1c2V1w=2tn/mm=210714mc1c16.5a)C1 =2520b)C1 =1080c)C2 =1296d)C2 =648V =3276C2 =648V =1872V =1872M =2275V =2808M =1950M =975W =13000M =1950W =9750W =975021071kgW =1300014868kg13245kg19486kg