Calculo Espectro de Respuesta

Sismo

donde tn es el periodo del modo de vibrar "n"s: coeficiente del suelo como se define en la siguiente tabla

A0 : Es la aceleracion efectiva como se define en la siguiente tabla.

k1: Coeficiente de importancia

EL puente a diseñar es una estructura escencial por lo que el coeficiente de importancia sera igual a 1,0

para encontrar el espectro de respuesta del suelo e ingresarlo a nuestro modelo se considera la seccion 3.1004 del manual de carreteras volumen 3. Se utiliza el modelo espectral 3.1004.309(3). La aceleracion Sa(tn) se obtiene con las siguientes expresiones

K2 =constante espectral (Tabla 3.1004.309(2).A). De acuerdo con el Informe Geotécnico el suelo seráclasificado tipo II para el análisis sísmico. Así que en nuestro caso se tiene: K2=0.672T1 = constante espectral (Tabla 3.1004.309(2).A). De acuerdo con el Informe Geotécnico el suelo seráclasificado tipo II para el análisis sísmico. Así que en nuestro caso se tiene: T1=0.30 seg

Suelo tipo II

Delta 0.01

k1 1S 1A0 0.4g 1t1 0.3k2 0.672

Grafico

Realizando una discretizacion de 0,01 (s), y calculando el espectro de aceleracion hasta los 4(s)

EL puente a diseñar es una estructura escencial por lo que el coeficiente de importancia sera igual a 1,0

para encontrar el espectro de respuesta del suelo e ingresarlo a nuestro modelo se considera la seccion 3.1004 del manual de carreteras volumen 3. Se utiliza el modelo espectral 3.1004.309(3). La aceleracion Sa(tn) se obtiene con las siguientes expresiones

El termino A0 elimina al g

0 1 2 3 4 5 60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Espectro de respuesta

Tn (seg)

Sa(g

)

K2 =constante espectral (Tabla 3.1004.309(2).A). De acuerdo con el Informe Geotécnico el suelo será

T1 = constante espectral (Tabla 3.1004.309(2).A). De acuerdo con el Informe Geotécnico el suelo será

Sa(g) Tn Tn Sa/m/s2)0.6 0 0 5.8860.6 0.01 0.01 5.8860.6 0.02 0.02 5.8860.6 0.03 0.03 5.8860.6 0.04 0.04 5.8860.6 0.05 0.05 5.8860.6 0.06 0.06 5.8860.6 0.07 0.07 5.8860.6 0.08 0.08 5.8860.6 0.09 0.09 5.8860.6 0.1 0.1 5.8860.6 0.11 0.11 5.8860.6 0.12 0.12 5.8860.6 0.13 0.13 5.8860.6 0.14 0.14 5.8860.6 0.15 0.15 5.8860.6 0.16 0.16 5.8860.6 0.17 0.17 5.8860.6 0.18 0.18 5.8860.6 0.19 0.19 5.8860.6 0.2 0.2 5.8860.6 0.21 0.21 5.8860.6 0.22 0.22 5.886

Realizando una discretizacion de 0,01 (s), y calculando el espectro de aceleracion hasta los 4(s) 0.6 0.23 0.23 5.8860.6 0.24 0.24 5.8860.6 0.25 0.25 5.8860.6 0.26 0.26 5.8860.6 0.27 0.27 5.8860.6 0.28 0.28 5.8860.6 0.29 0.29 5.8860.6 0.3 0.3 5.886

0.5868424 0.31 0.31 5.75692370.5745519 0.32 0.32 5.63635430.5628854 0.33 0.33 5.52190560.5517936 0.34 0.34 5.41309510.5412325 0.35 0.35 5.30949120.5311627 0.36 0.36 5.21070640.5215486 0.37 0.37 5.1163917

0.512358 0.38 0.38 5.0262321

0 1 2 3 4 5 60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Espectro de respuesta

Tn (seg)

Sa(g

)

0.5035619 0.39 0.39 4.93994220.4951338 0.4 0.4 4.85726290.4870498 0.41 0.41 4.77795840.4792878 0.42 0.42 4.70181360.4718279 0.43 0.43 4.62863180.4646516 0.44 0.44 4.55823260.4577422 0.45 0.45 4.4904507

0.451084 0.46 0.46 4.42513360.4446627 0.47 0.47 4.3621410.4384652 0.48 0.48 4.30134340.4324792 0.49 0.49 4.24262080.4266934 0.5 0.5 4.18586230.4210973 0.51 0.51 4.13096470.4156812 0.52 0.52 4.07783240.4104359 0.53 0.53 4.0263763

0.405353 0.54 0.54 3.97651320.4004247 0.55 0.55 3.92816580.3956434 0.56 0.56 3.88126160.3910023 0.57 0.57 3.835733

0.386495 0.58 0.58 3.79151640.3821154 0.59 0.59 3.74855250.3778578 0.6 0.6 3.70678540.3737169 0.61 0.61 3.66616250.3696875 0.62 0.62 3.62663470.3657651 0.63 0.63 3.5881554

0.361945 0.64 0.64 3.55068070.3582232 0.65 0.65 3.51416950.3545956 0.66 0.66 3.47858260.3510584 0.67 0.67 3.44388310.3476082 0.68 0.68 3.41003630.3442415 0.69 0.69 3.37700890.3409551 0.7 0.7 3.34476990.3377461 0.71 0.71 3.31328940.3346116 0.72 0.72 3.28253930.3315487 0.73 0.73 3.252493

0.328555 0.74 0.74 3.22312480.325628 0.75 0.75 3.1944108

0.3227653 0.76 0.76 3.16632780.3199647 0.77 0.77 3.1388540.3172241 0.78 0.78 3.11196860.3145414 0.79 0.79 3.08565150.3119148 0.8 0.8 3.05988390.3093423 0.81 0.81 3.03464760.3068221 0.82 0.82 3.00992520.3043527 0.83 0.83 2.9857003

0.3019324 0.84 0.84 2.9619570.2995596 0.85 0.85 2.9386802

0.297233 0.86 0.86 2.91585530.2949509 0.87 0.87 2.89346860.2927122 0.88 0.88 2.87150660.2905155 0.89 0.89 2.84995670.2883595 0.9 0.9 2.82880670.2862431 0.91 0.91 2.80804470.2841651 0.92 0.92 2.78765950.2821244 0.93 0.93 2.76764030.2801199 0.94 0.94 2.74797660.2781507 0.95 0.95 2.72865860.2762158 0.96 0.96 2.70967650.2743141 0.97 0.97 2.69102120.2724448 0.98 0.98 2.67268360.2706071 0.99 0.99 2.6546553

0.2688 1 1 2.6369280.2670228 1.01 1.01 2.61949370.2652747 1.02 1.02 2.60234470.2635549 1.03 1.03 2.58547370.2618627 1.04 1.04 2.56887350.2601975 1.05 1.05 2.55253720.2585584 1.06 1.06 2.53645810.2569449 1.07 1.07 2.52062990.2553564 1.08 1.08 2.50504640.2537922 1.09 1.09 2.48970150.2522517 1.1 1.1 2.47458940.2507344 1.11 1.11 2.45970460.2492397 1.12 1.12 2.44504160.2477671 1.13 1.13 2.4305952

0.246316 1.14 1.14 2.41636040.244886 1.15 1.15 2.4023321

0.2434766 1.16 1.16 2.38850570.2420873 1.17 1.17 2.37487650.2407176 1.18 1.18 2.36144010.2393672 1.19 1.19 2.34819210.2380355 1.2 1.2 2.33512840.2367222 1.21 1.21 2.32224490.2354269 1.22 1.22 2.30953770.2341491 1.23 1.23 2.29700280.2328886 1.24 1.24 2.28463670.2316448 1.25 1.25 2.27243570.2304176 1.26 1.26 2.26039620.2292064 1.27 1.27 2.2485150.2280111 1.28 1.28 2.2367887

0.2268312 1.29 1.29 2.22521410.2256665 1.3 1.3 2.2137880.2245166 1.31 1.31 2.20250760.2233812 1.32 1.32 2.19136970.2222601 1.33 1.33 2.18037160.2211529 1.34 1.34 2.16951040.2200595 1.35 1.35 2.15878350.2189794 1.36 1.36 2.14818820.2179125 1.37 1.37 2.1377220.2168585 1.38 1.38 2.12738230.2158172 1.39 1.39 2.11716680.2147883 1.4 1.4 2.1070730.2137715 1.41 1.41 2.09709870.2127667 1.42 1.42 2.08724150.2117736 1.43 1.43 2.07749940.2107921 1.44 1.44 2.06787020.2098218 1.45 1.45 2.05835180.2088626 1.46 1.46 2.04894220.2079143 1.47 1.47 2.03963930.2069767 1.48 1.48 2.03044140.2060496 1.49 1.49 2.02134650.2051328 1.5 1.5 2.01235270.2042261 1.51 1.51 2.00345830.2033294 1.52 1.52 1.99466150.2024425 1.53 1.53 1.98596070.2015652 1.54 1.54 1.97735410.2006973 1.55 1.55 1.96884020.1998387 1.56 1.56 1.96041740.1989892 1.57 1.57 1.9520840.1981487 1.58 1.58 1.9438387

0.197317 1.59 1.59 1.93567980.196494 1.6 1.6 1.9276061

0.1956795 1.61 1.61 1.9196160.1948734 1.62 1.62 1.91170820.1940756 1.63 1.63 1.90388130.1932858 1.64 1.64 1.89613410.1925041 1.65 1.65 1.88846520.1917302 1.66 1.66 1.88087330.1909641 1.67 1.67 1.87335730.1902055 1.68 1.68 1.8659160.1894544 1.69 1.69 1.85854810.1887108 1.7 1.7 1.85125250.1879743 1.71 1.71 1.8440281

0.187245 1.72 1.72 1.83687370.1865228 1.73 1.73 1.8297884

0.1858074 1.74 1.74 1.8227710.1850989 1.75 1.75 1.81582050.1843971 1.76 1.76 1.80893580.1837019 1.77 1.77 1.80211610.1830133 1.78 1.78 1.7953602

0.182331 1.79 1.79 1.78866740.1816551 1.8 1.8 1.78203650.1809854 1.81 1.81 1.77546680.1803218 1.82 1.82 1.76895730.1796643 1.83 1.83 1.76250710.1790128 1.84 1.84 1.75611540.1783671 1.85 1.85 1.74978140.1777272 1.86 1.86 1.74350410.1770931 1.87 1.87 1.73728290.1764645 1.88 1.88 1.73111680.1758415 1.89 1.89 1.7250052

0.175224 1.9 1.9 1.71894720.1746118 1.91 1.91 1.7129421

0.174005 1.92 1.92 1.70698920.1734034 1.93 1.93 1.7010878

0.172807 1.94 1.94 1.69523710.1722157 1.95 1.95 1.68943650.1716295 1.96 1.96 1.68368520.1710482 1.97 1.97 1.67798260.1704718 1.98 1.98 1.67232810.1699002 1.99 1.99 1.66672090.1693334 2 2 1.66116050.1687713 2.01 2.01 1.65564630.1682138 2.02 2.02 1.65017760.1676609 2.03 2.03 1.64475390.1671126 2.04 2.04 1.63937440.1665687 2.05 2.05 1.63403880.1660292 2.06 2.06 1.6287464

0.165494 2.07 2.07 1.62349660.1649632 2.08 2.08 1.61828890.1644366 2.09 2.09 1.61312270.1639141 2.1 2.1 1.60799760.1633958 2.11 2.11 1.60291310.1628816 2.12 2.12 1.59786850.1623714 2.13 2.13 1.59286340.1618652 2.14 2.14 1.58789730.1613629 2.15 2.15 1.58296980.1608645 2.16 2.16 1.57808030.1603699 2.17 2.17 1.57322840.1598791 2.18 2.18 1.5684136

0.159392 2.19 2.19 1.56363550.1589086 2.2 2.2 1.55889360.1584289 2.21 2.21 1.55418750.1579528 2.22 2.22 1.54951680.1574802 2.23 2.23 1.5448810.1570112 2.24 2.24 1.54027970.1565456 2.25 2.25 1.53571250.1560835 2.26 2.26 1.53117910.1556248 2.27 2.27 1.52667890.1551694 2.28 2.28 1.52221160.1547173 2.29 2.29 1.51777690.1542685 2.3 2.3 1.5133744

0.153823 2.31 2.31 1.50900360.1533807 2.32 2.32 1.50466430.1529415 2.33 2.33 1.5003560.1525054 2.34 2.34 1.49607840.1520725 2.35 2.35 1.49183120.1516426 2.36 2.36 1.4876140.1512158 2.37 2.37 1.48342650.1507919 2.38 2.38 1.4792684

0.150371 2.39 2.39 1.47513920.149953 2.4 2.4 1.4710387

0.1495379 2.41 2.41 1.46696670.1491257 2.42 2.42 1.46292260.1487162 2.43 2.43 1.45890640.1483096 2.44 2.44 1.45491760.1479058 2.45 2.45 1.45095590.1475047 2.46 2.46 1.44702110.1471063 2.47 2.47 1.44311290.1467106 2.48 2.48 1.43923090.1463175 2.49 2.49 1.4353750.1459271 2.5 2.5 1.43154480.1455392 2.51 2.51 1.42774

0.145154 2.52 2.52 1.42396040.1447712 2.53 2.53 1.4202057

0.144391 2.54 2.54 1.41647570.1440133 2.55 2.55 1.4127701

0.143638 2.56 2.56 1.40908860.1432651 2.57 2.57 1.4054310.1428947 2.58 2.58 1.4017970.1425267 2.59 2.59 1.3981865

0.142161 2.6 2.6 1.39459910.1417976 2.61 2.61 1.39103460.1414366 2.62 2.62 1.38749280.1410778 2.63 2.63 1.3839735

0.1407213 2.64 2.64 1.38047640.1403671 2.65 2.65 1.37700130.1400151 2.66 2.66 1.3735480.1396653 2.67 2.67 1.37011630.1393176 2.68 2.68 1.36670590.1389721 2.69 2.69 1.36331670.1386288 2.7 2.7 1.35994840.1382875 2.71 2.71 1.35660080.1379484 2.72 2.72 1.35327380.1376113 2.73 2.73 1.34996710.1372763 2.74 2.74 1.34668050.1369433 2.75 2.75 1.34341380.1366123 2.76 2.76 1.34016690.1362833 2.77 2.77 1.33693950.1359563 2.78 2.78 1.33373150.1356313 2.79 2.79 1.33054270.1353081 2.8 2.8 1.32737280.1349869 2.81 2.81 1.32422180.1346676 2.82 2.82 1.32108940.1343502 2.83 2.83 1.31797540.1340346 2.84 2.84 1.31487980.1337209 2.85 2.85 1.3118022

0.133409 2.86 2.86 1.30874260.133099 2.87 2.87 1.3057008

0.1327907 2.88 2.88 1.30267660.1324842 2.89 2.89 1.29966980.1321794 2.9 2.9 1.29668040.1318765 2.91 2.91 1.2937080.1315752 2.92 2.92 1.29075270.1312757 2.93 2.93 1.28781410.1309778 2.94 2.94 1.28489230.1306816 2.95 2.95 1.28198690.1303871 2.96 2.96 1.27909790.1300943 2.97 2.97 1.27622520.1298031 2.98 2.98 1.27336850.1295135 2.99 2.99 1.27052770.1292256 3 3 1.26770280.1289392 3.01 3.01 1.26489340.1286544 3.02 3.02 1.26209960.1283712 3.03 3.03 1.25932120.1280895 3.04 3.04 1.2565580.1278094 3.05 3.05 1.253810.1275308 3.06 3.06 1.25107680.1272537 3.07 3.07 1.24835860.1269781 3.08 3.08 1.2456551

0.126704 3.09 3.09 1.24296610.1264314 3.1 3.1 1.24029160.1261602 3.11 3.11 1.23763150.1258905 3.12 3.12 1.23498550.1256222 3.13 3.13 1.23235370.1253553 3.14 3.14 1.22973590.1250899 3.15 3.15 1.22713190.1248259 3.16 3.16 1.22454160.1245632 3.17 3.17 1.2219650.1243019 3.18 3.18 1.2194019

0.124042 3.19 3.19 1.21685220.1237835 3.2 3.2 1.21431570.1235262 3.21 3.21 1.21179250.1232704 3.22 3.22 1.20928230.1230158 3.23 3.23 1.20678510.1227626 3.24 3.24 1.20430070.1225106 3.25 3.25 1.20182910.1222599 3.26 3.26 1.19937010.1220106 3.27 3.27 1.19692360.1217624 3.28 3.28 1.19448960.1215156 3.29 3.29 1.1920679

0.12127 3.3 3.3 1.18965850.1210256 3.31 3.31 1.18726120.1207825 3.32 3.32 1.18487590.1205405 3.33 3.33 1.18250260.1202998 3.34 3.34 1.18014120.1200603 3.35 3.35 1.1777915

0.119822 3.36 3.36 1.17545340.1195848 3.37 3.37 1.17312690.1193488 3.38 3.38 1.1708119

0.119114 3.39 3.39 1.16850830.1188803 3.4 3.4 1.1662160.1186478 3.41 3.41 1.16393490.1184164 3.42 3.42 1.16166490.1181861 3.43 3.43 1.159406

0.117957 3.44 3.44 1.15715790.1177289 3.45 3.45 1.1549208

0.117502 3.46 3.46 1.15269450.1172761 3.47 3.47 1.15047880.1170514 3.48 3.48 1.14827380.1168277 3.49 3.49 1.1460793

0.116605 3.5 3.5 1.14389520.1163834 3.51 3.51 1.14172150.1161629 3.52 3.52 1.13955820.1159434 3.53 3.53 1.137405

0.115725 3.54 3.54 1.1352620.1155075 3.55 3.55 1.1331290.1152911 3.56 3.56 1.13100610.1150757 3.57 3.57 1.1288930.1148613 3.58 3.58 1.1267898

0.114648 3.59 3.59 1.12469640.1144355 3.6 3.6 1.12261270.1142241 3.61 3.61 1.12053860.1140137 3.62 3.62 1.1184740.1138042 3.63 3.63 1.11641890.1135956 3.64 3.64 1.11437330.1133881 3.65 3.65 1.11233690.1131814 3.66 3.66 1.11030990.1129757 3.67 3.67 1.1082921

0.112771 3.68 3.68 1.10628340.1125672 3.69 3.69 1.10428380.1123642 3.7 3.7 1.10229320.1121622 3.71 3.71 1.10031150.1119611 3.72 3.72 1.09833880.1117609 3.73 3.73 1.09637480.1115616 3.74 3.74 1.09441960.1113632 3.75 3.75 1.09247310.1111657 3.76 3.76 1.0905353

0.110969 3.77 3.77 1.0886060.1107732 3.78 3.78 1.08668520.1105783 3.79 3.79 1.08477280.1103842 3.8 3.8 1.0828689

0.110191 3.81 3.81 1.08097330.1099986 3.82 3.82 1.0790859

0.109807 3.83 3.83 1.07720680.1096163 3.84 3.84 1.07533580.1094264 3.85 3.85 1.0734730.1092373 3.86 3.86 1.07161820.1090491 3.87 3.87 1.06977130.1088616 3.88 3.88 1.0679325

0.108675 3.89 3.89 1.06610150.1084891 3.9 3.9 1.06427830.1083041 3.91 3.91 1.06246290.1081198 3.92 3.92 1.06065520.1079363 3.93 3.93 1.05885520.1077536 3.94 3.94 1.05706280.1075717 3.95 3.95 1.0552780.1073905 3.96 3.96 1.05350070.1072101 3.97 3.97 1.05173080.1070304 3.98 3.98 1.0499684

0.1068515 3.99 3.99 1.04821330.1066734 4 4 1.04646560.1064959 4.01 4.01 1.04472510.1063192 4.02 4.02 1.04299180.1061433 4.03 4.03 1.04126570.1059681 4.04 4.04 1.03954680.1057936 4.05 4.05 1.03783490.1056198 4.06 4.06 1.036130.1054467 4.07 4.07 1.03443210.1052743 4.08 4.08 1.03274120.1051027 4.09 4.09 1.03105710.1049317 4.1 4.1 1.02937990.1047614 4.11 4.11 1.02770950.1045918 4.12 4.12 1.02604590.1044229 4.13 4.13 1.0243890.1042547 4.14 4.14 1.02273880.1040872 4.15 4.15 1.02109510.1039203 4.16 4.16 1.01945810.1037541 4.17 4.17 1.01782760.1035885 4.18 4.18 1.01620370.1034237 4.19 4.19 1.01458610.1032594 4.2 4.2 1.0129750.1030959 4.21 4.21 1.01137030.1029329 4.22 4.22 1.0097720.1027706 4.23 4.23 1.0081799

0.102609 4.24 4.24 1.00659410.102448 4.25 4.25 1.0050145

0.1022876 4.26 4.26 1.00344110.1021278 4.27 4.27 1.00187380.1019687 4.28 4.28 1.00031260.1018101 4.29 4.29 0.99875760.1016522 4.3 4.3 0.99720850.1014949 4.31 4.31 0.99566540.1013383 4.32 4.32 0.99412830.1011822 4.33 4.33 0.99259710.1010267 4.34 4.34 0.99107180.1008718 4.35 4.35 0.98955230.1007175 4.36 4.36 0.98803870.1005638 4.37 4.37 0.98653080.1004107 4.38 4.38 0.98502870.1002581 4.39 4.39 0.98353220.1001062 4.4 4.4 0.98204150.0999548 4.41 4.41 0.9805563

0.099804 4.42 4.42 0.97907680.0996537 4.43 4.43 0.9776028

0.099504 4.44 4.44 0.97613440.0993549 4.45 4.45 0.97467150.0992063 4.46 4.46 0.9732140.0990583 4.47 4.47 0.9717620.0989108 4.48 4.48 0.97031540.0987639 4.49 4.49 0.96887420.0986176 4.5 4.5 0.96743830.0984717 4.51 4.51 0.96600770.0983264 4.52 4.52 0.96458240.0981817 4.53 4.53 0.96316230.0980375 4.54 4.54 0.96174740.0978938 4.55 4.55 0.96033780.0977506 4.56 4.56 0.95893320.0976079 4.57 4.57 0.95753390.0974658 4.58 4.58 0.95613960.0973242 4.59 4.59 0.95475030.0971831 4.6 4.6 0.95336610.0970425 4.61 4.61 0.95198690.0969024 4.62 4.62 0.95061270.0967628 4.63 4.63 0.94924350.0966238 4.64 4.64 0.94787910.0964852 4.65 4.65 0.94651970.0963471 4.66 4.66 0.94516510.0962095 4.67 4.67 0.94381530.0960724 4.68 4.68 0.94247040.0959358 4.69 4.69 0.94113020.0957997 4.7 4.7 0.9397948

0.095664 4.71 4.71 0.93846410.0955289 4.72 4.72 0.93713810.0953942 4.73 4.73 0.9358168

0.09526 4.74 4.74 0.93450020.0951262 4.75 4.75 0.93318810.0949929 4.76 4.76 0.93188070.0948601 4.77 4.77 0.93057780.0947278 4.78 4.78 0.92927950.0945959 4.79 4.79 0.92798570.0944645 4.8 4.8 0.92669630.0943335 4.81 4.81 0.9254115

0.094203 4.82 4.82 0.92413110.0940729 4.83 4.83 0.92285510.0939433 4.84 4.84 0.92158350.0938141 4.85 4.85 0.92031630.0936854 4.86 4.86 0.91905340.0935571 4.87 4.87 0.91779490.0934292 4.88 4.88 0.9165406

0.0933018 4.89 4.89 0.91529070.0931748 4.9 4.9 0.91404490.0930483 4.91 4.91 0.91280350.0929221 4.92 4.92 0.91156620.0927964 4.93 4.93 0.91033310.0926712 4.94 4.94 0.90910410.0925463 4.95 4.95 0.90787940.0924219 4.96 4.96 0.90665870.0922979 4.97 4.97 0.90544210.0921743 4.98 4.98 0.90422960.0920511 4.99 4.99 0.90302110.0919283 5 5 0.9018167