EJERCICIO 1DATOS DEL PROBLEMAH (m)B (m)E (GPA)20E (N/m)20000000000AREA AFER.2 (m)40VIGA0.30.25W2 CUBIERTA (KG/M)550AREA AFER. 1 (m)40COLUMNA0.30.3W1 ENTREPISO (KG/M)750

DETERMINACION DE LA MATRIZ DE MASASMATRIZ MASAM2 (KG)22000220000M1 (KG)30000030000DETERMINACION DE LA MATRIZ DE RIGIDEZDATOS HORIZONTALES MATRIZ DE RIGIDEZMATRIZ DE RIGIDEZINERCIA VIGAS (m^4)0.0005625AE/L37500000037500000000-3750000000037500000000-37500000000INERCIA COLUMNAS (m^4)0.0006752EI/L56250000210937542187500-210937542187500210937542187500-21093754218750AREA VIGAS (M)0.0754EI/L1125000004218750112500000-4218750562500004218750112500000-4218750300000000AREA COLUMA (M)0.096EI/L4218750-3750000000037500000000-3750000000037500000000LONGITUD VIGA (M)412EI/L21093750-2109375-421875002109375-42187500-2109375-421875002109375-4218750LONGITUD COLUMNA (M)30421875056250000-421875011250000042187503000000000-421875011250000E (N/m)20000000000# ELEMENTOS6DATOS VERTICALES MATRIZ DE RIGIDEZMATRIZ DE RIGIDEZ# NODOS6AE/L600000000-0-1000060000000000-60000000000600000009000000-6000000-090000002EI/L90000001-000000600000090000000-600000090000000600000000-0-0-600000000-04EI/L18000000TETA4.712388980400100009000000180000000-900000090000009000000-018000000-9000000090000006EI/L9000000000-0-10-6000000000060000000000-6000000-0-900000060000000-900000012EI/L60000000001-000-6000000-900000006000000-9000000-0-6000000000060000000000000010-900000090000000-900000018000000-900000009000000-9000000018000000ENSAMBLE DE LA MATRIZ DE RIGIDEZTRANSPUESTAY11Y12Y13Y21Y22Y23Y31Y32Y33Y41Y42Y43-01000038100000009000000-37500000000-6000000-09000000000000000-1-00000060210937542187500-21093754218750-0-600000000-000000000000100090000004218750292500000-4218750300000000-900000009000000000000000000-010-3750000000038100000009000000000-6000000-09000000000000000-1-000-2109375-42187500602109375-4218750000-0-600000000-0000000000001042187503000000009000000-421875029250000000-900000009000000000000-6000000-0-900000000038700000000-37500000000-6000000-09000000000-0-60000000000000120210937542187500-21093754218750-0-600000000-000090000000900000000004218750472500000-4218750300000000-900000009000000000000-6000000-0-9000000-3750000000038700000000000-6000000-09000000000-0-60000000000-2109375-421875001202109375-4218750000-0-600000000-0000900000009000000042187503000000000-421875047250000000-900000009000000000000-6000000-0-900000000060000000-9000000000000000-0-600000000000006000000000000000000-900000009000000000-9000000018000000000000000000-6000000-0-900000000060000000-9000000000000000-0-600000000000006000000000000000000-900000009000000000-9000000018000000MATRIZ Y12=Y22=Y32=Y42=0MATRIZ Y21=Y11MATRIZ ORDENADAY11Y13Y21Y23Y31Y33Y41Y43Y11Y13Y23Y31Y33Y43Y11Y31Y13Y23Y33Y43Y113810000009000000-3750000000-6000000900000000Y111200000090000009000000-1200000090000009000000Y1112000000-120000009000000900000090000009000000Y139000000292500000300000000-9000000900000000Y13900000029250000300000000-900000090000000Y31-1200000024000000-9000000-900000000Y21-3750000000381000000900000000-60000009000000Y23900000030000000029250000-900000009000000Y139000000-900000029250000562500090000000Y23030000000090000002925000000-90000009000000Y31-12000000-9000000-90000002400000000Y239000000-900000056250002925000009000000Y31-6000000-9000000003870000000-3750000000Y33900000090000000047250000300000000Y339000000090000000472500005625000Y3390000009000000000472500000300000000Y43900000009000000030000000047250000Y439000000009000000562500047250000Y4100-6000000-9000000-37500000003870000000Y4300900000090000000300000000047250000MATRIZ KSS1200000090000009000000-12000000900000090000000.0000000381-0.0000000081-0.00000000750.0000000024-12000000-9000000-90000002400000000-0.00000000810.00000003810.0000000024-0.0000000075900000029250000300000000-900000090000000-0.00000000750.00000000240.000000023-0.00000000326000000900000060000009000000-60000009000000-60000009000000900000030000000029250000-9000000090000000.0000000024-0.0000000075-0.00000000320.0000000239000000292500000300000000-9000000900000000900000090000000047250000300000000030000000090000002925000000-90000009000000900000009000000030000000047250000MATRIZ -KSS * KSPMATRIZ -KPS*KSS* KSPMATRIZ CONDENSADA PORTICOMATRIZ ESTRUCTURA-6000000-9000000-6000000-9000000120000000120000000-0.2239770280.2699210337-6409188.80114864031586.503948315590811.1988514-7968413.4960516916772433.5965542-23905240.488155190000009000000000472500000300000000-0.2239770280.26992103374031586.50394831-4858578.60732232-7968413.4960516919141421.3926777-23905240.488155157424264.17803300900000090000000300000000047250000-0.1320890165-0.0459440057-0.1320890165-0.0459440057FRECUENCIA DE VIBRACION16772433.5965542-23905240.4881551*W220000-23905240.488155157424264.178033030000

EJERCICIO 2DATOS DEL PROBLEMAH (m)B (m)E (GPA)20E (KN/m)20000000000VIGA0.40.3W2 CUBIERTA (KN/M)3COLUMNA0.30.4W1 ENTREPISO (KN/M)5LONG AFERENTE5

DETERMINACION DE LA MATRIZ DE MASASMATRIZ DE MASASM2 (KG)6116.216116.20795107030M1 (KG)22935.78022935.7798165138DETERMINACION DE LA MATRIZ DE RIGIDEZ INERCIA VIGAS (m^4)0.0016INERCIA COLUMNAS (m^4)0.0009AREA VIGAS (M)0.12DATOS HORIZONTALES MATRIZ DE RIGIDEZMATRIZ DE RIGIDEZ ELEMENTOS HORIZONTALES 1, 2, 3AREA COLUMA (M)0.12AE/L60000000060000000000-60000000000LONGITUD VIGA(M)42EI/L1600000006000000120000000-600000012000000LONGITUD COLUMNA (M)74EI/L32000000012000000320000000-1200000016000000E (N/m)200000000006EI/L12000000-6000000000060000000000# ELEMENTOS812EI/L60000000-6000000-1200000006000000-12000000# NODOS8012000000160000000-1200000032000000DATOS VERTICALES MATRIZ DE RIGIDEZMATIZ DE COSENOS YSENOSMATRIZ RIGIDEZ LOCALTRANSPUESTAAE/L342857142.857143-0-10000342857142.85714300-342857142.85714300-0100002EI/L5142857.142857141-000000629737.6093294462204081.632653060-629737.6093294462204081.63265306-1-000004EI/L10285714.285714300100002204081.6326530610285714.28571430-2204081.632653065142857.142857140010006EI/L2204081.63265306000-0-10-342857142.85714300342857142.85714300000-01012EI/L629737.6093294460001-000-629737.609329446-2204081.632653060629737.609329446-2204081.63265306000-1-00TETA4.712388980400000102204081.632653065142857.142857140-2204081.6326530610285714.2857143000001MATRIZ DE RIGIDEZ ELEMENTOS VERTICALES 4, 5, 6, 7 ,8629737.610.002204081.63-629737.61-0.002204081.630.00342857142.86-0.00-0.00-342857142.86-0.002204081.63-0.0010285714.29-2204081.630.005142857.14ECUACIONES DE MOVIMIENTO-629737.61-0.00-2204081.63629737.610.00-2204081.63-0.00-342857142.860.000.00342857142.860.006116.20795107030Y22204081.63-0.005142857.14-2204081.630.0010285714.29022935.7798165138Y1ENSAMBLE DE LA MATRIZY11Y12Y13Y21Y22Y23Y31Y32Y33Y41Y42Y43Y51Y52Y53Y11Y12Y13Y21Y22Y23Y31Y32Y33Y41Y42Y43Y51Y52Y53Y11600629737.610.002204081.63-600000000.000.000.00-629737.61-0.002204081.630.000.000.000.000.000.00Y11629737.610.002204081.63629737.610.002204081.63-629737.61-0.002204081.63-629737.61-0.002204081.630.000.000.00Y120.00348857142.8612000000.000.00-6000000.0012000000.00-0.00-342857142.86-0.000.000.000.000.000.000.00Y120.00347857142.8610000000.000.00-5000000.0010000000.00-0.00-342857142.86-0.000.000.000.000.000.000.00Y132204081.6312000000.0042285714.290.00-12000000.0016000000.00-2204081.630.005142857.140.000.000.000.000.000.00Y132204081.6310000000.0036952380.950.00-10000000.0013333333.33-2204081.630.005142857.140.000.000.000.000.000.00Y21-600000000.000.000.00600629737.610.002204081.630.000.000.00-629737.61-0.002204081.630.000.000.00Y220.00-5000000.00-10000000.000.00347857142.86-10000000.000.000.000.00-0.00-342857142.86-0.000.000.000.00Y220.00-6000000.00-12000000.000.00348857142.86-12000000.000.000.000.00-0.00-342857142.86-0.000.000.000.00Y230.0010000000.0013333333.332204081.63-10000000.0036952380.950.000.000.00-2204081.630.005142857.140.000.000.00Y230.0012000000.0016000000.002204081.63-12000000.0042285714.290.000.000.00-2204081.630.005142857.140.000.000.00Y31-629737.61-0.00-2204081.63-629737.61-0.00-2204081.631259475.220.000.001259475.220.000.00629737.610.002204081.63Y31-629737.61-0.00-2204081.630.000.000.00601259475.220.000.00-600000000.000.000.000.000.000.00Y32-0.00-342857142.860.000.000.000.000.00690714285.7110000000.000.00-5000000.0010000000.000.000.000.00Y32-0.00-342857142.860.000.000.000.000.00691714285.7112000000.000.00-6000000.0012000000.000.000.000.00Y332204081.63-0.005142857.140.000.000.000.0010000000.0047238095.240.00-10000000.0013333333.330.000.000.00Y332204081.63-0.005142857.140.000.000.000.0012000000.0052571428.570.00-12000000.0016000000.000.000.000.00Y420.000.000.00-0.00-342857142.860.000.00-5000000.00-10000000.000.00695714285.71-0.000.00-5000000.0010000000.00Y410.000.000.00-629737.61-0.00-2204081.63-600000000.000.000.001201259475.220.000.00-600000000.000.000.00Y430.000.000.002204081.63-0.005142857.140.0010000000.0013333333.330.00-0.0073904761.900.00-10000000.0013333333.33Y420.000.000.00-0.00-342857142.860.000.00-6000000.00-12000000.000.00697714285.71-0.000.00-6000000.0012000000.00Y520.000.000.000.000.000.000.000.000.000.00-5000000.00-10000000.000.00347857142.86-10000000.00Y430.000.000.002204081.63-0.005142857.140.0012000000.0016000000.000.00-0.0084571428.570.00-12000000.0016000000.00Y530.000.000.000.000.000.000.000.000.000.0010000000.0013333333.332204081.63-10000000.0036952380.95Y510.000.000.000.000.000.000.000.000.00-600000000.000.000.00600629737.610.002204081.63Y520.000.000.000.000.000.000.000.000.000.00-6000000.00-12000000.000.00348857142.86-12000000.00Y530.000.000.000.000.000.000.000.000.000.0012000000.0016000000.002204081.63-12000000.0042285714.290.000.000.000.000.000.00-629737.61-0.00-2204081.630.000.000.000.000.000.000.000.000.000.000.000.00-0.00-342857142.860.000.000.000.000.000.000.000.000.000.000.000.000.002204081.63-0.005142857.140.000.000.000.000.000.00MATRIZ Y12=Y22=Y32=Y42=Y52=0MATRIZ Y11=Y21; Y31=Y41=Y51MATRIZ ORDENADAY11Y13Y21Y23Y31Y33Y41Y43Y51Y53Y11Y13Y23Y31Y33Y43Y53Y11Y31Y13Y23Y33Y43Y53Y11629737.612204081.63629737.612204081.63-629737.612204081.63-629737.612204081.630.000.00Y111259475.218658922204081.632653062204081.63265306-1259475.218658892204081.632653062204081.632653060Y111259475.21865892-1259475.218658892204081.632653062204081.632653062204081.632653062204081.632653060Y120.0010000000.000.0010000000.00-0.00-0.000.000.000.000.00Y132204081.6326530636952380.95238113333333.3333333-2204081.632653065142857.1428571400Y31-1259475.21865889-2204081.6326530636952380.95238113333333.33333335142857.1428571400Y132204081.6336952380.950.0013333333.33-2204081.635142857.140.000.000.000.00Y232204081.6326530613333333.333333336952380.952381-2204081.6326530605142857.142857140Y132204081.63265306-2204081.6326530613333333.333333336952380.95238105142857.142857140Y220.00-10000000.000.00-10000000.000.000.00-0.00-0.000.000.00Y31-1259475.21865889-2204081.63265306-2204081.632653063148688.04664731002204081.63265306Y232204081.632653063148688.04664731-2204081.63265306-2204081.63265306002204081.63265306Y230.0013333333.332204081.6336952380.950.000.00-2204081.635142857.140.000.00Y332204081.632653065142857.142857140047238095.238095213333333.33333330Y332204081.6326530605142857.14285714047238095.238095213333333.33333330Y31-629737.61-2204081.63-629737.61-2204081.631259475.220.001259475.220.00629737.612204081.63Y432204081.6326530605142857.14285714013333333.333333373904761.904761913333333.3333333Y432204081.63265306005142857.1428571413333333.333333373904761.904761913333333.3333333Y32-0.000.000.000.000.0010000000.000.0010000000.000.000.00Y530002204081.63265306013333333.333333336952380.952381Y5302204081.6326530600013333333.333333336952380.952381Y332204081.635142857.140.000.000.0047238095.240.0013333333.330.000.00Y420.000.00-0.000.000.00-10000000.000.00-0.000.0010000000.001259475.218658922204081.632653062204081.63265306-1259475.218658892204081.632653062204081.632653060Y430.000.002204081.635142857.140.0013333333.330.0073904761.900.0013333333.33-1259475.21865889-2204081.63265306-2204081.632653063148688.04664731002204081.63265306Y520.000.000.000.000.000.000.00-10000000.000.00-10000000.002204081.6326530636952380.95238113333333.3333333-2204081.632653065142857.1428571400Y530.000.000.000.000.000.000.0013333333.332204081.6336952380.952204081.6326530613333333.333333336952380.952381-2204081.6326530605142857.1428571402204081.632653065142857.142857140047238095.238095213333333.33333330Y11Y13Y23Y31Y33Y43Y532204081.6326530605142857.14285714013333333.333333373904761.904761913333333.3333333Y111259475.222204081.632204081.63-1259475.222204081.632204081.630.000002204081.63265306013333333.333333336952380.952381Y120.0010000000.0010000000.00-0.00-0.000.000.00Y132204081.6336952380.9513333333.33-2204081.635142857.140.000.00Y220.00-10000000.00-10000000.00-0.000.00-0.000.00Y232204081.6313333333.3336952380.95-2204081.630.005142857.140.00Y31-1259475.22-2204081.63-2204081.633148688.050.000.002204081.63Y32-0.000.000.000.0010000000.0010000000.000.00Y332204081.635142857.140.000.0047238095.2413333333.330.00Y42-0.000.000.000.00-10000000.00-0.0010000000.00Y432204081.630.005142857.140.0013333333.3373904761.9013333333.33Y520.000.000.000.000.00-10000000.00-10000000.00Y530.000.000.002204081.630.0013333333.3336952380.95MATRIZ ORDENADAMATRIZ [KSS]MATRIZ -[KSS]*[KSP]Y11Y31Y13Y23Y33Y43Y53-0.0000000409-0.00000069740.0000000015-0.00000000530.00000004351.63564590112.0100870597Y111259475.21865892-1259475.218658892204081.632653062204081.632653062204081.632653062204081.6326530600.00000004240.00000025660.0000000001-0.0000000002-0.0000000152-0.6587331198-0.6810140428Y31-1259475.21865889-2204081.6326530636952380.95238113333333.33333335142857.14285714000.00000000560.0000000860.0000000222-0.0000000037-0.0000000038-0.2427935013-0.2500145722Y132204081.63265306-2204081.6326530613333333.333333336952380.95238105142857.142857140-0.0000000042-0.0000000357-0.00000000430.0000000152-0.00000000340.06398457750.1104466186Y232204081.632653063148688.04664731-2204081.63265306-2204081.63265306002204081.632653060.00000000150.00000001290.0000000015-0.00000000550.0000000283-0.0230872187-0.0994984117Y332204081.6326530605142857.14285714047238095.238095213333333.33333330Y432204081.63265306005142857.1428571413333333.333333373904761.904761913333333.3333333Y5302204081.6326530600013333333.333333336952380.952381MATRIZ -[KPS]* [kSS]*[KSP]MATRIZ CONDENSADA DEL PORTICO3605097.088198044430395.968236854864572.306856973170920.74957796-24341757.1890105-9080187.23769306-25601232.4076694-11284268.8703461

Hoja2

Hoja1

Hoja3