Analisi de viguetas aligeradas Matriz Global

DATOSB= 0.3 v1 Ɵ1 v2 Ɵ2 v1H= 0.6 2200.9 4401.8 -2200.9 4401.8 v1 2200.9i= 0.0054 4401.8 11738.0 -4401.8 5869.0 Ɵ1 4401.8fć= 210 k12= -2200.9 -4401.8 2200.9 -4401.8 v2 k= -2200.9E= 2173706.512 4401.8 5869.0 -4401.8 11738.0 Ɵ2 4401.8EI= 11738.01516 v2 Ɵ2 v3 Ɵ3 0L1= 4 1126.8 2817.1 -1126.8 2817.1 v2 0L2= 5 2817.1 9390.4 -2817.1 4695.2 Ɵ2

k23= -1126.8 -2817.1 1126.8 -2817.1 v32817.1 4695.2 -2817.1 9390.4 Ɵ3

Ɵ1 v2 Ɵ2 v3 Ɵ34401.8 -2200.9 4401.8 0 0 v1

11738.0 -4401.8 5869.0 0 0 Ɵ1-4401.8 3327.7 -1584.6 -1126.8 2817.1 v25869.0 -1584.6 21128.4 -2817.1 4695.2 Ɵ2

0 -1126.8 -2817.1 1126.8 -2817.1 v30 2817.1 4695.2 -2817.1 9390.4 Ɵ3

DATOSB= 0.3 v1 Ɵ1 v2 Ɵ2 v1H= 0.6 1545.7 3477.9 -1545.7 3477.9 v1 1545.7i= 0.0054 3477.9 10433.8 -3477.9 5216.9 Ɵ1 3477.9fć= 210 k12= -1545.7 -3477.9 1545.7 -3477.9 v2 k= -1545.7E= 2173706.51 3477.9 5216.9 -3477.9 10433.8 Ɵ2 3477.9EI= 11738.0152 v2 Ɵ2 v3 Ɵ3 0L1= 4.5 1126.8 2817.1 -1126.8 2817.1 v2 0L2= 5 2817.1 9390.4 -2817.1 4695.2 Ɵ2 0L3= 4 k23= -1126.8 -2817.1 1126.8 -2817.1 v3 0

2817.1 4695.2 -2817.1 9390.4 Ɵ3v3 Ɵ3 v4 Ɵ4

2200.9 4401.8 -2200.9 4401.8 v34401.8 11738.0 -4401.8 5869.0 Ɵ3

k23= -2200.9 -4401.8 2200.9 -4401.8 v44401.8 5869.0 -4401.8 11738.0 Ɵ4

Ɵ1 Ɵ2 Ɵ3M1 10433.8 5216.9 0 Ɵ1 1.0125M2 5216.9 19824.2 4695.2 Ɵ2 0.5643M3 0 4695.2 21128.4 Ɵ3 -0.5643

Ɵ1 Ɵ2 Ɵ3Y1 3477.9 3477.9 0 V1 1.0125Y2 -3477.9 -660.8 2817.1 V2 3.5125Y3 0 -2817.1 1584.6 V3 4.863Y4 0 0 -4401.8 V4 1.0125M4 0 0 5869.0 Ɵ4 -1.0125

Ɵ1 v2 Ɵ2 v3 Ɵ3 V4 Ɵ43477.9 -1545.7 3477.9 0 0 0 0 v1

10433.8 -3477.9 5216.9 0 0 0 0 Ɵ1-3477.9 2672.6 -660.8 -1126.8 2817.1 0 0 v25216.9 -660.8 19824.2 -2817.1 4695.2 0 0 Ɵ2

0 -1126.8 -2817.1 3327.7 1584.6 -2200.9 4401.8 v30 2817.1 4695.2 1584.6 21128.4 -4401.8 5869.0 Ɵ30 0 0 -2200.9 -4401.8 2200.9 -4401.8 V40 0 0 4401.8 5869.0 -4401.8 11738.0 Ɵ4

MINV DESPLA0.000111 -3.09E-05 6.87E-06 9.13687611E-05-3.09E-05 6.183E-05 -1.37E-05 1.13434164E-05

0.0 0.0 5.038E-05 -2.9228852E-05

0.357226 1.4-0.407611 3.1-0.078273 4.80.128658 1.1

-0.171544 -1.2

PRACTICA DE ESTRUCTURAS II

ALUMNO: ING. JOSE G ARICA NECIOSUPDOCENTE: ING SEGUNDO PAICO GASCOFECHA : AGOSTO 2012

w= 2.5 t

w= 3.0 t/m

4.00 mts 5.00 mts 3.00 mt

Calculo de Momentos de empotramiento

2.5 2.534

1 2 2 5 3 3 3 4

Calculo de Momentos 1-2 Calculo de Momentos 2-3 Calculo de Momentos 3-4

M1-2 = 4.0000 M 2-3 = 2.0833 M 3-4 = 1.1250M2-1 = -4.0000 M 3-2 = -3.1250 M 4-3= -0.7500Y 1= 6.0000 Y2 = 1.8750 Y3 2.6250Y2= 6.0000 Y3= 4.3750 Y4 1.1250

Calculo de MatricesMATRIZ GLOBAL

B= 0.3000 v1 Ɵ1 v2 Ɵ2 v1 Ɵ1 v2 Ɵ2 v3 Ɵ3 V4 Ɵ4H= 0.6000 2200.8778 4401.7557 -2200.8778 4401.7557 v1 2200.8778 4401.7557 -2200.8778 4401.7557 0.0000 0.0000 0.0000 0.0000 v1I = 0.0054 TRAMO 1-2 4401.7557 11738.0152 -4401.7557 5869.0076 Ɵ1 4401.7557 11738.0152 -4401.7557 5869.0076 0.0000 0.0000 0.0000 0.0000 Ɵ1fć= 210.0000 k12= -2200.8778 -4401.7557 2200.8778 -4401.7557 v2 k= -2200.8778 -4401.7557 3327.7273 -1584.6320 -1126.8495 2817.1236 0.0000 0.0000 v2E= 2173706.5119 4401.7557 5869.0076 -4401.7557 11738.0152 Ɵ2 4401.7557 5869.0076 -1584.6320 21128.4273 -2817.1236 4695.2061 0.0000 0.0000 Ɵ2

EI= 11738.0152 v2 Ɵ2 v3 Ɵ3 0.0000 0.0000 -1126.8495 -2817.1236 6343.7451 5008.2198 -5216.8956 7825.3434 v3L1= 4.0000 1126.8495 2817.1236 -1126.8495 2817.1236 v2 0.0000 0.0000 2817.1236 4695.2061 5008.2198 25041.0990 -7825.3434 7825.3434 Ɵ3L2= 5.0000 TRAMO 2-3 2817.1236 9390.4121 -2817.1236 4695.2061 Ɵ2 0.0000 0.0000 0.0000 0.0000 -5216.8956 -7825.3434 5216.8956 -7825.3434 V4L3= 3.0000 k23= -1126.8495 -2817.1236 1126.8495 -2817.1236 v3 0.0000 0.0000 0.0000 0.0000 7825.3434 7825.3434 -7825.3434 15650.6869 Ɵ4

2817.1236 4695.2061 -2817.1236 9390.4121 Ɵ3

v3 Ɵ3 v4 Ɵ45216.8956 7825.3434 -5216.8956 7825.3434 v3

TRAMO 3-4 7825.3434 15650.6869 -7825.3434 7825.3434 Ɵ3k34= -5216.8956 -7825.3434 5216.8956 -7825.3434 v4

7825.3434 7825.3434 -7825.3434 15650.6869 Ɵ4

Ɵ2 Ɵ3 v4 Ɵ4M2=0 21128.4273 4695.2061 0.0000 0.0000 Ɵ2 M2= 1.9167M3=0 4695.2061 25041.0990 -7825.3434 7825.3434 Ɵ3 M3= 2.0000Y4=0 0.0000 -7825.3434 5216.8956 -7825.3434 v4 Y4= -1.1250

M4=0 0.0000 7825.3434 -7825.3434 15650.6869 Ɵ4 M4= 0.7500

Calculo de desplazamientos

0.0001 0.0000 -0.0001 0.0000 M2= 1.91670.0000 0.0001 0.0004 0.0001 * M3= 2.0000

-0.0001 0.0004 0.0018 0.0007 Y4= -1.12500.0000 0.0001 0.0007 0.0004 M4= 0.7500

Ɵ2 0.0001Ɵ3 -0.0001v4 -0.0010Ɵ4 -0.0004

Determinacion de fuerzas y momentos desconocidos

Ɵ2 Ɵ3 v4 Ɵ4Y1 4401.7557 0.0000 0.0000 0.0000 v1 M2= 0.0001 6.0000M1 5869.0076 0.0000 0.0000 0.0000 Ɵ1 M3= -0.0001 4.0000

Y2 -1584.6320 2817.1236 0.0000 0.0000 Y4= -0.0010 + 7.8750Y3 -2817.1236 5008.2198 -5216.8956 7825.3434 v3 M4= -0.0004 7.0000

Y1 0.5225 6.0000

M1 0.6966 + 4.0000Y2 -0.5428 7.8750Y3 1.1453 7.0000

Y1 6.5225M1 4.6966Y2 7.3322 22.0000Y3 8.1453

REACCIONES

v2 *

CORTANTES

MOMENTOS

1.5 21.5

41 2 2 4 3 3 5 4

Calculo de Momentos 1-2 Calculo de Momentos 2-3 Calculo de Momentos 3-4

M1-2 = 2.0000 M 2-3 = 2.0000 M 3-4 = 4.1667M2-1 = -2.0000 M 3-2 = -2.0000 M 4-3= -4.1667Y 1= 3.0000 Y2 = 3.0000 Y3 5.0000Y2= 3.0000 Y3= 3.0000 Y4 5.0000

Calculo de MatricesMATRIZ GLOBAL

B= 0.3000 v1 Ɵ1 v2 Ɵ2 v1 Ɵ1 v2 Ɵ2 v3 Ɵ3 V4 Ɵ4H= 0.6000 2200.8778 4401.7557 -2200.8778 4401.7557 v1 2200.8778 4401.7557 -2200.8778 4401.7557 0.0000 0.0000 0.0000 0.0000 v1I = 0.0054 TRAMO 1-2 4401.7557 11738.0152 -4401.7557 5869.0076 Ɵ1 4401.7557 11738.0152 -4401.7557 5869.0076 0.0000 0.0000 0.0000 0.0000 Ɵ1fć= 210.0000 k12= -2200.8778 -4401.7557 2200.8778 -4401.7557 v2 k= -2200.8778 -4401.7557 4401.7557 0.0000 -2200.8778 4401.7557 0.0000 0.0000 v2E= 2173706.5119 4401.7557 5869.0076 -4401.7557 11738.0152 Ɵ2 4401.7557 5869.0076 0.0000 23476.0303 -4401.7557 5869.0076 0.0000 0.0000 Ɵ2

EI= 11738.0152 v2 Ɵ2 v3 Ɵ3 0.0000 0.0000 -2200.8778 -4401.7557 3327.7273 -1584.6320 -1126.8495 2817.1236 v3L1= 4.0000 2200.8778 4401.7557 -2200.8778 4401.7557 v2 0.0000 0.0000 4401.7557 5869.0076 -1584.6320 21128.4273 -2817.1236 4695.2061 Ɵ3L2= 4.0000 TRAMO 2-3 4401.7557 11738.0152 -4401.7557 5869.0076 Ɵ2 0.0000 0.0000 0.0000 0.0000 -1126.8495 -2817.1236 1126.8495 -2817.1236 V4L3= 5.0000 k23= -2200.8778 -4401.7557 2200.8778 -4401.7557 v3 0.0000 0.0000 0.0000 0.0000 2817.1236 4695.2061 -2817.1236 9390.4121 Ɵ4

4401.7557 5869.0076 -4401.7557 11738.0152 Ɵ3

v3 Ɵ3 v4 Ɵ41126.8495 2817.1236 -1126.8495 2817.1236 v3

TRAMO 3-4 2817.1236 9390.4121 -2817.1236 4695.2061 Ɵ3k34= -1126.8495 -2817.1236 1126.8495 -2817.1236 v4

2817.1236 4695.2061 -2817.1236 9390.4121 Ɵ4

Ɵ1 Ɵ2 Ɵ3 Ɵ4M1=0 11738.0152 5869.0076 0.0000 0.0000 Ɵ1 M1= -2.0000M2=0 5869.0076 23476.0303 5869.0076 0.0000 Ɵ2 M2= 0.0000M3=0 0.0000 5869.0076 21128.4273 4695.2061 Ɵ3 M3= -2.1667M4=0 0.0000 0.0000 4695.2061 9390.4121 Ɵ4 M4= 4.1667

Calculo de desplazamientos

0.0001 0.0000 0.0000 0.0000 M1= -2.0000M2 0.0000 0.0001 0.0000 0.0000 * M2= 0.0000

0.0000 0.0000 0.0001 0.0000 M3= -2.16670.0000 0.0000 0.0000 0.0001 M4= 4.1667

Ɵ1 -0.00023261Ɵ2 0.00012445Ɵ3 -0.00026518

Ɵ4 0.00057631

Determinacion de fuerzas y momentos desconocidos

v1 v2 v3 V4Y1 2200.8778 -2200.8778 0.0000 0.0000 v1 Ɵ1 -0.0002 3.0000Y2 -2200.8778 4401.7557 -2200.8778 0.0000 v2 Ɵ2 0.0001 6.0000

Y3 0.0000 -2200.8778 3327.7273 -1126.8495 v3 Ɵ3 -0.0003 + 8.0000Y4 0.0000 0.0000 -1126.8495 1126.8495 V4 Ɵ4 0.0006 5.0000

Y1 -0.7858 3.0000

Y2 1.6434 + 6.0000Y3 -1.8058 8.0000Y4 0.9482 5.0000

Y1 2.2142Y2 7.6434Y3 6.1942 22.0000Y4 5.9482

REACCIONES

MOMENTOS

DATOSB= 0.3 v1 Ɵ1 v2 Ɵ2H= 0.6 18996433.8 18521522.9 -18996433.8 18521522.9i= 0.0054 18521522.9 24077979.8 -18521522.9 12038989.9fć= 2.10E+02 k12= -18996433.8 -18521522.9 18996433.8 -18521522.9E= 2.17E+09 18521522.9 12038989.9 -18521522.9 24077979.8EI= 11738015.2 v2 Ɵ2 v3 Ɵ3L1= 1.95 11576903.3 13313438.7 -11576903.3 13313438.7L2= 2.3 13313438.7 20413939.4 -13313438.7 10206969.7L3= 1.35 k23= -11576903.3 -13313438.7 11576903.3 -13313438.7L4= 2.3 13313438.7 10206969.7 -13313438.7 20413939.4L5= 1.95 v3 Ɵ3 v4 Ɵ4

57249883.4 38643671.3 -57249883.4 38643671.338643671.3 34779304.2 -38643671.3 17389652.1

k34= -57249883.4 -38643671.3 57249883.4 -38643671.338643671.3 17389652.1 -38643671.3 34779304.2

v4 Ɵ4 v5 Ɵ511576903.3 13313438.7 -11576903.3 13313438.713313438.7 20413939.4 -13313438.7 10206969.7

k45= -11576903.3 -13313438.7 11576903.3 -13313438.713313438.7 10206969.7 -13313438.7 20413939.4

v5 Ɵ5 v6 Ɵ618996433.8 18521522.9 -18996433.8 18521522.918521522.9 24077979.8 -18521522.9 12038989.9

k56= -18996433.8 -18521522.9 18996433.8 -18521522.918521522.9 12038989.9 -18521522.9 24077979.8

Calculo de desplazamiento

Ɵ2 Ɵ3 Ɵ4 Ɵ5M2=0 44491919.24 10206969.7 0.0 0.0M3=0 10206969.71 55193243.61 17389652.10 0.0M4=0 0.0 17389652.1 55193243.61 10206969.7M5=0 0.0 0.0 10206969.7 44491919.24

Ɵ2 2.35926856E-08 -4.867641E-09 1.60158843E-09 -3.67423229E-10Ɵ3 = -4.86764096E-09 2.1217922E-08 -6.9812829E-09 1.60158843E-09Ɵ4 1.60158843E-09 -6.9812829E-09 2.12179221E-08 -4.86764096E-09Ɵ5 -3.67423229E-10 1.6015884E-09 -4.867641E-09 2.35926856E-08

Ɵ2 -1.9348413E-07Ɵ3 3.5793976E-07Ɵ4 -3.58027274E-07Ɵ5 1.93616587E-07

v1 Ɵ1 v2 Ɵ2v1 18996433.79 18521522.94 -18996433.79 18521522.94Ɵ1 18521522.94 24077979.82 -18521522.94 12038989.91v2 k= -18996433.79 -18521522.94 30573337.05 -5208084.19Ɵ2 18521522.94 12038989.91 -5208084.19 44491919.24

0.00 0.00 -11576903.26 -13313438.75v2 0.00 0.00 13313438.75 10206969.71Ɵ2 0.00 0.00 0.00 0.00v3 0.00 0.00 0.00 0.00Ɵ3 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00v3 0 0 0 0Ɵ3 0 0 0 0v4Ɵ4

v4Ɵ4v5Ɵ5

v5Ɵ5v6Ɵ6

Ɵ2 M2= -4.96Ɵ3 M3= 11.56Ɵ4 M4= -11.56Ɵ5 M5= 4.96

-1M2= -4.96M3= 11.56M4= -11.56M5= 4.96

v3 Ɵ3 V4 Ɵ4 v5 Ɵ5 v60.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00

-11576903.26 13313438.75 0.00 0.00 0.00 0.00 0.00-13313438.75 10206969.71 0.00 0.00 0.00 0.00 0.0068826786.70 25330232.57 -57249883.44 ### 0.00 0.00 0.0025330232.57 55193243.61 -38643671.32 ### 0.00 0.00 0.00

-57249883.44 -38643671.32 68826786.70 ### ### ### 0.0038643671.32 17389652.10 -25330232.57 ### ### ### 0.00

0.00 0.00 -11576903.26 ### ### 5208084.19 ###0.00 0.00 13313438.75 ### 5208084.19 ### ###

0 0 0 0 -18996433.8 -18521522.9 18996433.80 0 0 0 18521522.9 12038989.9 -18521522.9

Ɵ60.00 v10.00 Ɵ10.00 v20.00 Ɵ20.00 v30.00 Ɵ30.00 V40.00 Ɵ4### v5### Ɵ5

-18521522.9 v624077979.8 Ɵ6

TRABAJO DE ESTRUCTURAS II

ALUMNO . ING JOSE G ARICA NECIOSUPDOCENTE: ING SEGUNDO PAICO GASCO

Calculo de reacciones momentos y desplazamiento de una vigueta de losa aligerada,

1.95 2.3 1.35 2.3 1.95

9.85

M1 M2=0 M3=0 M4=0 M5=0 M6

1.95 2.3 1.35 2.3 1.951 2 3 4 5 6

9.85

R1 R2 R3 R4 R5 R6V1=0 V2=0 V3=0 V4=0 V5=0 V6=0Ɵ1=0 Ɵ2 Ɵ3 Ɵ4 Ɵ5 Ɵ6=0

CALCULOS PRELIMINARES

DATOSB= v1 Ɵ1 v2 Ɵ2 v1 Ɵ1 v2 Ɵ2 v3H= 373948.3 364599.6 -373948.3 364599.6 v1 373948.32 364599.61 -373948.32 364599.61 0.00i= 0.0001063 364599.6 473979.5 -364599.6 236989.7 Ɵ1 364599.61 473979.49 -364599.61 236989.75 0.00fć= 2.10E+02 k12= -373948.3 -364599.6 373948.3 -364599.6 v2 k= -373948.32 -364599.61 601841.80 -102522.10 -227893.48E= 2.17E+09 364599.6 236989.7 -364599.6 473979.5 Ɵ2 364599.61 236989.75 -102522.10 875831.67 -262077.51EI= 231065.002 v2 Ɵ2 v3 Ɵ3 0.00 0.00 -227893.48 -262077.51 1354868.04L1= 1.95 227893.5 262077.5 -227893.5 262077.5 v2 0.00 0.00 262077.51 200926.09 498630.32L2= 2.3 262077.5 401852.2 -262077.5 200926.1 Ɵ2 0.00 0.00 0.00 0.00 -1126974.56L3= 1.35 k23= -227893.5 -262077.5 227893.5 -262077.5 v3 0.00 0.00 0.00 0.00 760707.83L4= 2.3 262077.5 200926.1 -262077.5 401852.2 Ɵ3 0.00 0.00 0.00 0.00 0.00L5= 1.95 v3 Ɵ3 v4 Ɵ4 0.00 0.00 0.00 0.00 0.00

1126974.6 760707.8 -1126974.6 760707.8 v3 0 0 0 0 0760707.8 684637.0 -760707.8 342318.5 Ɵ3 0 0 0 0 0

k34= -1126974.6 -760707.8 1126974.6 -760707.8 v4760707.8 342318.5 -760707.8 684637.0 Ɵ4

v4 Ɵ4 v5 Ɵ5227893.5 262077.5 -227893.5 262077.5 v4262077.5 401852.2 -262077.5 200926.1 Ɵ4

k45= -227893.5 -262077.5 227893.5 -262077.5 v5262077.5 200926.1 -262077.5 401852.2 Ɵ5

v5 Ɵ5 v6 Ɵ6373948.3 364599.6 -373948.3 364599.6 v5364599.6 473979.5 -364599.6 236989.7 Ɵ5

k56= -373948.3 -364599.6 373948.3 -364599.6 v6364599.6 236989.7 -364599.6 473979.5 Ɵ6

Calculo de desplazamiento

Ɵ2 Ɵ3 Ɵ4 Ɵ5M2=0 875831.67 200926.1 0.0 0.0 Ɵ2 M2= -4.955M3=0 200926.09 1086489.22 342318.52 0.0 Ɵ3 M3= 11.555M4=0 0.0 342318.5 1086489.22 200926.1 Ɵ4 M4= -11.560M5=0 0.0 0.0 200926.1 875831.67 Ɵ5 M5= 4.960

-1Ɵ2 1.19849955E-06 -2.4727433E-07 8.13600898E-08 -1.86649618E-08 M2= -4.955Ɵ3 = -2.47274329E-07 1.07786246E-06 -3.5464655E-07 8.136008975E-08 M3= 11.555Ɵ4 8.13600898E-08 -3.5464655E-07 1.07786246E-06 -2.47274329E-07 M4= -11.560Ɵ5 -1.86649618E-08 8.13600898E-08 -2.4727433E-07 1.198499552E-06 M5= 4.960

Ɵ2 -9.8289E-06Ɵ3 1.8183E-05Ɵ4 -1.8188E-05Ɵ5 9.8356E-06

Resultado con SAP 2000 v14TABLE: Joint Displacements

Joint OutputCase CaseType U1 U2 U3 R1 R2 R3Text Text Text m m m Radians Radians Radians

1 DEAD LinStatic 0.00 0.00 0.00 0.00 0.00 0.002 DEAD LinStatic 0.00 0.00 0.00 0.00 9.94E-06 0.003 DEAD LinStatic 0.00 0.00 0.00 0.00 -1.80E-05 0.004 DEAD LinStatic 0.00 0.00 0.00 0.00 1.80E-05 0.00

5 DEAD LinStatic 0.00 0.00 0.00 0.00 -9.94E-06 0.006 DEAD LinStatic 0.00 0.00 0.00 0.00 0.00 0.00

Determinacion de reacciones y momentos en cada tramo

TRAMO 1-2 MATRIZ PARCIAL TRAMO ROTACIONES MOMENTOS EMPOTRAMIENTOS

v1 Ɵ1 v2 Ɵ2R12= 373948.3 364599.6 -373948.3 364599.6 v1 0.0 39.000M12= + 364599.6 473979.5 -364599.6 236989.7 Ɵ1 * 0.0 + 12.675R21= -373948.3 -364599.6 373948.3 -364599.6 v2 0.0 39.000M21 364599.6 236989.7 -364599.6 473979.5 Ɵ2 -9.8289E-06 -12.675

R12= -3.58362075443 39.000M12= -2.32935349038 + 12.675R21= 3.583620754434 39.000M21 -4.65870698076 -12.675

R12= 35.41637924557M12= 10.34564650962R21= 42.58362075443M21 -17.3337069808


v2 Ɵ2 v3 Ɵ3R23= 227893.4845579 262077.507242 -227893.484558 262077.5072416 v2 0.000 46.000M23= 262077.5072416 401852.17777 -262077.507242 200926.0888852 Ɵ2 * -9.8289E-06 + 17.630R32= -227893.484558 -262077.50724 227893.4845579 -262077.507242 v3 0.000 46.000M32= 262077.5072416 200926.088885 -262077.507242 401852.1777704 Ɵ3 1.8183E-05 -17.630

R23= 2.189469959547 46.000M23= -0.29629301924 17.630R32= -2.18946995955 46.000M32= 5.332073926195 -17.630

R23= 48.18946995955M23= 17.33370698076R32= 43.81053004045M32= -12.2979260738

TRAMO 3-4

MATRIZ PARCIAL TRAMO ROTACIONES MOMENTOS EMPOTRAMIENTOS

v3 Ɵ3 v4 Ɵ4R34= 1126974.557381 760707.826232 -1126974.55738 760707.8262321 v3 0.000 27.000M34= 760707.8262321 684637.043609 -760707.826232 342318.5218044 Ɵ3 * 1.8183E-05 + 6.075R43= -1126974.55738 -760707.82623 1126974.557381 -760707.826232 v4 0.000 27.000M43= 760707.8262321 342318.521804 -760707.826232 684637.0436089 Ɵ4 -1.8188E-05 -6.075

R34= -0.00338184133 27.000M34= 6.222926073805 + 6.075R43= 0.003381841334 27.000M43= -6.22749155961 -6.075

R34= 26.99661815867M34= 12.2979260738R43= 27.00338184133M43= -12.3024915596

TRAMO 4-5

MATRIZ PARCIAL TRAMO ROTACIONES MOMENTOS EMPOTRAMIENTOS

v4 Ɵ4 v5 Ɵ5R45= 227893.4845579 262077.507242 -227893.484558 262077.5072416 v4 0.000 46.000M45= 262077.5072416 401852.17777 -262077.507242 200926.0888852 Ɵ4 * -1.8188E-05 + 17.630R54= -227893.484558 -262077.50724 227893.4845579 -262077.507242 v5 0.0000 46.000M54= 262077.5072416 200926.088885 -262077.507242 401852.1777704 Ɵ5 9.8356E-06 -17.630

R45= -2.18887161213 46.000

M45= -5.33250844039 + 17.630R54= 2.188871612126 46.000M54= 0.298103732504 -17.630

R45= 43.81112838787M45= 12.29749155961R54= 48.18887161213M54= -17.3318962675


v5 Ɵ5 v6 Ɵ6R56= 373948.3169461 364599.609022 -373948.316946 364599.6090225 v5 0.0000 39.000M56= 364599.6090225 473979.491729 -364599.609022 236989.7458646 Ɵ5 9.8356E-06 + 12.670R65= -373948.316946 -364599.60902 373948.3169461 -364599.609022 v6 * 0.0000 39.000M65= 364599.6090225 236989.745865 -364599.609022 473979.4917292 Ɵ6 0.0000 -12.670

R56= 3.58607405192 39.000M56= 4.661896267496 + 12.670R65= -3.58607405192 39.000M65= 2.330948133748 -12.670

R56= 42.58607405192M56= 17.3318962675R65= 35.41392594808M65= -10.3390518663

RESULTADOS FINALES TABLE: Joint ReactionsJoint OutputCase CaseType F1 F2 F3 M1 M2 M3

M1= 10.345647 Text Text Text Kgf Kgf Kgf Kgf-m Kgf-m Kgf-mM2= 0.000000 1 DEAD LinStatic 0.00000 35.52000 0.00000 -10.46000 0.00000 0.00000M3= 0.000000 2 DEAD LinStatic 0.00000 0.00000 90.62000 0.00000 0.00000 0.00000M4= -0.005000 3 DEAD LinStatic 0.00000 0.00000 70.87000 0.00000 0.00000 0.00000M5= 0.000000 4 DEAD LinStatic 0.00000 0.00000 70.87000 0.00000 0.00000 0.00000M6 -10.339052 5 DEAD LinStatic 0.00000 0.00000 90.62000 0.00000 0.00000 0.00000R1= 35.416379 6 DEAD LinStatic 0.00000 -35.52000 0.00000 10.46000 0.00000 0.00000R2= 90.773091R3= 70.813912

R4= 70.814510R5= 90.774946R6= 35.413926

Ɵ3 V4 Ɵ4 v5 Ɵ5 v6 Ɵ60.00 0.00 0.00 0.00 0.00 0.00 0.00 v10.00 0.00 0.00 0.00 0.00 0.00 0.00 Ɵ1

262077.51 0.00 0.00 0.00 0.00 0.00 0.00 v2200926.09 0.00 0.00 0.00 0.00 0.00 0.00 Ɵ2498630.32 -1126974.56 760707.83 0.00 0.00 0.00 0.00 v3

1086489.22 -760707.83 342318.52 0.00 0.00 0.00 0.00 Ɵ3-760707.83 1354868.04 -498630.32 -227893.48 262077.51 0.00 0.00 V4342318.52 -498630.32 1086489.22 -262077.51 200926.09 0.00 0.00 Ɵ4

0.00 -227893.48 -262077.51 601841.80 102522.10 -373948.32 364599.61 v50.00 262077.51 200926.09 102522.10 875831.67 -364599.61 236989.75 Ɵ5

0 0 0 -373948.3 -364599.6 373948.3 -364599.6 v60 0 0 364599.6 236989.7 -364599.6 473979.5 Ɵ6

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