METODO DE ELEMENTOS FINITOS (ELEMENTO TRIANGULAR)

COORDENADAS DE LOS NUDOSNODO X Y

1 0 6.52 1.4 6.53 1.4 74 0 75 2.6 6.56 2.6 77 4 6.58 4 79 0 5.5

10 1.4 5.511 2.6 5.512 4 5.513 0 3.514 1.4 3.515 2.6 3.516 4 3.517 0 318 1.4 319 2.6 320 4 321 0 222 1.4 223 2.6 224 4 225 0 026 1.4 027 2.6 028 4 0

CONECTIVIDAD DE LOS ELEMENTOSELEMENTO NODO

1 1 2 32 1 3 43 2 6 34 2 5 65 5 8 66 5 7 87 9 2 18 9 10 29 11 7 5

10 11 12 711 13 10 912 13 14 1013 14 11 10

14 14 15 1115 15 12 1116 15 16 1217 17 14 1318 17 18 1419 18 15 1420 18 19 1521 19 16 1522 19 20 1623 21 18 1724 21 22 1825 23 20 1926 23 24 2027 25 22 2128 25 26 2229 26 23 2230 26 27 2331 27 24 2332 27 28 24

PROPIEDADES GENERALESt= 0.2v= 0.2

f'c= 280E= 2509980.08 tn/m2

250998.01 kg/m2

MATRIZ CONSTITUTIVA2614562.582919 522912.5165838 0

DD= 522912.5165838 2614562.582919 00 0 1045825.0331676

NODOS CON RESTRICCIONNODO X Y

25 1 126 1 127 1 128 1 1

FUERZAS NODALESCargas Puntuales

X YF= 50 0 4

30 0 13

MATRIZ JACOVIANA DE CADA ELEMENTO-1.4 -0.5

JJ1= 0 -0.5

JJ2= 0 -0.51.4 0

JJ3= 0 -0.51.2 0

JJ4= -1.2 -0.50 -0.5

JJ5= 0 -0.51.4 0

JJ6= -1.4 -0.50 -0.5

JJ7= 0 -11.4 0

JJ8= -1.4 -10 -1

JJ9= 0 -11.4 0

JJ10= -1.4 -10 -1

JJ11= 0 -21.4 0

JJ12= -1.4 -20 -2

JJ13= 0 -21.2 0

JJ14= -1.2 -20 -2

JJ15= 0 -21.4 0

JJ16= -1.4 -20 -2

JJ17= 0 -0.51.4 0

JJ18= -1.4 -0.50 -0.5

JJ19= 0 -0.51.2 0

JJ20= -1.2 -0.50 -0.5

JJ21= 0 -0.51.4 0

JJ22= -1.4 -0.50 -0.5

JJ23= 0 -11.4 0

JJ24= -1.4 -10 -1

JJ25= 0 -11.4 0

JJ26= -1.4 -10 -1

JJ27= 0 -21.4 0

JJ28= -1.4 -20 -2

JJ29= 0 -21.2 0

JJ30= -1.2 -20 -2

JJ31= 0 -21.4 0

JJ32= -1.4 -20 -2

MATRIZ "B" DE CADA ELEMENTO

B= 1 Y2-Y3 0 Y3-Y1 0Det(JJi) 0 X3-X2 0 X1-X3

X3-X2 Y2-Y3 X1-X3 Y1-Y2

-0.714285714286 0 0.7142857142857 0 0B1= 0 0 0 -2 0

0 -0.714285714286 -2 0.714285714 2

0 0 0.7142857142857 0 -0.714285714286B2= 0 -2 0 0 0

-2 0 0 0.714285714 2

0 0 0.8333333333333 0 -0.833333333333B3= 0 -2 0 0 0

-2 0 0 0.833333333 2

-0.833333333333 0 0.8333333333333 0 0B4= 0 0 0 -2 0

0 -0.833333333333 -2 0.833333333 2

0 0 0.7142857142857 0 -0.714285714286B5= 0 -2 0 0 0

-2 0 0 0.714285714 2

-0.714285714286 0 0.7142857142857 0 0B6= 0 0 0 -2 0

0 -0.714285714286 -2 0.714285714 2

0 0 0.7142857142857 0 -0.714285714286B7= 0 -1 0 0 0

-1 0 0 0.714285714 1

-0.714285714286 0 0.7142857142857 0 0B8= 0 0 0 -1 0

0 -0.714285714286 -1 0.714285714 1

0 0 0.7142857142857 0 -0.714285714286B9= 0 -1 0 0 0

-1 0 0 0.714285714 1

-0.714285714286 0 0.7142857142857 0 0B10= 0 0 0 -1 0

0 -0.714285714286 -1 0.714285714 1

0 0 0.7142857142857 0 -0.714285714286B11= 0 -0.5 0 0 0

-0.5 0 0 0.714285714 0.5

-0.714285714286 0 0.7142857142857 0 0B12= 0 0 0 -0.5 0

0 -0.714285714286 -0.5 0.714285714 0.5

0 0 0.8333333333333 0 -0.5B13= 0 -0.5 0 0 0

-0.5 0 0 0.833333333 0.5

-0.833333333333 0 0.8333333333333 0 0B14= 0 0 0 -0.5 0

0 -0.833333333333 -0.5 0.833333333 0.5

0 0 0.7142857142857 0 -0.714285714286B15= 0 -0.5 0 0 0

-0.5 0 0 0.714285714 0.5

-0.714285714286 0 0.7142857142857 0 0B16= 0 0 0 -0.5 0

0 -0.714285714286 -0.5 0.714285714 0.5

0 0 0.7142857142857 0 -0.714285714286B17= 0 -2 0 0 0

-2 0 0 0.714285714 2

-0.714285714286 0 0.7142857142857 0 0B18= 0 0 0 -2 0

0 -0.714285714286 -2 0.714285714 2

0 0 0.8333333333333 0 -0.833333333333B19= 0 -2 0 0 0

-2 0 0 0.833333333 2

-0.833333333333 0 0.8333333333333 0 15B20= 0 0 0 -2 0

0 -0.833333333333 -2 0.833333333 2

0 0 0.7142857142857 0 -0.714285714286B21= 0 -2 0 0 0

-2 0 0 0.714285714 2

-0.714285714286 0 0.7142857142857 0 0B22= 0 0 0 -2 0

0 -0.714285714286 -2 0.714285714 2

0 0 0.7142857142857 0 -0.714285714286B23= 0 -1 0 0 0

-1 0 0 0.714285714 1

-0.714285714286 0 0.7142857142857 0 0B24= 0 0 0 -1 0

0 -0.714285714286 -1 0.714285714 1

0 0 0.7142857142857 0 -0.714285714286B25= 0 -1 0 0 0

-1 0 0 0.714285714 1

-0.714285714286 0 0.7142857142857 0 0B26= 0 0 0 -1 0

0 -0.714285714286 -1 0.714285714 1

0 0 0.7142857142857 0 -0.714285714286B27= 0 -0.5 0 0 0

-0.5 0 0 0.714285714 0.5

-0.714285714286 0 0.7142857142857 0 0B28= 0 0 0 -0.5 0

0 -0.714285714286 -0.5 0.714285714 0.5

0 0 0.8333333333333 0 -0.833333333333B29= 0 -0.5 0 0 0

-0.5 0 0 0.833333333 0.5

-0.833333333333 0 0.8333333333333 0 0B30= 0 0 0 -0.5 0

0 -0.833333333333 -0.5 0.833333333 0.5

0 0 0.7142857142857 0 -0.714285714286B31= 0 -0.5 0 0 0

-0.5 0 0 0.714285714 0.5

-0.714285714286 0 0.7142857142857 0 0B32= 0 0 0 -0.5 0

0 -0.714285714286 -0.5 0.714285714 0.5

AREA DE CADA ELEMENTO

A1= 0.35 A17= 0.35

A2= 0.35 A18= 0.35

A3= 0.3 A19= 0.3

A4= 0.3 A20= 0.3

A5= 0.35 A21= 0.35

A6= 0.35 A22= 0.35

A7= 0.7 A23= 0.7

A8= 0.7 A24= 0.7

A9= 0.7 A25= 0.7

A10= 0.7 A26= 0.7

A11= 1.4 A27= 1.4

A12= 1.4 A28= 1.4

A13= 1.2 A29= 1.2

A14= 1.2 A30= 1.2

A15= 1.4 A31= 1.4

A16= 1.4 A32= 1.4

MATRIZ DE RIGIDEZ DE CADA ELEMENTO

-0.714285714286 0 0 00 0 -0.714285714286 0

B*T1= 0.7142857142857 0 -2 B*T17= 0.71428571428570 -2 0.7142857142857 00 0 2 -0.7142857142860 2 0 0

0 0 -2 -0.7142857142860 -2 0 0

B*T2= 0.7142857142857 0 0 B*T18= 0.71428571428570 0 0.7142857142857 0

-0.714285714286 0 2 00 2 -0.714285714286 0

0 0 -2 00 -2 0 0

B*T3= 0.8333333333333 0 0 0.83333333333330 0 0.8333333333333 B*T19= 0

-0.833333333333 0 2 -0.8333333333330 2 -0.833333333333 0

KL=t(A)(BˆT)(DD)(B)

-0.833333333333 0 0 -0.8333333333330 0 -0.833333333333 0

B*T4= 0.8333333333333 0 -2 B*T20= 0.83333333333330 -2 0.8333333333333 00 0 2 150 2 0 0

0 0 -2 00 -2 0 0

B*T5= 0.7142857142857 0 0 B*T21= 0.71428571428570 0 0.7142857142857 0

-0.714285714286 0 2 -0.7142857142860 2 -0.714285714286 0

-0.714285714286 0 0 -0.7142857142860 0 -0.714285714286 0

B*T6= 0.7142857142857 0 -2 B*T22= 0.71428571428570 -2 0.7142857142857 00 0 2 00 2 0 0

0 0 -1 00 -1 0 0

B*T7= 0.7142857142857 0 0 B*T23= 0.71428571428570 0 0.7142857142857 0

-0.714285714286 0 1 -0.7142857142860 1 -0.714285714286 0

-0.714285714286 0 0 -0.7142857142860 0 -0.714285714286 0

B*T8= 0.7142857142857 0 -1 B*T24= 0.71428571428570 -1 0.7142857142857 00 0 1 00 1 0 0

0 0 -1 00 -1 0 0

B*T9= 0.7142857142857 0 0 B*T25= 0.71428571428570 0 0.7142857142857 0

-0.714285714286 0 1 -0.7142857142860 1 -0.714285714286 0

-0.714285714286 0 0 -0.7142857142860 0 -0.714285714286 0

B*T10= 0.7142857142857 0 -1 B*T26= 0.71428571428570 -1 0.7142857142857 00 0 1 00 1 0 0

0 0 -0.5 00 -0.5 0 0

B*T11= 0.7142857142857 0 0 B*T27= 0.71428571428570 0 0.7142857142857 0

-0.714285714286 0 0.5 -0.7142857142860 0.5 -0.714285714286 0

-0.714285714286 0 0 -0.7142857142860 0 -0.714285714286 0

B*T12= 0.7142857142857 0 -0.5 B*T28= 0.71428571428570 -0.5 0.7142857142857 00 0 0.5 00 0.5 0 0

0 0 -0.5 00 -0.5 0 0

B*T13= 0.8333333333333 0 0 B*T29= 0.83333333333330 0 0.8333333333333 0

-0.5 0 0.5 -0.8333333333330 0.5 -0.5 0

-0.833333333333 0 0 -0.8333333333330 0 -0.833333333333 0

B*T14= 0.8333333333333 0 -0.5 B*T30= 0.83333333333330 -0.5 0.8333333333333 00 0 0.5 00 0.5 0 0

0 0 -0.5 00 -0.5 0 0

B*T15= 0.7142857142857 0 0 B*T31= 0.71428571428570 0 0.7142857142857 0

-0.714285714286 0 0.5 -0.7142857142860 0.5 -0.714285714286 0

-0.714285714286 0 0 -0.7142857142860 0 -0.714285714286 0

B*T16= 0.7142857142857 0 -0.5 B*T32= 0.71428571428570 -0.5 0.7142857142857 00 0 0.5 00 0.5 0 0

PROCEDEMOS A CREAR LAS MATRICES DE RIGIDEZ PARA CADA ELEMENTO1

-1867544.702085 -373508.940417 0 93377.235104250 0 -747017.880834 0

1867544.702085 373508.940417 -2091650.066335 KL1= -93377.23510425

(B*T)(DD)= -1045825.033168 -5229125.165838 747017.880834 52291.251658380 0 2091650.0663352 0

1045825.0331676 5229125.165838 0 -52291.251658381

0 0 -2091650.066335 292831.00928693-1045825.033168 -5229125.165838 0 0

(B*T)(DD)= 1867544.702085 373508.940417 0 KL2= 00 0 747017.880834 -104582.5033168

-1867544.702085 -373508.940417 2091650.0663352 -292831.00928691045825.0331676 5229125.165838 -747017.880834 104582.50331676

30 0 -2091650.066335 250998.00796022

-1045825.033168 -5229125.165838 0 0(B*T)(DD)= 2178802.1524325 435760.4304865 0 KL3= 0

0 0 871520.860973 -104582.5033168-2178802.152432 -435760.4304865 2091650.0663352 -250998.00796021045825.0331676 5229125.165838 -871520.860973 104582.50331676

3-2178802.152432 -435760.4304865 0 108940.10762162

0 0 -871520.860973 02178802.1524325 435760.4304865 -2091650.066335 KL4= -108940.1076216

(B*T)(DD)= -1045825.033168 -5229125.165838 871520.860973 52291.251658380 0 2091650.0663352 0

1045825.0331676 5229125.165838 0 -52291.251658389

0 0 -2091650.066335 292831.00928693-1045825.033168 -5229125.165838 0 01867544.702085 373508.940417 0 KL5= 0

(B*T)(DD)= 0 0 747017.880834 -104582.5033168-1867544.702085 -373508.940417 2091650.0663352 -292831.00928691045825.0331676 5229125.165838 -747017.880834 104582.50331676

9-1867544.702085 -373508.940417 0 93377.23510425

0 0 -747017.880834 0(B*T)(DD)= 1867544.702085 373508.940417 -2091650.066335 KL6= -93377.23510425

-1045825.033168 -5229125.165838 747017.880834 52291.251658380 0 2091650.0663352 0

1045825.0331676 5229125.165838 0 -52291.2516583817

0 0 -1045825.033168 146415.50464346-522912.5165838 -2614562.582919 0 0

(B*T)(DD)= 1867544.702085 373508.940417 0 KL7= 00 0 747017.880834 -104582.5033168

-1867544.702085 -373508.940417 1045825.0331676 -146415.5046435522912.5165838 2614562.582919 -747017.880834 104582.50331676

17-1867544.702085 -373508.940417 0 186754.4702085

0 0 -747017.880834 0

(B*T)(DD)= 1867544.702085 373508.940417 -1045825.033168 KL8= -186754.4702085-522912.5165838 -2614562.582919 747017.880834 52291.25165838

0 0 1045825.0331676 0522912.5165838 2614562.582919 0 -52291.25165838

210 0 -1045825.033168 149403.5761668

-522912.5165838 -2614562.582919 0 0(B*T)(DD)= 1867544.702085 373508.940417 0 KL9= 0

0 0 747017.880834 -106716.8401191-1867544.702085 -373508.940417 1045825.0331676 -149403.5761668522912.5165838 2614562.582919 -747017.880834 106716.84011914

21-1867544.702085 -373508.940417 0 186754.4702085

(B*T)(DD)= 0 0 -747017.880834 01867544.702085 373508.940417 -1045825.033168 KL10= -186754.4702085

-522912.5165838 -2614562.582919 747017.880834 52291.251658380 0 1045825.0331676 0

522912.5165838 2614562.582919 0 -52291.2516583825

0 0 -522912.5165838 73207.752321732-261456.2582919 -1307281.291459 0 0

(B*T)(DD)= 1867544.702085 373508.940417 0 KL11= 00 0 747017.880834 -104582.5033168

-1867544.702085 -373508.940417 522912.5165838 -73207.75232173261456.2582919 1307281.2914595 -747017.880834 104582.50331676

25-1867544.702085 -373508.940417 0 373508.940417

0 0 -747017.880834 0(B*T)(DD)= 1867544.702085 373508.940417 -522912.5165838 KL12= -373508.940417

-261456.2582919 -1307281.291459 747017.880834 52291.251658380 0 522912.5165838 0

261456.2582919 1307281.2914595 0 -52291.2516583827

0 0 -522912.5165838 62749.501990056-261456.2582919 -1307281.291459 0 0

(B*T)(DD)= 2178802.1524325 435760.4304865 0 KL13= 00 0 871520.860973 -104582.5033168

-1307281.291459 -261456.2582919 522912.5165838 -62749.50199006261456.2582919 1307281.2914595 -522912.5165838 62749.501990056

27-2178802.152432 -435760.4304865 0 435760.4304865

0 0 -871520.860973 0(B*T)(DD)= 2178802.1524325 435760.4304865 -522912.5165838 KL14= -435760.4304865

-261456.2582919 -1307281.291459 871520.860973 52291.251658380 0 522912.5165838 0

261456.2582919 1307281.2914595 0 -52291.2516583829

0 0 -522912.5165838 73207.752321732

-261456.2582919 -1307281.291459 0 0(B*T)(DD)= 1867544.702085 373508.940417 0 KL15= 0

0 0 747017.880834 -104582.5033168-1867544.702085 -373508.940417 522912.5165838 -73207.75232173261456.2582919 1307281.2914595 -747017.880834 104582.50331676

29-1867544.702085 -373508.940417 0 373508.940417

0 0 -747017.880834 0(B*T)(DD)= 1867544.702085 373508.940417 -522912.5165838 KL16= -373508.940417

-261456.2582919 -1307281.291459 747017.880834 52291.251658380 0 522912.5165838 0

261456.2582919 1307281.2914595 0 -52291.2516583833

0 0 -2091650.066335 292831.00928693-1045825.033168 -5229125.165838 0 0

(B*T)(DD)= 1867544.702085 373508.940417 0 KL17= 00 0 747017.880834 -104582.5033168

-1867544.702085 -373508.940417 2091650.0663352 -292831.00928691045825.0331676 5229125.165838 -747017.880834 104582.50331676

33-1867544.702085 -373508.940417 0 93377.23510425

0 0 -747017.880834 0(B*T)(DD)= 1867544.702085 373508.940417 -2091650.066335 KL18= -93377.23510425

-1045825.033168 -5229125.165838 747017.880834 52291.251658380 0 2091650.0663352 0

1045825.0331676 5229125.165838 0 -52291.2516583835

0 0 -2091650.066335 250998.00796022-1045825.033168 -5229125.165838 0 0

(B*T)(DD)= 2178802.1524325 435760.4304865 0 KL19= 00 0 871520.860973 -104582.5033168

-2178802.152432 -435760.4304865 2091650.0663352 -250998.00796021045825.0331676 5229125.165838 -871520.860973 104582.50331676

35-2178802.152432 -435760.4304865 0 108940.10762162

0 0 -871520.860973 0(B*T)(DD)= 2178802.1524325 435760.4304865 -2091650.066335 KL20= -108940.1076216

-1045825.033168 -5229125.165838 871520.860973 52291.2516583839218438.743785 7843687.748757 2091650.0663352 -1960921.9371891045825.0331676 5229125.165838 15687375.497514 -52291.25165838

370 0 -2091650.066335 292831.00928693

-1045825.033168 -5229125.165838 0 0(B*T)(DD)= 1867544.702085 373508.940417 0 KL21= 0

0 0 747017.880834 -104582.5033168-1867544.702085 -373508.940417 2091650.0663352 -292831.00928691045825.0331676 5229125.165838 -747017.880834 104582.50331676

37

-1867544.702085 -373508.940417 0 93377.23510425(B*T)(DD)= 0 0 -747017.880834 0

1867544.702085 373508.940417 -2091650.066335 KL22= -93377.23510425-1045825.033168 -5229125.165838 747017.880834 52291.25165838

0 0 2091650.0663352 01045825.0331676 5229125.165838 0 -52291.25165838

410 0 -1045825.033168 146415.50464346

-522912.5165838 -2614562.582919 0 0(B*T)(DD)= 1867544.702085 373508.940417 0 KL23= 0

0 0 747017.880834 -104582.5033168-1867544.702085 -373508.940417 1045825.0331676 -146415.5046435522912.5165838 2614562.582919 -747017.880834 104582.50331676

41-1867544.702085 -373508.940417 0 186754.4702085

0 0 -747017.880834 0(B*T)(DD)= 1867544.702085 373508.940417 -1045825.033168 KL24= -186754.4702085

-522912.5165838 -2614562.582919 747017.880834 52291.251658380 0 1045825.0331676 0

522912.5165838 2614562.582919 0 -52291.2516583845

0 0 -1045825.033168 146415.50464346-522912.5165838 -2614562.582919 0 0

(B*T)(DD)= 1867544.702085 373508.940417 0 KL25= 00 0 747017.880834 -104582.5033168

-1867544.702085 -373508.940417 1045825.0331676 -146415.5046435522912.5165838 2614562.582919 -747017.880834 104582.50331676

45-1867544.702085 -373508.940417 0 186754.4702085

0 0 -747017.880834 0(B*T)(DD)= 1867544.702085 373508.940417 -1045825.033168 KL26= -186754.4702085

-522912.5165838 -2614562.582919 747017.880834 52291.251658380 0 1045825.0331676 0

522912.5165838 2614562.582919 0 -52291.2516583849

0 0 -522912.5165838 73207.752321732-261456.2582919 -1307281.291459 0 0

(B*T)(DD)= 1867544.702085 373508.940417 0 KL27= 00 0 747017.880834 -104582.5033168

-1867544.702085 -373508.940417 522912.5165838 -73207.75232173261456.2582919 1307281.2914595 -747017.880834 104582.50331676

49-1867544.702085 -373508.940417 0 373508.940417

0 0 -747017.880834 0(B*T)(DD)= 1867544.702085 373508.940417 -522912.5165838 KL28= -373508.940417

-261456.2582919 -1307281.291459 747017.880834 52291.251658380 0 522912.5165838 0

261456.2582919 1307281.2914595 0 -52291.25165838

510 0 -522912.5165838 62749.501990056

-261456.2582919 -1307281.291459 0 0(B*T)(DD)= 2178802.1524325 435760.4304865 0 KL29= 0

0 0 871520.860973 -104582.5033168-2178802.152432 -435760.4304865 522912.5165838 -62749.50199006261456.2582919 1307281.2914595 -871520.860973 104582.50331676

51-2178802.152432 -435760.4304865 0 435760.4304865

0 0 -871520.860973 0(B*T)(DD)= 2178802.1524325 435760.4304865 -522912.5165838 KL30= -435760.4304865

-261456.2582919 -1307281.291459 871520.860973 52291.251658380 0 522912.5165838 0

261456.2582919 1307281.2914595 0 -52291.2516583853

0 0 -522912.5165838 73207.752321732-261456.2582919 -1307281.291459 0 0

(B*T)(DD)= 1867544.702085 373508.940417 0 KL31= 00 0 747017.880834 -104582.5033168

-1867544.702085 -373508.940417 522912.5165838 -73207.75232173261456.2582919 1307281.2914595 -747017.880834 104582.50331676

53-1867544.702085 -373508.940417 0 373508.940417

0 0 -747017.880834 0(B*T)(DD)= 1867544.702085 373508.940417 -522912.5165838 KL32= -373508.940417

-261456.2582919 -1307281.291459 747017.880834 52291.251658380 0 522912.5165838 0

261456.2582919 1307281.2914595 0 -52291.25165838

GRADOS DE LIBERTAD DEL SISTEMA

Numero total de Grados de Libertad NGL= 56

Numero de Grados de Libertad RestringidosNGLR= 8

Numero de Grados de Libertad no restringidosNGLNR= 48

ENSAMBLAJE DE LA MATRIZ DE RIGIDEZ DEL SISTEMA

1 2 3 4 5

719378.21924314 -156873.7549751 -280131.7053127 156873.755 0-156873.7549751 1210168.9669511 156873.75497514 -112052.6821 -156873.7549751-280131.7053127 156873.75497514 1079316.334825 -156873.755 -543829.0172471

156873.75497514 -112052.6821251 -156873.7549751 1881240.03 156873.754975140 -156873.7549751 -543829.0172471 156873.755 386208.24439118

-156873.7549751 0 156873.75497514 -1359572.543 -156873.7549751-292831.0092869 52291.25165838 0 0 -93377.23510425104582.50331676 -732077.5232173 0 0 52291.25165838

0 0 -108940.1076216 104582.5033 00 0 52291.25165838 -43576.04305 00 0 0 -156873.755 -108940.10762160 0 -156873.7549751 0 104582.503316760 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 0

-146415.5046435 104582.50331676 0 -156873.755 052291.25165838 -366038.7616087 -156873.7549751 0 0

0 0 -146415.5046435 52291.25166 00 0 104582.50331676 -366038.7616 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 0

0 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 0

CARGAS PUNTUALES

0 10 20 30 40 50 6

50 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 24

30 250 260 27

FN= 0 280 290 300 310 320 330 340 350 360 370 380 390 40

0 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 56

FUERZA TOTAL(SIN CONSIDERAR FUERZAS DE CUERPO)

0 10 20 30 40 50 6

50 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 23

Fu= 30 240 250 260 270 280 29

0 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 48

DETERMINACION DE LOS DESPLAZAMIENTOS DE CADA NODO

1 2 3 4 5719378.21924314 -156873.7549751 -280131.7053127 156873.755 0-156873.7549751 1210168.9669511 156873.75497514 -112052.6821 -156873.7549751-280131.7053127 156873.75497514 1079316.334825 -156873.755 -543829.0172471156873.75497514 -112052.6821251 -156873.7549751 1881240.03 156873.75497514

0 -156873.7549751 -543829.0172471 156873.755 386208.24439118-156873.7549751 0 156873.75497514 -1359572.543 -156873.7549751-292831.0092869 52291.25165838 0 0 -93377.23510425104582.50331676 -732077.5232173 0 0 52291.25165838

0 0 -108940.1076216 104582.5033 00 0 52291.25165838 -43576.04305 00 0 0 -156873.755 -108940.10762160 0 -156873.7549751 0 104582.503316760 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 0

-146415.5046435 104582.50331676 0 -156873.755 052291.25165838 -366038.7616087 -156873.7549751 0 0

0 0 -146415.5046435 52291.25166 00 0 104582.50331676 -366038.7616 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 0

Kuu= 0 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 0

6.799535802E-07 -4.555347142E-07 -1.41982934E-06 -7.93283E-08 -2.815100223E-06-5.782366087E-07 5.032968688E-06 -1.346951412E-06 2.209121E-06 -9.176338447E-07-1.424924473E-06 -1.213842195E-06 -9.429368794E-07 -1.41958E-08 -2.874417576E-06-5.629050096E-08 2.29678345E-06 1.741212854E-08 3.781692E-06 3.993734512E-07

-2.87369236E-06 -7.262563638E-07 -2.92971609E-06 3.134634E-07 -3.39904311E-06-4.943906319E-08 2.339980003E-06 -1.553502867E-07 3.694133E-06 3.386424177E-07-2.946242363E-07 2.184416235E-07 -2.098602613E-06 -3.94121E-07 -3.295358249E-06-5.097572382E-07 5.058052292E-06 -1.324883702E-06 2.190334E-06 -9.148808061E-07-1.405034141E-06 -1.009967377E-06 -1.249871952E-06 -1.5207E-08 -2.330061949E-06

4.07199899E-07 8.581127569E-07 6.091995648E-07 1.0197E-06 4.541070622E-07-1.782606073E-06 -7.362418026E-07 -1.637015282E-06 5.842701E-07 -2.638664428E-064.803902803E-07 8.833219194E-07 7.196457401E-07 1.112504E-06 4.660382621E-07

-1.332325089E-06 -9.812990995E-07 -1.242150442E-06 -3.3287E-08 -2.169292827E-061.007037506E-06 7.834398553E-07 1.047798287E-06 3.425998E-07 1.368356711E-06

-1.613535369E-06 -9.052416005E-07 -1.471344172E-06 2.868142E-07 -2.531965138E-061.027851171E-06 7.491347518E-07 1.083965212E-06 2.997202E-07 1.355574755E-06

-1.507189838E-07 -1.190742347E-06 -5.840120688E-07 3.222966E-07 -1.644797544E-06-6.306346682E-07 2.765715753E-06 -8.154350119E-07 1.694652E-06 -8.357020015E-07-3.402133503E-07 -1.501501498E-06 -5.120826842E-07 -1.33641E-07 -1.549331508E-067.189909654E-08 1.806525926E-06 6.794535345E-08 1.87963E-06 5.389887739E-07

-4.768743511E-07 -8.97284409E-07 -5.083731132E-07 -2.40763E-07 -1.122957702E-062.346009032E-07 7.079683094E-07 3.31358489E-07 6.185381E-07 4.309023665E-07

-6.030399569E-07 -9.075675282E-07 -6.244388665E-07 -2.6864E-07 -1.245069854E-06

7.721752326E-07 8.121940549E-07 8.122078469E-07 3.740811E-07 1.181643042E-06Kuu*-1= 3.27000095E-07 -5.840694902E-08 3.453278116E-07 1.530576E-07 5.167108889E-07

-1.556064732E-07 1.627104534E-08 -1.725424336E-07 1.253708E-07 -3.185696029E-072.090392774E-07 -2.452487187E-07 1.979758457E-07 -7.83648E-08 2.000045565E-071.097312828E-07 3.376429402E-07 1.214829337E-07 1.817669E-07 2.90605289E-071.415614915E-08 -3.789907179E-08 1.27866749E-08 -1.14528E-08 6.041094955E-09

3.0826605E-08 9.465995467E-08 3.377305872E-08 3.15412E-08 7.748931269E-08-3.155169306E-07 -3.834874447E-08 -3.224333549E-07 -5.74738E-08 -4.890152436E-072.052367562E-07 4.669257098E-07 2.164229557E-07 1.359774E-07 4.476649365E-07

4.57931198E-07 4.020043627E-07 4.77833867E-07 1.891478E-07 8.54012928E-07-9.685418417E-08 -8.412642602E-08 -1.044375964E-07 1.950626E-09 -2.013932872E-074.678471019E-07 1.707139729E-07 4.704319949E-07 5.761763E-08 7.446969574E-071.881760885E-07 3.342846616E-07 1.985064026E-07 1.346752E-07 4.021095566E-071.776394786E-07 5.934842029E-07 1.885352889E-07 1.493159E-07 4.600346946E-07

-1.442094212E-07 -2.99865454E-07 -1.531756467E-07 -9.63578E-08 -3.224972989E-07-1.648598623E-08 1.20592924E-06 -4.556729153E-10 2.533971E-07 3.794353155E-071.660398401E-07 4.349311862E-07 1.753566137E-07 1.192477E-07 3.912949417E-071.537716783E-06 1.845631036E-06 1.599065101E-06 6.609481E-07 2.9889157E-06

1.47391824E-07 1.314803031E-07 1.501724648E-07 5.284781E-08 2.611558674E-071.52615159E-06 2.078575965E-06 1.584791917E-06 6.7532E-07 3.027958009E-06

3.430418657E-07 6.459323311E-07 3.585285097E-07 1.94913E-07 7.378761197E-079.276155994E-07 1.858662506E-06 9.712643625E-07 5.375417E-07 2.034462312E-06

-9.142997354E-08 -8.139197794E-09 -9.363564901E-08 -1.61009E-08 -1.430697769E-076.56279583E-07 1.856933094E-06 6.945498623E-07 4.953259E-07 1.621556486E-06

-4.788184422E-08 -8.346716602E-08 -5.001647272E-08 -2.49262E-08 -1.024717797E-07

HALLANDO DESPLAZAMIENTOS

8.248453236E-06 12.371137832E-05 2-8.08840241E-05 3

-6.867873712E-06 4-0.00013418199 5

-1.28625497E-05 60.0001261545738 75.565479572E-05 8-9.80163501E-05 95.17663184E-05 10

-0.000126441893 115.459335632E-05 12-0.000102368393 130.0001355828042 14-0.000131268564 15

Du= (Kuu*-1)(Fu)

0.0001358107135 16-3.778773122E-05 17-4.281939813E-06 18-4.603242269E-05 191.555326804E-05 20

-3.930646782E-05 214.218918925E-05 22

Du= -4.233347596E-05 230.0001359496989 241.704891223E-05 25

-1.019536411E-05 269.610757342E-06 271.092219988E-05 285.996110029E-07 293.591633032E-06 30

-2.142932983E-05 312.503694463E-05 323.330523456E-05 33-7.37417759E-06 343.205870323E-05 35

1.63026161E-05 362.041969619E-05 37

-1.295600157E-05 381.447498851E-05 391.837459205E-05 400.0001205519355 411.101160576E-05 420.0001237753855 433.039438004E-05 448.384563455E-05 45

-5.806669668E-06 466.621157576E-05 47

-3.7393542E-06 48

CALCULO DE REACCIONES

0 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

-47.74314039869 49

Fre=(Kru)(Du)

-13.91943280646 50-16.97429980962 512.1315935085728 52

Re= -27.91194911421 533.5557798834134 54-5.042736150249 557.6089466313376 56

DESPLAZAMIENTOS DE CADA ELEMENTO

8.248453236E-06 1 8.248453E-06 12.371137832E-05 2 2.371138E-05 2-8.08840241E-05 3 -8.0884E-05 3

Db1= -6.867873712E-06 4 Db17= -6.86787E-06 4-0.00013418199 5 -0.000134182 5

-1.28625497E-05 6 -1.28625E-05 6

8.248453236E-06 1 8.248453E-06 12.371137832E-05 2 2.371138E-05 2-8.08840241E-05 5 -8.0884E-05 3

Db2= -6.867873712E-06 6 Db18= -6.86787E-06 4-0.00013418199 7 -0.000134182 5

-1.28625497E-05 8 -1.28625E-05 6

8.248453236E-06 3 8.248453E-06 12.371137832E-05 4 2.371138E-05 2-8.08840241E-05 11 Db19= -8.0884E-05 3

Db3= -6.867873712E-06 12 -6.86787E-06 4-0.00013418199 5 -0.000134182 5

-1.28625497E-05 6 -1.28625E-05 6

8.248453236E-06 3 8.248453E-06 12.371137832E-05 4 2.371138E-05 2

Db4= -8.08840241E-05 9 Db20= -8.0884E-05 3-6.867873712E-06 10 -6.86787E-06 4

-0.00013418199 11 -0.000134182 5-1.28625497E-05 12 -1.28625E-05 6

8.248453236E-06 9 8.248453E-06 12.371137832E-05 10 2.371138E-05 2

Db5= -8.08840241E-05 15 -8.0884E-05 3-6.867873712E-06 16 Db21= -6.86787E-06 4

-0.00013418199 11 -0.000134182 5-1.28625497E-05 12 -1.28625E-05 6

8.248453236E-06 9 8.248453E-06 12.371137832E-05 10 2.371138E-05 2

-8.08840241E-05 13 Db22= -8.0884E-05 3Db6= -6.867873712E-06 14 -6.86787E-06 4

-0.00013418199 15 -0.000134182 5-1.28625497E-05 16 -1.28625E-05 6

8.248453236E-06 17 8.248453E-06 12.371137832E-05 18 2.371138E-05 2-8.08840241E-05 3 Db23= . 3

Db7= -6.867873712E-06 4 -6.86787E-06 4-0.00013418199 1 -0.000134182 5

-1.28625497E-05 2 -1.28625E-05 6

8.248453236E-06 17 8.248453E-06 12.371137832E-05 18 2.371138E-05 2

Db8= -8.08840241E-05 19 Db24= -8.0884E-05 3-6.867873712E-06 20 -6.86787E-06 4

-0.00013418199 3 -0.000134182 5-1.28625497E-05 4 -1.28625E-05 6

8.248453236E-06 21 8.248453E-06 12.371137832E-05 22 2.371138E-05 2

Db9= -8.08840241E-05 13 Db25= -8.0884E-05 3-6.867873712E-06 14 -6.86787E-06 4

-0.00013418199 9 -0.000134182 5-1.28625497E-05 10 -1.28625E-05 6

8.248453236E-06 21 8.248453E-06 12.371137832E-05 22 2.371138E-05 2

Db10= -8.08840241E-05 23 Db26= -8.0884E-05 3-6.867873712E-06 24 -6.86787E-06 4

-0.00013418199 13 -0.000134182 5-1.28625497E-05 14 -1.28625E-05 6

8.248453236E-06 25 8.248453E-06 12.371137832E-05 26 2.371138E-05 2-8.08840241E-05 3 -8.0884E-05 3

Db11= -6.867873712E-06 4 Db27= -6.86787E-06 4-0.00013418199 5 -0.000134182 5

-1.28625497E-05 6 -1.28625E-05 6

8.248453236E-06 1 8.248453E-06 12.371137832E-05 2 2.371138E-05 2-8.08840241E-05 3 Db28= -8.0884E-05 3

Db12= -6.867873712E-06 4 -6.86787E-06 4-0.00013418199 5 -0.000134182 5

-1.28625497E-05 6 -1.28625E-05 6

8.248453236E-06 1 8.248453E-06 1

2.371137832E-05 2 2.371138E-05 2-8.08840241E-05 3 Db29= -8.0884E-05 3

Db13= -6.867873712E-06 4 -6.86787E-06 4-0.00013418199 5 -0.000134182 5

-1.28625497E-05 6 -1.28625E-05 6

8.248453236E-06 1 8.248453E-06 12.371137832E-05 2 2.371138E-05 2-8.08840241E-05 3 Db30= -8.0884E-05 3

Db14= -6.867873712E-06 4 -6.86787E-06 4-0.00013418199 5 -0.000134182 5

-1.28625497E-05 6 -1.28625E-05 6

8.248453236E-06 1 8.248453E-06 12.371137832E-05 2 2.371138E-05 2

Db15= -8.08840241E-05 3 Db31= -8.0884E-05 3-6.867873712E-06 4 -6.86787E-06 4

-0.00013418199 5 -0.000134182 5-1.28625497E-05 6 -1.28625E-05 6

8.248453236E-06 1 8.248453E-06 12.371137832E-05 2 2.371138E-05 2

Db16= -8.08840241E-05 3 Db32= -8.0884E-05 3-6.867873712E-06 4 -6.86787E-06 4

-0.00013418199 5 -0.000134182 5-1.28625497E-05 6 -1.28625E-05 6

METODO DE ELEMENTOS FINITOS (ELEMENTO TRIANGULAR)

Y1-Y2 00 X2-X1

X2-X1 Y1-Y2

020

02

-0.714285714286

02

-0.833333333333

020

02

-0.714285714286

020

01

-0.714285714286

010

01

-0.714285714286

010

00.5

-0.714285714286

00.5

0

00.5

-0.5

00.5

0

00.5

-0.714285714286

00.5

0

02

-0.714285714286

020

02

-0.833333333333

02

15

02

-0.714285714286

020

01

-0.714285714286

010

01

-0.714285714286

010

00.5

-0.714285714286

00.5

0

00.5

-0.833333333333

00.5

0

00.5

-0.714285714286

00.5

0

0 -2-2 00 00 0.71428571428570 22 -0.714285714286

0 00 -0.7142857142860 -2

-2 0.71428571428570 22 0

0 -2-2 00 00 0.83333333333330 22 -0.833333333333

0 00 -0.8333333333330 -2

-2 0.83333333333330 22 15

0 -2-2 00 00 0.71428571428570 22 -0.714285714286

0 00 -0.7142857142860 -2

-2 0.71428571428570 22 0

0 -1-1 00 00 0.71428571428570 11 -0.714285714286

0 00 -0.7142857142860 -1

-1 0.71428571428570 11 0

0 -1-1 00 00 0.71428571428570 11 -0.714285714286

0 00 -0.7142857142860 -1

-1 0.71428571428570 11 0

0 -0.5-0.5 0

0 00 0.71428571428570 0.5

0.5 -0.714285714286

0 00 -0.7142857142860 -0.5

-0.5 0.71428571428570 0.5

0.5 0

0 -0.5-0.5 0

0 00 0.83333333333330 0.5

0.5 -0.833333333333

0 00 -0.8333333333330 -0.5

-0.5 0.83333333333330 0.5

0.5 0

0 -0.5-0.5 0

0 00 0.71428571428570 0.5

0.5 -0.714285714286

0 00 -0.7142857142860 -0.5

-0.5 0.71428571428570 0.5

0.5 0

2 3 4 5 60 -93377.23510425 52291.25165838 0 -52291.25165838

37350.8940417 104582.50331676 -37350.8940417 -104582.5033168 0104582.50331676 386208.24439118 -156873.7549751 -292831.0092869 52291.25165838

-37350.8940417 -156873.7549751 769428.41725902 104582.50331676 -732077.5232173-104582.5033168 -292831.0092869 104582.50331676 292831.00928693 0

0 52291.25165838 -732077.5232173 0 732077.523217322 5 6 7 80 0 -104582.5033168 -292831.0092869 104582.50331676

732077.52321732 -52291.25165838 0 52291.25165838 -732077.5232173-52291.25165838 93377.23510425 0 -93377.23510425 52291.25165838

0 0 37350.8940417 104582.50331676 -37350.894041752291.25165838 -93377.23510425 104582.50331676 386208.24439118 -156873.7549751-732077.5232173 52291.25165838 -37350.8940417 -156873.7549751 769428.41725902

4 11 12 5 60 0 -104582.5033168 -250998.0079602 104582.50331676

627495.01990056 -52291.25165838 0 52291.25165838 -627495.0199006-52291.25165838 108940.10762162 0 -108940.1076216 52291.25165838

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74701.7880834 104582.50331676 -74701.7880834 -104582.5033168 0

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38 39 40 31 32

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1.506785092E-07 2.964526639E-07 4.324129357E-07 -1.448931369E-07 1.346885564E-078.783066652E-07 2.14139096E-06 1.823127575E-06 -1.043874225E-06 7.905980532E-077.235466482E-08 1.9014256E-07 1.295947591E-07 -1.108588504E-07 7.264936937E-089.008744264E-07 2.199233054E-06 2.056571675E-06 -1.109524775E-06 8.184691113E-072.512278631E-07 5.432892686E-07 6.407656645E-07 -2.743266431E-07 2.111104989E-076.940829297E-07 1.504876828E-06 1.844600962E-06 -7.575082036E-07 5.829999818E-07

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Du= (Kuu*-1)(Fu)

0 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 0

Fre=(Kru)(Du)

123

456

125678

34111256

349101112

91015161112

91013141516

17183412

1718

192034

21221314910

212223241314

252619201718

252627281920

272821221920

272829302122

29

3023242122

293031322324

333427282526

333435362728

353629302728

353637382930

373831322930

373839403132

414235363334

414243443536

454639403738

454647483940

495043444142

495051524344

515245464344

515253544546

535447484546

535455564748

11 12 13 14 15

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21 22 23 24 25

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