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    ANALISIS ESTRUCTURAL DEL PÓRTICO 3(EJE 1)

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    f'c= 210 kg/cm2

    E= 2173706.512

    columna H= 0.25 viga b= 0.25 ANGULO INERCIA

    b= 0.5 h= 0.6 0 0.0006510

    AREA= 0.13 m2 AREA= 0 m2 0.002604

    INERCIA= 0.000651 m4 INERCIA= 0.0045 m4

    AE= 271713.31 AE= 0

    EI= 1415.17 EI= 9781.6793

    L (columnas)= 3.00 L (vigas)= 6

    L (columnas)= 2.5

    Pórtico con coordenadas globales

    Matriz de elementos de las columnas 1 y 2

    90571.10 0.00 0.00 -90571.10 0.00 0.00

    0.00 628.97 943.45 0.00 -628.97 943.45

    [k]1 y 2 = 0.00 943.45 1886.90 0.00 -943.45 943.45

    -90571.10 0.00 0.00 90571.10 0.00 0.000.00 -628.97 -943.45 0.00 628.97 -943.45

    0.00 943.45 943.45 0.00 -943.45 1886.90

    Matriz de elementos de las columnas 3 y 4

    108685.33 0.00 0.00 -108685.33 0.00 0.00

    0.00 1086.85 1358.57 0.00 -1086.85 1358.57

    [k]3 y 4 = 0.00 1358.57 2264.28 0.00 -1358.57 1132.14

    -108685.33 0.00 0.00 108685.33 0.00 0.00

    0.00 -1086.85 -1358.57 0.00 1086.85 -1358.57

    0.00 1358.57 1132.14 0.00 -1358.57 2264.28

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    Datos para la matriz de transformación R

    ELEM X Y L

    m m m

    1 0 3 3

    2 0 3 3

    3 0 2.5 2.5

    4 0 2.5 2.5

    5 6 0 6

    6 6 0 6

    Matriz de transformación para las columnas 1,2,3 y 4

    0.000 1.000 0.000 0.000 0.000 0.000

    -1.000 0.000 0.000 0.000 0.000 0.000

    [R]1, 2,3,4 = 0.000 0.000 1.000 0.000 0.000 0.000

    0.000 0.000 0.000 0.000 1.000 0.000

    0.000 0.000 0.000 -1.000 0.000 0.000

    0.000 0.000 0.000 0.000 0.000 1.000

    Matriz de transformación para las columnas 5 y 6

    1.000 0.000 0.000 0.000 0.000 0.000

    0.000 1.000 0.000 0.000 0.000 0.000

    [R] 5 y 6 = 0.000 0.000 1.000 0.000 0.000 0.000

    0.000 0.000 0.000 1.000 0.000 0.000

    0.000 0.000 0.000 0.000 1.000 0.0000.000 0.000 0.000 0.000 0.000 1.000

    Matriz de rigidez de cada elemento:

    [∗] = {}[]{} 

    7 8 9 10 11 12

    628.97 0 -943.45 -628.97 0.00 -943.45 7

    0 90571.10 0 0 -90571.10 0 8

    [k*]1 =-943.45 0 1886.90 943.45 0 943.45 9

    -628.97 0 943.45 628.97 0 943.45 10

    0 -90571.10 0.00 0 90571.10 0 11

    -943.45 0.00 943.45 943.45 0 1886.90 12

    16 17 18 1 3 4

    628.97 0.00 -943.45 -628.97 0.00 -943.45 16

    0.00 90571.10 0.00 0.00 -90571.10 0.00 17

    [k*]2 = -943.45 0.00 1886.90 943.45 0.00 943.45 18

    -628.97 0.00 943.45 628.97 0.00 943.45 1

    0.00 -90571.10 0.00 0.00 90571.10 0.00 3

    -943.45 0.00 943.45 943.45 0.00 1886.90 4

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    10 11 12 13 14 15

    1086.85 0.00 -1358.57 -1086.85 0.00 -1358.57 10

    0.00 108685.33 0.00 0.00 -108685.33 0.00 11

    [k*]3 = -1358.57 0.00 2264.28 1358.57 0.00 1132.14 12

    -1086.85 0.00 1358.57 1086.85 0.00 1358.57 13

    0.00 -108685.33 0.00 0.00 108685.33 0.00 14

    -1358.57 0.00 1132.14 1358.57 0.00 2264.28 15

    1 3 4 2 5 6

    1086.85 0.00 -1358.57 -1086.85 0.00 -1358.57 1

    0.00 108685.33 0.00 0.00 -108685.33 0.00 3

    [k*]4 = -1358.57 0.00 2264.28 1358.57 0.00 1132.14 4

    -1086.85 0.00 1358.57 1086.85 0.00 1358.57 2

    0.00 -108685.33 0.00 0.00 108685.33 0.00 5

    -1358.57 0.00 1132.14 1358.57 0.00 2264.28 6

    10 11 12 1 3 4

    0.00 0.00 0.00 0.00 0.00 0.00 10

    0.00 543.43 1630.28 0.00 -543.43 1630.28 11

    [k*]5 = 0.00 1630.28 6521.12 0.00 -1630.28 3260.56 12

    0.00 0.00 0.00 0.00 0.00 0.00 1

    0.00 -543.43 -1630.28 0.00 543.43 -1630.28 3

    0.00 1630.28 3260.56 0.00 -1630.28 6521.12 4

    13 14 15 2 5 6

    0.00 0.00 0.00 0.00 0.00 0.00 13

    0.00 543.43 1630.28 0.00 -543.43 1630.28 14

    [k*]6 = 0.00 1630.28 6521.12 0.00 -1630.28 3260.56 15

    0.00 0.00 0.00 0.00 0.00 0.00 2

    0.00 -543.43 -1630.28 0.00 543.43 -1630.28 5

    0.00 1630.28 3260.56 0.00 -1630.28 6521.12 6

    Ensamblamos la matriz del pórtico K

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    1 3 4 2 5 6 10 11 12 13 14 15

    1715.8 0.0 -415.1 -1086.9 0.0 -1358.6 0.0 0.0 0.0 0.0 0.0 0.0 1

    0.0 199799.9 -1630.3 0.0 -108685.3 0.0 0.0 -543.4 -1630.3 0.0 0.0 0.0 3

    -415.1 -1630.3 10672.3 1358.6 0.0 1132.1 0.0 1630.3 3260.6 0.0 0.0 0.0 4

    -1086.9 0.0 1358.6 1086.9 0.0 1358.6 0.0 0.0 0.0 0.0 0.0 0.0 2

    0.0 -108685.3 0.0 0.0 109228.8 -1630.3 0.0 0.0 0.0 0.0 -543.4 -1630.3 5

    [K]= -1358.6 0.0 1132.1 1358.6 -1630.3 8785.4 0.0 0.0 0.0 0.0 1630.3 3260.6 6

    0.0 0.0 0.0 0.0 0.0 0.0 1715.8 0.0 -415.1 -1086.9 0.0 -1358.6 10

    0.0 -543.4 1630.3 0.0 0.0 0.0 0.0 199799.9 1630.3 0.0 -108685.3 0.0 11

    0.0 -1630.3 3260.6 0.0 0.0 0.0 -415.1 1630.3 10672.3 1358.6 0.0 1132.1 12

    0.0 0.0 0.0 0.0 0.0 0.0 -1086.9 0.0 1358.6 1086.9 0.0 1358.6 13

    0.0 0.0 0.0 0.0 -543.4 1630.3 0.0 -108685.3 0.0 0.0 109228.8 1630.3 14

    0.0 0.0 0.0 0.0 -1630.3 3260.6 -1358.6 0.0 1132.1 1358.6 1630.3 8785.4 15

    Ahora hallamos la matriz de transformación [R[ para condensar:

    La matriz de transformación será:

    Hallamos solo matriz de coordenadas libres

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      1* 2* 3* 4* 5* 6* 11* 12* 14* 15*

    1 0 0 0 0 0 0 0 0 0 1

    0 0 1 0 0 0 0 0 0 0 3

    0 0 0 1 0 0 0 0 0 0 4

    0 1 0 0 0 0 0 0 0 0 2

    0 0 0 0 1 0 0 0 0 0 5

    R = 0 0 0 0 0 1 0 0 0 0 6

    1 0 0 0 0 0 0 0 0 0 10

    0 0 0 0 0 0 1 0 0 0 110 0 0 0 0 0 0 1 0 0 12

    0 1 0 0 0 0 0 0 0 0 13

    0 0 0 0 0 0 0 0 1 0 14

    0 0 0 0 0 0 0 0 0 1 15

    Finalmente nuestra matriz quedaría:

    1* 2* 3* 4* 5* 6* 11* 12* 14* 15*

    3431.64 -2173.71 0 -415.117563 0 -1358.57 0.00 -415 0.00 -1358.57

    -2173.71 2173.71 0 1358.56657 0 1358.57 0.00 1359 0.00 1358.57

    0 0 199799.86 -1630.28 -108685.33 0 -543 -1630.28 0.00 0

    -

    415.1175631358.56657 -1630.28 10672.30 0 1132.14 1630.28 3260.56 0.00 0.00

    Kuu = 0 0 -108685.33 0 109228.75 -1630.28 0 0 -543 -1630

    -

    1358.566571358.56657 0 1132.14 -1630.28 8785.40 0.00 0 1630 3260.56

    0 0 -543.426628 1630.28 0 0.00 199799.86 1630 -108685.33 0.00

    -

    415.1175631358.56657 -1630.279884 3260.56 0 0 1630 10672.30 0.00 1132.14

    0 0 0 0.00 -543.426628 1630 -108685.33 0.00 109228.75 1630.28

    -

    1358.566571358.56657 0 0.00

    -

    1630.2798843260.56 0.00 1132 1630.28 8785.40

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    Por la fórmula:

    [K]L = 3106.83 -1807.91

    -1807.91 1637.28

    [] =  []   [] .  []−1[] 

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    ANALISIS ESTRUCTURAL DEL PÓRTICO 4 Y 5(EJES A Y B)

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    DATOS:

    HALLAMOS LOS k DE CADA ELEMENTO

    Para las columnas 1,2 y 3

    Para las columnas 4,5 y 6

    Para las vigas 7, 8,9 y 10

    MATRIZ DE TRANFORMACION [R]i

    Para las columnas 1, 2,3 ,4 ,5 y 6

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    Para las vigas 7, 8, 9, 10

    MATRIZ DE RIGIDEZ DEL ELEMENTO [k*]i

    De cada elemento

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    1 2 3 4 5 6   7 8 9   10 11 12 13 14 15   16 17 18   19 20 21 22 23 24   25 26 27

    2259.25 -1086.85 0.00 1215.16 0.00 -1358.57 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -543.43 0.00 1630.28 0.00 0.00 0.00 -628.97 0.00 943.45   1

    -1086.85 1630.28 0.00 1358.57 0.00 2988.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -543.43 0.00 1630.28 0.00 0.00 0.00   2

    0.00 0.00 199256.43 0.00 -108685.33 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -90571.10 0.00   3

    1215.16 1358.57 0.00 10672.30 0.00 1132.14 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -1630.28 0.00 3260.56 0.00 0.00 0.00 -943.45 0.00 943.45   4

    0.00 0.00 -108685.33 0.00 108685.33 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00   5

    -1358.57 2988.85 0.00 1132.14 0.00 8785.40 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 - 1630.28 0.00 3260.56 0 .00 0.00 0.00   6

    0.00 0.00 0.00 0.00 0.00 0.00 628.97 0.00 -943.45 -628.97 0.00 -943.45 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00   7

    0.00 0.00 0.00 0.00 0.00 0.00 0.00 9 0571.10 0.00 0.00 -90571.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00   8

    0.00 0.00 0.00 0.00 0.00 0.00 -943.45 0.00 1886.90 943.45 0.00 943.45 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00   9

    0.00 0.00 0.00 0.00 0.00 0.00 -628.97 0.00 943.45 2259.25 0.00 -2045.40 -1086.85 0.00 -1358.57 0.00 0.00 0.00 -543.43 0.00 -1630.28 0.00 0.00 0.00 0.00 0.00 0.00   10

    0.00 0.00 0.00 0.00 0.00 0.00 0.00 - 90571.10 0.00 0.00 199256.43 0.00 0.00 -108685.33 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00   11

    0.00 0.00 0.00 0.00 0.00 0.00 -943.45 0.00 943.45 -2045.40 0.00 10672.30 1358.57 0.00 1132.14 0.00 0.00 0.00 1630.28 0.00 3260.56 0.00 0.00 0.00 0.00 0.00 0.00   12

    0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -1086.85 0.00 1358.57 1630.28 0.00 -271.71 0.00 0.00 0.00 0.00 0.00 0.00 -543.43 0.00 -1630.28 0.00 0.00 0.00   13

    0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -108685.33 0 .00 0.00 108685.33 0 .00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00   14

    0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -1358.57 0.00 1132.14 -271.71 0.00 8785.40 0.00 0.00 0.00 0.00 0.00 0.00 1630.28 0.00 3260.56 0 .00 0.00 0.00   15

    0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 628.97 0.00 -943.45 -628.97 0.00 -943.45 0.00 0.00 0.00 0.00 0.00 0.00   16

    0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 90571.10 0.00 0.00 -90571.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00   17

    0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -943.45 0.00 1886.90 943.45 0.00 943.45 0.00 0.00 0.00 0.00 0.00 0.00   18

    - 543.43 0.00 0.00 -1630.28 0.00 0.00 0.00 0. 00 0.00 -543.43 0.00 1630.28 0. 00 0. 00 0.00 - 628. 97 0. 00 943. 45 2802. 67 0. 00 -415.12 -1086. 85 0.00 -1358.57 0 .00 0.00 0. 00   19

    0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -90571.10 0.00 0.00 199256.43 0.00 0.00 -108685.33 0.00 0.00 0.00 0.00   20

    1630. 28 0.00 0.00 3260.56 0.00 0.00 0.00 0. 00 0.00 -1630.28 0.00 3260.56 0. 00 0. 00 0.00 - 943. 45 0. 00 943. 45 -415. 12 0. 00 17193. 41 1358. 57 0.00 1132.14 0.00 0.00 0. 00   21

    0.00 -543.43 0.00 0.00 0.00 -1630.28 0.00 0.00 0.00 0.00 0.00 0.00 -543.43 0.00 1630.28 0.00 0.00 0.00 - 1086.85 0.00 1358.57 2173.71 0.00 1358.57 0.00 0.00 0.00   22

    0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 - 108685.33 0.00 0.00 108685.33 0.00 0.00 0.00 0.00   23

    0. 00 1630. 28 0.00 0.00 0.00 3260. 56 0.00 0. 00 0.00 0.00 0.00 0.00 -1630. 28 0. 00 3260.56 0.00 0. 00 0.00 -1358.57 0. 00 1132.14 1358. 57 0.00 15306.52 0.00 0.00 0. 00   24

    -628.97 0.00 0.00 -943.45 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 628.97 0.00 -943.45   25

    0.00 0.00 -90571.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 90571.10 0.00   26

    943.45 0.00 0.00 943.45 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 - 943.45 0.00 1886.90   27

    [K]P=

    MATRIZ DE RIGIDEZ DEL PORTICO [k]i

    AHORA HALLAMOS LA MATRIZ DE TRANSFORMACIÓN [R] PARA CONDENSAR:

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    Nuestra matriz final:

    =      .  −1 

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    ANALISIS ESTRUCTURAL DEL PÓRTICO 6(EJE C)

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    DATOS:

    HALLAMOS LOS k DE CADA ELEMENTO

    Para las columnas 1 y 2

    90571.1047 0 0 -90571.10466 0 0

    0 628.966005 943.449007 0 -628.9660046 943.449007

    [k]1, 2= 0 943.449007 1886.89801 0 -943.4490069 943.449007

    -90571.104 0 0 90571.10466 0 0

    0 -628.96605 -943.44900 0 628.9660046 -943.44900

    0 943.449007 943.449007 0 -943.4490069 1886.89801

    Para la viga 3

    1 8 9 1 2 3

    0 0 0 0 0 0 1

    0 543.426628 1630.27988 0 -543.426628 1630.27988 8

    [k]3=[k]*3= 0 1630.27988 6521.11954 0 -1630.279884 3260.55977 9

    0 0 0 0 0 0 1

    0 -543.4266 -1630.279 0 543.4266 -1630.279 2

    0 1630.27988 3260.55977 0 -1630.279884 6521.11954 3

    MATRIZ DE TRANFORMACION [R]i

    Para la columna 1 y 2 0 1 0 0 0 0

    -1 0 0 0 0 0

    [R]1 y 2= 0 0 1 0 0 0

    0 0 0 0 1 0

    0 0 0 -1 0 0

    0 0 0 0 0 1

    MATRIZ DE RIGIDEZ DEL ELEMENTO [k*]i

    f'c= 210 kg/cm2

    E= 2173706.51

    columna h= 0.25 viga b= 0.25 ANGULO INERCIA

    b= 0.5 h= 0.6 0 0.00065104

    AREA= 0.125 m2 AREA= 0 m2 0.00260417

    INERCIA= 0.00065104 m4 INERCIA= 0.0045 m4

    AE= 271713.314 AE= 0

    EI= 1415.17351 EI= 9781.679304

    L (colum)= 3 L (vigas)= 6

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    De cada elemento

    4 5 6 1 8 9

    628.966005 0 -943.4490 -628.9660046 0 -943.4490 4

    0 90571.1047 0 0 -90571.10466 0 5

    [k]*1= -943.4490 0 1886.89801 943.4490069 0 943.449007 6

    -628.9660 0 943.449007 628.9660046 0 943.449007 1

    0 -90571.10 0 0 90571.10466 0 8

    -943.4490 0 943.449007 943.4490069 0 1886.89801 9

    10 11 12 1 2 3

    628.966005 0 -943.4490 -628.96606 0 -943.4490 100 90571.1047 0 0 -90571.10466 0 11

    [k]*2= -943.44900 0 1886.89801 943.4490069 0 943.449007 12

    -628.9660 0 943.449007 628.9660046 0 943.449007 1

    0 -90571.104 0 0 90571.10466 0 2

    -943.44900 0 943.449007 943.4490069 0 1886.89801 3

    ENSAMBLAMOS LAS COORDENADAS LIBRES

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    Nuestra matriz final:

    1 2 3 7 8

    1257.93201 0 943.449 0 943.449 1

    0 90571.1047 -1630.28 -543.427 -1630.28 2

    K= 943.449 -1630.28 8408.109 1630.28 3260.56 3

    0 -543.427 1630.28 91114.5313 1630.28 7

    943.449 -1630.28 3260.56 1630.28 8408.018 8

    Kp= 1103.833

    [] =  []   [] .  []−1[] 


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