METODO DE KANIDATOS

COLUMNASPISO TRAMOS SECCION (m) LONGITUD (m)

1

AD 0.40 0.80 3.00BE 0.40 0.80 3.00CF 0.40 0.80 3.00DG 0.40 0.80 3.00

2

DH 0.40 0.80 3.00EI 0.40 0.80 3.00FJ 0.40 0.80 3.00GK 0.40 0.80 3.00

VIGASPISO TRAMOS SECCION (m) LONGITUD (m) CARGA (kg/m)

1

DE 0.40 0.80 8.00 9728.00EF 0.40 0.80 8.00 9728.00FG 0.40 0.80 7.00 7486.00

2

HI 0.40 0.80 8.00 9728.00IJ 0.40 0.80 8.00 9728.00JK 0.40 0.80 7.00 7486.00

RIGIDEZ RELATIVA (K)

COLUMNASPISO TRAMOS SECCION (m) LONGITUD (m) K

1

AD 0.40 0.80 3.00 0.0683BE 0.40 0.80 3.00 0.0683CF 0.40 0.80 3.00 0.0683DG 0.40 0.80 3.00 0.0683

2

DH 0.40 0.80 3.00 0.0683EI 0.40 0.80 3.00 0.0683FJ 0.40 0.80 3.00 0.0683GK 0.40 0.80 3.00 0.0683

VIGASPISO TRAMOS SECCION (m) LONGITUD (m) K

1

DE 0.40 0.80 8.00 0.0256EF 0.40 0.80 8.00 0.0256FG 0.40 0.80 7.00 0.02925714285714

2

HI 0.40 0.80 8.00 0.0256IJ 0.40 0.80 8.00 0.0256JK 0.40 0.80 7.00 0.02925714285714

NUDO D:

TRAMO K (ᶙij)DA 0.0683 -0.211

-0.500DE 0.0256 -0.079DH 0.0683 -0.211

NUDO E:

TRAMO K (ᶙij)EB 0.0683 -0.182

-0.500EF 0.0256 -0.068EI 0.0683 -0.182ED 0.0256 -0.068

COFICIENTE DE GIRO (ᶙ)

∑(ᶙij)

∑(ᶙij)

NUDO F:

TRAMO K (ᶙij)FC 0.0683 -0.178

-0.500FG 0.0293 -0.076FJ 0.0683 -0.178FE 0.0256 -0.067

NUDO G:

TRAMO K (ᶙij)GD 0.0683 -0.206

-0.500GK 0.0683 -0.206GF 0.0293 -0.088

NUDO H:

TRAMO K (ᶙij)HD 0.0683 -0.364

-0.500HI 0.0256 -0.136

NUDO I:

TRAMO K (ᶙij)IE 0.0683 -0.286

-0.500IJ 0.0256 -0.107IH 0.0256 -0.107

NUDO J:

TRAMO K (ᶙij)JF 0.0683 -0.277

-0.500JK 0.0293 -0.119JI 0.0256 -0.104

NUDO K:

TRAMO K (ᶙij)

∑(ᶙij)

∑(ᶙij)

∑(ᶙij)

∑(ᶙij)

∑(ᶙij)

∑(ᶙij)

KG 0.0683 -0.277-0.396

KJ 0.0293 -0.119

MOMENTO DE EMPOTRAMIENTO (Mij)

TRAMOS W (kg/m) L (m) Mij (kg.m)DE 9728.00 8.00 51882.67ED 9728.00 8.00 -51882.67EF 9728.00 8.00 51882.67FE 9728.00 8.00 -51882.67FG 7486.00 7.00 30567.83GF 7486.00 7.00 -30567.83HI 9728.00 8.00 51882.67IH 9728.00 8.00 -51882.67IJ 9728.00 8.00 51882.67JI 9728.00 8.00 -51882.67JK 7486.00 7.00 30567.83KJ 7486.00 7.00 -30567.83

TRAMO Kij (ϒij)AD 0.0683 -0.375BE 0.0683 -0.375CF 0.0683 -0.375DG 0.0683 -0.375DH 0.0683 -0.375EI 0.0683 -0.375FJ 0.0683 -0.375GK 0.0683 -0.375

COEFICIENTES DE DEZPLAZAMIENTOS (ϒij)

Mij = w * 𝐿^2 12

METODO DE KANYH I J K

0.000 51882.67 37013.82 -51882.7 51882.67 -51882.67 30567.83 -30567.83 -6460.451882.67 -0.1364 -0.107143 0.00 -0.1071429 -0.104 -21314.83 -0.11881 -0.1188 -30567.83

-0.363636 -5585.455 361.0 -0.2857 0.00 2215.9 -0.2772277 2189.79084 2884.1 -0.2772277-14894.5 -7029.2 -226.3 962.7 -356.3 2446.0 5109.5 2837.8 3558.1 6729.6-18744.6 -7301.0 -193.3 -603.4 -226.2 2410.6 6621.4 2739.5 3666.1 8302.2-19469.4 -7346.0 -176.7 -515.5 -185.2 2376.8 6392.2 2711.4 3688.0 8554.2-19589.3 -7350.1 -170.2 -471.3 -171.5 2367.9 6326.7 2704.5 3692.5 8605.4-19600.4 -7349.3 -168.4 -453.7 -168.5 2366.0 6310.6 2703.7 3694.5 8615.8-19598.3 -7519.5 -7519.5 -449.1 6308.6 6399.1 6399.1 8619.6-17415.6 37013.8 -59570.6 -20474.2 5394.3-37013.8 14013.8

-0.375 9204.0 6384.5 -0.375 -8180.5 -0.375 -7703.1 -0.37511246.9 7438.6 -8716.6 -9221.811358.4 7560.3 -8745.3 -9291.711321.8 7524.1 -8770.0 -9304.411295.7 7496.3 -8788.2 -9311.3

-9112.967 -932.29143 3829.72 6085.964-9126.696 -940.94911 3821.11 6082.525-9177.229 -953.7252 3800.67 6078.958-9362.516 -941.64239 3735.96 6095.536-9899.934 -743.798 3534.08 6133.802

-10922.7 M E 310.50098 F 2409.1 G 6293.377-0.210526 51882.7 -51882.7 -0.1818 51882.67 -51882.7 -0.1783439 30567.83 -30567.83 -0.2058824

51882.7 -0.0789 -0.068182 0.00 -0.0681818 -0.0669 -21314.83 -0.07643 -0.0882 -30567.8-0.210526 -4096 116.4 -0.1818 0.00 1425.51 -0.1783439 1032.4708 2697.2 -0.2058824

-10922.7 -3712.5 -278.9 310.5 -287.1 1306.1 2409.1 1514.6 2628.8 6293.4-9899.9 -3510.9 -353.1 -743.8 -346.6 1401.0 3534.1 1605.7 2612.4 6133.8-9362.5 -3441.5 -357.6 -941.6 -356.0 1424.6 3746.6 1628.9 2605.3 6095.5-9177.2 -3422.5 -352.9 -953.7 -352.3 1433.2 3800.7 1637.6 2606.8 6079.0-9126.7 -3417.4 -349.6 -940.9 -349.4 1436.3 3821.1 1641.3 2608.6 6082.5-9113.0 -932.3 3829.7 6086.7

-0.375 716.1 716.1 -0.375 716.1 -0.375 716.1 -0.375365.9 365.9 365.9 365.9173.3 173.3 173.3 173.3

94.2 94.2 94.2 94.261.5 61.5 61.5 61.548.3 48.3 48.3 48.3

A B C D

PRIMERO SEGUNDO TERCEROCUARTOQUINTO

.

METODO PENDIENTE Y DEFLEXION

DATOS

COLUMNASPISO TRAMOS SECCION (m) LONGITUD (m)

1 AD 0.40 0.80 3.00BE 0.40 0.80 3.00CF 0.40 0.80 3.00DG 0.40 0.80 3.00

2 DH 0.40 0.80 3.00EI 0.40 0.80 3.00FJ 0.40 0.80 3.00GK 0.40 0.80 3.00

VIGASPISO TRAMOS SECCION (m) LONGITUD (m) CARGA (kg/m)

1 DE 0.40 0.80 8.00 9728.00EF 0.40 0.80 8.00 9728.00FG 0.40 0.80 7.00 7486.00

2 HI 0.40 0.80 8.00 9728.00IJ 0.40 0.80 8.00 9728.00JK 0.40 0.80 7.00 7486.00

MOMENTO DE INERCIA (I ij)

COLUMNASPISO TRAMOS SECCION (m) LONGITUD (m) kij(m3)

1

AD 0.40 0.80 3.00 0.0171 0.00569BE 0.40 0.80 3.00 0.0171 0.00569CF 0.40 0.80 3.00 0.0171 0.00569DG 0.40 0.80 3.00 0.0171 0.00569

2

DH 0.40 0.80 3.00 0.0171 0.00569EI 0.40 0.80 3.00 0.0171 0.00569FJ 0.40 0.80 3.00 0.0171 0.00569GK 0.40 0.80 3.00 0.0171 0.00569

VIGASPISO TRAMOS SECCION (m) LONGITUD (m) Iij (m4) kij(m3)

1DE 0.40 0.80 8.00 0.0171 0.00213EF 0.40 0.80 8.00 0.0171 0.00213FG 0.40 0.80 7.00 0.0171 0.00244

2HI 0.40 0.80 8.00 0.0171 0.00213IJ 0.40 0.80 8.00 0.0171 0.00213JK 0.40 0.80 7.00 0.0171 0.00244

Iij (m4)

Iij = b * ℎ^2 12

K ij = I ij L

MOMENTO DE ENPOTRATAMIENTO FIJO (M ij)

VIGASPISO TRAMOS LONGITUD (m) CARGA (kg/m) Mij (kg.m)

1

DE 8.00 9728.00 -51882.67ED 8.00 9728.00 51882.67EF 8.00 9728.00 -51882.67FE 8.00 9728.00 51882.67FG 7.00 7486.00 -30567.83GF 7.00 7486.00 30567.83

2

HI 8.00 9728.00 -51882.67IH 8.00 9728.00 51882.67IJ 8.00 9728.00 -51882.67JI 8.00 9728.00 51882.67JK 7.00 7486.00 -30567.83KJ 7.00 7486.00 30567.83

Mij = w * 𝐿^2 12

ECUACIONES DEL PORTICO

M ij = MEF ij + 2 EI ij ( 2 θ i + θ j - 3 Δ ij ₎L ij L ij

M AM = MEF AM + 2 EI AM ( 2 θ A + θ M - 3 Δ AM ₎L AM L AM

M AM = 0 AM + 2 EI AM ( 2 0 A + θ M - 3 0 AM ₎3 AM 3 AM

M AM - 0.6667 EI θ M = 0 ………… ECUACION 01

M MA = MEF MA + 2 EI MA ( 2 θ M + θ A - 3 Δ MA ₎L MA L MA

M MA = 0 MA + 2 EI MA ( 2 θ M + 0 A - 3 0 MA ₎3 MA 3 MA

M MA - 1.3333 EI θ D = 0 ………… ECUACION 02

M ME = MEF ME + 2 EI ME ( 2 θ M + θ E - 3 Δ ME ₎L ME L ME

M ME = -51883 ME + 2 EI ME ( 2 θ M + θ E - 3 0 ME ₎8 ME 8 ME

M ME - 0.50 EI θ M - 0.25 EI θ E = -51883 ME ………… ECUACION 03

M EM = MEF EM + 2 EI EM ( 2 θ E + θ M - 3 Δ EM ₎L EM L EM

M EM = 51883 EM + 2 EI EM ( 2 θ E + θ M - 3 0 EM ₎8 EM 8 EM

M EM - 0.50 EI θ E - 0.25 EI θ M = 51883 EM ………… ECUACION 04

M MH = MEF MH + 2 EI MH ( 2 θ M + θ H - 3 Δ MH ₎L MH L MH

M MH = 0 MH + 2 EI MH ( 2 θ M + θ H - 3 0 MH ₎3 MH 3 MH

M MH - 1.33 EI θ M - 0.67 EI θ H = 0 MH ………… ECUACION 05

M HD = MEF HD + 2 EI HD ( 2 θ H + θ D - 3 Δ HD ₎L HD L HD

M HD = 0 HD + 2 EI HD ( 2 θ H + θ D - 3 0 HD ₎3 HD 3 HD

M HD - 1.33 EI θ H - 0.67 EI θ D = 0 HD ………… ECUACION 06

M HI = MEF HI + 2 EI HI ( 2 θ H + θ I - 3 Δ HI ₎L HI L HI

M HI = -51883 HI + 2 EI HI ( 2 θ H + θ I - 3 0 HI ₎8 HI 8 HI

M HI - 0.50 EI θ H - 0.25 EI θ I = -51883 HI ………… ECUACION 07

M IH = MEF IH + 2 EI IH ( 2 θ I + θ H - 3 Δ IH ₎L IH L IH

M IH = 51883 IH + 2 EI IH ( 2 θ I + θ H - 3 0 IH ₎8 IH 8 IH

M IH - 0.50 EI θ I - 0.25 EI θ H = 51883 IH ………… ECUACION 08

M BE = MEF BE + 2 EI BE ( 2 θ B + θ E - 3 Δ BE ₎L BE L BE

M BE = 0 BE + 2 EI BE ( 2 0 B + θ E - 3 0 BE ₎3 BE 3 BE

M BE - 1.33 EI 0 B - 0.67 EI θ E = 0 BE ………… ECUACION 09

M EB = MEF EB + 2 EI EB ( 2 θ E + θ B - 3 Δ EB ₎L EB L EB

M EB = 0 EB + 2 EI EB ( 2 θ E + 0 B - 3 0 EB ₎3 EB 3 EB

M EB - 1.33 EI θ E - 0.67 EI 0 B = 0 EB ………… ECUACION 10

M EF = MEF EF + 2 EI EF ( 2 θ E + θ F - 3 Δ EF ₎L EF L EF

M EF = -51883 EF + 2 EI EF ( 2 θ E + θ F - 3 0 EF ₎8 EF 8 EF

M EF - 0.50 EI θ E - 0.25 EI θ F = -51883 EF ………… ECUACION 11

M FE = MEF FE + 2 EI FE ( 2 θ F + θ E - 3 Δ FE ₎L FE L FE

M FE = 51883 FE + 2 EI FE ( 2 θ F + θ E - 3 0 FE ₎8 FE 8 FE

M FE - 0.50 EI θ F - 0.25 EI θ E = 51883 FE ………… ECUACION 12

M EI = MEF EI + 2 EI EI ( 2 θ E + θ I - 3 Δ EI ₎L EI L EI

M EI = 0 EI + 2 EI EI ( 2 θ E + θ I - 3 0 EI ₎3 EI 3 EI

M EI - 1.33 EI θ E - 0.67 EI θ I = 0 EI ………… ECUACION 13

M IE = MEF IE + 2 EI IE ( 2 θ I + θ E - 3 Δ IE ₎L IE L IE

M IE = 0 IE + 2 EI IE ( 2 θ I + θ E - 3 0 IE ₎3 IE 3 IE

M IE - 1.33 EI θ I - 0.67 EI θ E = 0 IE ………… ECUACION 14

M IJ = MEF IJ + 2 EI IJ ( 2 θ I + θ J - 3 Δ IJ ₎L IJ L IJ

M IJ = -51883 IJ + 2 EI IJ ( 2 θ I + θ J - 3 0 IJ ₎8 IJ 8 IJ

M IJ - 0.50 EI θ I - 0.25 EI θ J = -51883 IJ ………… ECUACION 15

M JI = MEF JI + 2 EI JI ( 2 θ J + θ I - 3 Δ JI ₎L JI L JI

M JI = 51883 JI + 2 EI JI ( 2 θ J + θ I - 3 0 JI ₎

8 JI( 8 JI

₎M JI - 0.50 EI θ J - 0.25 EI θ I = 51883 JI ………… ECUACION 16

M CF = MEF CF + 2 EI CF ( 2 θ C + θ F - 3 Δ CF ₎L CF L CF

M CF = 0 CF + 2 EI CF ( 2 0 C + θ F - 3 0 CF ₎3 CF 3 CF

M CF - 1.33 EI 0 C - 0.67 EI θ F = 0 CF ………… ECUACION 17

M FC = MEF FC + 2 EI FC ( 2 θ F + θ C - 3 Δ FC ₎L FC L FC

M FC = 0 FC + 2 EI FC ( 2 θ F + 0 C - 3 0 FC ₎3 FC 3 FC

M FC - 1.33 EI θ F - 0.67 EI 0 C = 0 FC ………… ECUACION 18

M FG = MEF FG + 2 EI FG ( 2 θ F + θ G - 3 Δ FG ₎L FG L FG

M FG = -30568 FG + 2 EI FG ( 2 θ F + θ G - 3 0 FG ₎7 FG 7 FG

M FG - 0.57 EI θ F - 0.29 EI θ G = -30568 FG ………… ECUACION 19

M GF = MEF GF + 2 EI GF ( 2 θ G + θ F - 3 Δ GF ₎L GF L GF

M GF = 30568 GF + 2 EI GF ( 2 θ G + θ F - 3 0 GF ₎7 GF 7 GF

M GF - 0.57 EI θ G - 0.29 EI θ F = 30568 GF ………… ECUACION 20

M FJ = MEF FJ + 2 EI FJ ( 2 θ F + θ J - 3 Δ FJ ₎L FJ L FJ

M FJ = 0 FJ + 2 EI FJ ( 2 θ F + θ J - 3 0 FJ ₎3 FJ 3 FJ

M FJ - 1.33 EI θ F - 0.67 EI θ J = 0 FJ ………… ECUACION 21

M JF = MEF JF + 2 EI JF ( 2 θ J + θ F - 3 Δ JF ₎L JF L JF

M JF = 0 JF + 2 EI JF ( 2 θ J + θ F - 3 0 JF ₎3 JF 3 JF

M JF - 1.33 EI θ J - 0.67 EI θ F = 0 JF ………… ECUACION 22

M JK = MEF JK + 2 EI JK ( 2 θ J + θ K - 3 Δ JK ₎L JK L JK

M JK = -30568 JK + 2 EI JK ( 2 θ J + θ K - 3 0 JK ₎7 JK 7 JK

M JK - 0.57 EI θ J - 0.29 EI θ K = -30568 JK ………… ECUACION 23

M KJ = MEF KJ + 2 EI KJ ( 2 θ K + θ J - 3 Δ KJ ₎L KJ L KJ

M KJ = 30568 KJ + 2 EI KJ ( 2 θ K + θ J - 3 0 KJ ₎7 KJ 7 KJ

M KJ - 0.57 EI θ K - 0.29 EI θ J = 30568 KJ ………… ECUACION 24

M DG = MEF DG + 2 EI DG ( 2 θ D + θ G - 3 Δ DG ₎L DG L DG

M DG = 0 DG + 2 EI DG ( 2 0 D + θ G - 3 0 DG ₎3 DG 3 DG

M DG - 1.33 EI 0 D - 0.67 EI θ G = 0 DG ………… ECUACION 25

M GD = MEF GD + 2 EI GD ( 2 θ G + θ D - 3 Δ GD ₎L GD L GD

M GD = 0 GD + 2 EI GD ( 2 θ G + 0 D - 3 0 GD ₎3 GD 3 GD

M GD - 1.33 EI θ G - 0.67 EI 0 D = 0 GD ………… ECUACION 26

M GK = MEF GK + 2 EI GK ( 2 θ G + θ K - 3 Δ GK ₎L GK L GK

M GK = 0 GK + 2 EI GK ( 2 θ G + θ K - 3 0 GK ₎3 GK 3 GK

M GK - 1.33 EI θ G - 0.67 EI θ K = 0 GK ………… ECUACION 27

M KG = MEF KG + 2 EI KG ( 2 θ K + θ G - 3 Δ KG ₎L KG L KG

M KG = 0 KG + 2 EI KG ( 2 θ K + θ G - 3 0 KG ₎3 KG 3 KG

M KG - 1.33 EI θ K - 0.67 EI θ G = 0 KG ………… ECUACION 28

M DA + M DE + M DH = 0 ……… ECUACION 29

M EB + M EF + M EI + M ED = 0 ……… ECUACION 30

M FC + M FG + M FJ + M FE = 0 ……… ECUACION 31

M GD + M GF + M GK = 0 ……… ECUACION 32

M IE + M IH + M IJ = 0 ……… ECUACION 33

M JF + M JI + M JK = 0 ……… ECUACION 34

M HD + M HI = 0 ……… ECUACION 35

M KG + M KJ = 0 ……… ECUACION 36

MATRIZ (36 x 36)MKG MGK MGD MDG MKJ MJK MJF MFJ MGF MFG MFC MCF MJI MIJ MIE MEI MFE MEF

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 01 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 10 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 1 00 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 00 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 01 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0

MATRIZ INVERSA (36 x 36)

MKG 0 0 0 0.003 0 0.002 0.002 -0.01 0 0.003 0.003 -0.011 0.003 -0.01 -0.01 0.088 0 -0.011MGK 0 6E-05 6E-05 0 6E-05 0 0 0 0 0 0 0.025 0 0 0 0.021 0 0.025MGD 0 0 0 0 0 0 0 0.005 0 0 0 0.041 0 0.005 0.005 -0.032 0 0.041MDG 0 0 0 0 0 0 0 0.002 0 0 0 0.021 0 0.002 0.002 -0.016 0 0.021MKJ 0 0.001 0.001 0 0.001 0 0 0.01 0 0 0 0.011 0 0.01 0.01 -0.088 0 0.011MJK 0 0.002 0.002 -0.008 0.002 0 0 0.028 0 -0.008 -0.008 0.041 -0.008 0.028 0.028 -0.237 0 0.041MJF 0 0.002 0.002 -0.006 0.002 -0.009 -0.009 0.062 0 -0.006 -0.006 -0.08 -0.006 0.062 0.062 -0.549 0 -0.08MFJ 0 0 0 0.02 0 0 0 0.015 0 0.02 0.02 -0.325 0.02 0.015 0.015 -0.192 0 -0.325MGF 0 0 0 0.005 0 0.001 0.001 0 0 0.005 0.005 -0.066 0.005 0 0 0.011 0 -0.066MFG 0 0 0 0.012 0 0.002 0.002 -0.008 0 0.012 0.012 -0.155 0.012 -0.008 -0.008 0.041 0 -0.155MFC 0 0 0 0.03 0 0.004 0.004 -0.021 0 0.03 0.03 -0.382 0.03 -0.021 -0.021 0.113 0 0.618MCF 0 0 0 0.015 0 0.002 0.002 -0.011 0 0.015 0.015 -0.192 0.015 -0.011 -0.011 0.057 1 -0.192MJI 0 0 0 0.014 0 0.014 0.014 -0.09 0 0.014 0.014 0.038 0.014 -0.09 -0.09 0.786 0 0.038MIJ 0 -0.01 -0.01 0.04 -0.01 0.034 0.034 -0.22 0 0.04 0.04 0.013 0.04 -0.22 0.78 -0.087 0 0.013MIE 0 -0.011 -0.011 -0.079 -0.011 0.081 0.081 -0.563 0 -0.079 -0.079 -0.006 -0.079 0.437 -0.563 0.062 0 -0.006MEI 0 0.022 0.022 -0.33 0.022 0.019 0.019 -0.196 0 -0.33 -0.33 0.02 0.67 -0.196 -0.196 0.015 0 0.02MFE 0 0.006 0.006 -0.062 0.006 0 0 0.014 0 -0.062 -0.062 0.862 -0.062 0.014 0.014 0.038 0 -0.138MEF 0 0.013 0.013 -0.141 0.013 -0.01 -0.01 0.04 0 -0.141 0.859 -0.06 -0.141 0.04 0.04 0.013 0 -0.06MEB 0 0.037 0.037 -0.389 0.037 -0.03 -0.03 0.117 0 0.611 -0.389 0.03 -0.389 0.117 0.117 -0.021 0 0.03MBE 0 0.019 0.019 -0.196 0.019 -0.015 -0.015 0.059 1 -0.196 -0.196 0.015 -0.196 0.059 0.059 -0.011 0 0.015MIH 0 0.021 0.021 0.039 0.021 -0.115 -0.115 0.784 0 0.039 0.039 -0.007 0.039 -0.216 -0.216 0.025 0 -0.007MHI 0 0.059 0.059 0.011 0.059 -0.284 0.716 -0.081 0 0.011 0.011 0 0.011 -0.081 -0.081 0.009 0 0MHM 0 -0.059 -0.059 -0.011 -0.059 0.284 -0.716 0.081 0 -0.011 -0.011 0.002 -0.011 0.081 0.081 -0.009 0 0.002MMH 0 -0.373 -0.373 0.022 0.627 -0.232 -0.232 0.019 0 0.022 0.022 0 0.022 0.019 0.019 0 0 0MEM 0 -0.073 -0.073 0.861 -0.073 0.021 0.021 0.039 0 -0.139 -0.139 0.011 -0.139 0.039 0.039 -0.007 0 0.011MME 0 -0.166 0.834 -0.059 -0.166 0.059 0.059 0.011 0 -0.059 -0.059 0.004 -0.059 0.011 0.011 0 0 0.004MMA 0 0.54 -0.46 0.037 -0.46 0.173 0.173 -0.03 0 0.037 0.037 0 0.037 -0.03 -0.03 0.004 0 0MAM 1 -0.232 -0.232 0.019 -0.232 0.087 0.087 -0.015 0 0.019 0.019 0 0.019 -0.015 -0.015 0.002 0 0EIθM 0 -0.346 -0.346 0.028 -0.346 0.13 0.13 -0.022 0 0.028 0.028 0 0.028 -0.022 -0.022 0.003 0 0EIθE 0 0.028 0.028 -0.293 0.028 -0.022 -0.022 0.088 0 -0.293 -0.293 0.023 -0.293 0.088 0.088 -0.016 0 0.023EIθH 0 0.13 0.13 -0.022 0.13 -0.604 -0.604 0.072 0 -0.022 -0.022 0.003 -0.022 0.072 0.072 -0.009 0 0.003EIθI 0 -0.022 -0.022 0.088 -0.022 0.072 0.072 -0.468 0 0.088 0.088 -0.016 0.088 -0.468 -0.468 0.054 0 -0.016EIθF 0 0 0 0.023 0 0.003 0.003 -0.016 0 0.023 0.023 -0.287 0.023 -0.016 -0.016 0.085 0 -0.287EIθJ 0 0.003 0.003 -0.016 0.003 -0.009 -0.009 0.054 0 -0.016 -0.016 0.085 -0.016 0.054 0.054 -0.455 0 0.085EIθG 0 0 0 0 0 0 0 0.003 0 0 0 0.031 0 0.003 0.003 -0.024 0 0.031EIθK 0 0 0 0.003 0 0.002 0.002 -0.009 0 0.003 0.003 -0.024 0.003 -0.009 -0.009 0.078 0 -0.024

MATRIZ (36 x 36)MEB MBE MIH MHI MHM MMH MEM MME MMA MAM EIθM EIθE EIθH EIθI EIθF EIθJ EIθG

0 0 0 0 0 0 0 0 0 1 -0.67 0 0 0 0 0 00 0 0 0 0 0 0 0 1 0 -1.33 0 0 0 0 0 00 0 0 0 0 0 0 1 0 0 -0.50 -0.25 0 0 0 0 00 0 0 0 0 0 1 0 0 0 -0.25 -0.50 0 0 0 0 00 0 0 0 0 1 0 0 0 0 -1.33 0 -0.67 0 0 0 00 0 0 0 1 0 0 0 0 0 -0.67 0 -1.33 0 0 0 00 0 0 1 0 0 0 0 0 0 0 0 -0.5 -0.25 0 0 00 0 1 0 0 0 0 0 0 0 0 0 -0.25 -0.50 0 0 00 1 0 0 0 0 0 0 0 0 0 -0.67 0 0 0 0 01 0 0 0 0 0 0 0 0 0 0 -1.33 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 -0.5 0 0 -0.25 0 00 0 0 0 0 0 0 0 0 0 0 -0.3 0 0 -0.50 0 00 0 0 0 0 0 0 0 0 0 0 -1.33 0 -0.67 0 0 00 0 0 0 0 0 0 0 0 0 0 -0.67 0 -1.33 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 -0.5 0 -0.25 00 0 0 0 0 0 0 0 0 0 0 0 0 -0.25 0 -0.50 00 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.67 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 -1.33 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.57 0 -0.290 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.29 0 -0.570 0 0 0 0 0 0 0 0 0 0 0 0 0 -1.33 -0.67 00 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.67 -1.33 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.57 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.29 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.670 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1.330 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1.330 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.670 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 01 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 00 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

MATRIZ INVERSA (36 x 36)

-0.011 -0.063 -0.011 0.088 0.088 -0.691 0 -0.063 -0.0631 0.30886 0.001 -0.00269 0.011023 0.0630777 -0.0016 0.0104 -0.0880.025 -0.367 0.025 0.021 0.021 -0.226 0 -0.367 0.63295 -0.22634 -6E-05 0.001371 -0.024933 0.3670539 -0.0002 0.0018 -0.0210.041 -0.449 0.041 -0.032 -0.032 0.163 0 0.551 -0.4493 0.16326 0.00 0.00365 -0.040853 0.4492978 0.00078 -0.005 0.0320.021 -0.226 0.021 -0.016 -0.016 0.082 1 -0.226 -0.2263 0.08224 0 0.00 -0.02058 0.226338 0.0004 -0.002 0.0160.011 0.063 0.011 -0.088 -0.088 0.691 0 0.063 0.06308 -0.30886 0 0.002686 -0.011023 -0.063078 0.00162 -0.01 0.0880.041 0.022 0.041 -0.237 0.763 -0.124 0 0.022 0.02205 -0.12424 0 0.008104 -0.041397 -0.022054 0.00444 -0.028 0.237-0.08 -0.011 -0.08 0.451 -0.549 0.088 0 -0.011 -0.011 0.08767 0 0.005999 0.079768 0.0110232 0.00931 -0.062 0.549

-0.325 0.025 0.675 -0.192 -0.192 0.021 0 0.025 0.02493 0.02058 0.001 -0.01951 0.325248 -0.02 0.00164 -0.015 0.192-0.066 0.816 -0.066 0.011 0.011 0.063 0 -0.184 -0.1836 0.06308 0.001 -0.00502 0.065786 0.1836483 -0.0006 0.0027 -0.0110.845 -0.08 -0.155 0.041 0.041 0.022 0 -0.08 -0.0805 0.02205 0.001 -0.01215 0.15481 0.0804586 -0.0016 0.0081 -0.041-0.382 0.041 -0.382 0.113 0.113 -0.032 0 0.041 0.04085 -0.0316 0.003 -0.0302 0.382007 -0.040853 -0.0041 0.0212 -0.113-0.192 0.021 -0.192 0.057 0.057 -0.016 0 0.021 0.02058 -0.01592 0.002 0.0 0.19244 -0.02058 0.00 0.0107 -0.0570.038 -0.011 0.038 -0.214 -0.214 0.037 0 -0.011 -0.011 0.03657 0.004 -0.0141 -0.038371 0.0110305 -0.0138 0.0899 0.2140.013 0 0.013 -0.087 -0.087 0.015 0 0 -0.0042 0.01472 0.01 -0.04017 -0.013205 0.0042395 -0.0339 0.2205 0.087-0.006 0.003 -0.006 0.062 0.062 -0.01 0 0.003 0.00269 -0.01035 0.011 0.078754 0.005999 -0.002686 -0.081 0.56 -0.0620.02 0 0.02 0.015 0.015 0 0 0 -0.0014 -0.00184 -0.022 0.330318 -0.019513 0.0013706 -0.0187 0.20 -0.015

-0.138 0.015 -0.138 0.038 0.038 -0.011 0 0.015 0.01467 -0.01103 -0.006 0.061859 0.137935 -0.014672 0.00403 -0.014 -0.038-0.06 0.006 -0.06 0.013 0.013 0 0 0.006 0.00631 -0.00424 -0.013 0.140747 0.060453 -0.006307 0.01037 -0.04 -0.0130.03 0 0.03 -0.021 -0.021 0.005 0 0 -0.0036 0.00452 -0.037 0.389485 -0.030199 0.0036499 0.02963 -0.117 0.021

0.015 0 0.015 -0.011 -0.011 0.002 0 0 -0.0018 0.00228 -0.019 0.196207 -0.015213 0.0018387 0.01492 -0.059 0.011-0.007 0.002 -0.007 0.025 0.025 0 0 0.002 0.00155 -0.00437 -0.021 -0.03859 0.007206 -0.001553 0.1149 0.216 -0.025

0 0.001 0 0.009 0.009 0 0 0.001 0.00056 -0.00162 -0.059 -0.01094 0.00245 -0.000555 0.28388 0.081 -0.0090.002 0 0.002 -0.009 -0.009 0.002 0 0 -0.0006 0.00162 0.059 0.01094 -0.00245 0.0005555 0.71612 -0.081 0.009

0 6E-05 0 0 0 0 0 6E-05 6E-05 0.00023 0.373 -0.02217 0.001196 -5.98E-05 0.23194 -0.019 0.0020.011 0 0.011 -0.007 -0.007 0.002 0 0 -0.0013 0.00155 0.073 0.13945 -0.010741 0.0012866 -0.0213 -0.039 0.0070.004 0 0.004 0 0 0.001 0 0 -0.0005 0.00056 0.166 0.059266 -0.004452 0.000515 -0.0593 -0.011 0.002

0 0 0 0.004 0.004 0 0 0 0.00046 -0.00078 0.46 -0.0371 0.003256 -0.000455 -0.1726 0.0296 00 0 0 0.002 0.002 0 0 0 0.00023 -0.0004 0.232 -0.01869 0.00164 -0.000229 -0.087 0.0149 00 0 0 0.003 0.003 0 0 0 0.00034 -0.00059 0.346 -0.02789 0.002448 -0.000342 -0.1298 0.0223 0

0.023 0 0.023 -0.016 -0.016 0.003 0 0 -0.0027 0.0034 -0.028 0.292846 -0.022706 0.0027443 0.02228 -0.088 0.0160.003 0 0.003 -0.009 -0.009 0.002 0 0 -0.0006 0.00151 -0.13 0.022276 -0.003075 0.00059 0.60382 -0.072 0.009-0.016 0.003 -0.016 0.054 0.054 -0.009 0 0.003 0.0034 -0.0095 0.022 -0.08831 0.015949 -0.003402 -0.0721 0.4681 -0.054-0.287 0.031 -0.287 0.085 0.085 -0.024 0 0.031 0.03072 -0.02376 0.002 -0.02271 0.287224 -0.030717 -0.0031 0.0159 -0.0850.085 -0.024 0.085 -0.455 -0.455 0.078 0 -0.024 -0.0238 0.07789 0 0.015949 -0.084716 0.023762 0.00855 -0.054 0.4550.031 -0.338 0.031 -0.024 -0.024 0.123 0 -0.338 -0.3378 0.12275 0 0.002744 -0.030717 0.3378179 0.00059 -0.003 0.024-0.024 0.123 -0.024 0.078 0.078 -0.581 0 0.123 0.12275 -0.58149 0.001 -0.0034 0.023762 -0.122752 -0.0015 0.0095 -0.078

EIθK0 00 00 -51882.670 51882.670 00 00 -51882.670 51882.670 00 00 -51882.670 51882.670 00 00 -51882.670 51882.670 00 00 -30567.830 30567.830 00 0

-0.29 -30567.83-0.57 30567.83

0 00 0

-0.67 0-1.33 0

0 00 00 00 00 00 00 00 0

0.691 -21476.160.226 -17183.60-0.163 -8529.28-0.082 -4296.710.309 21476.160.124 -37712.19-0.088 -10701.11-0.021 -9496.03-0.063 25712.88-0.022 -34785.320.032 -5501.34 .0.016 -2771.35-0.037 48413.30-0.015 -54349.740.01 -2682.77

0.002 -1477.720.011 49782.690.004 -52980.36

0 -169.190 -85.23

0.004 57032.510.002 -40118.22

0 40118.220 31358.340 54627.280 -46298.04

0.001 14939.710 7526.02

0.001 11232.860 -127.210 24505.42

0.009 -1953.030.024 -4136.35-0.078 -5962.22-0.123 -6413.000.581 -12916.88

.

RESULTADO FINAL DE MOMENTOS

= -21476.1622 = -17183.5965 = -8529.2847 = -4296.70733 = 21476.1622 = -37712.1926 = -10701.1084 = -9496.03195 ; = 25712.8812 = -34785.3174 = -5501.34337 = -2771.35343 = 48413.3009 = -54349.7418 = -2682.76571 = -1477.72412 = 49782.6928 = -52980.3632 = -169.192175 = -85.2321483 = 57032.5075 = -40118.2204 = 40118.2204 = 31358.3352 = 54627.2795 = -46298.0419 = 14939.7067 = 7526.01769 = 11232.8622 = -127.212162 = 24505.4156 = -1953.03275 = -4136.3484 = -5962.22175 = -6412.99601 = -12916.8833

.

MKG

MGK

MGD

MDG

MKJ

MJK

MJF

MFJ

MGF

MFG

MFC

MCF

MJI

MIJ

MIE

MEI

MFE

MEF

MEB

MBE

MIH

MHI

MHM

MMH

MEM

MME

MMA

MAM

EIθM

EIθE

EIθH

EIθI

EIθF

EIθJ

EIθG

EIθK