EJERCICIOS VIGAS CONTINUAS

ELEMENTO EI L 12EI/L^3 6EI/L^2 4EI/L 2EI/L

AB 1.00 4 0.19 0.38 1.00 0.50

BC 1.00 4 0.19 0.38 1.00 0.50

BC 1.00 2 1.50 1.50 2.00 1.00

Ma-b = 1.50 Tn-m Ra-b =Mb-a = -1.50 Tn-m Rb-a =

Mb-c = 4.00 Tn-m Rb-c =Mc-b = -4.00 Tn-m Rc-b =

Mc-d = 0 Tn-m Rc-d =Md-c = 0 Tn-m Rd-c =

MATRICES LOCALES:

Va θa Vb θbR(AB) 0.19 0.38 -0.19 0.38 0.00M(AB) = 0.38 1.00 -0.38 0.50 0.00R(BA) -0.19 -0.38 0.19 -0.38 0.00M(BA) 0.38 0.50 -0.38 1.00 -2.57

Vb θb Vc θcR(BC) 0.19 0.38 -0.1875 0.38 0.00M(BC) = 0.38 1.00 -0.375 0.50 -2.57R(CB) -0.19 -0.38 0.1875 -0.38 0.00M(CB) 0.38 0.50 -0.375 1.00 5.29

Vc θc Vd θdR(CD) 1.50 1.50 -1.5 1.50 0.00M(CD) = 1.50 2.00 -1.5 1.00 5.29R(DC) -1.50 -1.50 1.5 -1.50 10.57M(DC) 1.50 1.00 -1.5 2.00 5.29

MATRIZ GLOBAL:

Va θa Vb θb VcRa - - - 0.38 -Ma - - - 0.50 -Rb = - - - 0.00 -

Mb = 0 - - - 2.00 -Rc - - - -0.38 -

Mc = 0 - - - 0.50 -Rd = 0 - - - 0.00 -Md = 0 - - - 0.00 -

θb θc Vd θd Va0 2.00 0.50 0.00 0.00 -0 0.50 3.00 -1.50 1.00 -0 0.00 -1.50 1.50 -1.50 -0 0.00 1.00 -1.50 2.00 -

Ra = 0.38 0 0 0 -Ma 0.50 0 0 0 -Rb 0.00 0.38 0.00 0.00 -Rc -0.38 1.13 -1.50 1.50 -

θb 0 2.50 2.00θc = 0 - -4.00 x 0.50Vd 0 0.00 0.00θd 0 0.00 0.00

θb -2.50 0.57142857 -0.28571429 -0.57142857

θc = 4.00 x -0.28571429 1.14285714 2.285714286Vd 0.00 -0.57142857 2.28571429 7.238095238θd 0.00 -0.28571429 1.14285714 4.285714286

θb -2.57E+00θc = 5.29E+00Vd 1.06E+01θd 5.2857142857

Ra 0.38 0.00 0.00 0.00Ma = 0.50 0.00 0.00 0.00 xRb 0.00 0.38 0.00 0.00Rc -0.38 1.13 -1.50 1.50

Ra -0.96 2Ma = -1.29 + 1.5Rb 1.98 8Rc -1.02 6

Ra 1.04 Tn Ma = 0.21 Tn - mRb 9.98 Tn Rc 4.98 Tn

16.00

EI = 1 tn-m2

2 Tn2 Tn

6 Tn6 Tn

0 Tn0 Tn

Va = 0 2.00 -0.96428571 2θa = 0 + 1.50 = -1.28571429 + 1.5Vb = 0 2.00 0.964285714 2.00

θb -1.50 -2.57142857 -1.50

Vb = 0 6 1.017857143 6θb + 4.00 = 0.071428571 + 4

Vc = 0 6.00 -1.01785714 6.00θc -4.00 4 -4.00

Vc = 0 0 0 0θc + 0.00 = 0 + 0Vd 0.00 0 0.00θd 0.00 0 0.00

θc Vd θd0 0 0 Va = 0 20 0 0 θa = 0 1.50

0.38 0.00 0.00 Vb = 0 8.000.50 0.00 0.00 θb + 2.501.13 -1.50 1.50 Vc = 0 6.003.00 -1.50 1.00 θc -4.00-1.50 1.50 -1.50 Vd 0.001.00 -1.50 2.00 θd 0.00

θa Vb Vc- - - θb 2.50- - - θc -4.00- - - Vd 0.00- - - θd 0.00- - - 0 + 2- - - 0 1.50- - - 0 8.00- - - 0 6

-10.50 0.00 0.003.00 -1.50 1.00-1.50 1.50 -1.501.00 -1.50 2.00

-0.28571429

1.1428571434.2857142863.142857143

-2.57E+00 25.29E+00 + 1.501.06E+01 8.005.29E+00 6

R(AB) 1.04= M(AB) 0.21

R(BA) 2.96M(BA) -4.07

R(BC) 7.02= M(BC) 4.07

R(CB) 4.98M(CB) 0.00

R(CD) 0.00= M(CD) 0.00

R(DC) 0.00M(DC) 0.00

ELEMENTO EI L 12EI/L^3 6EI/L^2 4EI/L

AB 1.00 2 1.50 1.50 2.00

BC 1.00 4 0.19 0.38 1.00

CD 1.00 5 0.10 0.24 0.80

Ma-b = 0.67 Tn-m Ra-bMb-a = -0.67 Tn-m Rb-a

Mb-c = 1.33 Tn-m Rb-cMc-b = -1.33 Tn-m Rc-b

Mc-d = 4.58 Tn-m Rc-dMd-c = -4.58 Tn-m Rd-c

MATRICES LOCALES:Va θa Vb θb

R(AB) 1.50 1.50 -1.50 1.50M(AB) = 1.50 2.00 -1.50 1.00R(BA) -1.50 -1.50 1.50 -1.50M(BA) 1.50 1.00 -1.50 2.00

Vb θb Vc θcR(BC) 0.19 0.38 -0.19 0.38

M(BC) = 0.38 1.00 -0.38 0.50R(CB) -0.19 -0.38 0.19 -0.38M(CB) 0.38 0.50 -0.38 1.00

Vc θc Vd θdR(CD) 0.10 0.24 -0.10 0.24M(CD) = 0.24 0.80 -0.24 0.40R(DC) -0.10 -0.24 0.10 -0.24M(DC) 0.24 0.40 -0.24 0.80

MATRIZ GLOBAL:Va θa Vb θb

Ra=0 1.50 1.50 - 1.50Ma=0 1.50 2.00 - 1.00

Rb = -1.50 -1.50 - -1.13Mb = 0 1.50 1.00 - 3.00

Rc 0 0 - -0.38Mc = 0 0 0 - 0.50

Rd 0 0 - 0.00Md=0 0 0 - 0.00

ORDENANDO MATRIZ GLOBAL:Va θa θb θc

0 1.50 1.50 1.50 0.000 1.50 2.00 1.00 0.000 1.50 1.00 3.00 0.500 = 0.00 0.00 0.50 1.800 0.00 0.00 0.00 0.40

Rb -1.50 -1.50 -1.13 0.38Rc 0.00 0.00 -0.38 -0.14Rd 0.00 0.00 0.00 -0.24

Va 0 2.00θa 0 0.67θb = 0 - 0.66 xθc 0 3.25θd 0 -4.58

Va -2.00 7.40740740741 -4.3703703704θa -0.67 -4.3703703704 3.18518518519θb = -0.66 x -2.3703703704 1.18518518519θc -3.25 0.74074074074 -0.3703703704θd 4.58 -0.3703703704 0.18518518519

Va -1.443E+01θa 7.88E+00θb = 5.22E+00θc -5.09E+00θd 8.27E+00

Rb -1.50 -1.50 -1.13 0.38Rc = 0.00 0.00 -0.38 -0.14Rd 0.00 0.00 0.00 -0.24

Rb 2.04638888889 4.00Rc = 0.7165 + 7.50Rd -0.7628888889 5.50

Rb 6.05Rc = 8.22Rd 4.74

19.00

2EI/L

1.00

0.50 EI = 1 tn-m20.40

= 2 Tn= 2 Tn

= 2 Tn= 2 Tn

= 5.5 Tn= 5.5 Tn

-14.43 Va 2 -27.88 θa + 0.67 = -0.67 +0.00 Vb = 0 2.00 25.22 θb -0.67 -3.33

0.00 Vb = 0 2 0.046388889

5.22 θb + 1.33 = 2.67 +0.00 Vc = 0 2.00 -0.04638889-5.09 θc -1.33 -2.48444444

0.00 Vc = 0 5.5 0.762888889-5.09 θc + 4.58 = -0.76555556 +0.00 Vd = 0 5.50 -0.762888898.27 θd -4.58 4.58

Vc θc Vd θd- 0.00 - 0 Va - 0.00 - 0 θa - 0.38 - 0 Vb = 0- 0.50 - 0 θb +- -0.14 - 0.24 Vc = 0- 1.80 - 0.40 θc - -0.24 - -0.24 Vd = 0- 0.40 - 0.80 θd

θd Vb Vc Vd0 - - - Va 0 - - - θa0 - - - θb

0.40 - - - θc +0.80 - - - θd0.00 - - - 00.24 - - - 0-0.24 - - - 0

-11.50 1.50 1.50 0.00 0.001.50 2.00 1.00 0.00 0.001.50 1.00 3.00 0.50 0.000.00 0.00 0.50 1.80 0.400.00 0.00 0.00 0.40 0.80

-2.3703703704 0.7407407407 -0.37037037041.18518518519 -0.3703703704 0.18518518521.18518518519 -0.3703703704 0.1851851852-0.3703703704 0.7407407407 -0.37037037040.18518518519 -0.3703703704 1.4351851852

0.00 -1.44E+01 4.000.24 x 7.88E+00 + 7.50-0.24 5.22E+00 5.50

-5.09E+008.27E+00

2 R(AB) 0.000.67 = M(AB) 0.002.00 R(BA) 4.00-0.67 M(BA) -4.00

2 R(BC) 2.05

1.33 = M(BC) 4.002.00 R(CB) 1.95-1.33 M(CB) -3.81

5.5 R(CD) 6.264.58 = M(CD) 3.815.50 R(DC) 4.74-4.58 M(DC) 0.00

20.674.000.667.503.255.50-4.58

2.000.670.663.25-4.584.007.505.50


AB 1.00 4 0.19 0.38 1.00

BC 1.00 4 0.19 0.38 1.00

CD 1.00 5 0.10 0.24 0.80

Ma-b = 1.60 Tn-m Ra-bMb-a = -2.40 Tn-m Rb-a

Mb-c = 2.40 Tn-m Rb-cMc-b = -1.60 Tn-m Rc-b

Mc-d = 1.56 Tn-m Rc-dMd-c = -1.56 Tn-m Rd-c


R(AB) 0.19 0.38 -0.19 0.38M(AB) = 0.38 1.00 -0.38 0.50R(BA) -0.19 -0.38 0.19 -0.38M(BA) 0.38 0.50 -0.38 1.00

Vb θb Vc θcR(BC) 0.19 0.38 -0.19 0.38

M(BC) = 0.38 1.00 -0.38 0.50R(CB) -0.19 -0.38 0.19 -0.38M(CB) 0.38 0.50 -0.38 1.00

Vc θc Vd θdR(CD) 0.10 0.24 -0.10 0.24M(CD) = 0.24 0.80 -0.24 0.40R(DC) -0.10 -0.24 0.10 -0.24M(DC) 0.24 0.40 -0.24 0.80


Ra - - - 0.38Ma - - - 0.50Rb = - - - 0.00

Mb = 0 - - - 2.00Rc - - - -0.38

Mc = 0 - - - 0.50Rd - - - 0.00

Md=0 - - - 0.00

ORDENANDO MATRIZ GLOBAL:θb θc θd Va

0 2.00 0.50 0.00 -0 0.50 1.80 0.40 -0 0.00 0.40 0.80 -

Ra = 0.38 0.00 0.00 -Ma 0.50 0.00 0.00 -Rb 0.00 0.38 0.00 -Rc -0.38 -0.14 0.24 -Rd 0.00 -0.24 -0.24 -

θb 0 0.00θc = 0 - -0.04 xθd 0 -1.56

θb 0.00 0.5423728813559 -0.16949153θc = 0.04 x -0.169491525424 0.677966102θd 1.56 0.0847457627119 -0.33898305

θb 1.254E-01θc = -5.02E-01

θd 2.20E+00

Ra 0.38 0.00 0.00Ma 0.50 0.00 0.00Rb = 0.00 0.38 0.00 x Rc -0.38 -0.14 0.24Rd 0.00 -0.24 -0.24

Ra 0.0470338983051 1.80Ma 0.0627118644068 1.60Rb = -0.18813559322 + 8.40Rc 0.5488983050847 3.05Rd -0.407796610169 1.25

Ra 1.85Ma 1.66Rb = 8.21Rc 3.60Rd 0.84

14.50

2EI/L

0.50

0.50

0.40 E = 1 tn-m2

= 1.8 Tn= 4.2 Tn

= 4.2 Tn= 1.8 Tn

= 1.25 Tn= 1.25 Tn

0.00 Va = 0 1.8 0.047033898 1.80.00 θa = 0 + 1.60 = 0.062711864 + 1.60 =0.00 Vb = 0 4.20 -0.0470339 4.200.13 θb -2.40 0.125423729 -2.40

0.00 Vb = 0 4.2 -0.14110169 4.2

0.13 θb + 2.40 = -0.12542373 + 2.4 =0.00 Vc = 0 1.80 0.141101695 1.80-0.50 θc -1.60 -0.43898305 -1.60

0.00 Vc = 0 1.25 -0.12040678 1.25-0.50 θc + 1.56 = -0.40135593 + 1.56 =0.00 Vd = 0 1.25 0.12040678 1.250.00 θd= 0 -1.56 -0.20067797 -1.56

Vc θc Vd θd- 0.00 - 0 Va = 0 1.8- 0.00 - 0 θa = 0 1.60- 0.38 - 0 Vb = 0 8.40- 0.50 - 0 θb + 0.00- -0.14 - 0.24 Vc = 0 3.05- 1.80 - 0.40 θc -0.04- -0.24 - -0.24 Vd = 0 1.25- 0.40 - 0.80 θd -1.56

θa Vb Vc Vd- - - - θb 0.00- - - - θc -0.04- - - - θd -1.56- - - - 0 + 1.80- - - - 0 1.60- - - - 0 8.40- - - - 0 3.05- - - - 0 1.25

2.00 0.50 0.00 -10.50 1.80 0.400.00 0.40 0.80

0.084745763-0.338983051.419491525

1.801.25E-01 1.60-5.02E-01 + 8.402.20E+00 3.05

1.25

R(AB) 1.85M(AB) 1.66R(BA) 4.15M(BA) -2.27

R(BC) 4.06

M(BC) 2.27R(CB) 1.94M(CB) -2.04

R(CD) 1.13M(CD) 1.16R(DC) 1.37M(DC) -1.76


AB 1.00 2 1.50 1.50 2.00 1.00

BC 1.00 4 0.19 0.38 1.00 0.50

CD 1.00 5 0.10 0.24 0.80 0.40

DE 1.00 2.5 0.77 0.96 1.60 0.80

Ma-b = 0.00 Tn-m Ra-b =Mb-a = 0.00 Tn-m Rb-a =


Mc-d = 3.13 Tn-m Rc-d =Md-c = -3.13 Tn-m Rd-c =

Md-e = 0.00 Tn-m Rd-e =Me-d = 0.00 Tn-m Re-d =


R(AB) 1.50 1.50 -1.50 1.50 7.49M(AB) = 1.50 2.00 -1.50 1.00 -3.74R(BA) -1.50 -1.50 1.50 -1.50 0.00M(BA) 1.50 1.00 -1.50 2.00 -3.74

Vb θb Vc θcR(BC) 0.19 0.38 -0.19 0.38 0.00M(BC) = 0.38 1.00 -0.38 0.50 -3.74R(CB) -0.19 -0.38 0.19 -0.38 0.00M(CB) 0.38 0.50 -0.38 1.00 -0.51

Vc θc Vd θdR(CD) 0.10 0.24 -0.10 0.24 0.00M(CD) = 0.24 0.80 -0.24 0.40 -0.51R(DC) -0.10 -0.24 0.10 -0.24 0.00M(DC) 0.24 0.40 -0.24 0.80 4.17

Vd θd Ve θeR(DE) 0.77 0.96 -0.77 0.96 0.00M(DE) = 0.96 1.60 -0.96 0.80 4.17R(ED) -0.77 -0.96 0.77 -0.96 10.42M(ED) 0.96 0.80 -0.96 1.60 4.17

MATRIZ GLOBAL:Va θa Vb θb Vc

Ra = -3 1.50 1.50 - 1.50 -Ma=0 1.50 2.00 - 1.00 -

Rb = -1.50 -1.50 - -1.13 -Mb =0 1.50 1.00 - 3.00 -

Rc 0 0 - -0.38 -Mc =0 0 0 - 0.50 -

Rd 0 0 - 0.00 -Md=0 0 0 - 0.00 -RE = -2 0 0 - 0.00 -Me = 0 0 0 - 0.00 -

ORDENANDO MATRIZ GLOBAL:Va θa θb θc θd

-3 1.50 1.50 1.50 0.00 00 1.50 2.00 1.00 0.00 0.000 1.50 1.00 3.00 0.50 0.000 0.00 0.00 0.50 1.80 0.400 0.00 0.00 0.00 0.40 2.40-2 = 0.00 0.00 0.00 0.00 -0.960 0.00 0.00 0.00 0.00 0.80

Rb -1.50 -1.50 -1.13 0.38 0.00Rc 0.00 0.00 -0.38 -0.14 0.24Rd 0.00 0.00 0.00 -0.24 0.72

Va 0.00 0.00 1.50θa 0 0.00 1.50θb 0 4.00 1.50θc = 0 - 1.13 x 0.00θd 0 -3.13 0.00Ve 0 0.00 0.00θe 0 0.00 0.00

Va 0.00 7.41 -4.37 -2.37θa 0.00 -4.37 3.19 1.19θb -4.00 -2.37 1.19 1.19θc = -1.13 x 0.74 -0.37 -0.37θd 3.13 -0.37 0.19 0.19Ve 0.00 -0.93 0.46 0.46θe 0.00 -0.37 0.19 0.19

Va 7.485185185θa -3.74259259θb -3.74259259θc = -0.51481481θd 4.169907407Ve 10.42θe 4.17

Rb -1.50 -1.50 -1.13 0.38 0.00Rc = 0.00 0.00 -0.38 -0.14 0.24Rd 0.00 0.00 0.00 -0.24 0.72

Rb -1.60 6.00Rc = 2.47 + 6.75Rd -0.88 3.75

Rb 4.40Rc = 9.22Rd 2.87

16.50

E = 1 tn-m2

0 Tn0 Tn

3 Tn3 Tn

3.75 Tn3.75 Tn

0 Tn0 Tn

Va 0 0 0θa + 0.00 = 0 + 0.00 =

Vb = 0 3.00 0 3.00θb 2.00 0 2.00

Vb = 0 3 -1.59652778 3θb + 2.00 = -4 + 2 =

Vc = 0 3.00 1.596527778 3.00θc -2.00 -2.38611111 -2.00

Vc = 0 3.75 0.877222222 3.75θc + 3.13 = 1.256111111 + 3.13 =

Vd = 0 3.75 -0.87722222 3.75θd -3.13 3.13 -3.13

Vd = 0 0 0 0θd + 0.00 = 0 + 0.00 =Ve 0.00 0 0.00θe 0.00 0 0.00

θc Vd θd Ve θe0.00 - 0 0 0 Va0.00 - 0 0 0 θa0.38 - 0 0 0 Vb0.50 - 0 0 0 θb +-0.14 - 0.24 0 0 Vc1.80 - 0.40 0 0 θc-0.24 - 0.72 -0.77 0.96 Vd0.40 - 2.40 -0.96 0.80 θd0.00 - -0.96 0.77 -0.96 Ve0.00 - 0.80 -0.96 1.60 θe

Ve θe Vb Vc Vd

0 0 - - - Va0 0 - - - θa0 0 - - - θb0 0 - - - θc

-0.96 0.80 - - - θd0.77 -0.96 - - - Ve +-0.96 1.60 - - - θe

0 0 - - - Vb0 0 - - - Vc

-0.77 0.96 - - - Vd

-11.50 1.50 0.00 0.00 0.00 0.002.00 1.00 0.00 0.00 0.00 0.001.00 3.00 0.50 0.00 0.00 0.000.00 0.50 1.80 0.40 0.00 0.000.00 0.00 0.40 2.40 -0.96 0.800.00 0.00 0.00 -0.96 0.77 -0.960.00 0.00 0.00 0.80 -0.96 1.60

0.74 -0.37 -0.93 -0.37-0.37 0.19 0.46 0.19-0.37 0.19 0.46 0.190.74 -0.37 -0.93 -0.37-0.37 1.44 3.59 1.44-0.93 3.59 14.18 6.71-0.37 1.44 6.71 3.94

0.00 0.00 7.49 6.000.00 0.00 x -3.74 + 6.75-0.77 0.96 -3.74 3.75

-0.514.17

10.424.17

R(AB) 0.00M(AB) 0.00R(BA) 3.00M(BA) 2.00

R(BC) 1.40M(BC) -2.00R(CB) 4.60M(CB) -4.39

R(CD) 4.63M(CD) 4.39R(DC) 2.87M(DC) 0.00

R(CD) 0.00M(CD) 0.00R(DC) 0.00M(DC) 0.00

00.006.004.006.751.133.75-3.130.000.00

0.000.004.001.13-3.130.000.006.006.753.75


AB 1.00 5 0.10 0.24 0.80 0.40

BC 1.00 4 0.19 0.38 1.00 0.50

CD 1.00 4 0.19 0.38 1.00 0.50





R(AB) 0.10 0.24 -0.10 0.24 0.00M(AB) = 0.24 0.80 -0.24 0.40 0.00R(BA) -0.10 -0.24 0.10 -0.24 0.00M(BA) 0.24 0.40 -0.24 0.80 -0.77

Vb θb Vc θcR(BC) 0.19 0.38 -0.19 0.38 0.00

M(BC) = 0.38 1.00 -0.38 0.50 -0.77R(CB) -0.19 -0.38 0.19 -0.38 0.00M(CB) 0.38 0.50 -0.38 1.00 0.69



Ra - - - 0.24 -Ma - - - 0.40 -Rb = - - - 0.14 -

Mb = 0 - - - 1.80 -Rc - - - -0.38 -

Mc = 0 - - - 0.50 -Rd - - - 0.00 -Md - - - 0.00 -

ORDENANDO MATRIZ GLOBAL:θb θc Va θa Vb

0 1.80 0.50 - - -0 0.50 2.00 - - -

Ra 0.24 0.00 - - -Ma = 0.40 0.00 - - -Rb 0.14 0.38 - - -Rc -0.38 0.00 - - -Rd 0.00 -0.38 - - -Md 0.00 0.50 - - -

θb = 0 - 1.04 x 1.80θc 0 -1.00 0.50

θb = -1.04 x 0.597014925 -0.14925373θc 1.00 -0.14925373 0.537313433

θb = -7.701E-01θc 6.93E-01

Ra 0.24 0.00Ma 0.40 0.00 -0.77

Rb = 0.14 0.38 x 0.69 +Rc -0.38 0.00Rd 0.00 -0.38Md 0.00 0.50

Ra -0.18483582 1.10Ma -0.3080597 1.44Rb = 0.155731343 + 3.70Rc 0.28880597 4.00Rd -0.25970149 1.00Md 0.346268657 -1.00

Ra 0.92Ma 1.13Rb = 3.86Rc 4.29Rd 0.74Md -0.65

5.90

E = 1 tn-m2

1.1 Tn0.7 Tn

3 Tn3 Tn

1 Tn1 Tn

Va = 0 1.1 -0.18483582 1.1θa = 0 + 1.44 = -0.3080597 + 1.44Vb = 0 0.70 0.184835821 0.70

θb -0.96 -0.6161194 -0.96

Vb = 0 3 -0.02910448 3

θb + 2.00 = -0.4238806 + 2Vc = 0 3.00 0.029104478 3.00

θc -2.00 0.307462687 -2.00

Vc = 0 1 0.259701493 1θc + 1.00 = 0.692537313 + 1

Vd = 0 1.00 -0.25970149 1.00θd= 0 -1.00 0.346268657 -1.00

θc Vd θd0.00 - - Va = 0 1.10.00 - - θa = 0 1.440.38 - - Vb = 0 3.700.50 - - θb + 1.040.00 - - Vc = 0 4.002.00 - - θc -1.00-0.38 - - Vd= 0 1.000.50 - - θd = 0 -1.00

Vc Vd θd- - - θb 1.04- - - θc -1.00- - - Va 1.10- - - θa + 1.44- - - Vb 3.70- - - Vc 4.00- - - Vd 1.00- - - θd -1.00

-10.502.00

1.101.44

3.704.001.00-1.00

R(AB) 0.92= M(AB) 1.13

R(BA) 0.88M(BA) -1.58

R(BC) 2.97

= M(BC) 1.58R(CB) 3.03M(CB) -1.69

R(CD) 1.26= M(CD) 1.69

R(DC) 0.74M(DC) -0.65


AB 1.00 4 0.19 0.38 1.00 0.50

BC 1.00 4 0.19 0.38 1.00 0.50

CD 1.00 4 0.19 0.38 1.00 0.50





R(AB) 0.19 0.38 -0.19 0.38 0.000M(AB) = 0.38 1.00 -0.38 0.50 -2.66R(BA) -0.19 -0.38 0.19 -0.38 0.00M(BA) 0.38 0.50 -0.38 1.00 0.66

Vb θb Vc θcR(BC) 0.19 0.38 -0.19 0.38 0

M(BC) = 0.38 1.00 -0.38 0.50 0.66R(CB) -0.19 -0.38 0.19 -0.38 0M(CB) 0.38 0.50 -0.38 1.00 -0.66

Vc θc Vd θdR(CD) 0.19 0.38 -0.19 0.38 0M(CD) = 0.38 1.00 -0.38 0.50 -0.66R(DC) -0.19 -0.38 0.19 -0.38 0M(DC) 0.38 0.50 -0.38 1.00 2.66


Ra - 0.38 - 0.38 -Ma=0 - 1.00 - 0.50 -

Rb - -0.38 - 0.00 -Mb = 0 = - 0.50 - 2.00 -

Rc - 0 - -0.38 -Mc = 0 - 0 - 0.50 -

Rd - 0 - 0.00 -Md=0 - 0 - 0.00 -

ORDENANDO MATRIZ GLOBAL:θa θb θc θd Va

0 1.00 0.50 0.00 0.00 -0 0.50 2.00 0.50 0.00 -0 0.00 0.50 2.00 0.50 -0 = 0.00 0.00 0.50 1.00 -

Ra 0.38 0.38 0.00 0.00 -Rb -0.38 0.00 0.38 0.00 -Rc 0.00 -0.38 0.00 0.38 -Rd 0.00 0.00 -0.38 -0.38 -

θa 0 2.33 1.00θb 0 0.34 0.50θc = 0 - -0.34 x 0.00θd 0 -2.33 0.00

θa -2.33 1.155555556 -0.31111111 0.088888889θb -0.34 -0.31111111 0.622222222 -0.17777778θc = 0.34 x 0.088888889 -0.17777778 0.622222222θd 2.33 -0.04444444 0.088888889 -0.31111111

θa -2.660E+00θb 6.60E-01θc = -6.60E-01θd 2.66E+00

Ra 0.38 0.38 0.00 0.00Rb = -0.38 0.00 0.38 0.00 x Rc 0.00 -0.38 0.00 0.38Rd 0.00 0.00 -0.38 -0.38

Ra -0.75 3.00Rb 0.75 7.00Rc = 0.75 + 7.00Rd -0.75 3.00

Ra 2.25Rb 7.75Rc = 7.75Rd 2.25

17.75

EI = 1 tn-m2

3 Tn3 Tn

4 Tn4 Tn

3 Tn3 Tn

Va = 0 3 -0.75 3θa + 2.33 = -2.33 + 2.33

Vb = 0 3.00 0.75 3.00θb -2.33 -0.67 -2.33

Vb = 0 4 0 4

θb + 2.67 = 0.33 + 2.67Vc = 0 4.00 0 4.00

θc -2.67 -0.33 -2.67

Vc = 0 3 0.75 3θc + 2.33 = 0.67 + 2.33

Vd = 0 3.00 -0.75 3.00θd -2.33 2.33 -2.33

θc Vd θd0.00 - 0 Va 30.00 - 0 θa 2.330.38 - 0 Vb = 0 7.000.50 - 0 θb + 0.340.00 - 0.38 Vc = 0 7.002.00 - 0.50 θc -0.34-0.38 - -0.38 Vd = 0 3.000.50 - 1.00 θd -2.33

Vb Vc Vd- - - θa 2.33- - - θb 0.34- - - θc -0.34- - - θd + -2.33- - - 0 3.00- - - 0 7.00- - - 0 7.00- - - 0 3.00

-10.50 0.00 0.002.00 0.50 0.000.50 2.00 0.500.00 0.50 1.00

-0.044444440.088888889-0.311111111.155555556

-2.66E+00 3.006.60E-01 + 7.00-6.60E-01 7.002.66E+00 3.00

R(AB) 2.25= M(AB) 0.00

R(BA) 3.75M(BA) -3.00

R(BC) 4.00

= M(BC) 3.00R(CB) 4.00M(CB) -3.00

R(CD) 3.75= M(CD) 3.00

R(DC) 2.25M(DC) 0.00


AB 1.00 3 0.44 0.67 1.33 0.67

BC 1.00 6 0.06 0.17 0.67 0.33

CD 1.00 4 0.19 0.38 1.00 0.50





R(AB) 0.44 0.67 -0.44 0.67 -18.20M(AB) = 0.67 1.33 -0.67 0.67 6.82R(BA) -0.44 -0.67 0.44 -0.67 0.00M(BA) 0.67 0.67 -0.67 1.33 3.67

Vb θb Vc θcR(BC) 0.06 0.17 -0.06 0.17 0.00

M(BC) = 0.17 0.67 -0.17 0.33 3.67R(CB) -0.06 -0.17 0.06 -0.17 0.00M(CB) 0.17 0.33 -0.17 0.67 -1.03

Vc θc Vd θdR(CD) 0.19 0.38 -0.19 0.38 0.00M(CD) = 0.38 1.00 -0.38 0.50 -1.03R(DC) -0.19 -0.38 0.19 -0.38 0.00M(DC) 0.38 0.50 -0.38 1.00 0.00


Ra=0 0.44 0.67 - 0.67 -Ma=0 0.67 1.33 - 0.67 -

Rb = -0.44 -0.67 - -0.50 -Mb = 0 0.67 0.67 - 2.00 -

Rc 0 0 - -0.17 -Mc = 0 0 0 - 0.33 -

Rd 0 0 - 0.00 -Md 0 0 - 0.00 -

ORDENANDO MATRIZ GLOBAL:Va θa θb θc Vb

0 0.44 0.67 0.67 0.00 -0 0.67 1.33 0.67 0.00 -0 0.67 0.67 2.00 0.33 -0 = 0.00 0.00 0.33 1.67 -

Rb -0.44 -0.67 -0.50 0.17 -Rc 0.00 0.00 -0.17 0.21 -Rd 0.00 0.00 0.00 -0.38 -Md 0.00 0.00 0.00 0.50 -

Va 0 1.10 0.44θa = 0 - 0.60 x 0.67θb 0 0.60 0.67θc 0 0.50 0.00

Va -1.10 24 -9.5 -5θa = -0.60 x -9.5 4.666666667 1.666666667θb -0.60 -5 1.666666667 1.666666667θc -0.50 1 -0.33333333 -0.33333333

Va -1.82E+01θa = 6.82E+00θb 3.67E+00θc -1.03E+00

Rb -0.44 -0.67 -0.50 0.17Rc = 0.00 0.00 -0.17 0.21 x Rd 0.00 0.00 0.00 -0.38Md 0.00 0.00 0.00 0.50

Rb 1.538888889 3.10Rc = -0.82638889 + 4.00Rd 0.3875 3.00Md -0.51666667 -2.00

Rb 4.64Rc = 3.17Rd 3.39Md -2.52

11.20

EI = 1 tn-m2

1.1 Tn2.1 Tn

1 Tn1 Tn

3 Tn3 Tn

Va 1.1 -1.1 1.1θa + 0.60 = -0.6 + 0.6

Vb = 0 2.10 1.1 2.10θb -0.90 -2.7 -0.90

Vb = 0 1 0.438888889 1

θb + 1.50 = 2.1 + 1.5Vc = 0 1.00 -0.43888889 1.00

θc -1.50 0.533333333 -1.50

Vc = 0 3 -0.3875 3θc + 2.00 = -1.03333333 + 2

Vd = 0 3.00 0.3875 3.00θd = 0 -2.00 -0.51666667 -2.00

θc Vd θd0.00 - - Va 1.10.00 - - θa 0.600.17 - - Vb = 0 3.100.33 - - θb + 0.600.21 - - Vc = 0 4.001.67 - - θc 0.50-0.38 - - Vd = 0 3.000.50 - - θd = 0 -2.00

Vc Vd θd- - - Va 1.10- - - θa 0.60- - - θb 0.60- - - θc + 0.50- - - 0 3.10- - - 0 4.00- - - 0 3.00- - - 0 -2.00

-10.67 0.67 0.001.33 0.67 0.000.67 2.00 0.330.00 0.33 1.67

1-0.33333333-0.333333330.666666667

-18.20 3.106.82 + 4.003.67 3.00-1.03 -2.00

R(AB) 0.00= M(AB) 0.00

R(BA) 3.20M(BA) -3.60

R(BC) 1.44

= M(BC) 3.60R(CB) 0.56M(CB) -0.97

R(CD) 2.61= M(CD) 0.97

R(DC) 3.39M(DC) -2.52


AB 1.00 3 0.44 0.67 1.33 0.67

BC 1.00 4 0.19 0.38 1.00 0.50

CD 1.00 4 0.19 0.38 1.00 0.50

DE 1.00 3 0.44 0.67 1.33 0.67




Md-e = 0.75 Tn-m Rd-e =Me-d = -0.75 Tn-m Re-d =


R(AB) 0.44 0.67 -0.44 0.67 -14.05M(AB) = 0.67 1.33 -0.67 0.67 5.81R(BA) -0.44 -0.67 0.44 -0.67 0.00M(BA) 0.67 0.67 -0.67 1.33 1.31

Vb θb Vc θcR(BC) 0.19 0.38 -0.19 0.38 0.00M(BC) = 0.38 1.00 -0.38 0.50 1.31R(CB) -0.19 -0.38 0.19 -0.38 0.00M(CB) 0.38 0.50 -0.38 1.00 0.61

Vc θc Vd θdR(CD) 0.19 0.38 -0.19 0.38 0.00M(CD) = 0.38 1.00 -0.38 0.50 0.61R(DC) -0.19 -0.38 0.19 -0.38 0.00M(DC) 0.38 0.50 -0.38 1.00 -3.73

Vd θd Ve θeR(DE) 0.44 0.67 -0.44 0.67 0.00M(DE) = 0.67 1.33 -0.67 0.67 -3.73R(ED) -0.44 -0.67 0.44 -0.67 -21.33M(ED) 0.67 0.67 -0.67 1.33 -8.23


Ra = 0 0.44 0.67 - 0.67 -Ma=0 0.67 1.33 - 0.67 -

Rb -0.44 -0.67 - -0.29 -Mb =0 0.67 0.67 - 2.33 -

Rc 0 0 - -0.38 -Mc =0 = 0 0 - 0.50 -

Rd 0 0 - 0.00 -Md=0 0 0 - 0.00 -RE = 0 0 0 - 0.00 -Me = 0 0 0 - 0.00 -


0 0.44 0.67 0.67 0.00 00 0.67 1.33 0.67 0.00 0.000 0.67 0.67 2.33 0.50 0.000 0.00 0.00 0.50 2.00 0.500 0.00 0.00 0.00 0.50 2.330 = 0.00 0.00 0.00 0.00 -0.670 0.00 0.00 0.00 0.00 0.67

Rb -0.44 -0.67 -0.29 0.38 0.00Rc 0.00 0.00 -0.38 0.00 0.38Rd 0.00 0.00 0.00 -0.38 0.29

Va 0.00 1.50 0.44θa 0 0.75 0.67θb 0 2.14 0.67θc = 0 - 0.00 x 0.00θd 0 -0.32 0.00Ve 0 1.50 0.00θe 0 -0.75 0.00

Va -1.50 19.50 -8.00 -3.50θa -0.75 -8.00 4.17 1.17θb -2.14 -3.50 1.17 1.17θc = 0.00 x 1.00 -0.33 -0.33θd 0.32 -0.50 0.17 0.17Ve -1.50 -1.50 0.50 0.50θe 0.75 -0.50 0.17 0.17

Va -14.045θa 5.806666667θb 1.306666667θc = 0.606666667θd -3.73333333Ve -21.32θe -8.23

Rb -0.44 -0.67 -0.29 0.38 0.00Rc = 0.00 0.00 -0.38 0.00 0.38Rd 0.00 0.00 0.00 -0.38 0.29

Rb 2.22 2.92Rc = -1.89 + 5.34Rd 2.67 2.70

Rb 5.14Rc = 3.45Rd 5.37

13.96

E = 1 tn-m2

1.5 Tn1.5 Tn

1.46 Tn2.8 Tn

2.54 Tn1.2 Tn

1.5 Tn1.5 Tn

Va 1.5 -1.5 1.5θa + 0.75 = -0.75 + 0.75

Vb = 0 1.46 1.5 1.46θb 1.07 -3.75 1.07

Vb = 0 1.46 0.7175 1.46θb + 1.07 = 1.61 + 1.07

Vc = 0 2.80 -0.7175 2.80θc -1.60 1.26 -1.60

Vc = 0 2.54 -1.1725 2.54θc + 1.60 = -1.26 + 1.6

Vd = 0 1.20 1.1725 1.20θd -1.07 -3.43 -1.07

Vd= 0 1.5 1.5 1.5θd + 0.75 = 3.75 + 0.75Ve 1.50 -1.5 1.50θe -0.75 0.75 -0.75

θc Vd θd Ve θe0.00 - 0 0 0 Va0.00 - 0 0 0 θa0.38 - 0 0 0 Vb0.50 - 0 0 0 θb0.00 - 0.38 0 0 Vc2.00 - 0.50 0 0 θc-0.38 - 0.29 -0.44 0.67 Vd0.50 - 2.33 -0.67 0.67 θd0.00 - -0.67 0.44 -0.67 Ve0.00 - 0.67 -0.67 1.33 θe

Ve θe Vb Vc Vd

0 0 - - - Va0 0 - - - θa0 0 - - - θb0 0 - - - θc

-0.67 0.67 - - - θd0.44 -0.67 - - - Ve-0.67 1.33 - - - θe

0 0 - - - Vb0 0 - - - Vc

-0.44 0.67 - - - Vd

-10.67 0.67 0.00 0.00 0.00 0.001.33 0.67 0.00 0.00 0.00 0.000.67 2.33 0.50 0.00 0.00 0.000.00 0.50 2.00 0.50 0.00 0.000.00 0.00 0.50 2.33 -0.67 0.670.00 0.00 0.00 -0.67 0.44 -0.670.00 0.00 0.00 0.67 -0.67 1.33

1.00 -0.50 -1.50 -0.50-0.33 0.17 0.50 0.17-0.33 0.17 0.50 0.170.67 -0.33 -1.00 -0.33-0.33 1.17 3.50 1.17-1.00 3.50 19.50 8.00-0.33 1.17 8.00 4.17

0.00 0.00 -14.05 2.920.00 0.00 x 5.81 + 5.34-0.44 0.67 1.31 2.70

0.61-3.73

-21.32-8.23

R(AB) 0.00= M(AB) 0.00

R(BA) 2.96M(BA) -2.68

R(BC) 2.18= M(BC) 2.68

R(CB) 2.08M(CB) -0.34

R(CD) 1.37= M(CD) 0.34

R(DC) 2.37M(DC) -4.50

R(CD) 3.00= M(CD) 4.50

R(DC) 0.00M(DC) 0.00

1.50.752.92

+ 2.145.340.002.70-0.321.50-0.75

1.500.752.140.00-0.32

+ 1.50-0.752.925.342.70


AB 1.00 5 0.10 0.24 0.80 0.40

BC 1.00 4 0.19 0.38 1.00 0.50

CD 1.00 5 0.10 0.24 0.80 0.40





R(AB) 0.10 0.24 -0.10 0.24 0.00M(AB) = 0.24 0.80 -0.24 0.40 0.00R(BA) -0.10 -0.24 0.10 -0.24 0.00M(BA) 0.24 0.40 -0.24 0.80 -0.13

Vb θb Vc θcR(BC) 0.19 0.38 -0.19 0.38 0.00

M(BC) = 0.38 1.00 -0.38 0.50 -0.13R(CB) -0.19 -0.38 0.19 -0.38 0.00M(CB) 0.38 0.50 -0.38 1.00 0.13



Ra - - - 0.24 -Ma - - - 0.40 -Rb - - - 0.14 -

Mb = 0 = - - - 1.80 -Rc - - -0.38 -

Mc = 0 - - - 0.50 -Rd - - - 0.00 -Md - - - 0.00 -


0 1.80 0.50 - - -0 0.50 1.80 - - -

Ra 0.24 0.00 - - -Ma = 0.40 0.00 - - -Rb 0.14 0.38 - - -Rc -0.38 -0.14 - - -Rd 0.00 -0.24 - - -Md 0.00 0.40 - - -

θb = 0 - 0.17 x 1.80θc 0 -0.17 0.50

θb = -0.17 x 0.60 -0.16722408θc 0.17 -0.17 0.602006689

θb = -0.13076923θc 0.130769231

Ra 0.24 0.00Ma 0.40 0.00

Rb = 0.14 0.38 x -0.13076923 +Rc -0.38 -0.14 0.130769231Rd 0.00 -0.24Md 0.00 0.40

Ra -0.03 1.84Ma -0.05 1.67Rb = 0.03 + 7.50Rc 0.03 7.16Rd -0.03 1.50Md 0.05 -1.67

Ra 1.81Ma 1.62Rb = 7.53Rc 7.19Rd 1.47Md -1.62

18.00

EI = 1 tn-m2

1.84 Tn3.5 Tn

4 Tn4 Tn

3.16 Tn1.5 Tn

Va = 0 1.84 -0.03138462 1.84θa = 0 + 1.67 = -0.05230769 + 1.67Vb = 0 3.50 0.031384615 3.50

θb -2.50 -0.10461538 -2.50

Vb = 0 4 0 4

θb + 2.67 = -0.06538462 + 2.67Vc = 0 4.00 0 4.00

θc -2.67 0.065384615 -2.67

Vc = 0 3.16 0.031384615 3.16θc + 2.50 = 0.104615385 + 2.5

Vd = 0 1.50 -0.03138462 1.50θd = 0 -1.67 0.052307692 -1.67

θc Vd θd0.00 - - Va = 0 1.840.00 - - θa = 0 1.670.38 - - Vb = 0 7.500.50 - - θb + 0.17-0.14 - - Vc = 0 7.161.80 - - θc -0.17-0.24 - - Vd = 0 1.500.40 - - θd = 0 -1.67

Vc Vd θd- - - θb 0.17- - - θc -0.17- - - 0 1.84- - - 0 + 1.67- - - 0 7.50- - - 0 7.16- - - 0 1.50- - - 0 -1.67

-10.501.80

1.841.67

7.507.161.50-1.67

R(AB) 1.81= M(AB) 1.62

R(BA) 3.53M(BA) -2.60

R(BC) 4.00

= M(BC) 2.60R(CB) 4.00M(CB) -2.60

R(CD) 3.19= M(CD) 2.60

R(DC) 1.47M(DC) -1.62


AB 1.00 4 0.19 0.38 1.00 0.50

BC 1.00 5 0.10 0.24 0.80 0.40

CD 1.00 3 0.44 0.67 1.33 0.67





R(AB) 0.19 0.38 -0.19 0.38 0.00M(AB) = 0.38 1.00 -0.38 0.50 -1.35R(BA) -0.19 -0.38 0.19 -0.38 0.00M(BA) 0.38 0.50 -0.38 1.00 1.20

Vb θb Vc θcR(BC) 0.10 0.24 -0.10 0.24 0.00

M(BC) = 0.24 0.80 -0.24 0.40 1.20R(CB) -0.10 -0.24 0.10 -0.24 0.00M(CB) 0.24 0.40 -0.24 0.80 -4.76

Vc θc Vd θdR(CD) 0.44 0.67 -0.44 0.67 0.00M(CD) = 0.67 1.33 -0.67 0.67 -4.76R(DC) -0.44 -0.67 0.44 -0.67 -24.41M(DC) 0.67 0.67 -0.67 1.33 -9.26


Ra - 0.38 - 0.38 -Ma=0 - 1.00 - 0.50 -

Rb - -0.38 - -0.14 -Mb = 0 = - 0.50 - 1.80 -

Rc - 0 - -0.24 -Mc = 0 - 0 - 0.40 -Rd = 0 - 0 - 0.00 -Md=0 - 0 - 0.00 -

ORDENANDO MATRIZ GLOBAL:θa θb θc Vd θd

0 1.00 0.50 0.00 0.00 00 0.50 1.80 0.40 0.00 00 0.00 0.40 2.13 -0.67 0.670 = 0.00 0.00 -0.67 0.44 -0.670 0.00 0.00 0.67 -0.67 1.33

Ra 0.38 0.38 0.00 0.00 0.00Rb -0.38 -0.14 0.24 0.00 0.00Rc 0.00 -0.24 0.43 -0.44 0.67

θa 0 0.75 1.00θb 0 0.42 0.50θc = 0 - -0.42 x 0.00Vd 0 1.50 0.00θd 0 -0.75 0.00

θa -0.75 1.185185185 -0.37037037 0.185185185θb -0.42 -0.37037037 0.740740741 -0.37037037θc = 0.42 x 0.185185185 -0.37037037 1.435185185Vd -1.50 0.555555556 -1.11111111 4.305555556θd 0.75 0.185185185 -0.37037037 1.435185185

θa -1.350E+00θb 1.20E+00θc = -4.76E+00Vd -2.44E+01θd -9.26E+00

Ra 0.38 0.38 0.00 0.00 0.00Rb = -0.38 -0.14 0.24 0.00 0.00Rc 0.00 -0.24 0.43 -0.44 0.67

Ra -0.05625 1.00Rb = -0.79875 + 2.88Rc 2.355 3.38

Ra 0.94Rb = 2.08Rc 5.73

8.76

EI = 1 tn-m2

1 Tn1 Tn

1.88 Tn1.88 Tn

1.5 Tn1.5 Tn

Va = 0 1 -0.05625 1θa + 0.75 = -0.75 + 0.75

Vb = 0 1.00 0.05625 1.00θb -0.75 0.525 -0.75

Vb = 0 1.88 -0.855 1.88

θb + 1.17 = -0.945 + 1.17Vc = 0 1.88 0.855 1.88

θc -1.17 -3.33 -1.17

Vc = 0 1.5 1.5 1.5θc + 0.75 = 3.75 + 0.75Vd 1.50 -1.5 1.50θd -0.75 0.75 -0.75

θc Vd θd0.00 0 0 Va = 0 10.00 0 0 θa 0.750.24 0 0 Vb = 0 2.880.40 0 0 θb + 0.420.43 -0.44 0.67 Vc = 0 3.382.13 -0.67 0.67 θc -0.42-0.67 0.44 -0.67 Vd 1.500.67 -0.67 1.33 θd -0.75

Va Vb Vc- - - θa 0.75- - - θb 0.42- - - θc -0.42- - - Vd + 1.50- - - θd -0.75- - - 0 1.00- - - 0 2.88- - - 0 3.38

-10.50 0.00 0.00 0.001.80 0.40 0.00 0.000.40 2.13 -0.67 0.670.00 -0.67 0.44 -0.670.00 0.67 -0.67 1.33

0.555555556 0.185185185-1.11111111 -0.370370374.305555556 1.43518518521.91666667 8.8055555568.805555556 4.435185185

-1.35E+00 1.00x 1.20E+00 + 2.88

-4.76E+00 3.38-2.44E+01-9.26E+00

R(AB) 0.94= M(AB) 0.00

R(BA) 1.06M(BA) -0.22

R(BC) 1.03

= M(BC) 0.23R(CB) 2.73M(CB) -4.50

R(CD) 3.00= M(CD) 4.50

R(DC) 0.00M(DC) 0.00


AB 1.00 2 1.50 1.50 2.00

BC 1.00 4 0.19 0.38 1.00

CD 1.00 2 1.50 1.50 2.00

Ma-b = 2.00 KN-m Ra-bMb-a = -2.00 KN-m Rb-a

Mb-c = 1.00 KN-m Rb-cMc-b = -1.00 KN-m Rc-b

Mc-d = 2.00 KN-m Rc-dMd-c = -2.00 KN-m Rd-c


R(AB) 1.50 1.50 -1.50 1.50

M(AB) = 1.50 2.00 -1.50 1.00R(BA) -1.50 -1.50 1.50 -1.50

M(BA) 1.50 1.00 -1.50 2.00

Vb θb Vc θcR(BC) 0.19 0.38 -0.19 0.38

M(BC) = 0.38 1.00 -0.38 0.50R(CB) -0.19 -0.38 0.19 -0.38

M(CB) 0.38 0.50 -0.38 1.00

Vc θc Vd θdR(CD) 1.50 1.50 -1.50 1.50

M(CD) = 1.50 2.00 -1.50 1.00R(DC) -1.50 -1.50 1.50 -1.50M(DC) 1.50 1.00 -1.50 2.00


Ra 1.50 1.50 -1.50 1.50Ma 1.50 2.00 -1.50 1.00

Rb=0 = -1.50 -1.50 1.69 -1.13Mb = 0 1.50 1.00 -1.13 3.00Rc=0 0 0 -0.19 -0.38

Mc = 0 0 0 0.38 0.50Rd=0 0 0 0 0.00Md=0 0 0 0 0.00

ORDENANDO MATRIZ GLOBAL:Vb θb Vc θc

Rb=0 1.69 -1.13 -0.19 0.38Mb=0 -1.13 3.00 -0.38 0.50Rc=0 -0.19 -0.38 1.69 1.13Mc=0 = 0.38 0.50 1.13 3.00Rd=0 0.00 0.00 -1.50 -1.50Md=0 0.00 0.00 1.50 1.00

Ra -1.50 1.50 0.00 0.00Ma -1.50 1.00 0.00 0.00

Vb 0 2.00θb 0 -1.00Vc = 0 - 2.00 xθc 0 1.00Vd 0 1.00θd 0 -2.00

Vb -2.00 #VALUE! #VALUE!θb 1.00 #VALUE! #VALUE!Vc = -2.00 x #VALUE! #VALUE!

θc -1.00 #VALUE! #VALUE!Vd -1.00 #VALUE! #VALUE!θd 2.00 #VALUE! #VALUE!

Vb = #VALUE!θb #VALUE!Vc #VALUE!θc #VALUE!Vd #VALUE!θd #VALUE!

Ra -1.50 1.50 0.00 0.00Ma = -1.50 1.00 0.00 0.00

Ra #VALUE! 1.00Ma = #VALUE! + 2.00

Ra 6.00Ma = 24.00

2EI/L

1.00

0.50

1.00

= 1 KN= 1 KN

= 1 KN= 1 KN

= 1 KN= 1 KN

0.000 Va = 0 1 50.00 θa = 0 + 2.00 = 22 +

-37.33 Vb 1.00 -5-3.40E+01 θb -2.00 -12

-3.733E+01 Vb 1 3-3.40E+01 θb + 1.00 = 13 +-2.45E+02 Vc 1.00 -3-6.20E+01 θc -1.00 -1

-2.45E+02 Vc 1 1-6.20E+01 θc + 2.00 = 0 +-3.68E+02 Vd 1.00 -1-6.00E+01 θd -2.00 2

Vc θc Vd θd0 0.00 0 0 Va = 00 0.00 0 0 θa = 0

-0.19 0.38 0 0 Vb = 0-0.38 0.50 0 0 θb +1.69 1.13 -1.50 1.50 Vc = 01.13 3.00 -1.50 1.00 θc -1.50 -1.50 1.50 -1.50 Vd= 01.50 1.00 -1.50 2.00 θd = 0

Vd θd Ra θa0 0 - - Vb0 0 - - θb

-1.50 1.50 - - Vc-1.50 1.00 - - θc +1.50 -1.50 - - Vd-1.50 2.00 - - Vb θd0.00 0 - - Vc Ra0.00 0 - - Vd θa

1.69 -1.13 -0.19 0.38 0.00 0.00-1.13 3.00 -0.38 0.50 0.00 0.00-0.19 -0.38 1.69 1.13 -1.50 1.500.38 0.50 1.13 3.00 -1.50 1.000.00 0.00 -1.50 -1.50 1.50 -1.500.00 0.00 1.50 1.00 -1.50 2.00

#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!

0.00 0.00 -3.73E+01 1.00 =0.00 0.00 #VALUE! + 2.00

#VALUE!#VALUE!#VALUE!#VALUE!

1 R(AB) 6.002 = M(AB) 24.00

1.00 R(BA) -4.00-2.00 M(BA) -14.00

1 R(BC) 4.001 = M(BC) 14.00

1.00 R(CB) -2.00-1.00 M(CB) -2.00

1 R(CD) 2.002 = M(CD) 2.00

1.00 R(DC) 0.00-2.00 M(DC) 0.00

12.002.00-1.002.001.001.00-2.00

2.00-1.002.001.001.00-2.001.002.00


AB 1.00 4 0.19 0.38 1.00

BC 1.00 5 0.10 0.24 0.80

CD 1.00 2.5 0.77 0.96 1.60




MATRICES LOCALES:

Va θa Vb θbR(AB) 0.19 0.38 -0.19 0.38

M(AB) = 0.38 1.00 -0.38 0.50R(BA) -0.19 -0.38 0.19 -0.38

M(BA) 0.38 0.50 -0.38 1.00

Vb θb Vc θcR(BC) 0.10 0.24 -0.10 0.24

M(BC) = 0.24 0.80 -0.24 0.40R(CB) -0.10 -0.24 0.10 -0.24

M(CB) 0.24 0.40 -0.24 0.80

Vc θc Vd θdR(CD) 0.77 0.96 -0.77 0.96

M(CD) = 0.96 1.60 -0.96 0.80R(DC) -0.77 -0.96 0.77 -0.96M(DC) 0.96 0.80 -0.96 1.60


Ra 0.19 0.38 -0.19 0.38Ma=0 0.38 1.00 -0.38 0.50

Rb = -0.19 -0.38 0.28 -0.14Mb = 0 0.38 0.50 -0.14 1.80

Rc 0 0 -0.10 -0.24Mc = 0 0 0 0.24 0.40Rd=0 0 0 0 0.00Md=0 0 0 0 0.00

ORDENANDO MATRIZ GLOBAL:θa θb θc Vd

Ma= 0 1.00 0.40 0.00 0.00Mb = 0 0.50 2.40 0.40 0.00Mc=0 0.00 0.80 2.40 -0.96Rd=0 = 0.00 0.00 -0.96 0.77Md=0 0.00 0.00 0.80 -0.96

Ra 0.38 0.38 0.00 0.00Rb -0.38 -0.14 0.24 0.00Rc 0.00 -0.24 0.72 -0.77

Ma= 0 0 2.00Mb = 0 0 2.38 xMc=0 = 0 - -3.59Rd=0 0 1.88

Md=0 0 -0.78

Ma= 0 -2.00 1.1111111111111 -0.22222222Mb = 0 -2.38 x -0.277777777778 0.555555556Mc=0 = 3.59 0.2777777777778 -0.55555556Rd=0 -1.88 0.6944444444444 -1.38888889Md=0 0.78 0.2777777777778 -0.55555556

Ma= 0 = -1.729E+00Mb = 0 -6.77E-01Mc=0 2.86E-01Rd=0 -6.611979166667Md=0 -3.622916666667

Ra 0.38 0.38 0.00 0.00Rb = -0.38 -0.14 0.24 0.00Rc 0.00 -0.24 0.72 -0.77

Ra -0.90234375 3.00Rb 0.80859375 7.75Rc = 1.96875 + 6.63

Ra 2.10Rb 8.56Rc = 8.59

2EI/L

0.50

0.40

0.80

= 3 KN= 3 KN

= 4.75 KN= 4.75 KN

= 1.875 KN= 1.875 KN

0.00 Va = 0 3 -0.90234375-1.73 θa = 0 + 2.00 = -2.06770833 +0.00 Vb = 0 3.00 0.90234375

-6.77E-01 θb -2.00 -1.54166667

0.00 Vb = 0 4.75 -0.09375-6.77E-01 θb + 4.38 = -0.42708333 +

0 Vc = 0 4.75 0.093752.86E-01 θc -4.38 -0.04166667

0 Vc = 0 1.875 1.8752.86E-01 θc + 0.78 = 3.9075 +

-6.61197917 Vd = 0 1.88 -1.875-3.62E+00 θd= 0 -0.78 0.78

Vc θc Vd θd0 0.00 0 0 Va 0 0.00 0 0 θa

-0.10 0.24 0 0 Vb -0.24 0.40 0 0 θb =0 +0.86 0.72 -0.77 0.96 Vc 0.72 2.40 -0.96 0.80 θc =0-0.77 -0.96 0.77 -0.96 Vd0.96 0.80 -0.96 1.60 θd = 0

θd Va Vb Vc 0 - - - θa

0.00 - - - θb 0.80 - - - θc -0.96 - - - Vd +1.60 - - - θd 0.00 - - - Va 0.00 - - - Vb 0.96 - - - Vc

1.00 0.40 0.00 0.00 0.000.50 2.40 0.40 0.00 0.000.00 0.80 2.40 -0.96 0.800.00 0.00 -0.96 0.77 -0.96

0.00 0.00 0.80 -0.96 1.60

0.111111111 0.277777778 0.111111111-0.27777778 -0.69444444 -0.277777781.527777778 3.819444444 1.5277777783.819444444 14.75694444 6.9444444441.527777778 6.944444444 4.027777778

0.00 -1.73E+00 3.000.00 -6.77E-01 + 7.750.96 2.86E-01 6.63

-6.61E+00-3.62E+00

3 R(AB) 2.102.00 = M(AB) -0.073.00 R(BA) 3.90-2.00 M(BA) -3.54

4.75 R(BC) 4.664.375 = M(BC) 3.954.75 R(CB) 4.84-4.38 M(CB) -4.42

1.875 R(CD) 3.750.78 = M(CD) 4.691.88 R(DC) 0.00-0.78 M(DC) 0.00

32.007.752.386.63-3.591.88-0.78

2.002.38-3.591.88-0.783.007.756.63


AB 1.00 5 0.10 0.24 0.80

BC 1.00 3 0.44 0.67 1.33

CD 1.00 5 0.10 0.24 0.80





R(AB) 0.10 0.24 -0.10 0.24

M(AB) = 0.24 0.80 -0.24 0.40R(BA) -0.10 -0.24 0.10 -0.24

M(BA) 0.24 0.40 -0.24 0.80

Vb θb Vc θcR(BC) 0.44 0.67 -0.44 0.67

M(BC) = 0.67 1.33 -0.67 0.67R(CB) -0.44 -0.67 0.44 -0.67

M(CB) 0.67 0.67 -0.67 1.33

Vc θc Vd θdR(CD) 0.10 0.24 -0.10 0.24

M(CD) = 0.24 0.80 -0.24 0.40R(DC) -0.10 -0.24 0.10 -0.24M(DC) 0.24 0.40 -0.24 0.80


Ra 0.10 0.24 -0.10 0.24Ma 0.24 0.80 -0.24 0.40

Rb=0 = -0.10 -0.24 0.54 0.43Mb = 0 0.24 0.40 0.43 2.13

Rc 0 0 -0.44 -0.67Mc = 0 0 0 0.67 0.67Rd=0 0 0 0 0.00Md=0 0 0 0 0.00

ORDENANDO MATRIZ GLOBAL:Vb θb θc Vd

Rb= 0 0.54 0.43 0.67 0.00Mb = 0 0.43 2.13 0.67 0.00Mc=0 0.67 0.67 2.13 -0.24Rd=0 = 0.00 0.00 -0.24 0.10Md=0 0.00 0.00 0.40 -0.24

Ra -0.10 0.24 0.00 0.00Ma -0.24 0.40 0.00 0.00Rc -0.44 -0.67 -0.43 -0.10

Rb= 0 0 3.11Mb = 0 0 0.75 xMc=0 = 0 - 2.67Rd=0 0 5.00Md=0 0 -4.17

Rb= 0 -3.11 #VALUE! #VALUE!Mb = 0 -0.75 x #VALUE! #VALUE!Mc=0 = -2.67 #VALUE! #VALUE!Rd=0 -5.00 #VALUE! #VALUE!Md=0 4.17 #VALUE! #VALUE!

Rb= 0 = #VALUE!Mb = 0 #VALUE!Mc=0 #VALUE!Rd=0 #VALUE!Md=0 #VALUE!

Ra -0.10 0.24 0.00 0.00Ma = -0.24 0.40 0.00 0.00Rc -0.44 -0.67 -0.43 -0.10

Ra #VALUE! 1.31Ma #VALUE! 2.20Rc = #VALUE! + 8.00

Ra -1.55Rb -5.76Rc = 18.97

2EI/L

0.40 viga = 0.3x 0.6 m

0.67 f´c = 210kg/cm20.40 E = 11738.015 tn/m2

I = 5.4 x 10^-3 m4

= 1.31 KN= 0.11 KN

= 3 KN= 3 KN

= 5 KN= 5 KN

0.00 Va = 0 1.31 -2.859726560.00 θa = 0 + 2.20 = -7.9578125 +

39.90 Vb = 0 0.11 2.8597265634.04E+00 θb -0.75 -6.34082031

39.90 Vb = 0 3 -5.96972656

4.04E+00 θb + 1.50 = 5.590820313 +0 Vc = 0 3.00 5.969726563

-3.96E+01 θc -1.50 -23.5

0 Vc = 0 5 5-3.96E+01 θc + 4.17 = 20.83 +

-354.177083 Vd = 0 5.00 -5-8.12E+01 θd= 0 -4.17 4.17

Vc θc Vd θd0 0.00 0 0 Va 0 0.00 0 0 θa

-0.44 0.67 0 0 Vb =0-0.67 0.67 0 0 θb =0 +0.54 -0.43 -0.10 0.24 Vc -0.43 2.13 -0.24 0.40 θc =0-0.10 -0.24 0.10 -0.24 Vd=00.24 0.40 -0.24 0.80 θd = 0

θd Va θa Vc 0 - - - Vb

0.00 - - - θb 0.40 - - - θc -0.24 - - - Vd +0.80 - - - θd 0.00 - - - Va 0.00 - - - θa 0.24 - - - Vc

0.54 0.43 0.67 0.00 0.000.43 2.13 0.67 0.00 0.000.67 0.67 2.13 -0.24 0.400.00 0.00 -0.24 0.10 -0.240.00 0.00 0.40 -0.24 0.80

#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!

0.00 3.99E+01 1.310.00 #VALUE! + 2.200.24 #VALUE! 8.00

#VALUE!#VALUE!

1.31 R(AB) -1.552.20 = M(AB) -5.760.11 R(BA) 2.97-0.75 M(BA) -7.09

3 R(BC) -2.97

1.5 = M(BC) 7.093.00 R(CB) 8.97-1.50 M(CB) -25.00

5 R(CD) 10.004.17 = M(CD) 25.005.00 R(DC) 0.00-4.17 M(DC) 0.00

1.312.203.110.758.002.675.00-4.17

3.110.752.675.00-4.171.312.208.00


AB 1.00 4 0.19 0.38 1.00

BC 1.00 6 0.06 0.17 0.67

CD 1.00 5 0.10 0.24 0.80





R(AB) 0.19 0.38 -0.19 0.38

M(AB) = 0.38 1.00 -0.38 0.50R(BA) -0.19 -0.38 0.19 -0.38

M(BA) 0.38 0.50 -0.38 1.00

Vb θb Vc θcR(BC) 0.06 0.17 -0.06 0.17

M(BC) = 0.17 0.67 -0.17 0.33R(CB) -0.06 -0.17 0.06 -0.17

M(CB) 0.17 0.33 -0.17 0.67

Vc θc Vd θdR(CD) 0.10 0.24 -0.10 0.24

M(CD) = 0.24 0.80 -0.24 0.40R(DC) -0.10 -0.24 0.10 -0.24M(DC) 0.24 0.40 -0.24 0.80


Ra 0.19 0.38 -0.19 0.38Ma 0.38 1.00 -0.38 0.50

Rb=0 = -0.19 -0.38 0.24 -0.21Mb = 0 0.38 0.50 -0.21 1.67

Rc 0 0 -0.06 -0.17Mc = 0 0 0 0.17 0.33Rd=0 0 0 0 0.00Md=0 0 0 0 0.00

ORDENANDO MATRIZ GLOBAL:θb θc Vd θd

Mb= 0 1.67 0.33 0.00 0.00Mc = 0 0.33 1.47 -0.24 0.40Rd=0 0.00 -0.24 0.10 -0.24Md=0 = 0.00 0.40 -0.24 0.00

Ra 0.38 0.00 0.00 0.00Ma 0.50 0.00 0.00 0.00Rb -0.21 0.17 0.00 0.00Rc -0.17 0.07 -0.10 0.24

Mb= 0 0 2.53Mc = 0 0 -1.93 xRd=0 = 0 - 3.50Md=0 0 -2.50

Mb= 0 -2.53 0.6461538461538 -0.23076923Mc = 0 1.93 x -0.230769230769 1.153846154Rd=0 = -3.50 -0.384615384615 1.923076923Md=0 2.50 0.0769230769231 -0.38461538

Mb= 0 = -5.438E-01Mc = 0 -4.88E+00Rd=0 -1.86E+01Md=0 12.04358974359

Ra 0.38 0.00 0.00 0.00Ma = 0.50 0.00 0.00 0.00Rb -0.21 0.17 0.00 0.00Rc -0.17 0.07 -0.10 0.24

Ra -0.203942307692 2.80Ma -0.271923076923 1.60Rb = -0.70016025641 + 4.80Rc 4.4041025641026 5.10

Ra 2.60Ma 1.33Rb = 4.10Rc 9.50

16.20

2EI/L

0.50 viga = 0.3x 0.6 m

0.33 f´c = 210kg/cm20.40 E = 11738.015 tn/m2

I = 5.4 x 10^-3 m4

= 2.8 KN= 1.2 KN

= 3.6 KN= 3.6 KN

= 1.5 KN= 3.5 KN

0.00 Va = 0 2.8 -1.830288460.00 θa = 0 + 1.60 = -2.44038462 +0.00 Vb = 0 1.20 1.830288462

-4.88E+00 θb -1.07 -4.88076923

0.00 Vb = 0 3.6 -3.90534188

-4.88E+00 θb + 3.60 = -9.43760684 +0 Vc = 0 3.60 3.90534188

-1.86E+01 θc -3.60 -13.9944444

0 Vc = 0 1.5 0.219076923-1.86E+01 θc + 1.67 = -5.57128205 +-1.86E+01 Vd = 0 3.50 -0.219076921.20E+01 θd= 0 -2.50 6.666666667

Vc θc Vd θd0 0.00 0 0 Va 0 0.00 0 0 θa

-0.06 0.17 0 0 Vb -0.17 0.33 0 0 θb =0 +0.15 0.07 -0.10 0.24 Vc 0.07 1.47 -0.24 0.40 θc =0-0.10 -0.24 0.10 -0.24 Vd=00.24 0.40 -0.24 0.80 θd = 0

Va θa Vb Vc - - - θb - - - θc - - - Vd- - - θd +- - - Va - - - θa - - - Vb - - - Vc

1.67 0.33 0.00 0.000.33 1.47 -0.24 0.400.00 -0.24 0.10 -0.240.00 0.40 -0.24 0.00

-0.38461538 0.0769230771.923076923 -0.384615383.205128205 -4.80769231-4.80769231 -1.53846154

-5.44E-01 2.80-4.88E+00 + 1.60-1.86E+01 4.801.20E+01 5.10

2.8 R(AB) 0.971.60 = M(AB) -0.841.20 R(BA) 3.03-1.07 M(BA) -5.95

3.6 R(BC) -0.31

3.6 = M(BC) -5.843.60 R(CB) 7.51-3.60 M(CB) -17.59

1.5 R(CD) 1.721.67 = M(CD) -3.903.50 R(DC) 3.28-2.50 M(DC) 4.17

2.81.604.802.535.10-1.933.50-2.50

2.53-1.933.50-2.502.801.604.805.10


AB 1.00 2.5 0.77 0.96 1.60 0.80

BC 1.00 5 0.10 0.24 0.80 0.40

CD 1.00 4 0.19 0.38 1.00 0.50

DE 1.00 2.5 0.77 0.96 1.60 0.80

Ma-b = 0.52 KN-m Ra-b =Mb-a = -0.52 KN-m Rb-a

Mb-c = 1.67 KN-m Rb-c =Mc-b = -2.50 KN-m Rc-b =

Mc-d = 1.60 KN-m Rc-d =Md-c = -1.07 KN-m Rd-c =

Me-d = 0.52 KN-m Re-d =Md-e = -0.52 KN-m Rd-e


R(AB) 0.77 0.96 -0.77 0.96 -8.33

M(AB) = 0.96 1.60 -0.96 0.80 3.98R(BA) -0.77 -0.96 0.77 -0.96 0.00

M(BA) 0.96 0.80 -0.96 1.60 1.38E+00

Vb θb Vc θcR(BC) 0.10 0.24 -0.10 0.24 0M(BC) = 0.24 0.80 -0.24 0.40 1.38E+00R(CB) -0.10 -0.24 0.10 -0.24 0M(CB) 0.24 0.40 -0.24 0.80 8.89E-01

Vc θc Vd θdR(CD) 0.19 0.38 -0.19 0.38 0M(CD) = 0.38 1.00 -0.38 0.50 8.89E-01R(DC) -0.19 -0.38 0.19 -0.38 0M(DC) 0.38 0.50 -0.38 1.00 -2.50E+00

Vd θd Ve θeR(DE) 0.77 0.96 -0.77 0.96 0M(DE) = 0.96 1.60 -0.96 0.80 -2.50E+00R(ED) -0.77 -0.96 0.77 -0.96 -11.14M(ED) 0.96 0.80 -0.96 1.60 -5.11E+00


Ra=0 0.77 0.96 -0.77 0.96 0Ma=0 0.96 1.60 -0.96 0.80 0

Rb = -0.77 -0.96 0.86 -0.72 -0.10Mb =0 0.96 0.80 -0.72 2.40 -0.24

Rc 0 0 -0.10 -0.24 0.28Mc =0 0 0 0.24 0.40 0.14

Rd 0 0 0 0.00 -0.19

Md=0 0 0 0 0.00 0.38RE=0 0 0 0 0.00 0.00Me=0 0 0 0 0.00 0.00


Ra=0 0.77 0.96 0.96 0.00 0Ma=0 0.96 1.60 0.80 0.00 0.00Mb =0 0.96 0.80 2.40 0.40 0.00Mc =0 = 0.00 0.00 0.40 1.80 0.50Md=0 0.00 0.00 0.00 0.50 2.60RE=0 0.00 0.00 0.00 0.00 -0.96Me=0 0.00 0.00 0.00 0.00 0.80

Rb -0.77 -0.96 -0.72 0.24 0.00Rc 0.00 0.00 -0.24 0.14 0.38Rd 0.00 0.00 0.00 -0.38 0.59

Ra=0 0.00 1.25 0.77Ma=0 0.00 0.52 0.96Mb =0 0.00 1.15 0.96Mc =0 = 0.00 - -0.90 x 0.00Md=0 0.00 -0.55 0.00RE=0 0.00 1.25 0.00Me=0 0.00 -0.52 0.00

Ra=0 -1.25 14.18 -6.71 -3.59Ma=0 -0.52 -6.71 3.94 1.44Mb =0 -1.15 -3.59 1.44 1.44Mc =0 = 0.90 x 0.93 -0.37 -0.37Md=0 0.55 -0.46 0.19 0.19RE=0 -1.25 -1.16 0.46 0.46Me=0 0.52 -0.46 0.19 0.19

Ra=0 -8.32860725Ma=0 3.982484568Mb =0 1.378317901Mc =0 = 0.889197531Md=0 -2.50376543RE=0 -11.14Me=0 -5.11

Rb -0.77 -0.96 -0.72 0.24 0.00Rc = 0.00 0.00 -0.24 0.14 0.38Rd 0.00 0.00 0.00 -0.38 0.59

Rb 1.79 2.75Rc = -1.15 + 6.30Rd 1.86 2.45

Rb 4.54Rc = 5.15Rd 4.31

14.00

1.25 KN1.25 KN

1.5 KN3.5 KN

2.8 KN1.2 KN

1.25 KN1.25 KN

Va = 0 1.25 -1.25 1.25θa = 0 + 0.52 = -0.52083333 + 0.52 =Vb = 0 1.25 1.25 1.25

θb -0.52 -2.60416667 -0.52

Vb = 0 1.5 0.544203704 1.5θb + 1.67 = 1.458333333 + 1.666666667 =

Vc = 0 3.50 -0.5442037 3.50θc -2.50 1.262685185 -2.50

Vc = 0 2.8 -0.60546296 2.8θc + 1.60 = -0.36268519 + 1.6 =

Vd = 0 1.20 0.605462963 1.20θd= 0 -1.07 -2.05916667 -1.07

Vd= 1 1.25 1.25 1.25θd + 0.52 = 2.605 + 0.52 =

Ve= 1 1.25 -1.25 1.25θe= 1 -0.52 0.52 -0.52

θc Vd θd Ve θe0.00 0 0 0 0 Va0.00 0 0 0 0 θa0.24 0 0 0 0 Vb0.40 0 0 0 0 θb +0.14 -0.19 0.38 0 0 Vc1.80 -0.38 0.50 0 0 θc-0.38 0.96 0.59 -0.77 0.96 Vd

0.50 0.59 2.60 -0.96 0.80 θd0.00 -0.77 -0.96 0.77 -0.96 Ve0.00 0.96 0.80 -0.96 1.60 θe

Ve θe Vb Vc Vd0 0 Va0 0 θa0 0 θb0 0 θc +

-0.96 0.80 θd0.77 -0.96 Ve-0.96 1.60 θe

0 0 Vb0 0 Vc

-0.77 0.96 Vd

0.96 0.96 0.00 0.00 0.00 0.00 -11.60 0.80 0.00 0.00 0.00 0.000.80 2.40 0.40 0.00 0.00 0.000.00 0.40 1.80 0.50 0.00 0.000.00 0.00 0.50 2.60 -0.96 0.800.00 0.00 0.00 -0.96 0.77 -0.960.00 0.00 0.00 0.80 -0.96 1.60

0.93 -0.46 -1.16 -0.46-0.37 0.19 0.46 0.19-0.37 0.19 0.46 0.190.74 -0.37 -0.93 -0.37-0.37 1.19 2.96 1.19-0.93 2.96 12.62 6.09-0.37 1.19 6.09 3.69

0.00 0.00 -8.33 2.750.00 0.00 x 3.98 + 6.30-0.77 0.96 1.38 2.45

0.89-2.50

-11.14-5.11

R(AB) 0.00M(AB) 0.00R(BA) 2.50M(BA) -3.12

R(BC) 2.04M(BC) 3.12R(CB) 2.96M(CB) -1.24

R(CD) 1.90M(CD) 1.24R(DC) 1.81M(DC) -3.13

R(CD) 2.50M(CD) 3.13R(DC) 0.00M(DC) 0.00

1.250.522.751.156.30-0.902.45

-0.551.25-0.52

1.250.521.15-0.90-0.551.25-0.522.756.302.45


AB 1.00 4.5 0.13 0.30 0.89 0.44

BC 1.00 4 0.19 0.38 1.00 0.50

CD 1.00 4 0.19 0.38 1.00 0.50

Ma-b = 0.84 KN-m Ra-b = 1.125Mb-a = -0.84 KN-m Rb-a = 1.125

Mb-c = 2.33 KN-m Rb-c = 3Mc-b = -2.33 KN-m Rc-b = 3

Mc-d = 1.00 KN-m Rc-d = 1Md-c = -1.00 KN-m Rd-c = 1


R(AB) 0.13 0.30 -0.13 0.30 0.000 Va = 0

M(AB) = 0.30 0.89 -0.30 0.44 -5.16E-01 θa = 0R(BA) -0.13 -0.30 0.13 -0.30 0.00 Vb = 0

M(BA) 0.30 0.44 -0.30 0.89 -8.58E-01 θb

Vb θb Vc θcR(BC) 0.19 0.38 -0.19 0.38 0 Vb = 0

M(BC) = 0.38 1.00 -0.38 0.50 -8.58E-01 θbR(CB) -0.19 -0.38 0.19 -0.38 0 Vc = 0

M(CB) 0.38 0.50 -0.38 1.00 7.19E-01 θc

Vc θc Vd θdR(CD) 0.19 0.38 -0.19 0.38 0 Vc = 0

M(CD) = 0.38 1.00 -0.38 0.50 7.19E-01 θcR(DC) -0.19 -0.38 0.19 -0.38 0 Vd = 0M(DC) 0.38 0.50 -0.38 1.00 6.40E-01 θd= 0

MATRIZ GLOBAL:Va θa Vb θb Vc θc

Ra=0 0.13 0.30 -0.13 0.30 0 0.00Ma=0 0.30 0.89 -0.30 0.44 0 0.00

Rb = -0.13 -0.30 0.32 0.08 -0.19 0.38Mb = 0 0.30 0.44 0.08 1.89 -0.38 0.50

Rc 0 0 -0.19 -0.38 0.38 0.00Mc = 0 0 0 0.38 0.50 0.00 2.00

Rd 0 0 0 0.00 -0.19 -0.38Md=0 0 0 0 0.00 0.38 0.50

ORDENANDO MATRIZ GLOBAL:θa θb θc θd Va Vb

Ma=0 0.89 0.44 0.00 0.00 -Mb = 0 0.44 1.89 0.50 0.00 -Mc = 0 0.00 0.50 2.00 0.50 -Md=0 = 0.00 0.00 0.50 1.00 -

Ra 0.30 0.30 0.00 0.00 -Rb -0.30 0.08 0.38 0.00 -Rc 0.00 -0.38 0.00 0.38 -Rd 0.00 0.00 -0.38 -0.38 -

Ma=0 0 0.84 0.89 0.44Mb = 0 0 1.49 0.44 1.89Mc = 0 = 0 - -1.33 x 0.00 0.50Md=0 0 -1.00 0.00 0.00

Ma=0 -0.84 1.2890625 -0.328125 0.09375 -0.046875Mb = 0 -1.49 -0.328125 0.65625 -0.1875 0.09375Mc = 0 = 1.33 x 0.09375 -0.1875 0.625 -0.3125Md=0 1.00 -0.046875 0.09375 -0.3125 1.15625

Ma=0 = -5.161E-01Mb = 0 -8.58E-01Mc = 0 7.19E-01Md=0 6.40E-01

Ra 0.30 0.30 0.00 0.00Rb = -0.30 0.08 0.38 0.00 x Rc 0.00 -0.38 0.00 0.38Rd 0.00 0.00 -0.38 -0.38

Ra -0.40708333 1.13Rb = 0.35516927 + 4.13Rc 0.56179688 4.00Rd -0.50988281 1.00

Rb 0.72Rc = 4.49Rd 4.56

0.49

KNKN

KNKN

KNKN

1.125 -0.40708333 1.125 R(AB) 0.72+ 0.84 = -0.84 + 0.84 = M(AB) 0.00

1.13 0.407083333 1.13 R(BA) 1.53-0.84 -0.991875 -0.84 M(BA) -1.83

3 -0.05191406 3 R(BC) 2.95

+ 2.33 = -0.498125 + 2.33 = M(BC) 1.833.00 0.051914063 3.00 R(CB) 3.05-2.33 0.29046875 -2.33 M(CB) -2.04

1 0.509882813 1 R(CD) 1.51+ 1.00 = 1.03953125 + 1 = M(CD) 2.04

1.00 -0.50988281 1.00 R(DC) 0.49-1.00 1 -1.00 M(DC) 0.00

Vd θd0 0 Va = 0 1.1250 0 θa = 0 0.840 0 Vb = 0 4.130 0 θb + 1.49

-0.19 0.38 Vc = 0 4.00-0.38 0.50 θc -1.330.19 -0.38 Vd= 0 1.00-0.38 1.00 θd = 0 -1.00

Vc Vd- - θa 0.84- - θb 1.49- - θc -1.33- - θd + -1.00- - Va 1.13- - Vb Vb 4.13- - Vc Vc 4.00- - Vd Vd 1.00

0.00 0.00 -10.50 0.002.00 0.500.50 1.00

-5.16E-01 1.13-8.58E-01 + 4.137.19E-01 4.00 =6.40E-01 1.00


AB 1.00 4 0.19 0.38 1.00 0.50

BC 1.00 4.5 0.13 0.30 0.89 0.44

CD 1.00 2.5 0.77 0.96 1.60 0.80

Ma-b = 1.50 KN-m Ra-b =Mb-a = -1.50 KN-m Rb-a =




R(AB) 0.19 0.38 -0.19 0.38 0.000

M(AB) = 0.38 1.00 -0.38 0.50 0.00E+00R(BA) -0.19 -0.38 0.19 -0.38 0.00

M(BA) 0.38 0.50 -0.38 1.00 -4.40E-01

Vb θb Vc θcR(BC) 0.13 0.30 -0.13 0.30 0

M(BC) = 0.30 0.89 -0.30 0.44 -4.40E-01R(CB) -0.13 -0.30 0.13 -0.30 0M(CB) 0.30 0.44 -0.30 0.89 -4.48E-01

Vc θc Vd θdR(CD) 0.77 0.96 -0.77 0.96 0M(CD) = 0.96 1.60 -0.96 0.80 -4.48E-01R(DC) -0.77 -0.96 0.77 -0.96 -6.49E+00M(DC) 0.96 0.80 -0.96 1.60 -3.38E+00


Ra 0.19 0.38 -0.19 0.38 0Ma 0.38 1.00 -0.38 0.50 0

Rb = 0 = -0.19 -0.38 0.32 -0.08 -0.13Mb = 0 0.38 0.50 -0.08 1.89 -0.30

Rc 0 0 -0.13 -0.30 0.90Mc = 0 0 0 0.30 0.44 0.66Rd = 0 0 0 0 0.00 -0.77Md=0 0 0 0 0.00 0.96

ORDENANDO MATRIZ GLOBAL:θb θc Vd θd Va

Mb = 0 1.89 0.44 0.00 0.00Mc = 0 0.44 2.49 -0.96 0.80Rd= 0 0.00 -0.96 0.77 -0.96Md=0 = 0.00 0.80 -0.96 1.60

Ra 0.38 0.00 0.00 0.00Ma 0.50 0.00 0.00 0.00Rb -0.08 0.30 0.00 0.00Rc -0.30 0.66 -0.77 0.96

Mb = 0 0 1.03 1.89Mc = 0 0 -2.22 0.44Rd= 0 = 0 - 1.31 x 0.00Md=0 0 -0.47 0.00

Mb = 0 -1.03 0.6 -0.3 -0.75Mc = 0 2.22 -0.3 1.275 3.1875Rd= 0 = -1.31 x -0.75 3.1875 13.17708333Md=0 0.47 -0.3 1.275 6.3125

Mb = 0 = -4.404E-01Mc = 0 -4.48E-01Rd= 0 -6.49E+00Md=0 -3.38E+00

Ra 0.38 0.00 0.00 0.00Ma = 0.50 0.00 0.00 0.00Rb -0.08 0.30 0.00 0.00Rc -0.30 0.66 -0.77 0.96

Ra -0.16515562 2.00Ma = -0.2202075 + 1.50Rb -0.09807438 5.38Rc 1.57573 3.94

Rb 1.83Rc = 1.28Rd 5.28

5.51

2 KN2 KN

3.375 KN3.375 KN

0.5625 KN1.3125 KN

Va = 0 2 -0.16515562 2θa = 0 + 1.50 = -0.2202075 + 1.5Vb = 0 2.00 0.165155625 2.00

θb -1.50 -0.440415 -1.50

Vb = 0 3.375 -0.26323 3.375

θb + 2.53 = -0.590585 + 2.531Vc = 0 3.38 0.26323 3.38

θc -2.53 -0.59395 -2.53

Vc = 0 0.5625 1.3125 0.5625θc + 0.31 = 2.81245 + 0.3125

Vd = 0 1.31 -1.3125 1.31θd= 0 -0.47 0.4688 -0.47

θc Vd θd0.00 0 0 Va = 0 20.00 0 0 θa = 0 1.500.30 0 0 Vb = 0 5.380.44 0 0 θb + 1.030.66 -0.77 0.96 Vc = 0 3.942.49 -0.96 0.80 θc -2.22-0.96 0.77 -0.96 Vd= 0 1.310.80 -0.96 1.60 θd = 0 -0.47

θa Vb Vc- - - θb 1.03- - - θc -2.22- - - Vd 1.31- - - θd + -0.47- - - Va 2.00- - - Vb θa 1.50- - - Vc Vb 5.38- - - Vd Vc 3.94

0.44 0.00 0.00 -12.49 -0.96 0.80-0.96 0.77 -0.960.80 -0.96 1.60

-0.31.275

6.31253.775

-4.40E-01 2.00x -4.48E-01 + 1.50

-6.49E+00 5.38 =-3.38E+00 3.94

R(AB) 1.83= M(AB) 1.28

R(BA) 2.17M(BA) -1.94

R(BC) 3.11

= M(BC) 1.94R(CB) 3.64M(CB) -3.12

R(CD) 1.87= M(CD) 3.12

R(DC) 0.00M(DC) 0.00


AB 1.00 3.5 0.28 0.49 1.14 0.57

BC 1.00 3 0.44 0.67 1.33 0.67

CD 1.00 4 0.19 0.38 1.00 0.50





R(AB) 0.28 0.49 -0.28 0.49 0.000

M(AB) = 0.49 1.14 -0.49 0.57 0.00R(BA) -0.28 -0.49 0.28 -0.49 0.00

M(BA) 0.49 0.57 -0.49 1.14 -1.05E+00

Vb θb Vc θcR(BC) 0.44 0.67 -0.44 0.67 0

M(BC) = 0.67 1.33 -0.67 0.67 -1.05E+00R(CB) -0.44 -0.67 0.44 -0.67 -5.93E+00M(CB) 0.67 0.67 -0.67 1.33 -9.82E-01

Vc θc Vd θdR(CD) 0.19 0.38 -0.19 0.38 -5.93E+00M(CD) = 0.38 1.00 -0.38 0.50 -9.82E-01R(DC) -0.19 -0.38 0.19 -0.38 0.00E+00M(DC) 0.38 0.50 -0.38 1.00 0.00E+00


Ra 0.28 0.49 -0.28 0.49 0Ma 0.49 1.14 -0.49 0.57 0

Rb = 0 = -0.28 -0.49 0.72 0.18 -0.44Mb = 0 0.49 0.57 0.18 2.48 -0.67

Rc 0 0 -0.44 -0.67 0.63Mc = 0 0 0 0.67 0.67 -0.29Rd = 0 0 0 0 0.00 -0.19Md=0 0 0 0 0.00 0.38

ORDENANDO MATRIZ GLOBAL:θb Vc θc Va θa

Mb = 0 2.48 -0.67 0.67Rc = 0 -0.67 0.63 -0.29Mc = 0 0.67 -0.29 2.33

Ra = 0.49 0.00 0.00Ma 0.57 0.00 0.00Rb 0.18 -0.44 0.67Rd 0.00 -0.19 -0.38Md 0.00 0.38 0.50

Mb = 0 0 -0.70 2.48Rc = 0 0 2.76 -0.67Mc = 0 = 0 - 1.26 x 0.67

Mb = 0 0.70 0.583333333 0.571428571 -0.0952381Rc = 0 -2.76 0.571428571 2.239067055 0.116618076Mc = 0 = -1.26 x -0.0952381 0.116618076 0.470359572

Mb = 0 = -1.050E+00Rc = 0 -5.93E+00Mc = 0 -9.82E-01

Ra 0.49 0.00 0.00Ma = 0.57 0.00 0.00 x Rb 0.18 -0.44 0.67Rd 0.00 -0.19 -0.38Md 0.00 0.38 0.50

Ra #VALUE! 1.75Ma = #VALUE! + 1.02Rb #VALUE! 3.14Rd #VALUE! 0.85Md #VALUE! -0.33

Ra 1.24Ma = #VALUE!Rb #VALUE!Rd 2.33Md -3.04

8.50

1.75 KN1.75 KN

1.39 KN0.61 KN

2.1485 KN0.8515 KN

Va = 0 1.75 -0.51412245 1.75θa = 0 + 1.02 = -0.59980952 + 1.020833333Vb = 0 1.75 0.514122449 1.75

θb -1.02 -1.19961905 -1.02

Vb = 0 1.386666667 1.28137415 1.386666667

θb + 0.32 = 1.899619048 + 0.32Vc = 0 0.61 -1.28137415 0.61

θc -0.16 1.944503401 -0.16

Vc = 0 2.1485 -1.48045918 2.1485θc + 1.42 = -3.2065034 + 1.422

Vd = 0 0.85 1.480459184 0.85θd= 0 -0.33 -2.71533333 -0.33

θc Vd θd0.00 0 0 Va 1.750.00 0 0 θa 1.020.67 0 0 Vb 3.140.67 0 0 θb = 0 + -0.70-0.29 -0.19 0.38 Vc = 0 2.762.33 -0.38 0.50 θc = 0 1.26-0.38 0.19 -0.38 Vd 0.850.50 -0.38 1.00 θd -0.33

Vb Vd θdθb -0.70Vc 2.76θc 1.26Va + 1.75θa 1.02

Vb Vb 3.14Vc Vd 0.85Vd θd -0.33

-0.67 0.67 -10.63 -0.29-0.29 2.33

-1.05E+00 1.75-5.93E+00 + 1.02-9.82E-01 3.14 =

0.85-0.33

R(AB) 1.24= M(AB) 0.42

R(BA) 2.26M(BA) -2.22

R(BC) 2.67

= M(BC) 2.22R(CB) -0.67M(CB) 1.78

R(CD) 0.67= M(CD) -1.78

R(DC) 2.33M(DC) -3.04


AB 1.00 2 1.50 1.50 2.00

BC 1.00 3.5 0.28 0.49 1.14

CD 1.00 5 0.10 0.24 0.80

DE 1.00 2.5 0.77 0.96 1.60




Me-d = 2.50 KN-m Re-dMd-e = -1.67 KN-m Rd-e


R(AB) 1.50 1.50 -1.50 1.50

M(AB) = 1.50 2.00 -1.50 1.00R(BA) -1.50 -1.50 1.50 -1.50

M(BA) 1.50 1.00 -1.50 2.00

Vb θb Vc θcR(BC) 0.28 0.49 -0.28 0.49

M(BC) = 0.49 1.14 -0.49 0.57R(CB) -0.28 -0.49 0.28 -0.49

M(CB) 0.49 0.57 -0.49 1.14

Vc θc Vd θdR(CD) 0.10 0.24 -0.10 0.24

M(CD) = 0.24 0.80 -0.24 0.40R(DC) -0.10 -0.24 0.10 -0.24

M(DC) 0.24 0.40 -0.24 0.80

Vd θd Ve θeR(DE) 0.77 0.96 -0.77 0.96

M(DE) = 0.96 1.60 -0.96 0.80R(ED) -0.77 -0.96 0.77 -0.96M(ED) 0.96 0.80 -0.96 1.60


Ra=0 1.50 1.50 -1.50 1.50Ma=0 1.50 2.00 -1.50 1.00

Rb = -1.50 -1.50 1.78 -1.01Mb =0 1.50 1.00 -1.01 3.14

Rc 0 0 -0.28 -0.49Mc =0 0 0 0.49 0.57

Rd 0 0 0 0.00Md=0 0 0 0 0.00

RE=0 0 0 0 0.00Me=0 0 0 0 0.00


Ra=0 1.50 1.50 1.50 0.00Ma=0 1.50 2.00 1.00 0.00Mb =0 1.50 1.00 3.14 0.57Mc =0 = 0.00 0.00 0.57 1.94Md=0 0.00 0.00 0.00 0.40RE=0 0.00 0.00 0.00 0.00Me=0 0.00 0.00 0.00 0.00

Rb -1.50 -1.50 -1.01 0.49Rc 0.00 0.00 -0.49 -0.25Rd 0.00 0.00 0.00 -0.24

Ra=0 0.00 0.55Ma=0 0.00 0.20Mb =0 0.00 0.35Mc =0 = 0.00 - 0.44 xMd=0 0.00 1.94RE=0 0.00 0.75Me=0 0.00 -1.67

Ra=0 -0.55 6.85 -4.09Ma=0 -0.20 -4.09 3.05Mb =0 -0.35 -2.09 1.05Mc =0 = -0.44 x 0.69 -0.34Md=0 -1.94 -0.34 0.17RE=0 -0.75 -0.86 0.43Me=0 1.67 -0.34 0.17

Ra=0 -1.78382353Ma=0 1.058578431Mb =0 0.358578431Mc =0 = 0.245343137Md=0 -2.80392157RE=0 -5.70Me=0 -0.97

Rb -1.50 -1.50 -1.01 0.49Rc = 0.00 0.00 -0.49 -0.25Rd 0.00 0.00 0.00 -0.24

Rb 0.85 2.06Rc = -0.91 + 6.00Rd 1.36 2.07

Rb 2.91Rc = 5.09Rd 3.43

2EI/L

1.00

0.57

0.40

0.80

= 0.55 KN1.05 KN

= 1.01 KN= 2.4 KN

= 2.2 KN= 0.4 KN

= 1.67 KN0.75 KN

-1.78 Va = 0 0.55 -0.551.06 θa = 0 + 0.20 = -0.2 +0.00 Vb = 0 1.05 0.55

3.59E-01 θb -0.30 -0.9

0 Vb = 0 1.01 0.2957983193.59E-01 θb + 0.65 = 0.55 +

0 Vc = 0 2.40 -0.295798322.45E-01 θc -1.20 0.485294118

0 Vc = 0 2.2 -0.614058822.45E-01 θc + 1.64 = -0.92529412 +

0 Vd = 0 0.40 0.614058824-2.80E+00 θd= 0 -0.56 -2.145

0 Vd= 1 1.67 0.75-2.80E+00 θd + 2.50 = 0.205 +

-5.70 Ve= 1 0.75 -0.75-9.73E-01 θe= 1 -1.67 1.67

Vc θc Vd θd Ve θe0 0.00 0 0 0 00 0.00 0 0 0 0

-0.28 0.49 0 0 0 0-0.49 0.57 0 0 0 00.38 -0.25 -0.10 0.24 0 0-0.25 1.94 -0.24 0.40 0 0-0.10 -0.24 0.86 0.72 -0.77 0.960.24 0.40 0.72 2.40 -0.96 0.80

0.00 0.00 -0.77 -0.96 0.77 -0.960.00 0.00 0.96 0.80 -0.96 1.60

θd Ve θe Vb Vc Vd0 0 0

0.00 0 00.00 0 00.40 0 02.40 -0.96 0.80-0.96 0.77 -0.960.80 -0.96 1.600.00 0 00.24 0 00.72 -0.77 0.96

1.50 1.50 1.50 0.00 0.00 0.00 0.001.50 2.00 1.00 0.00 0.00 0.00 0.001.50 1.00 3.14 0.57 0.00 0.00 0.000.00 0.00 0.57 1.94 0.40 0.00 0.000.00 0.00 0.00 0.40 2.40 -0.96 0.800.00 0.00 0.00 0.00 -0.96 0.77 -0.960.00 0.00 0.00 0.00 0.80 -0.96 1.60

-2.09 0.69 -0.34 -0.86 -0.341.05 -0.34 0.17 0.43 0.171.05 -0.34 0.17 0.43 0.17-0.34 0.69 -0.34 -0.86 -0.340.17 -0.34 1.42 3.55 1.420.43 -0.86 3.55 14.09 6.680.17 -0.34 1.42 6.68 3.92

0.00 0.00 0.00 -1.78 2.060.24 0.00 0.00 x 1.06 + 6.000.72 -0.77 0.96 0.36 2.07

0.25-2.80-5.70-0.97

0.55 R(AB) 0.000.20 = M(AB) 0.001.05 R(BA) 1.60-0.30 M(BA) -1.20

1.01 R(BC) 1.310.65 = M(BC) 1.202.40 R(CB) 2.10-1.20 M(CB) -0.71

2.2 R(CD) 1.901.64 = M(CD) 0.710.40 R(DC) 1.01-0.56 M(DC) -2.70

1.67 R(CD) 2.422.50 = M(CD) 2.700.75 R(DC) 0.00-1.67 M(DC) 0.00

Va 0.55θa 0.20Vb 2.06θb + 0.35Vc 6.00θc 0.44Vd 2.07θd 1.94

Ve 0.75θe -1.67

Va 0.55θa 0.20θb 0.35θc + 0.44θd 1.94Ve 0.75θe -1.67Vb 2.06Vc 6.00Vd 2.07

-1


AB 1.00 4 0.19 0.38 1.00 0.50

BC 1.00 5 0.10 0.24 0.80 0.40

CD 1.00 3 0.44 0.67 1.33 0.67





R(AB) 0.19 0.38 -0.19 0.38 0.000

M(AB) = 0.38 1.00 -0.38 0.50 0.00R(BA) -0.19 -0.38 0.19 -0.38 0.00

M(BA) 0.38 0.50 -0.38 1.00 4.69E+00

Vb θb Vc θcR(BC) 0.10 0.24 -0.10 0.24 0

M(BC) = 0.24 0.80 -0.24 0.40 4.69E+00R(CB) -0.10 -0.24 0.10 -0.24 -1.63E+01M(CB) 0.24 0.40 -0.24 0.80 -5.80E+01

Vc θc Vd θdR(CD) 0.44 0.67 -0.44 0.67 -1.63E+01M(CD) = 0.67 1.33 -0.67 0.67 -5.80E+01R(DC) -0.44 -0.67 0.44 -0.67 0.00E+00M(DC) 0.67 0.67 -0.67 1.33 0.00E+00


Ra 0.19 0.38 -0.19 0.38 0Ma 0.38 1.00 -0.38 0.50 0

Rb = 0 = -0.19 -0.38 0.28 -0.14 -0.10Mb = 0 0.38 0.50 -0.14 1.80 -0.24

Rc 0 0 -0.10 -0.24 0.54Mc = 0 0 0 0.24 0.40 0.43Rd = 0 0 0 0 0.00 -0.44Md=0 0 0 0 0.00 0.67


Mb = 0 1.80 0.40 0.00 0.00Mc = 0 0.40 2.13 -0.67 0.67Rd = 0 0.00 -0.67 0.44 -0.67Md = 0 = 0.00 0.67 -0.67 1.33

Ra 0.38 0.00 0.00 0.00Ma 0.50 0.00 0.00 0.00Rb -0.14 0.24 0.00 0.00Rc -0.24 0.43 -0.44 0.67

Mb = 0 0 -1.92 1.80Mc = 0 0 11.18 0.40Rd = 0 = 0 - -2.00 x 0.00Md = 0 0 6.00 0.00

Mb = 0 1.92 0.625 -0.3125 -0.9375Mc = 0 -11.18 -0.3125 1.40625 4.21875Rd = 0 = 2.00 x -0.9375 4.21875 21.65625Md = 0 -6.00 -0.3125 1.40625 8.71875

Mb = 0 = 4.694E+00Mc = 0 -1.63E+01Rd = 0 -5.80E+01Md = 0 -2.53E+01

Ra 0.38 0.00 0.00 0.00Ma = 0.50 0.00 0.00 0.00 x Rb -0.14 0.24 0.00 0.00Rc -0.24 0.43 -0.44 0.67

Ra 1.76015625 6.00Ma = 2.346875 + 4.00Rb -4.55090625 12.81Rc 0.79075 3.35

Ra 7.76Ma = 6.35Rb 8.26Rc 4.14

6 KN6 KN

6.81 KN4.37 KN

6.81 KN3.35 KN

Va = 0 6 1.76015625 6θa = 0 + 4.00 = 2.346875 + 4Vb = 0 6.00 -1.76015625 6.00

θb -4.00 4.69375 -4.00

Vb = 0 6.81 -11.21835 6.81

θb + 2.08 = -15.514 + 2.08Vc = 0 4.37 11.21835 4.37

θc -3.13 -40.57775 -3.13

Vc = 0 6.81 -45.8979167 6.81θc + 1.13 = -88.16875 + 1.13

Vd = 0 3.35 45.89791667 3.35θd= 0 -0.75 -49.525 -0.75

θc Vd θd0.00 0 0 Va 60.00 0 0 θa 4.000.24 0 0 Vb 12.810.40 0 0 θb = 0 + -1.920.43 -0.44 0.67 Vc = 0 11.182.13 -0.67 0.67 θc = 0 -2.00-0.67 0.44 -0.67 Vd 3.350.67 -0.67 1.33 θd -0.75

θa Vb Vcθb -1.92θc 11.18Vd -2.00θd + 6.00Va 4.00

Vb θa 12.81Vc Vb 3.35Vd Vc -0.75

0.40 0.00 0.002.13 -0.67 0.67-0.67 0.44 -0.670.67 -0.67 1.33

-0.31251.406258.718754.40625

4.69E+00 6.00-1.63E+01 + 4.00-5.80E+01 12.81-2.53E+01 3.35

R(AB) 7.76= M(AB) 6.35

R(BA) 4.24M(BA) 0.69

R(BC) -4.41

= M(BC) -13.43R(CB) 15.59M(CB) -43.71

R(CD) -39.09= M(CD) -87.04

R(DC) 49.25M(DC) -50.27


AB 1.00 4.5 0.13 0.30 0.89 0.44

BC 1.00 5 0.10 0.24 0.80 0.40

CD 1.00 4 0.19 0.38 1.00 0.50





R(AB) 0.13 0.30 -0.13 0.30 0.000

M(AB) = 0.30 0.89 -0.30 0.44 0.00R(BA) -0.13 -0.30 0.13 -0.30 0.00

M(BA) 0.30 0.44 -0.30 0.89 9.36E-01

Vb θb Vc θcR(BC) 0.10 0.24 -0.10 0.24 0

M(BC) = 0.24 0.80 -0.24 0.40 9.36E-01R(CB) -0.10 -0.24 0.10 -0.24 -3.13E+00M(CB) 0.24 0.40 -0.24 0.80 1.18E+00

Vc θc Vd θdR(CD) 0.19 0.38 -0.19 0.38 -3.13E+00M(CD) = 0.38 1.00 -0.38 0.50 1.18E+00R(DC) -0.19 -0.38 0.19 -0.38 0.00E+00M(DC) 0.38 0.50 -0.38 1.00 0.00E+00


Ra 0.13 0.30 -0.13 0.30 0Ma 0.30 0.89 -0.30 0.44 0Rb = -0.13 -0.30 0.23 -0.06 -0.10Mb 0.30 0.44 -0.06 1.69 -0.24Rc 0 0 -0.10 -0.24 0.28

Mc 0 0 0.24 0.40 0.14Rd 0 0 0 0.00 -0.19Md 0 0 0 0.00 0.38

ORDENANDO MATRIZ GLOBAL:θa θb θc Va Vb

Ma = 0 0.89 0.44 0.00Mb = 0 0.44 1.69 0.40Mc = 0 0.00 0.40 1.80

Ra = 0.30 0.30 0.00Rb -0.30 -0.06 0.24Rc 0.00 -0.24 0.14Rd 0.00 0.00 -0.38Md 0.00 0.00 0.50

Ma = 0 0 0.56 0.89Mb = 0 0 4.40 0.44Mc = 0 = 0 - -0.88 x 0.00

Ma = 0 -0.56 1.306451613 -0.36290323 0.080645161Mb = 0 -4.40 -0.36290323 0.725806452 -0.16129032Mc = 0 = 0.88 x 0.080645161 -0.16129032 0.591397849

Ma = 0 = 9.361E-01Mb = 0 -3.13E+00Mc = 0 1.18E+00

Ra 0.30 0.30 0.00Rb = -0.30 -0.06 0.24 x Rc 0.00 -0.24 0.14Rd 0.00 0.00 -0.38Md 0.00 0.00 0.50

Ra -0.6507049 1.24Rb = 0.18335006 + 1.01Rc 0.911709677 4.87Rd -0.44435484 0.90Md 0.592473118 -0.80

Ra 0.59Rb = 1.19Rc 5.78Rd 0.46Md -0.21

1.24 KN2.37 KN

2.5 KN2.5 KN

1.9 KN0.9 KN

Va = 0 1.24 0.277371565 1.24θa = 0 + 1.01 = 0.416057348 + 1.01Vb = 0 2.37 -0.27737157 2.37

θb -1.52 0.832114695 -1.52

Vb = 0 2.5 0.809754839 2.5

θb + 2.08 = 1.974623656 + 2.08Vc = 0 2.50 -0.80975484 2.50

θc -2.08 2.074150538 -2.08

Vc = 0 1.9 -0.14294355 1.9θc + 1.20 = 0.010349462 + 1.2

Vd = 0 0.90 0.142943548 0.90θd= 0 -0.80 -0.58212366 -0.80

θc Vd θd0.00 0 0 Va 1.240.00 0 0 θa 1.010.24 0 0 Vb 4.870.40 0 0 θb = 0 + 0.560.14 -0.19 0.38 Vc = 0 4.401.80 -0.38 0.50 θc = 0 -0.88-0.38 0.19 -0.38 Vd 0.900.50 -0.38 1.00 θd -0.80

Vc Vd θdθa 0.56θb 4.40θc -0.88Va + 1.24Vb 1.01

Vb Vc 4.87Vc Vd 0.90Vd θd -0.80

0.44 0.001.69 0.400.40 1.80

9.36E-01 1.24-3.13E+00 + 1.011.18E+00 4.87 =

0.90-0.80

R(AB) 1.52= M(AB) 1.43

R(BA) 2.09M(BA) -0.69

R(BC) 3.31

= M(BC) 4.05R(CB) 1.69M(CB) -0.01

R(CD) 1.76= M(CD) 1.21

R(DC) 1.04M(DC) -1.38


AB 1.00 5 0.10 0.24 0.80 0.40

BC 1.00 4 0.19 0.38 1.00 0.50

CD 1.00 6 0.06 0.17 0.67 0.33





R(AB) 0.10 0.24 -0.10 0.24 0.000

M(AB) = 0.24 0.80 -0.24 0.40 0.00R(BA) -0.10 -0.24 0.10 -0.24 0.00

M(BA) 0.24 0.40 -0.24 0.80 7.49E+00

Vb θb Vc θcR(BC) 0.19 0.38 -0.19 0.38 0

M(BC) = 0.38 1.00 -0.38 0.50 7.49E+00R(CB) -0.19 -0.38 0.19 -0.38 -2.35E+00M(CB) 0.38 0.50 -0.38 1.00 0.00E+00



Ra 0.10 0.24 -0.10 0.24 0Ma 0.24 0.80 -0.24 0.40 0Rb = -0.10 -0.24 0.28 0.14 -0.19Mb 0.24 0.40 0.14 1.80 -0.38Rc 0 0 -0.19 -0.38 0.24

Mc 0 0 0.38 0.50 -0.21Rd 0 0 0 0.00 -0.06Md 0 0 0 0.00 0.17


Mb = 0 0.14 0.38Mc = 0 -0.38 -0.21

Ra 0.24 0.00Ma = 0.40 0.00Rb 1.80 0.50Rc 0.50 1.67Rd 0.00 -0.17Md 0.00 0.33

Mb = 0 0 -0.13 0.14Mc = 0 0 2.32 -0.38

Mb = 0 0.13 -1.85185185 -3.33333333Mc = 0 -2.32 x 3.333333333 1.2

Mb = 0 = 7.493E+00Mc = 0 -2.35E+00

Ra 0.24 0.00Ma = 0.40 0.00 x Rb 1.80 0.50Rc 0.50 1.67Rd 0.00 -0.17Md 0.00 0.33

Ra 1.798222222 0.86Ma = 2.997037037 + 1.75Rb 12.31133333 1.02Rc -0.17148148 2.93Rd 0.391777778 1.05Md -0.78355556 -0.98

Ra 2.66Ma = 4.75Rb 13.33Rc 2.76Rd 1.44Md -1.76

1.75 KN1.75 KN

1.18 KN0.52 KN

1.8 KN1.05 KN

Va = 0 1.75 1.798222222 1.75θa = 0 + 1.02 = 2.997037037 + 1.02Vb = 0 1.75 -1.79822222 1.75

θb -1.02 5.994074074 -1.02

Vb = 0 1.18 3.250472222 1.18

θb + 0.89 = 8.374092593 + 0.89Vc = 0 0.52 -3.25047222 0.52

θc -0.44 4.627796296 -0.44

Vc = 0 1.8 -0.13059259 1.8θc + 1.30 = -0.39177778 + 1.3

Vd = 0 1.05 0.130592593 1.05θd= 0 -0.98 -0.39177778 -0.98


Vc Vd θdθa -0.13θb 2.32θc 0.86Va + 1.75Vb 1.02

Vb Vc 2.93Vc Vd 1.05Vd θd -0.98

0.38-0.21

7.49E+00 0.86-2.35E+00 + 1.75

1.02 =2.931.05-0.98

R(AB) 3.55= M(AB) 4.02

R(BA) -0.05M(BA) 4.97

R(BC) 4.43

= M(BC) 9.26R(CB) -2.73M(CB) 4.19

R(CD) 1.67= M(CD) 0.91

R(DC) 1.18M(DC) -1.37


AB 1.00 5 0.10 0.24 0.80 0.40

BC 1.00 4 0.19 0.38 1.00 0.50

CD 1.00 5 0.10 0.24 0.80 0.40





R(AB) 0.10 0.24 -0.10 0.24 0.000

M(AB) = 0.24 0.80 -0.24 0.40 0.00R(BA) -0.10 -0.24 0.10 -0.24 0.00

M(BA) 0.24 0.40 -0.24 0.80 9.90E-01

Vb θb Vc θcR(BC) 0.19 0.38 -0.19 0.38 0

M(BC) = 0.38 1.00 -0.38 0.50 9.90E-01R(CB) -0.19 -0.38 0.19 -0.38 -1.66E+00M(CB) 0.38 0.50 -0.38 1.00 5.27E-01

Vc θc Vd θdR(CD) 0.10 0.24 -0.10 0.24 -1.66E+00M(CD) = 0.24 0.80 -0.24 0.40 5.27E-01R(DC) -0.10 -0.24 0.10 -0.24 0.00E+00M(DC) 0.24 0.40 -0.24 0.80 0.00E+00


Ra 0.10 0.24 -0.10 0.24 0Ma 0.24 0.80 -0.24 0.40 0

Rb = 0 = -0.10 -0.24 0.28 0.14 -0.19Mb = 0 0.24 0.40 0.14 1.80 -0.38

Rc 0 0 -0.19 -0.38 0.28Mc = 0 0 0 0.38 0.50 -0.14Rd = 0 0 0 0 0.00 -0.10Md=0 0 0 0 0.00 0.24


Ma= 0 0.80 0.40 0.00 0.00Mb = 0 0.40 1.80 0.50 0.00Mc = 0 0.00 0.50 1.80 0.40Md = 0 = 0.00 0.00 0.40 0.80

Ra 0.24 0.24 0.00 0.00Rb -0.24 0.14 0.38 0.00Rc 0.00 -0.38 -0.14 0.24Rd 0.00 0.00 -0.24 -0.24

Ma= 0 0 -0.13 0.80Mb = 0 0 2.32 0.40Mc = 0 = 0 - 0.86 x 0.00Md = 0 0 1.75 0.00

Ma= 0 0.13 1.423160173 -0.34632035 0.108225108Mb = 0 -2.32 -0.34632035 0.692640693 -0.21645022Mc = 0 = -0.86 x 0.108225108 -0.21645022 0.692640693Md = 0 -1.75 -0.05411255 0.108225108 -0.34632035

Ma= 0 = 9.901E-01Mb = 0 -1.66E+00Mc = 0 5.27E-01Md = 0 -2.45E+00

Ra 0.24 0.24 0.00 0.00Rb = -0.24 0.14 0.38 0.00 x Rc 0.00 -0.38 -0.14 0.24Rd 0.00 0.00 -0.24 -0.24

Ra -0.15962338 1.75Rb = -0.26359091 + 1.02Rc -0.03859091 2.93Rd 0.461805195 1.05

Ra 1.59Rb = 0.76Rc 2.89Rd 1.51

1.75 KN1.75 KN

1.18 KN0.52 KN

1.8 KN1.05 KN

Va = 0 1.75 0.237623377 1.75θa = 0 + 1.02 = 0.396038961 + 1.02Vb = 0 1.75 -0.23762338 1.75

θb -1.02 0.792077922 -1.02

Vb = 0 1.18 0.879119318 1.18

θb + 0.89 = 1.874107143 + 0.89Vc = 0 0.52 -0.87911932 0.52

θc -0.44 1.64237013 -0.44

Vc = 0 1.8 -0.03250909 1.8θc + 1.30 = 0.024051948 + 1.3

Vd = 0 1.05 0.032509091 1.05θd= 0 -0.98 -0.1865974 -0.98


Vb Vc Vdθa -0.13θb 2.32θc 0.86θd + 1.75Va 1.02

Vb Vb 2.93Vc Vc 1.05Vd Vd -0.98

0.40 0.00 0.001.80 0.50 0.000.50 1.80 0.400.00 0.40 0.80

-0.054112550.108225108-0.346320351.423160173

9.90E-01 1.75-1.66E+00 + 1.025.27E-01 2.93 =

-2.45E+00 1.05

R(AB) 1.99= M(AB) 1.42

R(BA) 1.51M(BA) -0.23

R(BC) 2.06

= M(BC) 2.76R(CB) -0.36M(CB) 1.20

R(CD) 1.77= M(CD) 1.32

R(DC) 1.08M(DC) -1.17


AB 1.00 2.1 1.30 1.36 1.90

BC 1.00 5 0.10 0.24 0.80

CD 1.00 5 0.10 0.24 0.80

DE 1.00 3 0.44 0.67 1.33




Me-d = 0.45 KN-m Rd-eMd-e = -0.68 KN-m Re-d


R(AB) 1.30 1.36 -1.30 1.36

M(AB) = 1.36 1.90 -1.36 0.95R(BA) -1.30 -1.36 1.30 -1.36

M(BA) 1.36 0.95 -1.36 1.90

Vb θb Vc θcR(BC) 0.10 0.24 -0.10 0.24

M(BC) = 0.24 0.80 -0.24 0.40R(CB) -0.10 -0.24 0.10 -0.24

M(CB) 0.24 0.40 -0.24 0.80

Vc θc Vd θdR(CD) 0.10 0.24 -0.10 0.24

M(CD) = 0.24 0.80 -0.24 0.40R(DC) -0.10 -0.24 0.10 -0.24

M(DC) 0.24 0.40 -0.24 0.80

Vd θd Ve θeR(DE) 0.44 0.67 -0.44 0.67

M(DE) = 0.67 1.33 -0.67 0.67R(ED) -0.44 -0.67 0.44 -0.67M(ED) 0.67 0.67 -0.67 1.33


Ra=0 1.30 1.36 -1.30 1.36Ma=0 1.36 1.90 -1.36 0.95

Rb = -1.30 -1.36 1.39 -1.12Mb =0 1.36 0.95 -1.12 2.70

Rc 0 0 -0.10 -0.24Mc =0 0 0 0.24 0.40

Rd 0 0 0 0.00Md=0 0 0 0 0.00

RE=0 0 0 0 0.00Me=0 0 0 0 0.00


Ra=0 1.30 1.36 1.36 0.00Ma=0 1.36 1.90 0.95 0.00Mb =0 1.36 0.95 2.70 0.40Mc =0 = 0.00 0.00 0.40 1.60Md=0 0.00 0.00 0.00 0.40RE=0 0.00 0.00 0.00 0.00Me=0 0.00 0.00 0.00 0.00

Rb -1.30 -1.36 -1.12 0.24Rc 0.00 0.00 -0.24 0.00Rd 0.00 0.00 0.00 -0.24

Ra=0 0.00 0.99Ma=0 0.00 0.33Mb =0 0.00 2.21Mc =0 = 0.00 - 0.00 xMd=0 0.00 -1.98RE=0 0.00 1.58Me=0 0.00 -0.68

Ra=0 -0.99 9.52 -5.27Ma=0 -0.33 -5.27 3.56Mb =0 -2.21 -3.06 1.46Mc =0 = 0.00 x 0.88 -0.42Md=0 1.98 -0.44 0.21RE=0 -1.58 -1.31 0.63Me=0 0.68 -0.44 0.21

Ra=0 -0.0110425Ma=0 0.386408333Mb =0 -1.10354167Mc =0 = 1.054583333Md=0 -3.11479167RE=0 -20.48Me=0 -8.18

Rb -1.30 -1.36 -1.12 0.24Rc = 0.00 0.00 -0.24 0.00Rd 0.00 0.00 0.00 -0.24

Rb 0.98 2.64Rc = -0.48 + 5.60Rd 2.07 3.03

Rb 3.62Rc = 5.11Rd 5.10

13.83

2EI/L

0.95

0.40

0.40

0.67

= 0.99 KN0.585 KN

= 2.052 KN= 2.948 KN

= 2.648 KN= 2.352 KN

= 0.675 KN1.575 KN

-0.01 Va = 0 0.99 -0.99 0.99 R(AB)0.39 θa = 0 + 0.33 = -0.33 + 0.33 = M(AB)0.00 Vb = 0 0.59 0.99 0.59 R(BA)

-1.10E+00 θb -0.22 -1.749 -0.22 M(BA)

0 Vb = 0 2.052 -0.01175 2.052 R(BC)

-1.10E+00 θb + 2.43 = -0.461 + 2.43 = M(BC)0 Vc = 0 2.95 0.01175 2.95 R(CB)

1.05E+00 θc -2.67 0.40225 -2.67 M(CB)

0 Vc = 0 2.648 -0.49445 2.648 R(CD)

1.05E+00 θc + 2.67 = -0.40225 + 2.67 = M(CD)0 Vd = 0 2.35 0.49445 2.35 R(DC)

-3.11E+00 θd= 0 -2.43 -2.07 -2.43 M(DC)

0 Vd= 1 0.675 1.575 0.675 R(CD)

-3.11E+00 θd + 0.45 = 4.05 + 0.45 = M(CD)-20.48 Ve= 1 1.58 -1.575 1.58 R(DC)

-8.18E+00 θe= 1 -0.68 0.675 -0.68 M(DC)

Vc θc Vd θd Ve θe0 0.00 0 0 0 0 Va 0.990 0.00 0 0 0 0 θa 0.33

-0.10 0.24 0 0 0 0 Vb 2.64-0.24 0.40 0 0 0 0 θb + 2.210.19 0.00 -0.10 0.24 0 0 Vc 5.600.00 1.60 -0.24 0.40 0 0 θc 0.00-0.10 -0.24 0.54 0.43 -0.44 0.67 Vd 3.030.24 0.40 0.43 2.13 -0.67 0.67 θd -1.98

0.00 0.00 -0.44 -0.67 0.44 -0.67 Ve 1.580.00 0.00 0.67 0.67 -0.67 1.33 θe -0.68

θd Ve θe Vb Vc Vd0 0 0 Va 0.99

0.00 0 0 θa 0.330.00 0 0 θb 2.210.40 0 0 θc + 0.002.13 -0.67 0.67 θd -1.98-0.67 0.44 -0.67 Ve 1.580.67 -0.67 1.33 θe -0.680.00 0 0 Vb 2.640.24 0 0 Vc 5.600.43 -0.44 0.67 Vd 3.03

1.30 1.36 1.36 0.00 0.00 0.00 0.00 -11.36 1.90 0.95 0.00 0.00 0.00 0.001.36 0.95 2.70 0.40 0.00 0.00 0.000.00 0.00 0.40 1.60 0.40 0.00 0.000.00 0.00 0.00 0.40 2.13 -0.67 0.670.00 0.00 0.00 0.00 -0.67 0.44 ###0.00 0.00 0.00 0.00 0.67 -0.67 1.33

-3.06 0.87 -0.44 -1.31 -0.441.46 -0.42 0.21 0.63 0.211.46 -0.42 0.21 0.63 0.21-0.42 0.83 -0.42 -1.25 -0.420.21 -0.42 1.46 4.38 1.460.63 -1.25 4.38 22.13 8.880.21 -0.42 1.46 8.88 4.46

0.00 0.00 0.00 -0.01 2.640.24 0.00 0.00 x 0.39 + 5.600.43 -0.44 0.67 -1.10 3.03

1.05-3.11###

-8.18

0.000.001.58-1.97

2.041.972.96-2.27

1.902.272.85-4.50

2.254.500.000.00


AB 1.00 5 0.10 0.24 0.80 0.40

BC 1.00 6 0.06 0.17 0.67 0.33

CD 1.00 3 0.44 0.67 1.33 0.67

Ma-b = 2.08 KN-m Ra-b = 2.5Mb-a = -2.08 KN-m Rb-a = 2.5

Mb-c = 2.67 KN-m Rb-c = 2Mc-b = -2.67 KN-m Rc-b = 2

Mc-d = 0.90 KN-m Rc-d = 2.1Md-c = -0.60 KN-m Rd-c = 2.4


R(AB) 0.10 0.24 -0.10 0.24 0.000 Va = 0

M(AB) = 0.24 0.80 -0.24 0.40 0.00 θa = 0R(BA) -0.10 -0.24 0.10 -0.24 0.00 Vb = 0

M(BA) 0.24 0.40 -0.24 0.80 1.40E+00 θb

Vb θb Vc θcR(BC) 0.06 0.17 -0.06 0.17 0 Vb = 0

M(BC) = 0.17 0.67 -0.17 0.33 1.40E+00 θbR(CB) -0.06 -0.17 0.06 -0.17 -7.95E+00 Vc = 0

M(CB) 0.17 0.33 -0.17 0.67 -4.27E+01 θc

Vc θc Vd θdR(CD) 0.44 0.67 -0.44 0.67 -7.95E+00 Vc = 0

M(CD) = 0.67 1.33 -0.67 0.67 -4.27E+01 θcR(DC) -0.44 -0.67 0.44 -0.67 0.00E+00 Vd = 0M(DC) 0.67 0.67 -0.67 1.33 0.00E+00 θd= 0

MATRIZ GLOBAL:Va θa Vb θb Vc θc

Ra 0.10 0.24 -0.10 0.24 0 0.00Ma 0.24 0.80 -0.24 0.40 0 0.00

Rb = 0 = -0.10 -0.24 0.15 -0.07 -0.06 0.17Mb = 0 0.24 0.40 -0.07 1.47 -0.17 0.33

Rc 0 0 -0.06 -0.17 0.50 0.50Mc = 0 0 0 0.17 0.33 0.50 2.00Rd = 0 0 0 0 0.00 -0.44 -0.67Md=0 0 0 0 0.00 0.67 0.67

ORDENANDO MATRIZ GLOBAL:θb θc Vd θd Va θa

Mb= 0 1.47 0.33 0.00 0.00Mc = 0 0.33 2.00 -0.67 0.67Rd = 0 0.00 -0.67 0.44 -0.67Md = 0 = 0.00 0.67 -0.67 1.33

Ra 0.24 0.00 0.00 0.00Ma 0.40 0.00 0.00 0.00Rb -0.07 0.17 0.00 0.00Rc -0.17 0.50 -0.44 0.67

Mb= 0 0 0.59 1.47 0.33Mc = 0 0 -1.77 0.33 2.00Rd = 0 = 0 - 2.40 x 0.00 -0.67Md = 0 0 -0.60 0.00 0.67

Mb= 0 -0.59 0.769230769 -0.38461538 -1.15384615 -0.38461538Mc = 0 1.77 -0.38461538 1.692307692 5.076923077 1.692307692Rd = 0 = -2.40 x -1.15384615 5.076923077 24.23076923 9.576923077Md = 0 0.60 -0.38461538 1.692307692 9.576923077 4.692307692

Mb= 0 = 1.404E+00Mc = 0 -7.95E+00Rd = 0 -4.27E+01Md = 0 -1.69E+01

Ra 0.24 0.00 0.00 0.00 1.40E+00Ma = 0.40 0.00 0.00 0.00 x -7.95E+00Rb -0.07 0.17 0.00 0.00 -4.27E+01Rc -0.17 0.50 -0.44 0.67 -1.69E+01

Ra 0.336923077 2.50Ma = 0.561538462 + 2.08Rb -1.4274359 4.50Rc 3.490512821 4.10

Ra 2.84Ma = 2.64Rb 3.07Rc 7.59

13.50

KNKN

KNKN

KNKN

2.5 0.336923077 2.5 R(AB)+ 2.08 = 0.561538462 + 2.08 = M(AB)

2.50 -0.33692308 2.50 R(BA)-2.08 1.123076923 -2.08 M(BA)

2 -6.44799145 2 R(BC)+ 2.67 = -11.9865385 + 2.67 = M(BC)

2.00 6.447991453 2.00 R(CB)-2.67 -26.7014103 -2.67 M(CB)

2.1 -32.025812 2.1 R(CD)+ 0.90 = -62.285641 + 0.9 = M(CD)

2.40 32.02581197 2.40 R(DC)-0.60 -33.7917949 -0.60 M(DC)

Vd θd0 0 Va 2.50 0 θa 2.080 0 Vb 4.500 0 θb = 0 + 0.59

-0.44 0.67 Vc = 0 4.10-0.67 0.67 θc = 0 -1.770.44 -0.67 Vd 2.40-0.67 1.33 θd -0.60

Vb Vcθa 0.59θb -1.77θc 2.40θd + -0.60Va 2.50

Vb Vb 2.08Vc Vc 4.50Vd Vd 4.10

0.00 0.00-0.67 0.670.44 -0.67-0.67 1.33

2.50+ 2.08

4.50 =4.10

2.842.642.16-0.96

-4.45-9.328.45

-29.37

-29.93-61.3934.43-34.39


AB 1.00 4 0.19 0.38 1.00 0.50

BC 1.00 6 0.06 0.17 0.67 0.33

CD 1.00 5 0.10 0.24 0.80 0.40





R(AB) 0.19 0.38 -0.19 0.38 0.000

M(AB) = 0.38 1.00 -0.38 0.50 0.00R(BA) -0.19 -0.38 0.19 -0.38 0.00

M(BA) 0.38 0.50 -0.38 1.00 8.58E-01

Vb θb Vc θcR(BC) 0.06 0.17 -0.06 0.17 0

M(BC) = 0.17 0.67 -0.17 0.33 8.58E-01R(CB) -0.06 -0.17 0.06 -0.17 -2.97E+00M(CB) 0.17 0.33 -0.17 0.67 2.66E+00



Ra 0.19 0.38 -0.19 0.38 0Ma 0.38 1.00 -0.38 0.50 0

Rb = 0 = -0.19 -0.38 0.24 -0.21 -0.06Mb = 0 0.38 0.50 -0.21 1.67 -0.17

Rc 0 0 -0.06 -0.17 0.15Mc = 0 0 0 0.17 0.33 0.07Rd = 0 0 0 0 0.00 -0.10Md=0 0 0 0 0.00 0.24


Ma= 0 1.00 0.50 0.00 0.00Mb = 0 0.50 1.67 0.33 0.00Mc = 0 0.00 0.33 1.47 0.40Md = 0 = 0.00 0.00 0.40 0.80

Ra 0.38 0.38 0.00 0.00Rb -0.38 -0.21 0.17 0.00Rc 0.00 -0.17 0.07 0.24Rd 0.00 0.00 -0.24 -0.24

Ma= 0 0 0.63 1.00Mb = 0 0 3.63 0.50Mc = 0 = 0 - -0.88 x 0.00Md = 0 0 3.00 0.00

Ma= 0 -0.63 1.188118812 -0.37623762 0.099009901Mb = 0 -3.63 -0.37623762 0.752475248 -0.1980198Mc = 0 = 0.88 x 0.099009901 -0.1980198 0.841584158Md = 0 -3.00 -0.04950495 0.099009901 -0.42079208

Ma= 0 = 8.583E-01Mb = 0 -2.97E+00Mc = 0 2.66E+00Md = 0 -5.08E+00

Ra 0.38 0.38 0.00 0.00Rb = -0.38 -0.21 0.17 0.00 x Rc 0.00 -0.17 0.07 0.24Rd 0.00 0.00 -0.24 -0.24

Ra -0.79061881 3.00Rb = 0.73879538 + 1.25Rc -0.5294934 4.25Rd 0.581316832 2.72

Ra 2.21Rb = 1.99Rc 3.72Rd 3.30

11.22

3 KN3 KN

1.25 KN1.25 KN

2.38 KN2.72 KN

Va = 0 3 0.321868812 3θa = 0 + 1.25 = 0.429158416 + 1.25Vb = 0 3.00 -0.32186881 3.00

θb -1.25 0.858316832 -1.25

Vb = 0 1.25 0.750481298 1.25

θb + 1.88 = 1.951881188 + 1.875Vc = 0 1.25 -0.7504813 1.25

θc -1.88 2.551006601 -1.88

Vc = 0 2.38 0.352569505 2.38θc + 1.00 = 1.412562376 + 1

Vd = 0 2.72 -0.3525695 2.72θd= 0 -1.20 0.350285149 -1.20

θc Vd θd0.00 0 0 Va 30.00 0 0 θa 1.250.17 0 0 Vb 4.250.33 0 0 θb = 0 + 0.630.07 -0.10 0.24 Vc = 0 3.631.47 -0.24 0.40 θc = 0 -0.88-0.24 0.10 -0.24 Vd 2.720.40 -0.24 0.80 θd -1.20

θa Vb Vcθa 0.63θb 3.63θc -0.88θd + 3.00Va 1.25

Vb Vb 4.25Vc Vc 2.72Vd Vd -1.20

0.50 0.00 0.001.67 0.33 0.000.33 1.47 0.400.00 0.40 0.80

-0.049504950.099009901-0.420792081.46039604

8.58E-01 3.00-2.97E+00 + 1.252.66E+00 4.25 =-5.08E+00 2.72

R(AB) 3.32= M(AB) 1.68

R(BA) 2.68M(BA) -0.39

R(BC) 2.00

= M(BC) 3.83R(CB) 0.50M(CB) 0.68

R(CD) 2.73= M(CD) 2.41

R(DC) 2.37M(DC) -0.85


AB 1.00 5 0.10 0.24 0.80 0.40

BC 1.00 5 0.10 0.24 0.80 0.40

CD 1.00 6 0.06 0.17 0.67 0.33





R(AB) 0.10 0.24 -0.10 0.24 0.000

M(AB) = 0.24 0.80 -0.24 0.40 0.00R(BA) -0.10 -0.24 0.10 -0.24 0.00

M(BA) 0.24 0.40 -0.24 0.80 9.50E+00

Vb θb Vc θcR(BC) 0.10 0.24 -0.10 0.24 0

M(BC) = 0.24 0.80 -0.24 0.40 9.50E+00R(CB) -0.10 -0.24 0.10 -0.24 5.42E-01M(CB) 0.24 0.40 -0.24 0.80 0.00E+00

Vc θc Vd θdR(CD) 0.06 0.17 -0.06 0.17 5.42E-01M(CD) = 0.17 0.67 -0.17 0.33 0.00E+00R(DC) -0.06 -0.17 0.06 -0.17 0.00E+00M(DC) 0.17 0.33 -0.17 0.67 0.00E+00


Ra 0.10 0.24 -0.10 0.24 0Ma 0.24 0.80 -0.24 0.40 0Rb = -0.10 -0.24 0.19 0.00 -0.10Mb 0.24 0.40 0.00 1.60 -0.24Rc 0 0 -0.10 -0.24 0.15

Mc 0 0 0.24 0.40 -0.07Rd 0 0 0 0.00 -0.06Md 0 0 0 0.00 0.17


Mb = 0 0.00 0.24Mc = 0 -0.24 -0.07

Ra 0.24 0.00Ma = 0.40 0.00Rb 1.60 0.40Rc 0.40 1.47Rd 0.00 -0.17Md 0.00 0.33

Mb = 0 0 -0.13 0.00Mc = 0 0 2.32 -0.24

Mb = 0 0.13 -1.27314815 -4.16666667Mc = 0 -2.32 x 4.166666667 0

Mb = 0 = 9.501E+00Mc = 0 5.42E-01

Ra 0.24 0.00Ma = 0.40 0.00 x Rb 1.60 0.40Rc 0.40 1.47Rd 0.00 -0.17Md 0.00 0.33

Ra 2.280277778 0.86Ma = 3.800462963 + 1.75Rb 15.41851852 1.02Rc 4.594907407 2.93Rd -0.09027778 1.05Md 0.180555556 -0.98

Ra 3.14Ma = 5.55Rb 16.44Rc 7.52Rd 0.96Md -0.80

1.75 KN1.75 KN

1.18 KN0.52 KN

1.8 KN1.05 KN

Va = 0 1.75 2.280277778 1.75θa = 0 + 1.02 = 3.800462963 + 1.02Vb = 0 1.75 -2.28027778 1.75

θb -1.02 7.600925926 -1.02

Vb = 0 1.18 2.228277778 1.18

θb + 0.89 = 7.470925926 + 0.89Vc = 0 0.52 -2.22827778 0.52

θc -0.44 3.670462963 -0.44

Vc = 0 1.8 0.030092593 1.8θc + 1.30 = 0.090277778 + 1.3

Vd = 0 1.05 -0.03009259 1.05θd= 0 -0.98 0.090277778 -0.98


Vc Vd θdθa -0.13θb 2.32θc 0.86Va + 1.75Vb 1.02

Vb Vc 2.93Vc Vd 1.05Vd θd -0.98

0.24-0.07

9.50E+00 0.865.42E-01 + 1.75

1.02 =2.931.05-0.98

R(AB) 4.03= M(AB) 4.82

R(BA) -0.53M(BA) 6.58

R(BC) 3.41

= M(BC) 8.36R(CB) -1.71M(CB) 3.23

R(CD) 1.83= M(CD) 1.39

R(DC) 1.02M(DC) -0.89


AB 1.00 5 0.10 0.24 0.80 0.40

BC 1.00 6 0.06 0.17 0.67 0.33

CD 1.00 3 0.44 0.67 1.33 0.67





R(AB) 0.10 0.24 -0.10 0.24 0.000

M(AB) = 0.24 0.80 -0.24 0.40 0.00R(BA) -0.10 -0.24 0.10 -0.24 0.00

M(BA) 0.24 0.40 -0.24 0.80 2.60E+00

Vb θb Vc θcR(BC) 0.06 0.17 -0.06 0.17 0

M(BC) = 0.17 0.67 -0.17 0.33 2.60E+00R(CB) -0.06 -0.17 0.06 -0.17 -9.19E+00M(CB) 0.17 0.33 -0.17 0.67 -3.36E+01



Ra 0.10 0.24 -0.10 0.24 0Ma 0.24 0.80 -0.24 0.40 0

Rb = 0 = -0.10 -0.24 0.15 -0.07 -0.06Mb = 0 0.24 0.40 -0.07 1.47 -0.17

Rc 0 0 -0.06 -0.17 0.50Mc = 0 0 0 0.17 0.33 0.50Rd = 0 0 0 0 0.00 -0.44Md=0 0 0 0 0.00 0.67


Mb = 0 1.47 0.33 0.00 0.00Mc = 0 0.33 2.00 -0.67 0.67Rd = 0 0.00 -0.67 0.44 -0.67Md = 0 = 0.00 0.67 -0.67 1.33

Ra 0.24 0.00 0.00 0.00Ma 0.40 0.00 0.00 0.00Rb -0.07 0.17 0.00 0.00Rc -0.17 0.50 -0.44 0.67

Mb = 0 0 -0.75 1.47Mc = 0 0 4.50 0.33Rd = 0 = 0 - -0.58 x 0.00Md = 0 0 2.50 0.00

Mb = 0 0.75 0.769230769 -0.38461538 -1.15384615Mc = 0 -4.50 -0.38461538 1.692307692 5.076923077Rd = 0 = 0.58 x -1.15384615 5.076923077 24.23076923Md = 0 -2.50 -0.38461538 1.692307692 9.576923077

Mb = 0 = 2.600E+00Mc = 0 -9.19E+00Rd = 0 -3.36E+01Md = 0 -1.41E+01

Ra 0.24 0.00 0.00 0.00Ma = 0.40 0.00 0.00 0.00 x Rb -0.07 0.17 0.00 0.00Rc -0.17 0.50 -0.44 0.67

Ra 0.624 2.50Ma = 1.04 + 2.08Rb -1.72233333 5.50Rc 0.518333333 1.50

Ra 3.12Ma = 3.12Rb 3.78Rc 2.02

2.5 KN2.5 KN

3 KN3 KN

1.5 KN1.5 KN

Va = 0 2.5 0.624 2.5θa = 0 + 2.08 = 1.04 + 2.08Vb = 0 2.50 -0.624 2.50

θb -2.08 2.08 -2.08

Vb = 0 3 -4.65611111 3

θb + 1.33 = -7.935 + 1.33Vc = 0 3.00 4.656111111 3.00

θc -1.33 -20.0016667 -1.33

Vc = 0 1.5 -26.4844444 1.5θc + 0.75 = -50.9266667 + 0.75

Vd = 0 1.50 26.48444444 1.50θd= 0 -0.75 -28.5266667 -0.75

θc Vd θd0.00 0 0 Va 2.50.00 0 0 θa 2.080.17 0 0 Vb 5.500.33 0 0 θb = 0 + -0.750.50 -0.44 0.67 Vc = 0 4.502.00 -0.67 0.67 θc = 0 -0.58-0.67 0.44 -0.67 Vd 1.500.67 -0.67 1.33 θd -0.75

θa Vb Vcθb -0.75θc 4.50Vd -0.58θd + 2.50Va 2.08

Vb θa 5.50Vc Vb 1.50Vd Vc -0.75

0.33 0.00 0.002.00 -0.67 0.67-0.67 0.44 -0.670.67 -0.67 1.33

-0.384615381.6923076929.5769230774.692307692

2.60E+00 2.50-9.19E+00 + 2.08-3.36E+01 5.50 =-1.41E+01 1.50

R(AB) 3.12= M(AB) 3.12

R(BA) 1.88M(BA) 0.00

R(BC) -1.66

= M(BC) -6.61R(CB) 7.66M(CB) -21.33

R(CD) -24.98= M(CD) -50.18

R(DC) 27.98M(DC) -29.28


AB 1.00 3 0.44 0.67 1.33 0.67

BC 1.00 6 0.06 0.17 0.67 0.33

CD 1.00 5 0.10 0.24 0.80 0.40





R(AB) 0.44 0.67 -0.44 0.67 0.000

M(AB) = 0.67 1.33 -0.67 0.67 0.00R(BA) -0.44 -0.67 0.44 -0.67 0.00

M(BA) 0.67 0.67 -0.67 1.33 3.10E+00

Vb θb Vc θcR(BC) 0.06 0.17 -0.06 0.17 0

M(BC) = 0.17 0.67 -0.17 0.33 3.10E+00R(CB) -0.06 -0.17 0.06 -0.17 -2.21E+01M(CB) 0.17 0.33 -0.17 0.67 -1.83E+02



Ra 0.44 0.67 -0.44 0.67 0Ma 0.67 1.33 -0.67 0.67 0

Rb = 0 = -0.44 -0.67 0.50 -0.50 -0.06Mb = 0 0.67 0.67 -0.50 2.00 -0.17

Rc 0 0 -0.06 -0.17 0.15Mc = 0 0 0 0.17 0.33 0.07Rd = 0 0 0 0 0.00 -0.10Md=0 0 0 0 0.00 0.24

ORDENANDO MATRIZ GLOBAL:Va θa θb θc Vb

Ra = 0 2.00 0.33 0.00 0.00Ma = 0 0.33 1.47 -0.24 0.40Mb = 0 0.00 -0.24 0.10 -0.24Mc = 0 = 0.00 0.40 -0.24 0.80

Rb 0.67 0.00 0.00 0.00Rc 0.67 0.00 0.00 0.00Rd -0.50 0.17 0.00 0.00Md -0.17 0.07 -0.10 0.24

Ra = 0 0 1.17 2.00Ma = 0 0 6.44 0.33Mb = 0 = 0 - 0.85 x 0.00Mc = 0 0 3.00 0.00

Ra = 0 -1.17 0.545454545 -0.27272727 -1.36363636Ma = 0 -6.44 -0.27272727 1.636363636 8.181818182Mb = 0 = -0.85 x -1.36363636 8.181818182 82.57575758Mc = 0 -3.00 -0.27272727 1.636363636 20.68181818

Ra = 0 = 3.095E+00Ma = 0 -2.21E+01Mb = 0 -1.83E+02Mc = 0 -4.77E+01

Rb 0.67 0.00 0.00 0.00Rc = 0.67 0.00 0.00 0.00 x Rd -0.50 0.17 0.00 0.00Md -0.17 0.07 -0.10 0.24

Rb 2.063636364 3.00Rc = 2.063636364 + 1.50Rd -5.22818182 5.00Md 4.014545455 3.83

Rb 5.06Rc = 3.56Rd -0.23Md 7.84

3 KN3 KN

2 KN2 KN

4.44 KN3.83 KN

Va = 0 3 2.063636364 3θa = 0 + 1.50 = 2.063636364 + 1.5Vb = 0 3.00 -2.06363636 3.00

θb -1.50 4.127272727 -1.50

Vb = 0 2 -28.8123232 2

θb + 2.67 = -55.3660101 + 2.67Vc = 0 2.00 28.81232323 2.00

θc -2.67 -117.507929 -2.67

Vc = 0 4.44 -46.1192145 4.44θc + 3.52 = -151.964097 + 3.52

Vd = 0 3.83 46.11921455 3.83θd= 0 -4.24 -78.6319758 -4.24

θc Vd θd0.00 0 0 Va 30.00 0 0 θa 1.500.17 0 0 Vb 5.000.33 0 0 θb = 0 + 1.170.07 -0.10 0.24 Vc = 0 6.441.47 -0.24 0.40 θc = 0 0.85-0.24 0.10 -0.24 Vd 3.830.40 -0.24 0.80 θd -4.24

Vc Vd θdVa 1.17θa 6.44θb 0.85θc + 3.00Vb 1.50

Vb Vc 5.00Vc Vd 3.83Vd θd -4.24

0.33 0.00 0.001.47 -0.24 0.40-0.24 0.10 -0.240.40 -0.24 0.80

-0.272727271.63636363620.681818186.636363636

3.10E+00 3.00-2.21E+01 + 1.50-1.83E+02 5.00 =-4.77E+01 3.83

R(AB) 5.06= M(AB) 3.56

R(BA) 0.94M(BA) 2.63

R(BC) -26.81

= M(BC) -52.70R(CB) 30.81M(CB) -120.18

R(CD) -41.68= M(CD) -148.44

R(DC) 49.95M(DC) -82.87


AB 1.00 4 0.19 0.38 1.00 0.50

BC 1.00 4 0.19 0.38 1.00 0.50

CD 1.00 5 0.10 0.24 0.80 0.40





R(AB) 0.19 0.38 -0.19 0.38 0.000

M(AB) = 0.38 1.00 -0.38 0.50 0.00R(BA) -0.19 -0.38 0.19 -0.38 0.00

M(BA) 0.38 0.50 -0.38 1.00 2.44E+00

Vb θb Vc θcR(BC) 0.19 0.38 -0.19 0.38 0

M(BC) = 0.38 1.00 -0.38 0.50 2.44E+00R(CB) -0.19 -0.38 0.19 -0.38 -4.88E+00M(CB) 0.38 0.50 -0.38 1.00 1.09E+00



Ra 0.19 0.38 -0.19 0.38 0Ma 0.38 1.00 -0.38 0.50 0

Rb = 0 = -0.19 -0.38 0.38 0.00 -0.19Mb = 0 0.38 0.50 0.00 2.00 -0.38

Rc 0 0 -0.19 -0.38 0.28Mc = 0 0 0 0.38 0.50 -0.14Rd = 0 0 0 0 0.00 -0.10Md=0 0 0 0 0.00 0.24


Ma= 0 1.00 0.50 0.00 0.00Mb = 0 0.50 2.00 0.50 0.00Mc = 0 0.00 0.50 1.80 0.40Md = 0 = 0.00 0.00 0.40 0.80

Ra 0.38 0.38 0.00 0.00Rb -0.38 0.00 0.38 0.00Rc 0.00 -0.38 -0.14 0.24Rd 0.00 0.00 -0.24 -0.24

Ma= 0 0 0.00 1.00Mb = 0 0 8.00 0.50Mc = 0 = 0 - 2.20 x 0.00Md = 0 0 3.00 0.00

Ma= 0 0.00 1.156862745 -0.31372549 0.098039216Mb = 0 -8.00 -0.31372549 0.62745098 -0.19607843Mc = 0 = -2.20 x 0.098039216 -0.19607843 0.68627451Md = 0 -3.00 -0.04901961 0.098039216 -0.34313725

Ma= 0 = 2.441E+00Mb = 0 -4.88E+00Mc = 0 1.09E+00Md = 0 -4.29E+00

Ra 0.38 0.38 0.00 0.00Rb = -0.38 0.00 0.38 0.00 x Rc 0.00 -0.38 -0.14 0.24Rd 0.00 0.00 -0.24 -0.24

Ra -0.91544118 3.00Rb = -0.50735294 + 2.00Rc 0.653382353 6.00Rd 0.769411765 5.00

Ra 2.08Rb = 1.49Rc 6.65Rd 5.77

3 KN3 KN

3 KN3 KN

5 KN5 KN

Va = 0 3 0.915441176 3θa = 0 + 2.00 = 1.220588235 + 2Vb = 0 3.00 -0.91544118 3.00

θb -2.00 2.441176471 -2.00

Vb = 0 3 2.238970588 3

θb + 2.00 = 4.816176471 + 2Vc = 0 3.00 -2.23897059 3.00

θc -2.00 4.139705882 -2.00

Vc = 0 5 -0.20752941 5θc + 4.20 = -0.30117647 + 4.2

Vd = 0 5.00 0.207529412 5.00θd= 0 -4.20 -0.73647059 -4.20

θc Vd θd0.00 0 0 Va 30.00 0 0 θa 2.000.38 0 0 Vb 6.000.50 0 0 θb = 0 + 0.00-0.14 -0.10 0.24 Vc = 0 8.001.80 -0.24 0.40 θc = 0 2.20-0.24 0.10 -0.24 Vd 5.000.40 -0.24 0.80 θd -4.20

Vb Vc Vdθa 0.00θb 8.00θc 2.20θd + 3.00Va 2.00

Vb Vb 6.00Vc Vc 5.00Vd Vd -4.20

0.50 0.00 0.002.00 0.50 0.000.50 1.80 0.400.00 0.40 0.80

-0.049019610.098039216-0.343137251.421568627

2.44E+00 3.00-4.88E+00 + 2.001.09E+00 6.00 =-4.29E+00 5.00

R(AB) 3.92= M(AB) 3.22

R(BA) 2.08M(BA) 0.44

R(BC) 5.24

= M(BC) 6.82R(CB) 0.76M(CB) 2.14

R(CD) 4.79= M(CD) 3.90

R(DC) 5.21M(DC) -4.94


AB 1.00 3 0.44 0.67 1.33

BC 1.00 4 0.19 0.38 1.00

CD 1.00 5 0.10 0.24 0.80

DE 1.00 2 1.50 1.50 2.00

Ma-b = 0.00 KN-m Ra-bMb-a = 0.00 KN-m Rb-a



Me-d = 0.00 KN-m Re-dMd-e = 0.00 KN-m Rd-e


R(AB) 0.44 0.67 -0.44 0.67

M(AB) = 0.67 1.33 -0.67 0.67R(BA) -0.44 -0.67 0.44 -0.67

M(BA) 0.67 0.67 -0.67 1.33

Vb θb Vc θcR(BC) 0.19 0.38 -0.19 0.38

M(BC) = 0.38 1.00 -0.38 0.50R(CB) -0.19 -0.38 0.19 -0.38

M(CB) 0.38 0.50 -0.38 1.00

Vc θc Vd θdR(CD) 0.10 0.24 -0.10 0.24

M(CD) = 0.24 0.80 -0.24 0.40R(DC) -0.10 -0.24 0.10 -0.24

M(DC) 0.24 0.40 -0.24 0.80

Vd θd Ve θeR(DE) 1.50 1.50 -1.50 1.50

M(DE) = 1.50 2.00 -1.50 1.00R(ED) -1.50 -1.50 1.50 -1.50M(ED) 1.50 1.00 -1.50 2.00


Ra=0 0.44 0.67 -0.44 0.67Ma=0 0.67 1.33 -0.67 0.67

Rb = -0.44 -0.67 0.63 -0.29Mb =0 0.67 0.67 -0.29 2.33

Rc 0 0 -0.19 -0.38Mc =0 0 0 0.38 0.50

Rd 0 0 0 0.00Md=0 0 0 0 0.00RE=0 0 0 0 0.00Me=0 0 0 0 0.00


Ra=-2 0.44 0.67 0.67 0.00Ma=0 0.67 1.33 0.67 0.00Mb =0 0.67 0.67 2.33 0.50Mc =0 = 0.00 0.00 0.50 1.80Md=0 0.00 0.00 0.00 0.40RE=-2 0.00 0.00 0.00 0.00Me=0 0.00 0.00 0.00 0.00

Rb -0.44 -0.67 -0.29 0.38Rc 0.00 0.00 -0.38 -0.14Rd 0.00 0.00 0.00 -0.24

Ra=0 -2.00 0.00Ma=0 0.00 0.00Mb =0 0.00 2.33Mc =0 = 0.00 - 0.71 xMd=0 0.00 -3.52RE=0 -2.00 0.00Me=0 0.00 0.00

Ra=0 -2.00 19.67 -8.06Ma=0 0.00 -8.06 4.19Mb =0 -2.33 -3.56 1.19Mc =0 = -0.71 x 1.11 -0.37Md=0 3.52 -0.56 0.19RE=0 -2.00 -1.11 0.37Me=0 0.00 -0.56 0.19

Ra=0 -31.5611 -2.69E-03Ma=0 13.5204 1.15E-03Mb =0 4.5204 3.85E-04Mc =0 = -1.7074 -1.45E-04Md=0 0.2579 2.20E-05RE=0 -4.8176 -4.10E-04Me=0 -3.7421 -3.19E-04

Rb -0.44 -0.67 -0.29 0.38Rc = 0.00 0.00 -0.38 -0.14Rd 0.00 0.00 0.00 -0.24

Rb 3.05 3.00Rc = -1.40 + 6.20Rd 2.35 3.80

Rb 6.05Rc = 4.80Rd 6.14

17.00

2EI/L

0.67

0.50

0.40

1.00

= 0 KN0 KN

= 3 KN= 3 KN

= 3.204 KN= 3.796 KN

= 0 KN0 KN

-31.56 Va = 0 0 -213.52 θa = 0 + 0.00 = 0 +0.00 Vb = 0 0.00 2

4.52E+00 θb 0.00 -6

0 Vb = 0 3 1.0548611114.52E+00 θb + 2.33 = 3.666666667 +

0 Vc = 0 3.00 -1.05486111-1.71E+00 θc -2.33 0.552777778

0 Vc = 0 3.204 -0.34788889-1.71E+00 θc + 3.04 = -1.26277778 +

0 Vd = 0 3.80 0.3478888892.58E-01 θd= 0 -3.52 -0.47666667

0 Vd= 1 0 22.58E-01 θd + 0.00 = 4 +

-4.82 Ve= 1 0.00 -2-3.74E+00 θe= 1 0.00 0

Vc θc Vd θd Ve θe0 0.00 0 0 0 00 0.00 0 0 0 0

-0.19 0.38 0 0 0 0-0.38 0.50 0 0 0 00.28 -0.14 -0.10 0.24 0 0-0.14 1.80 -0.24 0.40 0 0

-0.10 -0.24 1.60 1.26 -1.50 1.500.24 0.40 1.26 2.80 -1.50 1.000.00 0.00 -1.50 -1.50 1.50 -1.500.00 0.00 1.50 1.00 -1.50 2.00

θd Ve θe Vb Vc Vd0 0 0

0.00 0 00.00 0 00.40 0 02.80 -1.50 1.00-1.50 1.50 -1.501.00 -1.50 2.000.00 0 00.24 0 01.26 -1.50 1.50

0.44 0.67 0.67 0.00 0.00 0.00 0.000.67 1.33 0.67 0.00 0.00 0.00 0.000.67 0.67 2.33 0.50 0.00 0.00 0.000.00 0.00 0.50 1.80 0.40 0.00 0.000.00 0.00 0.00 0.40 2.80 -1.50 1.000.00 0.00 0.00 0.00 -1.50 1.50 -1.500.00 0.00 0.00 0.00 1.00 -1.50 2.00

-3.56 1.11 -0.56 -1.11 -0.561.19 -0.37 0.19 0.37 0.191.19 -0.37 0.19 0.37 0.19-0.37 0.74 -0.37 -0.74 -0.370.19 -0.37 1.44 2.87 1.440.37 -0.74 2.87 8.41 4.870.19 -0.37 1.44 4.87 3.44

0.00 0.00 0.00 -31.56 3.000.24 0.00 0.00 x 13.52 + 6.201.26 -1.50 1.50 4.52 3.80

-1.710.26-4.82-3.74

0 R(AB) -2.000.00 = M(AB) 0.000.00 R(BA) 2.000.00 M(BA) -6.00

3 R(BC) 4.052.333333333 = M(BC) 6.00

3.00 R(CB) 1.95-2.33 M(CB) -1.78

3.204 R(CD) 1.903.043333333 = M(CD) 1.78

3.80 R(DC) 4.14-3.52 M(DC) -4.00

0 R(CD) 2.000.00 = M(CD) 4.000.00 R(DC) -2.000.00 M(DC) 0.00

Va 0θa 0.00Vb 3.00θb + 2.33Vc 6.20θc 0.71

Vd 3.80θd -3.52Ve 0.00θe 0.00

Va 0.00θa 0.00θb 2.33θc + 0.71θd -3.52Ve 0.00θe 0.00Vb 3.00Vc 6.20Vd 3.80

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EJERCICIOS VIGAS CONTINUAS

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