2 Practica

BARRA N SENTIDOINICIO FINAL

a b Barra 1a c Barra 2b c Barra 3a d Barra 4a e Barra 5b d Barra 6b f Barra 7c f Barra 8c d Barra 9d e Barra 10e f Barra 11f d Barra 12

Matriz de Continuidad

0 0 00 0 00 0 0

0.485 0.485 0.7280 0 0

a -0.640 0.426 0.6400 0 00 0.000 0.000

-0.137 -0.549 0.824-1.000 0.000 0.000

0 0 0-0.447 -0.894 0.000

Dx y z

Matriz de Rigidez

0.067 0 00 0.071 00 0 0.0710 0 00 0 0

k 0 0 00 0 00 0 00 0 00 0 00 0 00 0 0

Fuerzas Externas

0 D0

-2000 E000 F000 C00 A0 B

Clculo de la Matriz Global de Rigidez

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

at 0 0 00 0 00 0 00 0.52999894 -0.52999894

]= ] ] ][ [ ^ [ [

0 0.847998304 0.847998304-1 -0.52999894 01 0 0.52999894

0 0 00 0 00 0 00 0 0

at*k 0 0 00 0 00 0 00 0 00 0 00 0.0374531835 -0.03745318350 0.0599250936 0.0599250936

-0.0666666667 -0.037453184 00.0666666667 0 0.0374531835

0.44278485 0.12580870 -0.010906060.12580870 0.29810247 0.00644815

-0.01090606 0.00644815 0.13407424-0.33333333 0.00000000 0.000000000.00000000 0.00000000 0.000000000.00000000 0.00000000 0.00000000

K -0.05962848 -0.11925696 0.00000000-0.11925696 -0.23851392 0.000000000.00000000 0.00000000 0.00000000

-0.00172781 -0.00691122 0.01036684-0.00691122 -0.02764489 0.04146734-0.01902240 -0.01902240 -0.02853360-0.02907282 0.01938188 0.02907282

Clculo de los Desplazamientos

### 1.47313081 1.050107010.71467675 23.31516177 -2.314524170.93662275 -2.31452417 9.03829474

### 1.47313081 1.050107012.63298909 4.35560099 0.40281442

K-1 0.00000000 3.79724234 -1.29186424### 20.43269159 -1.66723158

1.34108107 13.83538138 -0.955854870.00000000 2.23948067 0.63792379

### 7.80707335 -2.72852509

[ ]= ]" [ " ^(1) ][

1.84487766 7.11693938 -2.86962625### 8.17410714 0.02678571### 1.14285714 -1.28571429

-210.0214014575462.9048337572

-1807.6589482663-210.0214014575

-80.5628842297u 258.3728480868

333.4463165295191.1709747638

-127.5847586082545.7050175194573.9252505883

-5.3571428571257.1428571429

Clculo de los Deformaciones de las Barras

262.50778.75333.75

-1190.000.00

e -660.000.000.00

-1325.000.000.000.00

Clculo de los Esfuerzos en las Barras

17.5055.0323.58

-96.21s 0.00

-46.90

]= ] ][ [ [

]= ][[ [ ]

]= ] ][ [ [

0.000.00

-121.340.000.000.00

COMPROBACIN

0.000.00

-200.000.000.00

F 0.000.000.000.000.000.000.000.00

Calculando Reacciones

0 0.000 0.0000.000 -0.848 0.0000.000 0 0

0 -0.485 -0.7280 -0.426 -0.6400 0 00 0 0

-0.949 0 0-0.824 0 0

0 0 00 0 00 0 0

C Az y z

0 0 0

]= ] ][ [ ^ []= ] ][ [ ^ [

[H]= [ _ ] ^ ] [

0 -0.847998304 0Aht 0 0 0

0 0 -0.8479983040 0 0

100.00 C z0.00 A y

H 70.00 z0.00 B y

30.00 z

E A COORDENADAST/m2 m2 Dx Dy

1 1 15 01 1 7.5 121 1 -7.5 121 1 6 61 1 9 61 1 -9 61 1 -7.5 91 1 0 -31 1 -1.5 -61 1 3 01 1 -1.5 31 1 -1.5 -3

APOYOS COORDENADASa 0 0b 15 0c 7.5 12d 6 6e 9 6f 7.5 9

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

0.640 0.426 0.640 00 0 0 00 0 0 -0.5080 0 0 0.000

0.000 0.000 0.000 0.0001.000 0.000 0.000 0.0000.447 -0.894 0.000 -0.447

0 0 0 0.447E Fx y z x

0 0 0 00 0 0 00 0 0 0

0.081 0 0 00 0.071 0 00 0 0.071 00 0 0 0.0680 0 0 00 0 0 00 0 0 00 0 0 00 0 0 0

0.4850712501 0 -0.6396021491 00.4850712501 0 0.4264014327 00.7276068751 0 0.6396021491 0

0 0.6396021491 0 00 0.4264014327 0 00 0.6396021491 0 00 0 0 -0.50767308260 0 0 0.60920769910 0 0 0.60920769910 0 0 0

0 0 0 0-0.4850712501 -0.6396021491 0 0

0 0 0.6396021491 0.5076730826

0.0392156863 0 -0.0454545455 00.0392156863 0 0.0303030303 00.0588235294 0 0.0454545455 0

0 0.0454545455 0 00 0.0303030303 0 00 0.0454545455 0 00 0 0 -0.03436426120 0 0 0.04123711340 0 0 0.04123711340 0 0 00 0 0 0

-0.0392156863 -0.0454545455 0 00 0 0.0454545455 0.0343642612

-0.33333333 0.00000000 0.00000000 -0.059628480.00000000 0.00000000 0.00000000 -0.119256960.00000000 0.00000000 0.00000000 0.000000000.42203464 -0.09987508 0.02907282 -0.05962848

-0.09987508 0.25143517 0.01938188 0.119256960.02907282 0.01938188 0.02907282 0.00000000

-0.05962848 0.11925696 0.00000000 0.136702770.11925696 -0.23851392 0.00000000 -0.020934970.00000000 0.00000000 0.00000000 -0.020934970.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 0.00000000 0.00000000

-0.02907282 -0.01938188 -0.02907282 0.000000000.00000000 0.00000000 0.00000000 -0.01744581

### 11.05311228 -10.65781270 ###0.71467675 4.35560099 3.79724234 20.963851300.93662275 0.40281442 -1.29186424 -2.34155687

### 12.55311228 -14.65781270 ###4.03724994 36.23056579 -33.83628709 -23.52136922

-4.18176874 -33.83628709 92.60279109 33.45414989### -15.41337757 21.87006677 ###

1.34108107 18.05469341 -12.77726239 0.447027020.00000000 -2.45721262 0.45370838 5.42568913

### 0.64225418 17.97659245 ###

1.84487766 4.34448021 -0.08382014 4.91967375### 2.87053571 20.99107143 ###### -2.28571429 15.42857143 ###

0.000 0.000 10 0 2

-0.848 0.000 30 0 40 0 5

-0.426 -0.640 6-0.609 -0.609 7

0 0 80 0 90 0 100 0 110 0 12

By z

0 0 0 0

-0.4850712501 -0.4264014327 0 0-0.7276068751 -0.6396021491 0 0

0 0 -0.4264014327 -0.60920769910 0 -0.6396021491 -0.6092076991

Sz 200.00

COORDENADAS L k = EA/L Ux UyDz m T/m0 15.000 0.067 1.000 0.0000 14.151 0.071 0.530 0.8480 14.151 0.071 -0.530 0.8489 12.369 0.081 0.485 0.4859 14.071 0.071 0.640 0.4269 14.071 0.071 -0.640 0.4269 14.773 0.068 -0.508 0.6099 9.487 0.105 0.000 -0.3169 10.920 0.092 -0.137 -0.5490 3.000 0.333 1.000 0.0000 3.354 0.298 -0.447 0.8940 3.354 0.298 -0.447 -0.894

COORDENADAS0 EJE00999

0 0 0 0 -1.0000 0 0.530 0.848 -0.5300 0 -0.530 0.848 00 0 0 0 -0.4850 0 0 0 -0.6400 0 0 0 0

0.609 0.609 0 0 0-0.316 0.949 0.000 0.316 00.000 0.000 0.137 0.549 00.000 0.000 0 0 00.894 0.000 0 0 00.894 0.000 0 0 0

C Ay z x y x

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

0.105 0 0 0 00 0.092 0 0 00 0 0.333 0 00 0 0 0.298 00 0 0 0 0.298

0 -0.1373605639 -1 0 -0.44721359550 -0.5494422558 0 0 -0.8944271910 0.8241633837 0 0 00 0 1 0.4472135955 00 0 0 -0.894427191 00 0 0 0 00 0 0 -0.4472135955 0.4472135955

-0.316227766 0 0 0.894427191 0.8944271910.9486832981 0 0 0 0

0 0.1373605639 0 0 0

0.316227766 0.5494422558 0 0 00 0 0 0 00 0 0 0 0

0 -0.0125786164 -0.333333333 0 -0.13333333330 -0.0503144654 0 0 -0.26666666670 0.0754716981 0 0 00 0 0.333333333 0.1333333333 00 0 0 -0.2666666667 00 0 0 0 00 0 0 -0.1333333333 0.1333333333

-0.0333333333 0 0 0.2666666667 0.26666666670.1 0 0 0 0

0 0.0125786164 0 0 00.0333333333 0.0503144654 0 0 0

0 0 0 0 00 0 0 0 0

-0.11925696 0.00000000 -0.00172781 -0.00691122 -0.01902240-0.23851392 0.00000000 -0.00691122 -0.02764489 -0.019022400.00000000 0.00000000 0.01036684 0.04146734 -0.028533600.11925696 0.00000000 0.00000000 0.00000000 -0.02907282

-0.23851392 0.00000000 0.00000000 0.00000000 -0.019381880.00000000 0.00000000 0.00000000 0.00000000 -0.02907282

-0.02093497 -0.02093497 0.00000000 0.00000000 0.000000000.51269073 -0.00650081 0.00000000 -0.01054093 0.00000000

-0.00650081 0.11999030 0.00000000 0.03162278 0.000000000.00000000 0.00000000 0.04142810 0.00691122 -0.01985015

-0.01054093 0.03162278 0.00691122 0.13981857 -0.031760240.00000000 0.00000000 -0.01985015 -0.03176024 0.134612040.02093497 0.02093497 -0.01985015 0.03176024 -0.06666667

7.40597869 -0.34681663 ### 2.44642857 ###13.83538138 2.23948067 7.62321866 7.11693938 6.90854191-0.95585487 0.63792379 -2.80986825 -2.86962625 -0.468311377.40597869 -0.34681663 ### 2.44642857 ###

18.05469341 -2.45721262 -9.47876073 4.34448021 -6.49470643-12.77726239 0.45370838 33.45414989 -0.08382014 33.45414989

5.51590413 5.12628915 ### 5.21888774 ###17.10965613 0.27934027 -0.44702702 5.73070980 0.44702702

0.27934027 10.08210073 -0.75356793 -1.85782715 -1.205708695.36752091 -1.18255256 ### 2.91517857 ###

5.73070980 -1.85782715 2.45983688 11.30419126 4.304714546.66517857 -1.53125000 ### 5.25892857 ###0.57142857 -2.00000000 ### 0.57142857 ###

-0.9486832981 -0.8241633837 0 0 0

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

Uz

0.0000.0000.0000.7280.6400.6400.6090.9490.8240.0000.0000.000

1.000 10 2

0.530 30 40 5

0.640 60.508 7

0 80 90 100 110 12

Bx

-0.029072820.019381880.029072820.000000000.000000000.00000000

-0.017445810.020934970.02093497

-0.019850150.03176024

-0.066666670.13303545

###1.19112792

-1.40493412###

-11.0585541925.09061242

###-4.91729727-1.65784946

###

0.00000000######

BARRA N SENTIDO E AINICIO FINAL T/m2 m2

B A Barra 1 1 1C A Barra 2 1 1C B Barra 3 1 1D B Barra 4 1 1A D Barra 5 1 1C D Barra 6 1 1

0 0 0 -0.948683298 -0.3162277660 0 0 0 0

a 0 0 0 -0.882352941 0.47058823530.4472135955 0 0.894427191 -0.447213595 0

-0.6666666667 -0.3333333333 0.666666667 0 0-0.6154574549 0.4923659639 0.615457455 0 0

D BX Y

Matriz de Rigidez

0.063 0 0 0 00 0.077 0 0 0

k 0 0 0.059 0 00 0 0 0.089 00 0 0 0 0.0670 0 0 0 0

Fuerzas Externas

200 D-350

0

0 B x0 y

Clculo de la Matriz Global de Rigidez

0 0 0 0.447213595 -0.66666666670 0 0 0 -0.3333333333

at 0 0 0 0.894427191 0.6666666667-0.9486832981 0 -0.882352941 -0.447213595 0

-0.316227766 0 0.470588235 0 0

0 0 0 0.04 -0.0444444444aT*k 0 0 0 0 -0.0222222222

0 0 0 0.08 0.0444444444-0.06 0 -0.051903114 -0.04 0-0.02 0 0.027681661 0 0

0.0708309558 -0.0038354111 -0.017165324 -0.017888544 0-0.0038354111 0.0223275881 0.003835411 0 0-0.0171653244 0.0038354111 0.124496587 -0.035777088 0

K -0.0178885438 0 -0.035777088 0.120606407 -0.0054513290 0 0 -0.005451329 0.0193512193

Clculo de los Desplazamientos

15.8100813687 2.1903505372 3.059102791 3.294387138 0.9280442606K-1 2.1903505372 45.352025312 -1.095175269 -7.8424E-017 0

3.0591027911 -1.0951752686 9.43459208 3.294387138 0.92804426063.2943871384 -1.37156E-016 3.294387138 9.883161415 2.78413278170.9280442606 -3.86376E-017 0.928044261 2.784132782 52.460633581

2395.4-15435.1

u 995.1658.9185.6

]= ] ] ][ [ ^ [ [

[ ]= ]" [ " ^(1) ][

Clculo de los Deformaciones de las Barras

-683.80.0

-494.0e 1666.7

4211.5-8461.5

Clculo de los Esfuerzos en las Barras

-43.20.0

-29.1s 149.1

280.8-520.8

COMPROBACIN

200.00F -350.00

0.000.000.00

Calculando Reacciones

0.000 0.949 0.316 0.000 00 0.000 1.000 0.000 0.000

Ah 0.000 0 0 0 0.882-0.894 0 0 0 0

0 0.667 0.333 -0.667 00 0 0 0 0.615

B A CZ X Y Z X

0 0 0 -0.894427191 00.9486832981 0 0 0 0.6666666667

0.316227766 1 0 0 0.3333333333ahT 0 0 0 0 -0.6666666667

0 0 0.882352941 0 0

]= ][[ [ ]

]= ] ][ [ [

]= ] ][ [ ^ [

[H]= [ _ ] ^ ] [

0 -1 -0.470588235 0 00 0 0 0 0

-133.33 B z146.15 A x SFx

79.91 yH -187.18 z SFy

-346.15 C x270.09 y SFz320.51 z

COORDENADAS L k = EA/L UxDx Dy Dz m T/m15 5 0 15.811 0.063 0.9490 13 0 13.000 0.077 0.000

-15 8 0 17.000 0.059 -0.882-5 0 -10 11.180 0.089 -0.447

-10 -5 10 15.000 0.067 -0.667-10 8 10 16.248 0.062 -0.615

APOYOS COORDENADASA 15 5 0B 0 0 0 EJEC 15 -8 0D 5 0 10

123456

00000

0.062

-0.615457450.492365960.61545745

00

-0.037878790.030303030.03787879

00

0 0 1-1.000 0.000 2-0.471 0.000 3

0 0 40 0 5

-0.492 -0.615 6

Y Z

0000

0.61545745

-0.49236596-0.61545745

-200.00

350.00

0.00

Uy Uz 0

0.316 0.0001.000 0.0000.471 0.0000.000 -0.894-0.333 0.6670.492 0.615

EJERCICIO 1EJERCICIO 2

Documents

2 Practica