examen escrito 17

Alumna: Colmenares Vasquez Dirze Malu

PRACTICA CALIFICADA - ANÁLISIS ESTRUCTURAL II

E,A I = Ctes

1. Calculamos coordenadas locales y coordenadas globales

ELEMENTOS 1 Y 2 ( COLUMNAS)

Coeficientes de rigidez

raz= 0.3333 EI r11x=r22x=

raax= 0.4444 EI r12x=r21x=

rabx=rbax= 0.6667 EI

Submatrices en coordenadas locales

0.3333 0 0

0 0.4444 0.6667 EI0 0.6667 1.3333

-0.3333 0 0

0 -0.4444 0.6667 EI0 -0.6667 0.6667

[K11]= [K21]=

[K12]= [K22]=

Submatrices en coordenadas globales

= 90° cos 0

0.3333 0 0 A=

0 0.4444 -0.6667 B=

0 -0.6667 1.3333 C=

0.4444 0 0.6667

0 0.3333 0.00000.6667 0 1.3333

ELEMENTOS 3 Y 4 ( COLUMNAS)

raz= 0.2500 EI rabx=rbax= 0.3750

raax= 0.1875 EI r11x=r22x= 1.0000

Submatrices en coordenadas locales

0.2500 0 0

0 0.1875 0.3750 EI0 0.3750 1.0000

-0.2500 0 0

0 -0.1875 0.3750 EI0 -0.3750 0.5000

Submatrices en coordenadas globales

= 90° cos 0

0.2500 0 0 A=

0 0.1875 0.3750 EI B=

0 0.3750 1.0000 C=

0.1875 0 -0.3750

0 0.2500 0.0000-0.3750 0 1.0000

-0.2500 0 0 A=

0 -0.1875 0.3750 B=

0 -0.3750 0.5000 C=

-0.1875 0 -0.3750

[K22]=

[K22]=

[K11]= [K21]=

[K12]= [K22]=

[K11]=

[K11]=

[K12]=

� �

� �� �

0 -0.2500 0.00000.3750 0 0.5000

-0.2500 0 0 A=

0 -0.1875 -0.3750 B=

0 0.3750 0.5000 C=

-0.1875 0 0.3750

0 -0.2500 0.0000-0.3750 0 0.5000

0.2500 0 0 A=

0 0.1875 -0.3750 B=

0 -0.3750 1.0000 C=

0.1875 0 0.3750

0 0.2500 0.00000.3750 0 1.0000

ELEMENTOS 5, 6, 7 y 8 ( VIGAS)

raz= 0.3333 EI r11x=r22x=

raax= 0.4444 EI r12x=r21x=

rabx=rbax= 0.6667 EI

Submatrices en coordenadas locales

0.3333 0 0

0 0.4444 0.6667 EI0 0.6667 1.3333

-0.3333 0 0

0 -0.4444 0.6667 EI0 -0.6667 0.6667

Submatrices en coordenadas globales

= 0 cos 1

0.3333 0 0.0000

0 0.4444 0.6667 EI0.0000 0.66666667 1.3333

-0.3333 0 0.0000

[K12]=

[K21]=

[K21]=

[K22]=

[K22]=

[K11]= [K21]=

[K12]= [K22]=

[K11]= [K21]=

� �� �

0 -0.4444 0.6667 EI0.0000 -0.66666667 0.6667

ELEMENTOS 9 Y 10 ( COLUMNAS)

raz= 0.1429 EI r11x=r22x=

raax= 0.0350 EI r12x=r21x=

rabx=rbax= 0.1224 EI

Submatrices en coordenadas locales

0.1429 0 0

0 0.0350 0.1224 EI0 0.1224 0.5714

-0.1429 0 0

0 -0.0350 0.1224 EI0 -0.1224 0.2857

Submatrices en coordenadas globales

= 90° cos 0

0.1429 0 0 A=

0 0.0350 -0.1224 B=

0 -0.1224 0.5714 C=

0.0350 0 0.1224

0 0.1429 0.00000.1224 0 0.5714

[K12]= [K22]=

[K11]= [K21]=

[K12]= [K22]=

[K22]=

[K22]=

� �

Alumna: Colmenares Vasquez Dirze Malu

PRACTICA CALIFICADA - ANÁLISIS ESTRUCTURAL II

1. Calculamos coordenadas locales y coordenadas globales

1.3333 EI

0.6667 EI

-0.3333 0 0

0 -0.4444 -0.6667 EI0 0.6667 0.6667

0.3333 0 0

0 0.4444 -0.6667 EI0 -0.6667 1.3333

sen 1

0.3333 D= -0.6667

0.4444 E= -0.66671.3333

EI

EI r12x=r21x= 0.5000 EI

EI

-0.2500 0 0

0 -0.1875 -0.3750 EI0 0.3750 0.5000

0.2500 0 0

0 0.1875 -0.3750 EI0 -0.3750 1.0000

sen 1

0.2500 D= 0.3750

0.1875 E= 0.37501.0000

EI

-0.2500 D= 0.3750

-0.1875 E= -0.37500.5000

�

��

EI

-0.2500 D= -0.3750

-0.1875 E= 0.37500.5000

EI

0.2500 D= -0.3750

0.1875 E= -0.37501.0000

EI

1.3333 EI

0.6667 EI

-0.3333 0 0

0 -0.4444 -0.6667 EI0 0.6667 0.6667

0.3333 0 0

0 0.4444 -0.6667 EI0 -0.6667 1.3333

sen 0

-0.3333 0 0.0000

0 -0.4444 -0.6667 EI0.0000 0.66666667 0.6667

0.3333 0 0.0000

��

0 0.4444 -0.6667 EI0.0000 -0.66666667 1.3333

0.5714 EI

0.2857 EI

-0.1429 0 0

0 -0.0350 -0.1224 EI0 0.1224 0.2857

0.1429 0 0

0 0.0350 -0.1224 EI0 -0.1224 0.5714

sen 1

0.1429 D= -0.1224

0.0350 E= -0.12240.5714

EI

�

z

Ensamble de la matriz de rigidez global K

[K]=

MATRIZ "K" DE RIGIDEZ GLOBAL

0.9653 0 0.2917 -0.3333 0 0 -0.1875 0 -0.3750 0 00 1.0278 0.6667 0 -0.4444 0.6667 0 -0.2500 0 0 0

0.2917 0.6667 3.6667 0 -0.6667 0.6667 0.3750 0 0.5000 0 0-0.3333 0 0 0.9653 0 0.2917 0 0 0 -0.1875 0

0 -0.4444 -0.6667 0 1.0278 -0.6667 0 0 0 0 -0.25000 0.6667 0.6667 0.2917 -0.6667 3.6667 0 0 0 0.3750 0

-0.1875 0 0.3750 0 0 0 0.5208 0 0.3750 -0.3333 0[K]= 0 -0.2500 0 0 0 0 0 0.6944 0.6667 0 -0.4444

-0.3750 0 0.5000 0 0 0 0.3750 0.6667 2.3333 0 -0.66670 0 0 -0.1875 0 0.3750 -0.3333 0 0 0.8542 00 0 0 0 -0.2500 0 0 -0.4444 -0.6667 0 1.13890 0 0 -0.3750 0 0.5000 0 0.6667 0.6667 0.3750 00 0 0 0 0 0 0 0 0 -0.3333 00 0 0 0 0 0 0 0 0 0 -0.44440 0 0 0 0 0 0 0 0 0 0.66670 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0

K11 K12 K13 K14 K15 K16

K21 K22 K23 K24 K25 K26

K31 K32 K33 K34 K35 K36

K41 K42 K43 K44 K45 K46

K51 K52 K53 K54 K55 K56

K61 K62 K63 K64 K65 K66

MINVERSA DE MATRIZ "K" DE RIGIDEZ GLOBAL

2.139 0.548 -0.528 1.260 -0.327 -0.385 2.650 0.401 -0.017 2.324 0.1140.548 2.338 -0.412 0.550 0.719 -0.410 1.954 2.142 -0.376 1.858 0.990-0.528 -0.412 0.536 -0.398 0.267 0.154 -1.324 -0.329 0.073 -1.087 -0.0111.260 0.550 -0.398 2.136 -0.360 -0.528 2.566 0.431 -0.248 2.573 0.014-0.327 0.719 0.267 -0.360 1.930 0.281 -0.836 0.985 0.102 -0.707 1.194-0.385 -0.410 0.154 -0.528 0.281 0.537 -1.199 -0.341 0.198 -1.261 0.0412.650 1.954 -1.324 2.566 -0.836 -1.199 10.136 2.789 -1.558 8.105 -0.1810.401 2.142 -0.329 0.431 0.985 -0.341 2.789 5.269 -1.002 2.636 2.029-0.017 -0.376 0.073 -0.248 0.102 0.198 -1.558 -1.002 1.013 -1.203 0.3642.324 1.858 -1.087 2.573 -0.707 -1.261 8.105 2.636 -1.203 8.780 0.0510.114 0.990 -0.011 0.014 1.194 0.041 -0.181 2.029 0.364 0.051 3.069-0.119 -0.319 0.108 0.015 -0.063 0.031 -0.736 -0.831 0.132 -0.812 -0.0602.030 1.679 -0.943 2.249 -0.528 -1.095 7.012 2.404 -1.012 7.615 0.282-0.084 0.212 0.111 -0.018 0.600 0.070 -0.904 0.288 0.339 -0.860 1.607-0.123 -0.228 0.046 -0.131 -0.158 0.053 -0.305 -0.393 -0.013 -0.370 -0.5071.904 1.592 -0.880 2.113 -0.461 -1.026 6.544 2.281 -0.933 7.113 0.356-0.431 -0.345 0.229 -0.426 0.220 0.230 -1.705 -0.586 0.299 -1.827 0.295-0.201 -0.218 0.082 -0.233 -0.048 0.104 -0.594 -0.315 0.051 -0.666 -0.305

[�]" " ^(−1)=

Ensamble de la matriz de rigidez global K

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

-0.3750 0 0 0 0 0 00 0 0 0 0 0 0

0.5000 0 0 0 0 0 00 0 0 0 0 0 0

0.6667 0 0 0 0 0 00.6667 0 0 0 0 0 00.3750 -0.3333 0 0 0 0 0

0 0 -0.4444 0.6667 0 0 03.6667 0 -0.6667 0.6667 0 0 0

0 0.7017 0 0.1224 -0.3333 0 0-0.6667 0 1.0317 0 0 -0.4444 0.66670.6667 0.1224 0 3.2381 0 -0.6667 0.6667

0 -0.3333 0 0 0.3683 0 0.12240 0 -0.4444 -0.6667 0 0.5873 -0.66670 0 0.6667 0.6667 0.1224 -0.6667 1.9048

-0.119 2.030 -0.084 -0.123 1.904 -0.431 -0.201-0.319 1.679 0.212 -0.228 1.592 -0.345 -0.2180.108 -0.943 0.111 0.046 -0.880 0.229 0.0820.015 2.249 -0.018 -0.131 2.113 -0.426 -0.233-0.063 -0.528 0.600 -0.158 -0.461 0.220 -0.0480.031 -1.095 0.070 0.053 -1.026 0.230 0.104-0.736 7.012 -0.904 -0.305 6.544 -1.705 -0.594-0.831 2.404 0.288 -0.393 2.281 -0.586 -0.3150.132 -1.012 0.339 -0.013 -0.933 0.299 0.051-0.812 7.615 -0.860 -0.370 7.113 -1.827 -0.666-0.060 0.282 1.607 -0.507 0.356 0.295 -0.3050.573 -0.675 0.513 -0.001 -0.608 0.379 -0.008-0.675 9.245 -0.634 -0.511 8.657 -2.052 -0.8740.513 -0.634 3.103 0.079 -0.446 2.001 -0.385-0.001 -0.511 0.079 0.584 -0.492 0.821 0.087-0.608 8.657 -0.446 -0.492 10.930 -2.191 -1.1410.379 -2.052 2.001 0.821 -2.191 5.289 1.004-0.008 -0.874 -0.385 0.087 -1.141 1.004 1.054

1. OBTENCIÓN DE LOS DESPLAZAMIENTOS Y GIROS GLOBALES

200000

100

[F]= 0 (Ton) [u]=000000000

2. CÁLCULO DE DEFORMACIONES EN COORDENADAS LOCALES Y ELEMENTOS MECÁNICOS

ELEMENTO 1 Angulo : 90°

0 1 0-1 0 0 [T]=0 0 1

00

[u]= 0 1/EI30.775220.6333

[ ]=� [�] [�]" " ^(−�−−−−−−−−−−− )

[�′]= ][� [u]

�=

-14.2975

0.333 0.000 0.000 -0.333 0.0000.000 0.444 0.667 0.000 -0.444

[k']= 0.000 0.667 1.333 0.000 -0.667-0.333 0.000 0.000 0.333 0.0000.000 -0.444 -0.667 0.000 0.4440.000 0.667 0.667 0.000 -0.667

ELEMENTO 2 Angulo : 90°

0 1 0-1 0 0 [T]=0 0 1

00

[u]= 0 1/EI28.1781-9.0133

-12.7606

0.333 0.000 0.000 -0.333 0.0000.000 0.444 0.667 0.000 -0.444

[k']= 0.000 0.667 1.333 0.000 -0.667-0.333 0.000 0.000 0.333 0.0000.000 -0.444 -0.667 0.000 0.4440.000 0.667 0.667 0.000 -0.667

ELEMENTO 3 Angulo : 90°

0 1 0-1 0 0 [T]=0 0 1

30.775220.6333

[u]= -14.2975 1/EI

[F']= ′][� [u']

�=

[F']= ′][� [u']

[�′]= ][� [u]

[�′]= ][� [u]

�=

106.657528.6944-15.6118

0.250 0.000 0.000 -0.250 0.0000.000 0.188 0.375 0.000 -0.188

[k']= 0.000 0.375 1.000 0.000 -0.375-0.250 0.000 0.000 0.250 0.0000.000 -0.188 -0.375 0.000 0.1880.000 0.375 0.500 0.000 -0.375

ELEMENTO 4 Angulo : 90°

0 1 0-1 0 0 [T]=0 0 1

28.1781-9.0133

[u]= -12.7606 1/EI85.6933-1.5811-7.5948

0.250 0.000 0.000 -0.250 0.0000.000 0.188 0.375 0.000 -0.188

[k']= 0.000 0.375 1.000 0.000 -0.375-0.250 0.000 0.000 0.250 0.0000.000 -0.188 -0.375 0.000 0.1880.000 0.375 0.500 0.000 -0.375

ELEMENTO 5 Angulo : 0

1 0 00 1 0 [T]=0 0 1

[F']= ′][� [u']

[�′]= ][� [u]

�=

[F']= ′][� [u']

[�′]= ][� [u]

�=

30.775220.6333

[u]= -14.2975 1/EI28.1781-9.0133

-12.7606

0.333 0.000 0.000 -0.333 0.0000.000 0.444 0.667 0.000 -0.444

[k']= 0.000 0.667 1.333 0.000 -0.667-0.333 0.000 0.000 0.333 0.0000.000 -0.444 -0.667 0.000 0.4440.000 0.667 0.667 0.000 -0.667

ELEMENTO 6 Angulo : 0

1 0 00 1 0 [T]=0 0 1

106.657528.6944

[u]= -15.6118 1/EI85.6933-1.5811-7.5948

0.333 0.000 0.000 -0.333 0.0000.000 0.444 0.667 0.000 -0.444

[k']= 0.000 0.667 1.333 0.000 -0.667-0.333 0.000 0.000 0.333 0.0000.000 -0.444 -0.667 0.000 0.4440.000 0.667 0.667 0.000 -0.667

ELEMENTO 7 Angulo : 0

1 0 00 1 0 [T]=0 0 1

[F']= ′][� [u']

[�′]= ][� [u]

�=

[F']= ′][� [u']

[�′]= ][� [u]

�=

85.6933-1.5811

[u]= -7.5948 1/EI74.1816-9.2038-3.2971

0.333 0.000 0.000 -0.333 0.0000.000 0.444 0.667 0.000 -0.444

[k']= 0.000 0.667 1.333 0.000 -0.667-0.333 0.000 0.000 0.333 0.0000.000 -0.444 -0.667 0.000 0.4440.000 0.667 0.667 0.000 -0.667

ELEMENTO 8 Angulo : 0

1 0 00 1 0 [T]=0 0 1

74.1816-9.2038

[u]= -3.2971 1/EI69.2446-17.9095-6.3444

0.333 0.000 0.000 -0.333 0.0000.000 0.444 0.667 0.000 -0.444

[k']= 0.000 0.667 1.333 0.000 -0.667-0.333 0.000 0.000 0.333 0.0000.000 -0.444 -0.667 0.000 0.4440.000 0.667 0.667 0.000 -0.667

ELEMENTO 9 Angulo : 90°

0 1 0

[F']= ′][� [u']

[�′]= ][� [u]

�=

[F']= ′][� [u']

[�′]= ][� [u]

-1 0 0 [T]=0 0 1

0.00000.0000

[u]= 0.0000 1/EI74.1816-9.2038-3.2971

0.143 0.000 0.000 -0.143 0.0000.000 0.035 0.122 0.000 -0.035

[k']= 0.000 0.122 0.571 0.000 -0.122-0.143 0.000 0.000 0.143 0.0000.000 -0.035 -0.122 0.000 0.0350.000 0.122 0.286 0.000 -0.122

ELEMENTO 10 Angulo : 90°

0 1 0-1 0 0 [T]=0 0 1

0.00000.0000

[u]= 0.0000 1/EI69.2446-17.9095-6.3444

0.143 0.000 0.000 -0.143 0.0000.000 0.035 0.122 0.000 -0.035

[k']= 0.000 0.122 0.571 0.000 -0.122-0.143 0.000 0.000 0.143 0.0000.000 -0.035 -0.122 0.000 0.0350.000 0.122 0.286 0.000 -0.122

�=

[F']= ′][� [u']

[�′]= ][� [u]

�=

[F']= ′][� [u']

30.775220.6333-14.297528.1781-9.0133

-12.7606106.657528.6944-15.6118 1/EI85.6933-1.5811-7.594874.1816-9.2038-3.297169.2446-17.9095-6.3444

2. CÁLCULO DE DEFORMACIONES EN COORDENADAS LOCALES Y ELEMENTOS MECÁNICOS

0 1 0 0 0 0-1 0 0 0 0 00 0 1 0 0 00 0 0 0 1 00 0 0 -1 0 00 0 0 0 0 1

00

[u']= 0 1/EI20.6333-30.7752

[ ]=� [�] [�]" " ^(−�−−−−−−−−−−− )

[�′]= ][� [u]

-14.2975

0.000 -6.87780.667 4.14620.667 [F']= 10.9852 1/EI0.000 6.8778-0.667 -4.14621.333 1.4535

0 1 0 0 0 0-1 0 0 0 0 00 0 1 0 0 00 0 0 0 1 00 0 0 -1 0 00 0 0 0 0 1

00

[u']= 0 1/EI-9.0133

-28.1781-12.7606

0.000 3.00440.667 4.01650.667 [F']= 10.2783 1/EI0.000 -3.0044-0.667 -4.01651.333 1.7713

0 1 0 0 0 0-1 0 0 0 0 00 0 1 0 0 00 0 0 0 1 00 0 0 -1 0 00 0 0 0 0 1

20.6333-30.7752

[u']= -14.2975 1/EI

[F']= ′][� [u']

[F']= ′][� [u']

[�′]= ][� [u]

[�′]= ][� [u]

28.6944-106.6575-15.6118

0.000 -2.01530.375 3.01190.500 [F']= 6.3525 1/EI0.000 2.0153-0.375 -3.01191.000 5.6953

0 1 0 0 0 0-1 0 0 0 0 00 0 1 0 0 00 0 0 0 1 00 0 0 -1 0 00 0 0 0 0 1

-9.0133-28.1781

[u']= -12.7606 1/EI-1.5811

-85.6933-7.5948

0.000 -1.85810.375 3.15080.500 [F']= 5.0102 1/EI0.000 1.8581-0.375 -3.15081.000 7.5931

1 0 0 0 0 00 1 0 0 0 00 0 1 0 0 00 0 0 1 0 00 0 0 0 1 00 0 0 0 0 1

[F']= ′][� [u']

[�′]= ][� [u]

[F']= ′][� [u']

[�′]= ][� [u]

30.775220.6333

[u']= -14.2975 1/EI28.1781-9.0133

-12.7606

0.000 0.86570.667 -4.86250.667 [F']= -7.8060 1/EI0.000 -0.8657-0.667 4.86251.333 -6.7814

1 0 0 0 0 00 1 0 0 0 00 0 1 0 0 00 0 0 1 0 00 0 0 0 1 00 0 0 0 0 1

106.657528.6944

[u']= -15.6118 1/EI85.6933-1.5811-7.5948

0.000 6.98810.667 -2.01530.667 [F']= -5.6953 1/EI0.000 -6.9881-0.667 2.01531.333 -0.3506

1 0 0 0 0 00 1 0 0 0 00 0 1 0 0 00 0 0 1 0 00 0 0 0 1 0

[F']= ′][� [u']

[�′]= ][� [u]

[F']= ′][� [u']

[�′]= ][� [u]

0 0 0 0 0 1

85.6933-1.5811

[u']= -7.5948 1/EI74.1816-9.2038-3.2971

0.000 3.83720.667 -3.87330.667 [F']= -7.2426 1/EI0.000 -3.8372-0.667 3.87331.333 -4.3774

1 0 0 0 0 00 1 0 0 0 00 0 1 0 0 00 0 0 1 0 00 0 0 0 1 00 0 0 0 0 1

74.1816-9.2038

[u']= -3.2971 1/EI69.2446-17.9095-6.3444

0.000 1.64570.667 -2.55850.667 [F']= -2.8220 1/EI0.000 -1.6457-0.667 2.55851.333 -4.8535

0 1 0 0 0 0-1 0 0 0 0 0

[F']= ′][� [u']

[�′]= ][� [u]

[F']= ′][� [u']

[�′]= ][� [u]

0 0 1 0 0 00 0 0 0 1 00 0 0 -1 0 00 0 0 0 0 1

0.00000.0000

[u']= 0.0000 1/EI-9.2038

-74.1816-3.2971

0.000 1.31480.122 2.19160.286 [F']= 8.1414 1/EI0.000 -1.3148-0.122 -2.19160.571 7.1994

0 1 0 0 0 0-1 0 0 0 0 00 0 1 0 0 00 0 0 0 1 00 0 0 -1 0 00 0 0 0 0 1

0.00000.0000

[u']= 0.0000 1/EI-17.9095-69.2446-6.3444

0.000 2.55850.122 1.64570.286 [F']= 6.6662 1/EI0.000 -2.5585-0.122 -1.64570.571 4.8535

[F']= ′][� [u']

[�′]= ][� [u]

[F']= ′][� [u']