Examen Escrito 17
28
Alumna: Colmenares Vasq PRACTICA CALIFICADA - ANÁLISIS ES E,A I = Ctes 1. Calculamos coordenadas locales y coordenadas 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 EI 0 0.6667 1.3333 -0.3333 0 0 0 -0.4444 0.6667 EI 0 -0.6667 0.6667 [K 11 ]= [K 21 ]= [K 12 ]= [K 22 ]=
description
examen de excel
Transcript of 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']
