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Metodo Matricial - Porticos 1
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Metodo Matricial - Porticos 1
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Luis Carrillo Cumpa
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I) CALCULO DE LA MATRIZ DE CADA ELEMENTO EN COORDENADAS GLOBALES ELEMENTO 1
dimenciones SEXAG 90
Ɵ=
RAD. 1. 1 .6
COS(Ɵ)= SEN(Ɵ)=
A= E= I= L=
0.00 1.00
a) matrisz de tansformacion (T).
T=
0.00 -1.00 0.00 0.00 0.00 0.00
1.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 -1.00 0.00
0.00 0.00 0.00 1.00 0.00 0.00
0 .0 0 0 .0 0 0 .0 0 0 .0 0 0 .0 0 1 .0 0
0.00 0.00 0.00 -1.00 0.00 0.00
0 .0 0 0 .0 0 0 .0 0 0 .0 0 0 .0 0 1 .0 0
b) matriz tanspuesta de la matriz de transformacion T T
T T=
0.00 1.00 0.00 0.00 0.00 0.00
-1.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 1.00 0.00
c) calculo de la matriz de rigidez del elemento en MN/m
b 0.3
h 0 .3
0.09 210000 0.000675 3.132
m2 T/m2 m4 m
dimenciones de la viga
ELEMENTO 2 SEXAG 90
Ɵ=
RAD. 1. 1 .6
COS(Ɵ)= SEN(Ɵ)=
b 0.3
A= E= I= L=
0.00 1.00
a) matrisz de tansformacion (T).
T=
0.00 -1.00 0.00 0.00 0.00 0.00
1.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 -1.00 0.00
0.00 0.00 0.00 1.00 0.00 0.00
0 .0 0 0 .0 0 0 .0 0 0 .0 0 0 .0 0 1 .0 0
0.00 0.00 0.00 -1.00 0.00 0.00
0 .0 0 0 .0 0 0 .0 0 0 .0 0 0 .0 0 1 .0 0
b) matriz tanspuesta de la matriz de transformacion T T
T T=
0.00 1.00 0.00 0.00 0.00 0.00
-1.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 1.00 0.00
c) calculo de la matriz de rigidez del elemento en T/m
h 0 .3
0.09 210000 0 .0 0 0 6 7 5 3 .0 1 6
m2 T/m2 m4 m
dimenciones de la viga
ELEMENTO 2 SEXAG 90
Ɵ=
RAD. 1. 1 .6
COS(Ɵ)= SEN(Ɵ)=
b 0.3
A= E= I= L=
0.00 1.00
a) matrisz de tansformacion (T).
T=
0.00 -1.00 0.00 0.00 0.00 0.00
1.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 -1.00 0.00
0.00 0.00 0.00 1.00 0.00 0.00
0 .0 0 0 .0 0 0 .0 0 0 .0 0 0 .0 0 1 .0 0
0.00 0.00 0.00 -1.00 0.00 0.00
0 .0 0 0 .0 0 0 .0 0 0 .0 0 0 .0 0 1 .0 0
b) matriz tanspuesta de la matriz de transformacion T T
T T=
0.00 1.00 0.00 0.00 0.00 0.00
-1.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 1.00 0.00
c) calculo de la matriz de rigidez del elemento en T/m
h 0 .3
0.09 210000 0 .0 0 0 6 7 5 3 .0 1 6
m2 T/m2 m4 m
dimenciones de la viga
ELEMENTO 3 SEXAG 0
Ɵ=
RAD. 0. 0 .0
COS(Ɵ)= SEN(Ɵ)=
b 0.3
A= E= I= L=
1.00 0.00
a) matrisz de tansformacion (T).
T=
1.00 0.00 0.00 0.00 0.00 0.00
0.00 1.00 0.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00 0.00
0.00 0.00 0.00 1.00 0.00 0.00
0.00 0.00 0.00 0.00 1.00 0.00
0 .0 0 0 .0 0 0 .0 0 0 .0 0 0 .0 0 1 .0 0
0.00 0.00 0.00 0.00 1.00 0.00
0 .0 0 0 .0 0 0 .0 0 0 .0 0 0 .0 0 1 .0 0
b) matriz tanspuesta de la matriz de transformacion T T
T T=
1.00 0.00 0.00 0.00 0.00 0.00
0.00 1.00 0.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00 0.00
0.00 0.00 0.00 1.00 0.00 0.00
c) calculo de la matriz de rigidez del elemento en T/m
h 0 .3
0 .0 9 210000 0 .0 0 0 6 7 5 4 .8 4
m2 T/m2 m4 m
dimenciones de la viga
ELEMENTO 4
Ɵ=
SEXAG 0
RAD. 0. 0 .0
COS(Ɵ)= SEN(Ɵ)=
b 0.3
A= E= I= L=
1.00 0.00
a) matrisz de tansformacion (T).
T=
1.00 0.00 0.00 0.00 0.00 0.00
0.00 1.00 0.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00 0.00
0.00 0.00 0.00 1.00 0.00 0.00
0.00 0.00 0.00 0.00 1.00 0.00
0 .0 0 0 .0 0 0 .0 0 0 .0 0 0 .0 0 1 .0 0
0.00 0.00 0.00 0.00 1.00 0.00
0 .0 0 0 .0 0 0 .0 0 0 .0 0 0 .0 0 1 .0 0
b) matriz tanspuesta de la matriz de transformacion T T
T T=
1.00 0.00 0.00 0.00 0.00 0.00
0.00 1.00 0.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00 0.00
0.00 0.00 0.00 1.00 0.00 0.00
c) calculo de la matriz de rigidez del elemento en T/m
h 0 .3
0 .0 9 210000 0 .0 0 0 6 7 5 4 .8 4
m2 T/m2 m4 m
dimenciones de la viga
ELEMENTO 5
Ɵ=
SEXAG 90
RAD. 1.6
COS(Ɵ)= SEN(Ɵ)=
b 0.3
A= E= I= L=
0.00 1.00
a) matrisz de tansformacion (T).
T=
0.00 -1.00 0.00 0.00 0.00 0.00
1.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 -1.00 0.00
0.00 0.00 0.00 1.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 1.00
0.00 0.00 0.00 -1.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 1.00
b) matriz tanspuesta de la matriz de transformacion T T
T T=
0.00 1.00 0.00 0.00 0.00 0.00
-1.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 1.00 0.00
c) calculo de la matriz de rigidez del elemento en T/m
h 0.3
0.09 210000 0.000675 3.132
m2 T/m2 m4 m
dimenciones de la viga
ELEMENTO 6
Ɵ=
SEXAG 90
RAD. 1.6
COS(Ɵ)= SEN(Ɵ)=
b 0.3
A= E= I= L=
0.00 1.00
a) matrisz de tansformacion (T).
T=
0.00 -1.00 0.00 0.00 0.00 0.00
1.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 -1.00 0.00
0.00 0.00 0.00 1.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 1.00
0.00 0.00 0.00 -1.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 1.00
b) matriz tanspuesta de la matriz de transformacion T T
T T=
0.00 1.00 0.00 0.00 0.00 0.00
-1.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 1.00 0.00
c) calculo de la matriz de rigidez del elemento en T/m
h 0.3
0.09 210000 0.000675 3.016
m2 T/m2 m4 m
dimenciones de la viga
ELEMENTO 7
Ɵ=
SEXAG 0
RAD. 0.0
COS(Ɵ)= SEN(Ɵ)=
b 0.3
A= E= I= L=
1.00 0.00
a) matrisz de tansformacion (T).
T=
1.00 0.00 0.00 0.00 0.00 0.00
0.00 1.00 0.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00 0.00
0.00 0.00 0.00 1.00 0.00 0.00
0.00 0.00 0.00 0.00 1.00 0.00
0.00 0.00 0.00 0.00 0.00 1.00
0.00 0.00 0.00 0.00 1.00 0.00
0.00 0.00 0.00 0.00 0.00 1.00
b) matriz tanspuesta de la matriz de transformacion T T
T T=
1.00 0.00 0.00 0.00 0.00 0.00
0.00 1.00 0.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00 0.00
0.00 0.00 0.00 1.00 0.00 0.00
c) calculo de la matriz de rigidez del elemento en T/m
h 0.3
0.09 210000 0.000675 5.98
m2 T/m2 m4 m
dimenciones de la viga
ELEMENTO 8
Ɵ=
SEXAG 0
RAD. 0.0
COS(Ɵ)= SEN(Ɵ)=
b 0.3
A= E= I= L=
1.00 0.00
a) matrisz de tansformacion (T).
T=
1.00 0.00 0.00 0.00 0.00 0.00
0.00 1.00 0.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00 0.00
0.00 0.00 0.00 1.00 0.00 0.00
0.00 0.00 0.00 0.00 1.00 0.00
0.00 0.00 0.00 0.00 0.00 1.00
0.00 0.00 0.00 0.00 1.00 0.00
0.00 0.00 0.00 0.00 0.00 1.00
b) matriz tanspuesta de la matriz de transformacion T T
T T=
1.00 0.00 0.00 0.00 0.00 0.00
0.00 1.00 0.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00 0.00
0.00 0.00 0.00 1.00 0.00 0.00
c) calculo de la matriz de rigidez del elemento en T/m
h 0.3
0.09 210000 0.000675 5.98
m2 T/m2 m4 m
dimenciones de la viga
ELEMENTO 9
Ɵ=
SEXAG 90
RAD. 1.6
COS(Ɵ)= SEN(Ɵ)=
b 0.3
A= E= I= L=
0.00 1.00
a) matrisz de tansformacion (T).
T=
0.00 -1.00 0.00 0.00 0.00 0.00
1.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 -1.00 0.00
0.00 0.00 0.00 1.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 1.00
0.00 0.00 0.00 -1.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 1.00
b) matriz tanspuesta de la matriz de transformacion T T
T T=
0.00 1.00 0.00 0.00 0.00 0.00
-1.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 1.00 0.00
c) calculo de la matriz de rigidez del elemento en T/m
h 0.3
0.09 210000 0.000675 3.132
m2 T/m2 m4 m
dimenciones de la viga
ELEMENTO 10
Ɵ=
SEXAG 90
RAD. 1.6
COS(Ɵ)= SEN(Ɵ)=
b 0.3
A= E= I= L=
0.00 1.00
a) matrisz de tansformacion (T).
T=
0.00 -1.00 0.00 0.00 0.00 0.00
1.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 -1.00 0.00
0.00 0.00 0.00 1.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 1.00
0.00 0.00 0.00 -1.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 1.00
b) matriz tanspuesta de la matriz de transformacion T T
T T=
0.00 1.00 0.00 0.00 0.00 0.00
-1.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 1.00 0.00
c) calculo de la matriz de rigidez del elemento en T/m
h 0.3
0.09 210000 0.000675 3.016
m2 T/m2 m4 m
III) CALCULO DE LOS MOMENTOS DE EMPOTRAMIENTO PERFECTO O DE FIJACION
9 181 6 151 152 24 182 27
MCF= MFC= MBE= MEB= MEH= MHE= MFI= MIF=
14.84 -14.84 23.54 -20.36 36.94 -34.05 22.65 -22.65
T.m T.m T.m T.m T.m T.m T.m T.m
8 171 5 141 142 23 172 26
YC YF` YB YE` YE`` YH YF`` YI
= = = = = = = =
18.39 18.39 28.77 24.17 35.41 32.39 22.72 22.72
III) CALCULO DE REACCIONES PROBOCADO POR LOS VOLADISOS(EXTERNAS) MB= MI=
52.67 T.m -34.2 T.m
RB= RI=
-31.50 T -22.80 T
IV) CALCULO DE LOS DESPLAZAMIENTOS
D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 D
0 0 0
0 0
D16 D17 D18 D19 D20 D21 D22 D23 D24 D25 D26
0 0 0
DESPEJANDO OBTENEMOS LOS DESPLAZAMIENTOS DESCONOCIDOS D4 D5 D6 D7 D8 D9 D13 D14 D15 D16 D17 D18 D22 D23 D24 D25 D26 D27
=
0.3569 -0.0109 -0.0367 0.7676 -0.0127 -0.1565 0.3592 -0.0174 -0.1346 0.7635 -0.0244 -0.0419 0.3620 -0.0143 -0.0292 0.7612 -0.0224 -0.1559
VI) CALCULO DE LAS REACCIONES PARA CADA ELEMENTO ELEMENTO 1 1 v1 2
2
3
4
5
6
55.37 0.00 0 00 6034 48
-86.70 0 00
-55.37 0 00
0.00 6034 5
-86.70 0 00
0.0000 0 0000
ELEMENTO 2 4 v4 v5 M6 v7 v8 M9
=
5
6
62.00 0.00 0.00 6266.58 -93.50 0.00 -62.00 0.00 0.00 -6266.6 -93.50 0.00
-93.50 0.00 188.00 93.50 0.00 94.00
7
8
9
-62.00 0.00 0.00 -6266.6 93.50 0.00 62.00 0.00 0.00 6266.58 93.50 0.00
-93.50 0.00 94.00 93.50 0.00 188.00
X
0.3569 -0.0109 -0.0367 0.7676 -0.0127 -0.1565
ENTONSES RESOLVIENDO v4 v5 M6 v7 v8 M9
-7.3992 11.36 16.788 7.3992 -11.36 5.5282
ELEMENTO 3
4
5
3905.0 0.0 0.0 -3905.0 0.0 0.0
0.0 15.0 36.3 0.0 -15.0 36.3
v4 v5 M6 v13 v14 M15
= = = = = =
=
6
13
14
15
0.0 -3905.0 36.3 0.0 117.1 0.0 0.0 3905.0 -36.3 0.0 58.6 0.0
0.0 -15.0 -36.3 0.0 15.0 -36.3
0.0 36.3 58.6 0.0 -36.3 117.1
ENTONSES RESOLVIENDO v4 5
-9.1742 6 1225
0 28 77
-9.1742 22.648
X
0.3569 -0.0109 -0.0367 0.3592 -0.0174 -0.1346
0 28.8 + 23.5 0 24.2 -20
ELEMENTO 5 10 v10 v11 M12 v13 v14 M15
11
12
55.37 0.00 -86.70 0.00 6034.48 0.00 -86.70 0.00 181.03 -55.37 0.00 86.70 0.00 -6034.5 0.00 -86.70 0.00 90.52
=
13
14
15
-55.37 0.00 -86.70 0.00 -6034.5 0.00 86.70 0.00 90.52 55.37 0.00 86.70 0.00 6034.48 0.00 86.70 0.00 181.03
X
0.0000 0.0000 0.0000 0.3592 -0.0174 -0.1346
ENTONSES RESOLVIENDO v10 v11 M12 v13 v14 M15
= = = = = =
ELEMENTO 6 V13 v14 M15 v16 v17 M18
=
-8.2163 105.2 18.959 8.2163 -105.2 6.774 13
14
15
62.0 0.0 0.0 6266.6 -93.5 0.0 -62.0 0.0 0.0 -6266.6 -93.5 0.0
-93.5 0.0 188.0 93.5 0.0 94.0
ENTONSES RESOLVIENDO V13 v14
-8.5592 43.419
16
17
18
-62.0 0.0 0.0 -6266.6 93.5 0.0 62.0 0.0 0.0 6266.6 93.5 0.0
-93.5 0.0 94.0 93.5 0.0 188.0
X
0.3592 -0.0174 -0.1346 0.7635 -0.0244 -0.0419
ELEMENTO 8 16 v16 v17 M18 v25 v26 M27
3160.54 0.00 0.00 -3160.5 0.00 0.00
=
17 0.00 7.95 23.78 0.00 -7.95 23.78
18
25
26
0.00 -3160.5 0.00 23.78 0.00 -7.95 94.82 0.00 -23.78 0.00 3160.54 0.00 -23.78 0.00 7.95 47.41 0.00 -23.78
27 0.00 23.78 47.41 0.00 -23.78 94.82
X
0.7635 -0.0244 -0.0419 0.7612 -0.0224 -0.1559
ENTONSES RESOLVIENDO v16 v17 M18 v25 v26 M27
7.4415 -4.7213 -11.416 -7.4415 4.7213 -16.818
ELEMENTO 9
19
V19 v20 M21 v22 v23 M24
= = = = = =
=
20
21
55.4 0.0 0.0 6034.5 -86.7 0.0 -55.4 0.0 0.0 -6034.5 -86.7 0.0
-86.7 0.0 181.0 86.7 0.0 90.5
ENTONSES RESOLVIENDO V19 v20
+
0 22.72 22.65 = 0 22.72 -22.65
-17.51 86.552
7.4415 17.999 11.234 -7.4415 27.441 -39.468 22
23
24
-55.4 0.0 0.0 -6034.5 86.7 0.0 55.4 0.0 0.0 6034.5 86.7 0.0
-86.7 0.0 90.5 86.7 0.0 181.0
X
0.0000 0.0000 0.0000 0.3620 -0.0143 -0.0292
0 22.7 + 22.7 0 22.7 -23
VI) RESUMEN DESPLAZAMIENTOS D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 D11 D12 D13 D14 D15
0 0 0
0.3569
-0.0109
-0.0367
0.7676
-0.0127
-0.1565 0 0 0
0.3592
-0.0174 -0.1346
D16 D17 D18 D19 D20 D21 D22 D23 D24 D25 D26 D27
0.7635
-0.0244 -0.0419 0 0 0
0.3620
-0.0143 -0.0292
0.7612
-0.0224 -0.1559
-0 -1 0 0 0 0
1 -0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 -0 1 0 0 -1 -0 0 0 0 0 1
-0 0 0 0 0 0
0 -0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 -0 0 0 0 0 -0 0 0 0 0 1
0
matriz general de rigidez del elemento 1 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
55.37
0.0
-86.7
0.0
6034
0.0
-55.4
0.0
-86.7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.0
-6034
0.0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-86.7
0.0
-55.4
0.0
181.0
86.7
0.0
90.5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
86.7
55.4
0.0
86.7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
12 UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO ESCUELA PROFESIONAL DE INGENIERIA CIVIL
matriz general de rigidez del elemento 2 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
0
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62.0
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188.0
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
13 UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO ESCUELA PROFESIONAL DE INGENIERIA CIVIL
matriz general de rigidez del elemento 3 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
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36.31
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36.31
117.15
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58.57
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14 UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO ESCUELA PROFESIONAL DE INGENIERIA CIVIL
matriz general de rigidez del elemento 4 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
15 UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO ESCUELA PROFESIONAL DE INGENIERIA CIVIL
matriz general de rigidez del elemento 5 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
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86.70
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90.52
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90.52
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0.00 181.03
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
16 UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO ESCUELA PROFESIONAL DE INGENIERIA CIVIL
matriz general de rigidez del elemento 6 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
17 UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO ESCUELA PROFESIONAL DE INGENIERIA CIVIL
matriz general de rigidez del elemento 7 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
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26
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
18 UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO ESCUELA PROFESIONAL DE INGENIERIA CIVIL
matriz general de rigidez del elemento 8 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
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26
27
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
19 UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO ESCUELA PROFESIONAL DE INGENIERIA CIVIL
matriz general de rigidez del elemento 9 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
20 UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO ESCUELA PROFESIONAL DE INGENIERIA CIVIL
matriz general de rigidez del elemento 10 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
21 UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO ESCUELA PROFESIONAL DE INGENIERIA CIVIL
I) MATRIZ DE RIGIDEZ DE LA ESTRUCTURA 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
55.4
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0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-62.0
0.0
93.5
3967
0.0
93.5
0.0
0.0
0.0
0.0
0.0
0.0
-3905
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-6267
0.0
0.0
6282
36.3
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-15.0
36.3
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-93.5
0.0
94.0
93.5
36.3
305.1
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-36.3
58.6
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
55.4
0.0
-86.7
-55.4
0.0
-86.7
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
6034
0.0
0.0
-6034
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-86.7
0.0
181.0
86.7
0.0
90.5
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-3905
0.0
0.0
0.0
0.0
0.0
-55.4
0.0
86.7
7183
0.0
-6.8
-62.0
0.0
-93.5
0.0
0.0
0.0
-3161
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-15.0
-36.3
0.0
0.0
0.0
0.0
-6034
0.0
0.0
12324
-12.5
0.0
-6267
0.0
0.0
0.0
0.0
0.0
-8.0
23.8
0.0
0.0
0.0
0.0
0.0
0.0
0.0
36.3
58.6
0.0
0.0
0.0
-86.7
0.0
90.5
-6.8
-12.5
581.0
93.5
0.0
94.0
0.0
0.0
0.0
0.0
-23.8
47.4
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-3905
0.0
0.0
0.0
0.0
0.0
-62.0
0.0
93.5
7127
0.0
93.5
0.0
0.0
0.0
0.0
0.0
0.0
-3161
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-15.0
-36.3
0.0
0.0
0.0
0.0
-6267
0.0
0.0
6290
-12.5
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-8.0
23.8
0.0
0.0
0.0
0.0
0.0
0.0
0.0
36.3
58.6
0.0
0.0
0.0
-93.5
0.0
94.0
93.5
-12.5
400.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-23.8
47.4
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
55.4
0.0
-86.7
-55.4
0.0
-86.7
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
6034
0.0
0.0
-6034
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-86.7
0.0
181.0
86.7
0.0
90.5
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-3161
0.0
0.0
0.0
0.0
0.0
-55.4
0.0
86.7
3278
0.0
-6.8
-62.0
0.0
-93.5
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-8.0
-23.8
0.0
0.0
0.0
0.0
-6034
0.0
0.0
12309
-23.8
0.0
-6267
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
23.8
47.4
0.0
0.0
0.0
-86.7
0.0
90.5
-6.8
-23.8
463.8
93.5
0.0
94.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-3161
0.0
0.0
0.0
0.0
0.0
-62.0
0.0
93.5
3223
0.0
93.5
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-8.0
-23.8
0.0
0.0
0.0
0.0
-6267
0.0
0.0
6275
-23.8
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
23.8
47.4
0.0
0.0
0.0
-93.5
0.0
94.0
93.5
-23.8
282.8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
22 UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO ESCUELA PROFESIONAL DE INGENIERIA CIVIL
entonses tenemos
4 5 6 7 8 9 13 14 15 16 17 18 22 23 24 25 26 27
0.00
5
6
7
8
9
13
14
15
16
17
18
22
23
24
25
26
27
4022
0.0
-6.8
-62.0
0.0
-93.5
-3905
0
0
0
0
0
0.0
0.0
0.0
0.0
0.0
0.0
-31.5
0.0
12316
36.3
0.0
-6267
0.0
0
-15
36
0
0
0
0.0
0.0
0.0
0.0
0.0
0.0
52.67
-6.8
36.3
486.2
93.5
0.0
94.0
0
-36
59
0
0
0
0.0
0.0
0.0
0.0
0.0
0.0
23.40
-62.0
0.0
93.5
3967
0.0
93.5
0
0
0
-3905
0
0
0.0
0.0
0.0
0.0
0.0
0.0
0.00
0.0
-6267
0.0
0.0
6282
36.3
0
0
0
0
-15
36
0.0
0.0
0.0
0.0
0.0
0.0
0.00
-93.5
0.0
94.0
93.5
36.3
305.1
0
0
0
0
-36
59
0.0
0.0
0.0
0.0
0.0
0.0
0.00
4
-3905
0
0
0
0
0
7183
0.0
-6.8
-62.0
0.0
-93.5
-3161
0
0
0
0
0
0
-15
-36
0
0
0
0.0
12324
-12.5
0.0
-6267
0.0
0
-8
24
0
0
0
0.00
0
36
59
0
0
0
-6.8
-12.5
581.0
93.5
0.0
94.0
0
-24
47
0
0
0
0.00
0
0
0
-3905
0
0
-62.0
0.0
93.5
7127
0.0
93.5
0
0
0
-3161
0
0
0.00
0
0
0
0
-15
-36
0.0
-6267
0.0
0.0
6290
-12.5
0
0
0
0
-8
24
0.00
0
0
0
0
36
59
-93.5
0.0
94.0
93.5
-12.5
400.0
0
0
0
0
-24
47
18.90
0.0
0.0
0.0
0.0
0.0
0.0
-3161
0.0
0.0
0.0
0.0
0.0
3278
0.0
-6.8
-62.0
0.0
-93.5
0.00
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-8.0
-23.8
0.0
0.0
0.0
0.0
12309
-23.8
0.0
-6267
0.0
0.00
0.0
0.0
0.0
0.0
0.0
0.0
0.0
23.8
47.4
0.0
0.0
0.0
-6.8
-23.8
463.8
93.5
0.0
94.0
0.00
=
0.00
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-3161
0.0
0.0
-62.0
0.0
93.5
3223
0.0
93.5
-22.8
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-8.0
-23.8
0.0
-6267
0.0
0.0
6275
-23.8
-34.2
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
23.8
47.4
-93.5
0.0
94.0
93.5
-23.8
282.8
X
D4 D5 D6 D7 D8 D9 D13 D14 D15 D16 D17 D18 D22 D23 D24 D25 D26 D27
0.00
28.77
23.54
0.00
18.39
14.84
+
0.00
59.58 16.58
0.00 41.11
7.81
0.00
32.39
-34.1
0.00
22.7
-22.7
4 5 6 7 8 9 13 14 15 16 17 18 22 23 24 25 26 27
23 UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO ESCUELA PROFESIONAL DE INGENIERIA CIVIL
NO IMPRIMIR
W D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 D11 D12 D13 D14 D15 D16 D17 D18 D19 D20 D21 D22 D23 D24 D25 D26 D27
= = = = = = = = = = = = = = = = = = = = = = = = = = =
0 0 0
0.357
-0.011
-0.037
0.768
-0.013
-0.157
0 0 0
0.359
-0.017
-0.135
0.764
-0.024
-0.042
0 0 0
0.36201
-0.01434
-0.02921
0.76117
-0.02236
-0.1559
q1 q2 M3 q4 q5 M6 q7 q8 M9 q10 q11 M12 q13 q14 q15 q16 q17 q18 q19 q20 M21 q22 q23 q24 q25 q26 q27
UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO ESCUELA PROFESIONAL DE INGENIERIA CIVIL
UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO ESCUELA PROFESIONAL DE INGENIERIA CIVIL
UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO ESCUELA PROFESIONAL DE INGENIERIA CIVIL
UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO ESCUELA PROFESIONAL DE INGENIERIA CIVIL
UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO ESCUELA PROFESIONAL DE INGENIERIA CIVIL
UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO ESCUELA PROFESIONAL DE INGENIERIA CIVIL
UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO ESCUELA PROFESIONAL DE INGENIERIA CIVIL
UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO ESCUELA PROFESIONAL DE INGENIERIA CIVIL
UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO ESCUELA PROFESIONAL DE INGENIERIA CIVIL
UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO ESCUELA PROFESIONAL DE INGENIERIA CIVIL
UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO ESCUELA PROFESIONAL DE INGENIERIA CIVIL
UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO ESCUELA PROFESIONAL DE INGENIERIA CIVIL
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