matriz ensamblada
DESCRIPTION
Matriz EnsambladaTRANSCRIPT
PROYECTO DE MADERASNombre: Univ. Juan Carlos Sanabria Coca C.I.
En el portico de la figura determinar1. Matriz de rigidez de cada barra2. Matriz ensamblada3. Vector de fuerzas4. Vector de momentos de emptramiento perfecto5. Matriz Reducida6. Despazamientos nodales7.reacciones
COORDENADAS
4m
1.5m
5m 5m
2.5m2m
5m
1.5T
q1=300kg/m
q2=250kg/m2T
1.5T
1.5plg:
9
x
y
4m
1.5m
5m 5m
2.5m2m
5m
1.5T
q1=300kg/m
q2=250kg/m2T
1.5T
1.5plg:
1
2
3
4 7
6 9
5 8
10
1
2 3
46
10
5 8
7
9
x
y
4m
1.5m
5m 5m
2.5m2m
5m
1.5T
q1=300kg/m
q2=250kg/m2T
1.5T
1.5plg:
1
2
3
4 7
6 9
5 8
10
1
2 3
46
10
5 8
7
PROYECTO DE MADERAS6581308
COORDENADAS
nudo x y1 0 12 0 53 2.5 6.54 5 55 5 2.56 5 07 10 58 10 2.59 10 0
10 12 5
9
x
y
4m
1.5m
5m 5m
2.5m2m
5m
1.5T
q1=300kg/m
q2=250kg/m2T
1.5T
1.5plg:
1
2
3
4 7
6 9
5 8
10
1
2 3
46
10
5 8
7
9
x
y
4m
1.5m
5m 5m
2.5m2m
5m
1.5T
q1=300kg/m
q2=250kg/m2T
1.5T
1.5plg:
1
2
3
4 7
6 9
5 8
10
1
2 3
46
10
5 8
7
MATRIZ DE RIGIDEZ DE CADA BARRAb= 0.3 m h= 0.4 m
Matriz de rididez de la barra 1-2ÁREA (m²) A 0.12 DX1 DY1 O1INERCIA (m^4) I= 0.0016 39 0 -78MODULO DE ELASTICIDAD E= 130000 0.00E+00 3900 0LONGITUD (m) L= 4 K1-2= -78 0 208ÁNGULO α= 90 -39 0 78COSENO α C= 0 0 -3900 0SENOα 1 -78 0 104
b= 0.3 m h= 0.4 mMatriz de rididez de la barra 2-3
ÁREA (m²) A 0.12 DX2 DY2 O2INERCIA (m^4) I= 0.0016 3955.12437 2312.5793 -75.29796141MODULO DE ELASTICIDAD E= 130000 2312.5793 1487.59407 125.5152546LONGITUD (m) L= 2.92 K2-3= -75.2979614 125.515255 284.9315068ÁNGULO α= 30.96 -3955.12437 -2312.5793 75.29796141COSENO α C=0.8575266562 -2312.5793 -1487.59407 -125.5152546SENOα 0.5144395338 -75.2979614 125.515255 142.4657534
b= 0.3 m h= 0.4 mMatriz de rididez de la barra 3-4
ÁREA (m²) A 0.12 DX3 DY3 O3INERCIA (m^4) I= 0.0016 3955.12437 -2312.5793 75.29796141MODULO DE ELASTICIDAD E= 130000 -2312.5793 1487.59407 125.5152546LONGITUD (m) L= 2.92 K3-4= 75.2979614 125.515255 284.9315068ÁNGULO α= 329.04 -3955.12437 2312.5793 -75.29796141COSENO α C=0.8575266562 2312.5793 -1487.59407 -125.5152546SENOα -0.514439534 75.2979614 125.515255 142.4657534
b= 0.3 m h= 0.4 m
Matriz de rididez de la barra 4-5ÁREA (m²) A 0.12 DX4 DY4 O4INERCIA (m^4) I= 0.0016 159.744 0 199.68MODULO DE ELASTICIDAD E= 130000 0 6240 0LONGITUD (m) L= 2.5 K4-5= 199.68 0 332.8ÁNGULO α= 270 -159.744 0 -199.68COSENO α C= 0 0 -6240 0SENOα -1 199.68 0 166.4
b= 0.3 m h= 0.4 mMatriz de rididez de la barra 5-6
ÁREA (m²) A 0.12 DX5 DY5 O5INERCIA (m^4) I= 0.0016 159.744 0 199.68MODULO DE ELASTICIDAD E= 130000 0 6240 0LONGITUD (m) L= 2.5 k5-6= 199.68 0 332.8ÁNGULO α= 270 -159.744 0 -199.68COSENO α C= 0 0 -6240 0SENOα -1 199.68 0 166.4
b= 0.3 m h= 0.4 mMatriz de rididez de la barra 4-7
ÁREA (m²) A 0.12 DX4 DY4 O4INERCIA (m^4) I= 0.0016 3120 0 0MODULO DE ELASTICIDAD E= 130000 0 19.968 49.92LONGITUD (m) L= 5 K4-7= 0 49.92 166.4ÁNGULO α= 0 -3120 0 0COSENO α C= 1 0 -19.968 -49.92SENOα 0 0 49.92 83.2
b= 0.3 m h= 0.4 mMatriz de rididez de la barra 5-8
ÁREA (m²) A 0.12 DX5 DY5 O5
INERCIA (m^4) I= 0.0016 3120 0 0MODULO DE ELASTICIDAD E= 130000 0 19.968 49.92LONGITUD (m) L= 5 K5-8= 0 49.92 166.4ÁNGULO α= 0 -3120 0 0COSENO α C= 1 0 -19.968 -49.92SENOα 0 0 49.92 83.2
b= 0.3 m h= 0.4 mMatriz de rididez de la barra 7-8
ÁREA (m²) A 0.12 DX7 DY7 O7INERCIA (m^4) I= 0.0016 159.744 0 199.68MODULO DE ELASTICIDAD E= 130000 0 6240 0LONGITUD (m) L= 2.5 K7-8= 199.68 0 332.8ÁNGULO α= 270 -159.744 0 -199.68COSENO α C= 0 0 -6240 0SENOα -1 199.68 0 166.4
b= 0.3 m h= 0.4 mMatriz de rididez de la barra 8-9
ÁREA (m²) A 0.12 DX8 DY8 O8INERCIA (m^4) I= 0.0016 159.744 0 199.68MODULO DE ELASTICIDAD E= 130000 0 6240 0LONGITUD (m) L= 2.5 K8-9= 199.68 0 332.8ÁNGULO α= 270 -159.744 0 -199.68COSENO α C= 0 0 -6240 0SENOα -1 199.68 0 166.4
b= 0.3 m h= 0.4 mMatriz de rididez de la barra 7-10
ÁREA (m²) A 0.12 DX7 DY7 O7INERCIA (m^4) I= 0.0016 7800 0 0MODULO DE ELASTICIDAD E= 130000 0 312 312
LONGITUD (m) L= 2 K7-10= 0 312 416ÁNGULO α= 0 -7800 0 0COSENO α C= 1 0 -312 -312SENOα 0 0 312 208
1 2 3 4 5 6 7DX1 DY1 O1 DX2 DY2 O2 DX3
DX1 39 0 -78 -39 0 -78 0DY1 0 3900 0 0 -3900 0 0O1 -78 0 208 78 0 104 0
DX2 -39 0 78 3994.12437 2312.5793 2.70203859 -3955.124372DY2 0 -3900 0 2312.5793 5387.59407 125.515255 -2312.579297O2 -78 0 104 2.70203859 125.515255 492.931507 75.29796141
DX3 0 0 0 -3955.12437 -2312.5793 75.2979614 7910.248745DY3 0 0 0 -2312.5793 -1487.59407 -125.515255 0O3 0 0 0 -75.2979614 125.515255 142.465753 150.5959228
DX4 0 0 0 0 0 0 -3955.124372DY4 0 0 0 0 0 0 2312.579297O4 0 0 0 0 0 0 75.29796141
DX5 0 0 0 0 0 0 0DY5 0 0 0 0 0 0 0O5 0 0 0 0 0 0 0
DX6 0 0 0 0 0 0 0DY6 0 0 0 0 0 0 0O6 0 0 0 0 0 0 0
DX7 0 0 0 0 0 0 0DY7 0 0 0 0 0 0 0O7 0 0 0 0 0 0 0
DX8 0 0 0 0 0 0 0DY8 0 0 0 0 0 0 0
O8 0 0 0 0 0 0 0DX9 0 0 0 0 0 0 0DY9 0 0 0 0 0 0 0O9 0 0 0 0 0 0 0
DX10 0 0 0 0 0 0 0DY10 0 0 0 0 0 0 0O10 0 0 0 0 0 0 0
MATRIZ DE RIGIDEZ DE CADA BARRA
DX2 DY2 O2 FN FEP-39 0 -78 DX1 0
0 -3900 0 DY1 078 0 104 O1 039 0 78 DX2 2
0 3900 0 DY2 078 0 208 O2 0
DX3 DY3 O3 FN FEP-3955.124372 -2312.579297 -75.29796141 DX2 2-2312.579297 -1487.594069 125.5152546 DY2 075.29796141 -125.5152546 142.4657534 O2 03955.124372 2312.579297 75.29796141 DX3 02312.579297 1487.594069 -125.5152546 DY3 075.29796141 -125.5152546 284.9315068 O3 0
DX4 DY4 O4 FN FEP-3955.124372 2312.579297 75.29796141 DX3 02312.579297 -1487.594069 125.5152546 DY3 -1.5
-75.29796141 -125.5152546 142.4657534 O3 03955.124372 -2312.579297 -75.29796141 DX4 0
-2312.579297 1487.594069 -125.5152546 DY4 0-75.29796141 -125.5152546 284.9315068 O4 0
DX5 DY5 O5 FN FEP-159.744 0 199.68 DX4 0
0 -6240 0 DY4 0-199.68 0 166.4 O4 0159.744 0 -199.68 DX5 0
0 6240 0 DY5 0-199.68 0 332.8 O25 0
DX6 DY6 O6 FN FEP-159.744 0 199.68 DX5 0
0 -6240 0 DY5 0-199.68 0 166.4 O5 0159.744 0 -199.68 DX6 0
0 6240 0 DY6 0-199.68 0 332.8 O6 0
DX7 DY7 O7 FN FEP-3120 0 0 DX4 0
0 -19.968 49.92 DY4 00 -49.92 83.2 O4 0
3120 0 0 DX7 00 19.968 -49.92 DY7 00 -49.92 166.4 O7 0
DX8 DY8 O8 FN FEP
-3120 0 0 DX5 00 -19.968 49.92 DY5 00 -49.92 83.2 O25 0
3120 0 0 DX8 00 19.968 -49.92 DY8 00 -49.92 166.4 O8 0
DX8 DY8 O8 FN FEP-159.744 0 199.68 DX7 0
0 -6240 0 DY7 0-199.68 0 166.4 O7 0159.744 0 -199.68 DX8 0
0 6240 0 DY8 0-199.68 0 332.8 O8 0
DX9 DY9 O9 FN FEP-159.744 0 199.68 DX8 0
0 -6240 0 DY8 0-199.68 0 166.4 O8 0159.744 0 -199.68 DX9 0
0 6240 0 DY9 0-199.68 0 332.8 O9 0
DX10 DY10 O10 FN FEP-7800 0 0 DX7 0
0 -312 312 DY7 0
0 -312 208 O7 07800 0 0 DX10 0
0 312 -312 DY10 -1.50 -312 416 O10 0
MATRIZ ENSAMBLADA EN COORDENADAS GLOBALES8 9 10 11 12 13 14 15
DY3 O3 DX4 DY4 O4 DX5 DY5 O50 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0
-2312.579297 -75.29796141 0 0 0 0 0 0-1487.594069 125.5152546 0 0 0 0 0 0-125.5152546 142.4657534 0 0 0 0 0 0
0 150.5959228 -3955.124372 2312.579297 75.29796141 0 0 02975.188139 0 2312.579297 -1487.594069 125.5152546 0 0 0
0 569.8630137 -75.29796141 -125.5152546 142.4657534 0 0 02312.579297 -75.29796141 7234.868372 -2312.579297 124.3820386 -159.744 0 199.68-1487.594069 -125.5152546 -2312.579297 7747.562069 -75.59525461 0 -6240 0125.5152546 142.4657534 124.3820386 -75.59525461 784.1315068 -199.68 0 166.4
0 0 -159.744 0 -199.68 3439.488 0 00 0 0 -6240 0 0 12499.968 49.920 0 199.68 0 166.4 0 49.92 8320 0 0 0 0 -159.744 0 -199.680 0 0 0 0 0 -6240 00 0 0 0 0 199.68 0 166.40 0 -3120 0 0 0 0 00 0 0 -19.968 -49.92 0 0 00 0 0 49.92 83.2 0 0 00 0 0 0 0 -3120 0 00 0 0 0 0 0 -19.968 -49.92
0 0 0 0 0 0 49.92 83.20 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0
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MATRIZ ENSAMBLADA EN COORDENADAS GLOBALES16 17 18 19 20 21 22 23 24
DX6 DY6 O6 DX7 DY7 O7 DX8 DY8 O80 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 -3120 0 0 0 0 00 0 0 0 -19.968 49.92 0 0 00 0 0 0 -49.92 83.2 0 0 0
-159.744 0 199.68 0 0 0 -3120 0 00 -6240 0 0 0 0 0 -19.968 49.92
-199.68 0 166.4 0 0 0 0 -49.92 83.2159.744 0 -199.68 0 0 0 0 0 0
0 6240 0 0 0 0 0 0 0-199.68 0 332.8 0 0 0 0 0 0
0 0 0 11079.744 0 199.68 -159.744 0 199.680 0 0 0 6571.968 262.08 0 -6240 00 0 0 199.68 262.08 915.2 -199.68 0 166.40 0 0 -159.744 0 -199.68 3439.488 0 00 0 0 0 -6240 0 0 12499.968 -49.92
0 0 0 199.68 0 166.4 0 -49.92 8320 0 0 0 0 0 -159.744 0 -199.680 0 0 0 0 0 0 -6240 00 0 0 0 0 0 199.68 0 166.40 0 0 -7800 0 0 0 0 00 0 0 0 -312 -312 0 0 00 0 0 0 312 208 0 0 0
233
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25 26 27 28 29 30DX9 DY9 O9 DX10 DY10 O10 FN FEP
0 0 0 0 0 0 DX1 00 0 0 0 0 0 DY1 00 0 0 0 0 0 O1 00 0 0 0 0 0 DX2 20 0 0 0 0 0 DY2 00 0 0 0 0 0 O2 00 0 0 0 0 0 DX3 00 0 0 0 0 0 DY3 1.50 0 0 0 0 0 O3 00 0 0 0 0 0 DX4 00 0 0 0 0 0 DY4 00 0 0 0 0 0 O4 00 0 0 0 0 0 DX5 00 0 0 0 0 0 DY5 00 0 0 0 0 0 O5 00 0 0 0 0 0 DX6 00 0 0 0 0 0 DY6 00 0 0 0 0 0 O6 00 0 0 -7800 0 0 DX7 00 0 0 0 -312 312 DY7 00 0 0 0 -312 208 O7 0
-159.744 0 199.68 0 0 0 DX8 00 -6240 0 0 0 0 DY8 0
-199.68 0 166.4 0 0 0 O8 0159.744 0 -199.68 0 0 0 DX9 0
0 6240 0 0 0 0 DY9 0-199.68 0 332.8 0 0 0 O9 0
0 0 0 7800 0 0 DX10 00 0 0 0 312 -312 DY10 1.50 0 0 0 -312 416 O10 0
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