Analisis estatico con brazo rigido_Rev0.pdf
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Transcript of Analisis estatico con brazo rigido_Rev0.pdf
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Universidad Jos Carlos Mariategui Anlisis Estructura II Pag. 1
4. Ejemplo de problema c/software
Problema 01
1.1.- Hallar la matriz de rigidez total
1.2.- Hallar la matriz de rigidez lateral
1.3.- Hallar desplazamiento lateral
30 Ton
Viga
Placa de CA Columna
Datos:
Viga = 30X70 cm
Columna = 30X70 cm
Placa = 20X200 cm
E = 2X106 Ton/m2
Cuando: Cuando: Cuando:
D1 = 1 D2 = 1 D3= 1
0 0 0 0 0 0 0 0 0
[A]1 = 0 0 0 [A]2 = 1 0 0 [A]3 = 0 0 0
0 0 -1 0 0 0 0 0 -1
1 0 0 0 1 0 0 1 0
2 m 8 m 0.7 m
4 m
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Universidad Jos Carlos Mariategui Anlisis Estructura II Pag. 2
Datos de los elementos:
Placa Viga Columna
2.00 0.70 0.70
0.20 0.30 0.30
a b
L = 1.00 0.00
A =
E =
I =
EI =
V =
f=
G =
g=
[K]v-brazo rgido =
[K]columna =
[K]placa =
65806.8928 185904.47 -65807 120097.6 0 0 0
0 0 0 1 185904.472 598239.49 -185904 266216.3 0 0 0
[K]T = 0 0 0 0 * -65806.893 -185904.47 65806.9 -120097.6 * 0 0 -1 +
0 0 -1 0 120097.579 266216.3 -120098 292237.4 1 0 0
0 1 0 0 353.497172 1829.3479 -353.5 1475.851 0 0 0
0 0 0 1 * 1829.34787 11520.767 -1829.3 5583.635 * 1 0 0 +
0 0 0 0 -353.49717 -1829.3479 353.497 -1475.851 0 0 0
1475.85069 5583.6351 -1475.9 8215.569 0 1 0
0 0 0 0 4232.20579 11955.981 -4232.2 7723.776 0 0 0
0 0 0 1 * 11955.9814 38474.277 -11956 17121.04 * 0 0 0
0 0 -1 0 -4232.2058 -11955.981 4232.21 -7723.776 0 0 -1
7723.77557 17121.036 -7723.8 18794.52 0 1 0
120097.5793 266216.3007 -120097.579 292237.4429 0 0 0 292237.44 0 120097.58
0 0 0 0 * 0 0 0 = 0 0 0
65806.89276 185904.472 -65806.8928 120097.5793 0 0 -1 120097.58 0 65806.893
1 0 0
1829.347866 11520.76742 -1829.34787 5583.635125 0 0 0 11520.767 5583.6351 0
1475.850694 5583.635125 -1475.85069 8215.568862 * 1 0 0 = 5583.6351 8215.5689 0
0 0 0 0 0 0 0 0 0 0
0 1 0
0 0 0 0 0 0 0 0 0 0
7723.775568 17121.03584 -7723.77557 18794.52055 * 0 0 0 = 0 18794.521 7723.7756
4232.20579 11955.98136 -4232.20579 7723.775568 0 0 -1 0 7723.7756 4232.2058
0 1 0
1475.85
5583.64
-1475.85
8215.57
-185904.47
65806.89
-120097.58
120097.58
266216.30
-120097.58
292237.44
7723.78
17121.04
-7723.78
18794.52
-353.50
-1829.35
353.50
-1475.85
-4232.21
-11955.98
4232.21
-7723.78
-65806.8965806.89
185904.47
-65806.89
120097.58
1829.35
11520.77
-1829.35
5583.64
11955.98
38474.28
-11955.98
17121.04
185904.47
598239.49
4232.21
11955.98
-4232.21
7723.78
353.50
1829.35
-353.50
1475.85
-185904.47
266216.30
Longitud de elemento (m)
Seccion de elemento (m2)
Modulo de elastisidad (tn/m2)
Momento de inercia (m4)
Producto EI (tn/m2)
Coeficiente de poison
Factor de forma
Modulo de corte
Factor de corte 0.40
Donde:
b*h
I=b*h3/12
G=E/(2+V)
g=6fEI/GAL2
0.20
1.20
909090.91
3.65
0.40
2000000.00
0.13333
266666.67
3.65
0.21
2000000.00
0.00858
17150.00
8.35
0.21
2000000.00
0.00858
17150.00
(m) (m)
Brazo
(m)
Viga Columna PlacaDescripcin
33 = 1 1 1+ 2
2 2+ 3 3 3
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Universidad Jos Carlos Mariategui Anlisis Estructura II Pag. 3
303758.2 5583.6 120097.6
[K]T = 5583.6 27010.1 7723.8
120097.6 7723.8 70039.1
Rigidez Lateral
[K]L = 70039.1 - 120097.6 7723.8 * 0.000003 -0.000001 * 120097.58
-0.000001 0.000037 7723.78
[K]L = 70039.1 - 0.4 0.2 * 120097.58 = 70039.1 - 48614.1
7723.78
[K]L = 21425.0 Ton/m
Si:
= 30 Ton
Entonces:
Despejando de la ecuacin tenemos:
0.00140 m Por lo tanto:
D3 = 0.00140 m
- 303758.2 5583.6 -1 120097.6
5583.6 27010.1 * 7723.8 * 0.001400
- 0.000003305 -0.000000683 120097.6
-0.000000683 0.000037164 * 7723.8 * 0.001400
- 0.3916039
0.2050050 * 0.001400
-0.0005483 Rad
-0.0002871 Rad
=
= - 1
=
=
= 1
=
12
=
12
=
12
=
