e Structur As
6
Para una viga de hormigon graficar el comportamiento sobre un lecho elastico, que tiene las siguientes caracteristicas: Datos geometricos: Base b 10cm Altura h 30cm Longitud L 12m Datos físicos: Modulo de elasticidad: E 2300MPa Coeficiente de balasto: k 2.0 kgf cm 2 Calculo de inercia de la seccion: I bh 3 12 2.25 10 4 cm 4 Ĭ 4 k 4E I 0.555 1 m Considerando el cambio de variable de: u Ĭx = Tenemos: IJu () e u cos u () ĸu () e u sin u () 0 2 4 6 1 0.5 0 0.5 1 1 0.5 0 0.5 1 IJu () ĸu () u You created this PDF from an application that is not licensed to print to novaPDF printer (http://www.novapdf.com)
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Transcript of e Structur As
Para una viga de hormigon graficar el comportamiento sobre un lecho elastico, que tiene las siguientescaracteristicas:
Datos geometricos: Base b 10cm
Altura h 30cm
Longitud L 12m
Datos físicos: Modulo de elasticidad: E 2300MPa
Coeficiente de balasto: k 2.0kgf
cm2
Calculo de inercia de la seccion: Ib h312
2.25 104 cm4
β4 k
4E I0.555
1m
Considerando el cambio de variable de: u βx=
Tenemos: θu( ) e u cos u( )
ξu( ) e u sin u( )
0 2 4 61
0.5
0
0.5
1
1
0.5
0
0.5
1
θu( ) ξu( )
u
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ϕu( ) e u cos u( ) sin u( )( )
ψu( ) e u cos u( ) sin u( )( )
0 2 4 61
0.5
0
0.5
1
1
0.5
0
0.5
1
ϕ u( ) ψu( )
u
Calculo del desplazamiento, giro, momento y cortante:
Desplazamiento: ωH C1 θu( ) C2 ξu( )=
uωH
dd
C1 β ϕu( ) C2 β ψu( )=Giro:
E I 2uωH
d
d
2 2 C1 β2
ξu( ) 2 C2 β2 θu( )=
Momento:
Cortante: E I 3uωH
d
d
3 2 C1 β3
ψu( ) 2 C2 β3 ϕu( )=
Viga en fundacion elastica con carga puntual P: P 10kgf
Caso 1: QoP
2 M 0 tenemos: C2 0 C1
Qo
2 E I β3
ωH u( ) C1 θu( ) C2 ξu( )
αu( ) C1 β ϕu( ) C2 β ψu( )
M u( )1
E I2 C1 β2
ξu( ) 2 C2 β2 θu( )
V u( )1
E I2 C1 β3
ψu( ) 2 C2 β3 ϕu( )
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0 2 4 61 10 4
0
1 10 4
2 10 4
0.0003
1.859 10 5
ω.H u( )
6.70 u
0 2 4 6
1.5 10 4
1 10 4
5 10 5
0
5 10 5
αu( )
u
0 2 4 61.5 10 10
1 10 10
5 10 11
0
5 10 11
M u( )
u
0 2 4 62 10 10
1 10 10
0
1 10 10
V u( )
u
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Caso 2: V 0 Mo 10kgf m C1Mo
2 E I β2
C2Mo
2 E I β2
ωH u( ) C1 θu( ) C2 ξu( )
αu( ) C1 β ϕu( ) C2 β ψu( )
M u( )1
E I2 C1 β2
ξu( ) 2 C2 β2 θu( )
V u( )1
E I2 C1 β3
ψu( ) 2 C2 β3 ϕu( )
0 2 4 64 10 4
2 10 4
0
2 10 4
ωH u( )
u
0 2 4 6
1 10 4
0
1 10 4
2 10 4
αu( )
u
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0 2 4 64 10 10
3 10 10
2 10 10
1 10 10
0
1 10 10
M u( )
u
0 2 4 61 10 10
0
1 10 10
2 10 10
3 10 10
V u( )
u
C1Qo
2 E I β3
Mo
2 E I β2
C2Mo
2 E I β2
Caso 3:
ωH u( ) C1 θu( ) C2 ξu( )
αu( ) C1 β ϕu( ) C2 β ψu( )
M u( )1
E I2 C1 β2
ξu( ) 2 C2 β2 θu( )
V u( )1
E I2 C1 β3
ψu( ) 2 C2 β3 ϕu( )
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0 2 4 62 10 4
1 10 4
0
1 10 4
2 10 4
ωH u( )
u
0 2 4 6
1 10 4
0
1 10 4
αu( )
u
0 2 4 63 10 10
2 10 10
1 10 10
0
1 10 10
M u( )
u
0 2 4 65 10 11
0
5 10 11
1 10 10
1.5 10 10
2 10 10
V u( )
u
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