distribucion de e.docx

8/17/2019 distribucion de e.docx

1/24

CALCULO DE LOS ESFUERZOS ALEJADOS DE LOS LÍMITESDE LA EXCAVACION

Observando la figura siguiente, podemos expresar las ecuaciones finales de la

solución bidimensional de la distribución de esfuerzos alrededor de una abertura

en un cuerpo elástico usando en este caso un sistema de coordenadas polares en

la cual los esfuerzos son definidos en técnicas de tracciones, actuando sobre las

caras de un elemento ubicado por un radio r y un ángulo polar θ.


2/24

ESFUERZOS ALEJADOS DE LOS LÍMITES DE LA EXCAVACIÓN

Componentes de los esfe!"os en el pnto #!$ θ %&

Esfuerzo radial: σ r 1

2 P

z[ (1+k )(1− a

2

r2 )+(1−k )(1− 4 a

2

r2 +

3a4

r4 )cos2θ]

Esfuerzo tangencial: σ θ 1

2 P z[ (1+k )(1+ a

2

r2 )−(1−k )(1+ 3a

4

r4 )cos2θ]

Esfuerzo de corte: τ rθ 1

2 P

z[−(1−k )(1+2a

2

r2 −

3a4

r4 )sen2θ]

Esfe!"os p!'n('p)les en el pnto #!$ θ %&

Esfuerzo principal máximo: σ !1

2 " σ r # σ θ $ #

τr θ

¿¿

14(σ r−σ θ )2+¿

√ ¿


3/24


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