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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.
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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+¿
√ ¿
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)exp"GSI −1009−3 D $
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Ro(): 3uarcita
Inse!t)ndo los d)tos en el p!o3!)m) Ro(l)0$ se o0t'ene (omo !eslt)do&
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*)ll)ndo los p)!2met!os del m)('"o !o(oso&
m b!4.exp"45−10028−4 (0) $+,&5.
)exp"45−1009−3(0) $,++.
a1
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−203 $,/5.
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