关键词: 莫尔圆, 极点, 平行线法, 法线法, 射线法

Abstract: Mohr circle is extensively used in strength theory of geotechnical materials, stress path and bearing capacity of foundations. The pole point is a special point on the Mohr circle. It is unique and can help to determine stresses acting on any plane. In particular, the pole point method is capable of solving complex stress problems. Based on the parallel line and normal line methods stated in textbooks of soil mechanics and material mechanics, a new method to find the pole point, i.e. the ray method, is put forward. The validity and the uniqueness of the ray method are proved by using the stress equilibrium method of the isolated element. It is concluded that the parallel line method and the normal line method are special cases of the ray method. The pole points obtained by using the parallel line method and the normal line method separately are not in the same position. But the desired stress state for any plane by using the two methods are the same. However, the parallel line method is relatively easy to use. Although the ray method is relatively complex to use, it can help to understand the concept of the pole point thoroughly.

Key words: Mohr circle, pole point, parallel line method, normal line method, ray method