主应力迹线的自动绘制

Automatic Portraying of Principal Stress Trace

主应力迹线是代表主应力方向的曲线簇。在土木建筑工程中主应力迹线是布筋方向的依据,但是在工程中通常都是徒手或用曲线板近似绘制主应力迹线。作者提出一种新的主应力迹线自动的绘制方法。该方法是根据主应力迹线满足过任意三条等倾线的主应力都可以用二次曲线来描述这一条件,再利用主应力迹线本身所具有的性质列出方程组解算出描述主应力迹线的一元二次方程,然后根据方程描绘出所求的主应力迹线。实验证明这种方法对于工程上进行主应力迹线的绘制很有效。

The principal stress traces represent the directions of principal stresses inside an object. In civil engineering, the disposing of reinforcing steel bars is often based on the analysis of the principal stress traces. The principal stress traces of an object are often drawn by hand, or at most drawn with a French curve, which induces the results very inaccurate. In this paper is presented an automatic way of drawing the lines. The new method gives out a set of equations based on the fundamental algebra rules that principal stress trace obeys and the essential attributes it possess, we then combine these equations with further information described in this paper leading to an exact description of the conic representing the principal stress traces. From the results of abundant experiments, this method is proved to be practically effective.