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本文介绍的降次迭代法,比牛顿法[1]有更好的收敛性。它使三次代数方程的求解变得简单容易。尤其用来解部分预应力混凝土梁开裂截面的中和轴方程,常能得到满意的结果。为了方便设计人员在结构验算中参考和掌握,本文先写出中和轴方程,然后介绍降次迭代的思路和方法,并附上工程实例。由于本文的性质,扼要叙述有关内容和结论,力求浅显、直观,而不拘泥于详细论述。
The reduced iteration method introduced in this paper has better convergence than Newton’s method [1]. It makes the solution of the cubic algebraic equation simple and easy. In particular, it can be used to solve the neutral axis equations of the cracked sections of partially prestressed concrete beams. In order to facilitate the designer’s reference and mastery in the structural calculations, this paper first writes out the neutral axis equations, then introduces the ideas and methods of degenerative iterations, and attaches engineering examples. Due to the nature of this article, it is necessary to describe the relevant contents and conclusions, strive to be simple and intuitive, and not rigidly discuss in detail.