圆形截面混凝土柱偏心受压算法研究

An algorithm study on circular section column under eccentric compression

圆形截面混凝土柱在实际工程中应用广泛,其偏心受压正截面承载力计算是一个常见问题。《混凝土结构设计规范》(GB 50010—2010)附录E.0.4给出了相关控制方程组,该方程组属于超越方程,不能采用通常的直接解法进行计算,必须进行近似处理或者借助于数值解法。本文不对该方程进行任何简化,而是直接采用迭代法进行求解,并证明了在每次迭代过程中控制方程有且仅有一个解,可保证计算稳定可靠。算例表明,该算法具有很好的适应能力,可快速收敛到指定精度。目前,该算法已在北京市建筑设计研究院有限公司自主研发的设计软件Paco中完整实现,取得了良好的应用效果。

Circular section concrete columns are widely used in the actual project,whose eccentric compression capacity is a common problem. Code for design of concrete structures(GB 50010—2010) appendix E. 0. 4 gives the relevant control equations,which are transcendental equations. Generally the direct method can't be used,and it must be approximated by means of numerical solution. This paper does not make any simplification of the equations,but solves it directly by iteration,and proves that the equations have one and only one solution to ensure stable and reliable computing. Numerical examples show that the iterative algorithm has a good ability to adapt and quickly converge to the exact solution. At present,the algorithm has complete implementation in Beijing Institute of Architectural Design self-developed design software Paco and achieved good effect.