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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 cross-section concrete columns are widely used in practical engineering. The calculation of bearing capacity of normal cross-section of eccentric compression is a common problem. Appendix E.0.4 of the Code for Design of Concrete Structures (GB 50010-2010) gives equations of relative governing equations that are transcendental and can not be calculated using the usual direct solution and must be approximated or numerically solved. This paper does not simplify the equation, but directly uses the iterative method to solve it. It proves that there is one and only one solution to the governing equations in each iteration, which guarantees the stability and reliability of the calculation. The example shows that the algorithm has good adaptability and can converge to the specified accuracy quickly. At present, the algorithm has been fully implemented in Paco, a self-developed design software developed by Beijing Institute of Architectural Design and Research Co., Ltd., and has achieved good application results.