A novel algorithm is proposed to analyze the reinforced concrete (RC) beam-columns (B-Cs), having rectangular or non-rectangular sections, subjected to monotonic or cyclic oblique shear and axial loading. B-Cs are discretized into the macro-elements (MEs) in the form of discrete finite-element (member) models, and their critical sections are discretized into fiber elements. A novel numerical convergence search method is proposed as the root-finding technique to reach the equilibrium state in each section. A three-loop iteration process is adapted employing three main characteristic strain variables, equilibrium functions, and reasonably acceptable tolerances. Based on the proposed algorithm, a computer program has been developed to simulate the non-linear behavior of B-Cs. A good agreement has been observed between the results obtained by applying the proposed algorithm and the experimental test results carried out by other researchers. The difference between the results of the ultimate strengths obtained using the proposed algorithm and the experimental tests on the B-Cs subjected to the oblique shear force and axial load is less than 5%. The results indicate that the ultimate strain of concrete at the most compressed corner of the critical section of B-C ranges from 0.0024 to 0.0038 under maximum to zero axial loads, respectively, and the application of 0.003 value given by ACI code for the ultimate strain of concrete can lead to unconventional non-conservative approximate results when B-C is subjected to an axial force larger than 70% of its axial load capacity.

提出了一种新颖的算法来分析具有矩形或非矩形截面的钢筋混凝土（RC）梁柱（B-Cs），该梁柱承受单调或周期性的斜向剪切力和轴向载荷。B-C以离散有限元（成员）模型的形式离散化为宏观元素（ME），其临界截面也离散化为纤维元素。提出了一种新颖的数值收敛搜索方法作为寻根技术，以使各部分达到平衡状态。采用三个主要特征应变变量，平衡函数和合理可接受的公差来调整三循环迭代过程。基于提出的算法，开发了计算机程序来模拟B-C的非线性行为。通过应用所提出的算法获得的结果与其他研究人员进行的实验测试结果之间已经观察到很好的一致性。使用所提出的算法获得的极限强度结果与承受斜剪力和轴向载荷的B-C的实验测试之间的差异小于5％。结果表明，在最大轴向载荷为零的情况下，BC临界段最大压缩角处的混凝土极限应变分别为0.0024至0.0038，ACI代码给出的0.003值应用于混凝土的极限应变。当BC承受的轴向力大于其轴向负载能力的70％时，可能会导致非常规的非保守近似结果。