This paper presents a mathematical model for the analysis of reinforced concrete (RC) uniaxial and biaxial columns. This proposed model is a quick and faster approach for the analysis and design of reinforced concrete rectangular columns without going through the interaction charts procedure as well as other iterative methods for the computation of required axial load capacity (Pc) and moment capacity (Mc). A simplified flow chart has also been developed to find the required column capacity using this mathematical model. Eight uniaxial columns (C-1 to C-8) and seven biaxial columns (CB-1 to CB-7) are analysed in this study. Each column is analysed having different steel reinforcement ratios with different loading conditions. In addition, the studied columns are subjected to both tension and compression failures. The detailed examples for both uniaxial and biaxial columns (one for each case) are also presented in this study. The studied columns are also analysed using computer software spColumn. The average variation of the mathematically computed values to the finite element software is not more than 10%, showing promising computational results.

中文翻译：

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钢筋混凝土单轴和双轴分析的数学模型

本文提出了用于分析钢筋混凝土（RC）单轴和双轴柱的数学模型。所提出的模型是一种快速而又快速的方法，无需进行交互作用图程序即可进行钢筋混凝土矩形柱的分析和设计，也无需其他迭代方法即可计算所需的轴向载荷能力（Pc）和弯矩能力（Mc）。还开发了简化流程图，以使用该数学模型找到所需的色谱柱容量。在此研究中分析了八个单轴柱（C-1至C-8）和七个双轴柱（CB-1至CB-7）。分析各列具有不同的钢筋比例在不同的加载条件下。另外，所研究的柱子承受拉伸和压缩破坏。本研究还介绍了单轴和双轴柱的详细示例（每种情况一个）。还使用计算机软件spColumn对研究的色谱柱进行了分析。有限元软件的数学计算值的平均变化不超过10％，显示出令人鼓舞的计算结果。