中文摘要：

在考虑材料非线性的有限元分析中，根据荷载进行相应的钢筋混凝土梁单元截面刚度的求解。通过对Cranston方法求解截面刚度的原理和步骤的分析，指出由于混凝土和钢筋的应力-应变关系曲线均为分段曲线，应用Cranston方法进行单元截面参考轴应变和曲率迭代计算时可能会出现不收敛的情况，依据函数的单调性和连续函数的介值定理，提出在该情况下可采用加速搜索区间法和二分法相结合进行钢筋混凝土梁单元刚度求解。基于该方法编写考虑材料非线性的平面杆系有限元程序，并用算例进行验证，表明其具有良好的收敛效果。

英文摘要：

The solution of corresponding element rigidity of reinforced concrete beams was discussed according to load in FEM program for which the material nonlinearity was taken into account. By the principle and process of Cranston method, it is pointed out that Cranston method sometimes will not converge when the strain and curve of the reference axis in the section is used to calculate as the curves of stress - strain of concrete and reinforcing bar are sectional. Based on the function monotonicity and the intermediate value theorem, the accelerating interval search method combined with dichotomy was put forward to resolve the element rigidity of RC beams. A FEM program was coded and proves that the new method has a satisfied convergence effect.