Abstract: In order to overcome the difficulty of elastic modulus adjustment procedures applied in reinforced concrete (RC) structures, a homogeneous generalized yield function is developed for RC eccentric compression member with rectangular section. The piecewise-smooth interaction equation of bearing capacity is developed for RC eccentric compression members with rectangular section using the quadratic function and their failure mechanism is considered. The partition expressions of sectional characteristic function are proposed through regression analysis to consider the influence of the sectional geometry and material property on the bearing capacity, hence the homogeneous generalized yield function is developed for these members by adopting the first order polynomials with fractional exponential power. Furthermore, an adaptive criterion for identification of highly stressed element is defined by using the element bearing ratio. The elastic modulus of the highly-stressed element is reduced strategically so that the ultimate bearing capacity of RC arches is evaluated by linear elastic iteration. Compared with the model test and the incremental non-linear finite element method, the proposed method proves to have high computational accuracy and efficiency.