In this paper, a set of general "internal force"-displacement constitutive formulas based on "yield surface equation" for beam-column elements regarded as "single-component model" is firstly derived (not to simplify/reduce the ground motion and "internal force" components, can be applied to R/C frame structures and steel frame structures, existing single "internal force" constitutive formula is their special case). Later, the graduate-textbooks of "Nonlinear analysis of concrete structures" (Liang Xingwen,Ye Yanxia; 2007) names my paper's method "Yield surface model of beam-column elements", to distinguish it from "Section fiber model", "Five-spring elements"...... For the formulas derived from the "yield surface equation", the final key is able to calculate the hardening modulus. Otherwise, the formulas can not be calculated. In this paper, the calculation of hardening modulus in general case is explored, an approximate (but theoretical) formula is given, and the applied conditions of the "simple curve" hardening law are discussed once again according to new viewpoint. In the end, a simple example is presented to illustrate the application of the method in this paper and some significant results are reached also. For the transition stage from elastic to plastic in numerical calculation, a concept of composite stiffness is used, needless to reduce the time step for finding the transition point of beam-column elements one by one, so that to save a lot of computer-time.
The relevant ideas of this paper can be extended to the similar elasto-plastic problems/expressions described by stress-strain relationships. Please see the "Section 10" of this paper: Section 10. [later supplement] The new thinking on plasticity-theory : "The theory of elasticity and plasticity based on the concept of yield surface"