The Second-order Effects And Design Method Of Reinforced Concrete Bent Frames

The design method of second-order effect of bent frames in current “Code for design of concrete structures” is still ?-l₀ method which relies heavily on empirical experience. The ?-l₀ method has not been revised for almost fifty years with theoretical flaws and lacks the effective analyses. This paper is part of the follow-up study of the questions left over from “Code for design of concrete structures” GB50010-2010 about second-order effect design method and aims to provide references for a new revision of the “Code for design of concrete structures” about second-order effect of bent frames.With the computer technology has been widely used in engineering design, the ?-l₀ method for considering second-order effect of bent frames has already been an old design method. But in order to optimize the ?-l₀ method, we still need to clarify the essence of second-order effect and provide reasonable effective length. At the same tine, the design methods apply to solve second-order effect questions provided by American codes are quite mature and widely adopted by other engineering world. So we need to learn form the design concept of American codes that employing stiffness reduction to solve material nonlinearity questions, and introduce the elastic second-order analysis method employing stiffness reduction. Thus the second-order effect questions would be solved in structural level and the second-order effect analysis would be restored to structural analysis. Moreover the old way that can only solve the adverse effects of second-order effect at section bearing capacity design would be changed. For these reasons, this paper launched a series of research work and obtained some academic results as follows.?1? The design ideas and the guidances, provided by American codes “ACI 318-14”, about solving second-order effect questions and the moment magnifier method of sway structures and nonsway structures have been clarified clearly. Meanwhile the rationalization of the ?-l₀ method used for bent frames has been demonstrated and the effective length has been back calculated by utilizing the axial force expression of moment magnifier.?2? Referencing the atlas of national standard and the existing research results of single span bent frames, 108 two span bent frames that have typtical engineering significance was designed. All kinds of loads, beared by bent frames, and the way they act has been clarified. After the load combinations, guided by new load codes, was fininshed, the worst-case load combinations corresponding to their section has been judged according to the elastic second-order analysis results.?3? According to the elastic first-order and the elastic second-order analysis results, at the worst-case load combinations, of the 108 bent frames, the moment magnifier coefficients and the effective lengths was figured out. The laws of second-order effect that impacted by span, crane tonnage, wind load and upper and lower column height ratio was studied systematically by using control variable method and explained.?4? The distribution law of the moment magnifier coefficients and the effective lengths of the bent frames was summarized then a practical suggestion of the effective length coefficient which takes both efficiency and precision into account has been given as follows: the value of upper of side column is 3.5; the value of lower of side column is 2.7; the value of upper of middle column is 1; the value of lower of middle column is 1.7. Meanwhile the relationship between the suggestion and the current codes has been explained and the ?-l₀ method has been optimized.?5? Explaining the properties of material and geometrical nonlinear of bent frames at ultimate capacity state. According to the analysis results of elastic second-order employing stiffness reduction and nonlinear second-order, learned from American codes, the rational stiffness reduction factor would be figured out by the equivalence of the structures entire second-order effect.?6? The distribution law of the stiffness reduction factors of the 34 typical bent frames was summarized then a practical suggestion of stiffness reduction has been given as follow: ? =0.85. Finally the rationalization of the suggestiong is verified by comparing the analysis results of elastic second-order employing stiffness reduction and nonlinear second-order.