| The occurrence and intensity of earthquake have the characteristic of highly uncertainty,and the current seismic design codes for building structures generally consider multiple earthquake levels and the corresponding seismic performance targets.However,these approaches can be classified as force-based elastic design method,such that it is difficult to consider the damage and performance evolution of a structure once the nonlinearity occur.Therefore,the displacement-based seismic design method was developed as the development direction of the next-generation structural seismic design code,in which the structural nonlinear performance under any intensity level of earthquake can be controlled by setting appropriate displacement targets.However,for reinforced concrete(RC)structures with multi-story and multi-span,the early displacement-based seismic design method determine the reinforcement of structural members by checking the displacement under earthquake action after the primary design is completed and employing some iteration.This indicate that it cannot directly be used to obtain the reinforcement of members,such that it is not convenient for practical application.To solve this problem,the direct displacement-based seismic design(DDBD)method was proposed subsequently.By using a predefined lateral displacement distribution curve,the DDBD method establishs an equivalent elastic single-degree-of-freedom(SDOF)system with higher equivalent damping ratio and equivalent period to represent the practical nonlinear multi-degree-of-freedom(MDOF)structure.The design base shear force of structure can be determined on the basis of the theory of static nonlinear analysis.Then,the internal force demand of the structure corresponding to the displacement target is required to be calculated and the arrangement of reinforcements of each member can be designed accordingly.The DDBD method is more suitable for the structures that the first order mode of vibration dominates the structural response.For the RC frame structure system,the current investigations about the DDBD method still have many shortcomings.Fist,almost all existing equivalent damping ratio models are derived based on the SDOF system with simplified hysteresis rules,which are hard to be used to reflect the global hysteretic characteristics of practical MDOF RC frame structure.Second,the existing lateral displacement distribution models usually use constant curve and do not consider the evolution of lateral displacement with the development of inelastic deformation and the increase of the number of plastic hinges.Third,when the structure is expected to exhibit nonlinearity,the corresponding internal force calculation method often do not follow the principle of structural mechanics strictly on the premise of considering the condition of predefined target displacement,such that the consistency of the calculated displacement distribution of structure and target displacement distribution is hard to be considered.To solve the above-mentioned problems,this study conducts in-depth research on DDBD method.The main research contents and conclusions are as follows:(1)A novel equivalent damping ratio model is proposed.66 RC frame structures with variation in bay widths,stories and design peak ground accelerations(PGA)are constructed initially.Those structures are designed according to the current seismic design standerd(GB 50011-2016).The OpenSees program is used to perform the monotonic and cyclic pushover analyses for the selected RC frame structures that have ductility deformation mechanism.Then,the unified hysteresis loop expression that can predict the cyclic pushover results of RC frame system is developed by studying the geometric characteristics of normalized hysteretic curves of the selected RC frame structures.Based on the developed expression and the principle of equating energy dissipation,a global equivalent damping ratio model is developed.By performing dynamic nonlinear analysis for the selected structures and taking the computed average peak displacement response as reference,the proposed global equivalent damping model is calibrated further.The example verifications show that the displacements obtained by the nonlinear static analysis using the proposed equivalent damping model are basically consistent with the average maximum displacement of multiple nonlinear dynamic analyses.This indicates that the proposed model has good applicability and can better reflect the energy dissipation characteristics of the global structure.The proposed model can be used for implement direct displacement design of middle-low rise RC frame structures.(2)A displacement profile expression of RC frame structure that can be used to predict the structural lateral displacement corresponding various damage state is proposed.To develop this expression,the deformation mechanism of RC frame structures is investigated firstly by performing pushover analyses for the selected 66 RC frame structures with variation design parameters according to the position and order of the occurrence of plastic hinges.For the structures with ductility deformation mechanism,it is found that the lateral displacement of the structure can be model approximately by the first order elastic mode of vibration is the structure is in elastic state,and gradually deviates from its first order elastic mode once inelastic deformation occur.Then,considering the effect of column-to-beam strength ratio,height-width ratio and so on,a refined displacement profile expression is established.The proposed expression is capable of describing the evolution process of the lateral displacement shape of RC frame structures from elastic state to inelastic stage.Finally,the lateral displacement curves obtained by the proposed expression are compared with those obtained by nonlinear time-history analyses,and the results show that the proposed lateral displacement expression can accurately simulate the lateral displacement profile of RC frame system under different maximum interstory drift ratio.As a result,the proposed expression can be used for the design of RC frame structures considering various performance levels.(3)By establishing ideal elasto-plastic analytical model of RC frame structure,a calculation method of the internal force for RC frame structure,which can make the calculated lateral displacement distribution consistent with the predefined lateral displacement distribution,is proposed.According to the deformation process of the RC frame structure from the elastic state to the elastic-plastic state under the earthquake action,the structural deformation process is simplified into two processes of the elastic stage and the incremental plastic stage.For the incremental plastic stage,based on the ideal elasto-plastic assumption of the plastic hinge area,the deformation of the structure can be treated as the sum of elastic displacement under the combined action of the same load and virtual external moment.Then,by introducing the principle of minimizing displacement deviation,the internal forces of the plastic hinge regions are determined through using structural mechanics method.Finally,by addting the internal force of the structure in elastic stage,the total internal force of the structural members can be obtained.The detailed calculation process of the proposed internal force calculation method is demonstrated by an example.Moreover,by using the calculation results to determine the bearing capacity of the structural plastic member,nonlinear structural analysis is carried out.The obtained lateral displacement distribution is basically consistent with the specified lateral displacement curve,which indicates the feasibility of the proposed internal force calculation method.(4)The models and expressions proposed in this paper are applied to DDBD of RC frame structures.According to the principle of DDBD method and considering multiple performance objectives under various seismic intensity levels,a direct displacement seismic design procedure is presented by integrating the proposed calculation models and methods,and a 6-story RC frame structure is selected as an example to perform the seismic design.By implementing nonlinear analysis for the designed structure,the applicability and rationality of the proposed models and methods are demonstrated.By comparing the seismic performance of the structure designed according to the proposed approach and that designed according to the traditional force-based base shear method,the differences between the design results are analyzed and discussed. |
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