错层钢筋混凝土（RC）框架结构因其灵活的空间布局和具有层次感的设计形式应用广泛，但楼板的错层会极大地影响荷载传递，同时错层处易产生短柱，对结构抗震不利。错层RC框架结构的现有研究多集中于错层节点和短柱，对短柱在结构整体中的抗震表现以及结构整体的抗震性能分析尚不完善。本文以在错层处带有钢管混凝土叠合柱的实际工程为背景，建立纤维模型单元，运用弹塑性时程分析法，对局部错层RC框架结构进行基于性能的抗震评估，然后研究错层柱的剪跨比、套箍系数以及错层高度对局部错层RC框架结构抗震性能的影响，主要研究内容和结论如下：

利用PERFORM-3D模拟钢管混凝土叠合柱的轴向受压试验。分别选用Simple模型、Mander模型和圆钢管混凝土单轴受压本构模型模拟非约束混凝土、约束混凝土和钢管内混凝土的材料特性，选用“EPP”模型模拟钢材的材料特性。结果表明：模拟与试验得到钢管混凝土叠合柱的荷载变形曲线相似，说明本文选用的材料本构、纤维划分及设置方式合理有效。

采用基于性能的抗震评估方法，对不同角度（0°、30°、60°和90°）地震波作用下的结构进行弹塑性时程分析，结果表明：结构第2、3和4层存在错层，导致这3层刚度突变；第4层的层间位移角最大，是结构的薄弱层；输入60°地震动时结构的层间位移角最大，说明60°为结构的最不利地震动输入角度。对构件的正、斜截面复核以及耗能分析的结果表明：构件的变形均符合性能水准4的要求，框架梁耗散了大部分地震作用的能量；在8度罕遇地震下，错层处按照现行规范设计的钢管混凝土叠合柱抗震性能表现良好。

在错层柱处考虑3组剪跨比、4组套箍系数以及2种错层高度，然后分别建立错层结构整体分析模型并进行弹塑性分析，结果表明：剪跨比减小，层间位移角减小。柱截面每增加100mm，剪跨比减少13%左右，错层柱的剪力增加7%~13%。套箍系数的增大使得钢管混凝土叠合柱延性增加，从而使其损坏程度减小。套箍系数分别增加6%、11%和22%时，钢管混凝土叠合柱承受剪力分别增加3%、23%和22%。局部错层高度减小会使得短柱效应明显，结构刚度增大，从而导致错层柱及结构整体的剪力增大，变形减小。楼层内力和局部错层柱剪力从大到小依次为1/4层高处设置错层的结构、1/2层高处设置错层的结构和无错层结构。1/2层高处设置错层的结构的错层柱剪力比无错层结构的错层柱剪力大19%左右，1/4层高处设置错层的结构的错层柱剪力比1/2层高处设置错层的结构的错层柱剪力大19%左右。在1/2层高处设置错层比在1/4层高处设置错层对结构抗震更有利。以上结论可为错层RC框架结构的相关设计提供参考。

Split-layer reinforced concrete (RC) frame structures are widely used because of their flexible spatial layout and hierarchical design forms, but the split layers of the floor slabs will greatly affect the load transmission, and the split layers are prone to short columns, which is not conducive to structural seismic resistance. The existing research on split-layer RC frame structures mostly focuses on split-level nodes and short columns, and the seismic performance analysis of short columns in the structure as a whole and the seismic performance of the structure as a whole is not yet perfect. In this paper, based on the actual engineering of steel pipe concrete superimposed columns at the split layer, the fiber model unit is established, and the performance-based seismic evaluation of the local split-layer RC frame structure is carried out by using the elastoplastic time history analysis method, and then the shear span ratio, hoop coefficient and split-layer height of the split-layer column are studied on the seismic performance of the local split-layer RC frame structure, and the main research contents and conclusions are as follows:

The axial compression test of steel pipe concrete superimposed column is simulated by PERFORM-3D. The Simple model, the Mander model and the round steel tube concrete uniaxial compression constitutive model were used to simulate the material properties of unconstrained concrete, constrained concrete and concrete in steel pipe, and the "EPP" model was used to simulate the material properties of steel. The results show that the load deformation curve of the steel pipe concrete superimposed column obtained by simulation and experiment is similar, indicating that the material constitutive, fiber division and setting method selected in this paper are reasonable and effective.

(2) Using the performance-based seismic evaluation method, the elastoplastic time course analysis of the structure under the action of seismic waves at different angles (0°, 30°, 60° and 90°) shows that there are fault layers in the second, third and fourth layers of the structure, resulting in the sudden change of stiffness of these three layers; the maximum interlayer displacement angle of the fourth layer is the weak layer of the structure; the interlayer displacement angle of the structure is the largest when the 60° seismic vibration is input, indicating that 60° is the most unfavorable seismic input angle of the structure. The results of the positive and oblique cross-sectional review and energy consumption analysis of the components show that the deformation of the components meets the requirements of performance level 4, and the frame beam dissipates most of the energy of seismic action; under the rare earthquake of 8 degrees, the seismic performance of the steel pipe concrete superimposed column designed according to the current specification at the split layer is good.

(3) At the split-level column, three sets of shear-span ratio, four sets of hoop coefficients and two kinds of split-layer heights were considered, and then the overall analysis model of the split-layer structure was established and the elastoplastic analysis was carried out, and the results showed that the shear-span ratio was reduced and the displacement angle between layers was reduced. For every 100 mm increase in the cross-section of the column, the shear-span ratio is reduced by about 13%, and the shear force of the split-layer column is increased by 7% to 13%. The increase of the hoop coefficient increases the ductility of the steel pipe concrete superimposed column, thereby reducing the degree of damage. When the coupling coefficient is increased by 6%, 11% and 22%, respectively, the shear force of the steel pipe concrete superimposed column is increased by 3%, 23% and 22%, respectively. The reduction of the local split-level height will make the short column effect obvious and the structural stiffness increase, resulting in an increase in the shear force of the split-layer column and the structure as a whole, and the deformation is reduced. The internal force of the floor and the shear force of the local split-level column are set up from large to small, and the split-level structure is set at the height of the 1/4 floor, and the split-level structure and the structure without the fault-level are set at the height of the 1/2 floor. The shear force of the split-layer column of the 1/2-story structure is about 19% greater than that of the split-level column without the split-layer structure, and the shear force of the split-layer column of the 1/4-story structure is about 19% greater than that of the split-layer column of the structure set at 1/2-story height. Setting a split layer at a height of 1/2 is more advantageous to the seismic resistance of the structure than setting a split layer at a height of 1/4. The above conclusions can provide reference for the design of split-layer RC frame structures.

[1] 罗开海，保海娥，左琼．不同设防烈度下RC框架结构抗震设计与控制因素分析[J].建筑结构学报，2021，42（11）：128-136.

[2] 刘会军，段永飞. 银川大阅城一期南区影院结构设计 [J] 建筑结构，2021,51（S1）：232-236.

[3] 曹赫. 钢筋混凝土错层框架结构抗震性能分析 [D]. 南昌：南昌航空大学，2019.

[4] Ghaemdoust M R, Narmashiri K, Yousefi O. Structural behaviors of deficient steel SHS shortcolumns strengthened using CFRP [J]. Construction & Building Materials, 2016, 126:1002-1011.

[5] 徐张伟. 多高层错层结构受力性能研究 [D] . 合肥：安徽建筑大学，2017.

[6] Jinkoo Kim, Yong Jun, Hyunkoo Kang. Seismic Behavior Factors of RC Staggered WallBuildings [J]. International Journal of Concrete Structures and Materials, 2016, 10 (3): 355-371.

[7] Gaia Barbieri, Massimiliano Bocciarelli. A numerical procedure for the pushover analysis ofmasonry towers[J]. Soil Dynamics and Earthquake Engineering,2016.

[8] CECS 188-2019. 钢管混凝土叠合柱结构技术规程 [S]. 北京：中国建筑工业出版社, 2019.

[9] 牛海成，高锦龙，吉珈琨，等.钢管高强再生混凝土叠合柱轴压性能[J/OL]复合材料学报，2021：1-12.

[10] Li Z X, Gao Y, Zhao Q H. A 3D Flexure-shear Fiber Element for Modeling the Seismic Behavior of Reinforced Concrete Columns[J]. Engineering Structures, 2016, 117：372-383.

[11] Feng D C, Wu G, Sun Z Y, et al. A Flexure-shear Timoshenko Fiber Beam Element Based on Softened Damage-plasticity Model[J]. Engineering Structures, 2017, 140：483-497.

[12] R. Nabouch, Q.B. Bui, O. Plé, P. Perrotin, C. Poinard, T. Goldin, J.P. Plassiard. SeismicAssessment of Rammed Earth Walls Using Pushover Tests[J]. Procedia Engineering,2016,145.

[13] Hema Mukundan, S.Manivel. Effect of Vertical Stiffness Irregularity on Multi-Storey ShearWall-framed Structures using Response Spectrum Analysis [J]. Engineering and Technology, 2015, 4(3):1186-1198.

[14] Kiran Kamath, H Sachin, Jose Camilo Karl Barbosa Noronha. An Analytical Study onPerformance of a Diagrid Structure Using Nonlinear static Pushover Analysis[J]. Perspectives inScience,2016.

[15] Szabolcs Varga, Cosmin G. Chiorean. Seismic Assessment of Reinforced ConcreteFrameworks through Advanced Pushover Analysis and Nonlinear Response of a SDOFO scillator[J]. Procedia Engineering,2016,161.

[16] Gaia Barbieri, Massimiliano Bocciarelli. A numerical procedure for the pushover analysis ofmasonry towers[J]. Soil Dynamics and Earthquake Engineering,2016.

[17] 王义俊. 高层错层结构受力性能研究 [D]. 长沙：湖南大学，2008.

[18] R.Park and T Paulay, Reinforced Concrete Structure [M].Canada:John Wiley& Sons, Inc.1975.

[19] 朱兰影. 钢筋混凝土框架完全错开300mm节点拟静力试验与非线性有限元分析 [D]. 重庆：重庆大学，2004.

[20] ACI Committee. Building code requirements for structural concrete (ACI318299) [S]. American Concrete Institute, Farmington Hills, Mich, 1999．

[21] 谢靖中，李国强，屠成松. 错层结构的几点分析 [J]. 建筑科学,2001(01)：35-37+41.

[22] 陈曦. 钢筋混凝土框架全错开节点拟静力试验与错层节点非线性有限元分析 [D]. 重庆：重庆大学，2002.

[23] 田必云. 钢筋混凝土框架错层节点的拟静力试验研究 [D]. 重庆：重庆大学，2002.

[24] 朱建本. 地震作用下质量分布对错层框架受力的影响分析 [D]. 重庆：重庆大学，2005.

[25] 余琼，边冯博. 某钢筋混凝土框架结构错层计算分析及处理 [J] . 结构工程师，2008 (04)：121-124.

[26] 赵德春，李章政. 钢筋混凝土框架错层节点非线性有限元分析 [J] . 工业建筑，2008 (S1)：264-267.

[27] 陈辉. 基于ABAQUS的错层结构地震响应的研究 [J] .建筑结构，2013，43 (S1)：610-613.

[28] 王硕. 对错层处形成短柱的框架结构抗震性能分析 [D] . 太原：太原理工大学，2014

[29] 张永山, 莊初立, 汪大洋, 等. 非线性黏滞阻尼器对某含较多短柱框架结构的减震控制研究 [J] . 建筑结构， 2015，45 (01)：43-46+36.

[30] 黄用军，尧国皇，宋宝东，厚童，彭肇才. 钢管混凝土叠合柱的计算与设计 [J]. 钢结构，2008(07)：12-14+19.

[31] 尧国皇，李永进，廖飞宇. 钢管混凝土叠合柱轴压性能研究 [J]. 建筑结构学报，2013，34(5)：114-121.

[32] 张文勇. 钢管混凝土叠合柱结构弹塑性分析 [D]. 大连：大连理工大学，2013.

[33] 赵均海，侯玉林，张常光. 方形高强钢管混凝土叠合柱轴压极限承载力分析 [J]. 土木建筑与环境工程，2016，38(05)：20-26.

[34] 钱炜武，李威，韩林海，等. 往复荷载作用下钢管混凝土叠合柱-钢梁连接节点力学性能研究 [J]. 土木工程学报，2017，50(07)：27-38.

[35] 黄登，黄远，陈桂榕，等. 钢管混凝土叠合柱受力性能研究 [J]. 地震工程与工程振动，2017(04)：131-139.

[36] 段雪晨. 钢管混凝土叠合柱局部受压的力学性能研究 [D]. 福建农林大学，2018.

[37] 周林聪. 钢筋混凝土结构非线性和可靠度分析方法研究 [D]. 上海交通大学，2007.

[38] Dehestani M, Mousavi S S. Modified Steel Bar Model Incorporating Bond-slip Effects for Embedded Element Method[J]. Construction and Building Materials, 2015, 81：284-290.

[39] Pan W H, Tao M X, Nie J G. Fiber Beam-column Element Model Considering Reinforcement Anchorage Slip in the Footing[J]. Bulletin of Earthquake Engineering, 2017, 15（3）：991-1018.

[40] Kang, Y.J., Nonlinear Geometric Material and Time-Dependent Analysis of Prestressed Concrete Frames，Ph.D，Thiesis， Engineering and Civil Engineering， Department of Civil Engineering, University of California，Berkeley，Report No.UC -SESM77-l, 1977.

[41] Chan, E.C., Nonlinear Geometric, Material and Time Dependent Analysis of Reinforced Concrete Shells with Edge Beams [R], Department of Civil Engineering, University of Califomia, Berkeley, 1982.

[42] Kaba S, Mahin S A. Refined Modeling of Reinforced Concrete Columns for Seismic Analysis [R]. Earthquake Engineering Research Center, University of California, Berkeley.2000.

[43] 陈滔. 基于有限单元柔度法的钢筋混凝土框架三维非弹性地震反应分析 [D]. 重庆：重庆大学，2003.

[44] 唐剑. 钢筋混凝土异形柱框架结构非线性地震反应分析研究 [D]. 重庆：重庆大学，2005.

[45] 孟春光. 复杂体型方钢管混凝土框架结构抗震性能和减震研究 [D]. 上海：同济大学，2006.

[46] 陈超. 钢筋混凝土框架结构抗连续性倒塌分析 [D]. 广州：华南理工大学，2010.

[47] 崔济东，沈雪龙. PERFORM-3D原理与实例 ［M］. 北京：中国建筑工业出版社；2017：103-104.

[48] 王丽萍，张伟，罗文文.地震作用下RC框架梁受弯损伤轴向伸长效应研究[J].建筑结构，2019,49（13）：98-105.

[49] GB50010-2010. 混凝土结构设计规范[S]. 北京：中国建筑工业出版社，2015.

[50] 赵金钢，杜斌，占玉林.OpenSees中Mander模型用于钢筋混凝土柱滞回性能的适用性[J].兰州理工大学学报，2017,43（05）：127-133.

[51] 吴代渊. 不同承载力和刚度调整方案对框架结构抗震性能影响规律的研究 [D]. 重庆：重庆大学，2016.

[52] 韩林海．钢管混凝土结构：理论与实践［M］．2版．北京：科学出版社，2007：101-110．

[53] 刘阳，郭子雄，贾磊鹏，陈庆猛. 核心钢管混凝土叠合短柱轴压性能及设计方法研究 [J]. 建筑结构学报，2015，36(12)：135-142.

[54] 贾磊鹏，郭子雄，刘阳，刘亚，高毅超. 核心钢管混凝土短柱轴压受力机理及设计方法研究 [J]. 地震工程与工程振动，2015，35(03)：79-85.

[55] 黄炳达，葛楠，姜畔等.变截面高耸结构振动瞬时主动最优控制研究[J].工程抗震加固与改造，2021,43（06）：25-31+11.

[56] 胡进军，靳超越，张辉等.匹配多目标参数的地震动合成方法[J].工程力学，2022,39（03）：126-136.

[57] GB50011-2010. 建筑抗震设计规范 [S]. 北京：中国建筑工业出版社,2016.

[58] DBJ/T15-151-2019，建筑工程混凝土结构抗震性能设计规程 [S]. 广州：广东省住房和城乡建设厅，2019.

[59] 淡凯. 框架—核心筒混合结构双向水平地震弹塑性性能研究 [D]. 西安：西安建筑科技大学，2014.

[60] 缪志伟，叶列平. 钢筋混凝土框架-联肢剪力墙结构的地震能量分布研究 [J]. 工程力学，2010，27(02)：130-141.

[61] 韩小雷，季静. 基于性能的钢筋混凝土结构抗震—理论研究、试验研究、设计方法研究与工程应用［M］. 北京：中国建筑工业出版社；2019：9-10.

[62] ASCE/SEI 41-13， Seismic Evaluation of Civil and Retrofit of Existing Building [S]. Reston，Virginia：America Society of Civil Engineers, 2014.

[63] 崔济东，韩小雷，季静等.RC梁的变形性能指标限值研究与试验验证[J]哈尔滨工业大学学报，2018,50（06）：169-176.

[64] 李安琪. 地震作用下框支剪力墙结构层间位移角限值的研究 [D]. 广州：华南理工大学，2020.

[65] 张鹏程，黄文锦，纪似玉. 装配式大跨度承重楼盖结构设计综合研究 [J].世界地震工程，2020，36（01）：1-7.

[66] 康洪震，钱稼茹. 钢管高强混凝土组合柱轴压承载力试验研究 [J]. 建筑结构，2011，41(06)：64-67.