MDOF系统构件地震能量反应研究
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(1 广州容柏生建筑结构设计事务所， 广州 510170; 2 合肥工业大学土木与水利工程学院， 合肥 230009)［摘要］基于有限元理论推导结构能量方程，提出构件能量反应的不平衡性。在地震动作用下，由于能量的往复传递，结构内部任何构件的能量反应几乎时刻均是不平衡的。构件的弹性行为是能量在构件间传递的途径和保障，而其塑性行为则是能量得以耗散的原因，据此定义吸能及耗能构件。通过不同场地条件记录、对不同剪切型多自由度体系展开的弹塑性时程反应统计分析，研究构件能量反应分布及传递特征。结果表明：刚度分布对结构耗能分布影响最大，即便是等屈服强度系数分布模型，底层最薄弱，耗能也最集中；构件的吸能及耗能特征与构件质量、结构刚度的分布关系密切，而滞回模型的选取及不同场地条件下的记录输入对构件能量反应分布的影响不大。［关键词］能量方程; 滞回耗能分布特征; 滞回模型; 弹塑性时程分析; 构件能量不平衡性中图分类号：P315.3+1， TU311.3 文献标识码：A 文章编号：1002-848X(2013)21-0078-08Research on component-based seismic energy response of MDOF systemChang Lei1,2(1 RBS Architectural Engineering Design Associates, Guangzhou 510170, China; 2 School of Civil and Hydraulic Engineering, Hefei University of Technology, Hefei 230009, China)Abstract: Structure’s energy equation was derived based on finite element method, with the component-based energy imbalance energy proposed. As energy transfers constantly under earthquake excitation, almost at any time any structural component has imbalanced energy response. The component’s elasticity ensures energy’s transferring while its plasticity renders energy’s dissipation, thus, the energy-producing and the energy-absorbing components were defined conceptually. Statistical analyses of the component-based energy’s distribution and energy’s transferring were carried out on the layered shear multi-degree of freedom (abbr. MDOF) system with its properties and input record’s site condition considered. The results show that: stiffness’ distribution of the MDOF system has the greatest influence on its energy distribution, and the bottom layer is the weakest where energy concentration happens, even to the equal yield strength coefficient model; component’s character of energy-producing or energy-absorbing highly depends on the component’s mass and system’s stiffness distribution, while selection of the hysteretic model and the input record’s site condition has little influence.Keywords: energy equation; hysteretic energy distribution; hysteretic model; elasto-plastic time history analysis; component-based imbalance energy response作者简介：常磊，博士，工程师，Email: changlei1218@163.com。参考文献［1］HOUSNER G W. Limit Design of Structures to Resist Earthquakes［C］//1st World Conference Earthquake Engineering, Berkeley, CA. EERI, 1956: 1-13.［2］MANFREDI GAETANO. Evaluation of seismic energy demand［J］. Earthquake Engineering & Structural Dynamics, 2001, 30(4): 485-499.［3］KUNNATH S K，CHAI Y H. Cumulative damage-based inelastic cyclic demand spectrum［J］. Earthquake Engineering & Structural Dynamics,2004,33(4):499-520.［4］ARROYO DANNY，ORDAZ MARIO. On the estimation of hysteretic energy demands for SDOF systems［J］. Earthquake Engineering & Structural Dynamics, 2007, 36（15）: 2365-2382.［5］程光煜，叶列平.弹性SDOF系统的地震输入能量谱［J］.工程抗震与加固改造，2006，28(5)：1-8.［6］程光煜，叶列平.弹塑性SDOF系统的地震输入能量谱［J］.工程力学，2008，25(2)：28-39.［7］周云，乐登，邓雪松.设计用地震动总输入能量谱研究［J］.工程抗震与加固改造，2008，30(5)：1-7.［8］滕军，董志君，容柏生，等.弹性单自由度体系能量反应谱研究［J］.建筑结构学报，2009，30(S1)：129-133.［9］叶献国.建筑结构弹塑性地震反应中的能量表达及应用［J］.合肥工业大学学报：自然科学版，1998，21(5)： 9-16.［10］程光煜，叶列平.弹塑性MDOF系统地震输入能量研究［J］.工程抗震与加固改造，2007，29(6)：29-35.［11］PRASANTH THOLEN,GHOSH SIDDHARTHA,COLLINS KEVIN R. Estimation of hysteretic energy demand using concepts of modal pushover analysis［J］. Earthquake Engineering & Structural Dynamics, 2008, 37(6): 975-990.［12］BENAVENT CLIMENT A，ZAHRAN R. An energy-based procedure for the assessment of seismic capacity of existing frames: Application to RC wide beam systems in Spain［J］. Soil Dynamics and Earthquake Engineering, 2010, 30(5): 354-367.［13］李宁，翟长海，谢礼立.基于能量的模态pushover分析方法［J］.建筑结构学报，2009，30(6)：101-106.［14］BATHE KLAUS-JURGEN. Finite element procedures［M］. New Jersey: Prentice-Hall Inc., 1996.［15］MAHIN S A，BERTERO V V. Nonlinear seismic response of a coupled wall system［J］. Journal of the Structural Division, ASCE, 1976, 102(9): 1759-1980.［16］MIRANDA EDUARDO，RUIZ-GARCIA JORGE. Influence of stiffness degradation on strength demands of structures built on soft soil sites［J］. Engineering Structures, 2002, 24(10): 1271-1281.［17］KUNNATH SASHI K, REINHORN ANDREI M，PARK YOUNG J. Analytical modeling of inelastic seismic response of RC structures［J］. Journal of Structural Engineering, 1990, 116(4): 996-1017.［18］常磊，叶献国，李康宁.高层混凝土基础隔震结构的损伤与耗能评价［J］.土木工程学报，2010，34(9)：22-31.［19］GB 50011—2010 建筑抗震设计规范［S］. 北京：中国建筑工业出版社，2010.
