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Article(id=1245390363846881829, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245390357958082790, articleNumber=null, orderNo=null, doi=10.13197/j.eeed.2024.0607, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1697904000000, receivedDateStr=2023-10-22, revisedDate=1701792000000, revisedDateStr=2023-12-06, acceptedDate=null, acceptedDateStr=null, onlineDate=1774853800974, onlineDateStr=2026-03-30, pubDate=null, pubDateStr=null, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774853800974, onlineIssueDateStr=2026-03-30, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774853800974, creator=13701087609, updateTime=1774853800974, updator=13701087609, issue=Issue{id=1245390357958082790, tenantId=1146029695717560320, journalId=1241701559352995854, year='2024', volume='44', issue='6', pageStart='1', pageEnd='237', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774853799571, creator=13701087609, updateTime=1774854467826, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1245393160877224589, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245390357958082790, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1245393160877224590, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245390357958082790, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=72, endPage=83, ext={EN=ArticleExt(id=1245390364144677416, articleId=1245390363846881829, tenantId=1146029695717560320, journalId=1241701559352995854, language=EN, title=Calculation model and application of buckling-restrained steel plate wall combined with friction damper, columnId=null, journalTitle=Earthquake Engineering and Engineering Dynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

For the large yield displacement of the buckling-restrained steel plate wall(BRW), only stiffness and bearing capacity can be provided in the small deformation stage. BRW can not dissipate energy in the small deformation stage. To solve this problem, the wall type friction damper (FD) and buckling-restrained steel plate wall are arranged in parallel in the thickness direction to form a new type of buckling-restrained steel plate wall combined with friction damper (FD-BRW). In the small deformation stage, the friction damper in the composite member slides to dissipate energy. As the deformation increases, the buckling-restrained steel plate wall yields, and the friction damper and the buckling-restrained steel plate wall dissipate energy together. Based on the test results of BRW, FD and FD-BRW, a simplified calculation model was established to simulate the mechanical properties of FD-BRW. The simplified calculation model consists of three springs. The calculation results of the simplified model were basically consistent with the experimental results, which can replace the solid finite element analysis and can be directly applied in the overall analysis of the structure. Based on the simplified model, taking the optimal additional damping as the control index, the reasonable ratio of the sliding friction force of friction damper to the yield bearing capacity of the buckling-restrained steel plate wall (slip-yield ratio) and the recommended value of the height-width ratio of the member were discussed through parametric analysis. The results showed that the height-width ratio is recommended to be less than 1.5, and the reasonable range of slip-yield ratio is 0.07~0.10.

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为解决防屈曲钢板墙屈服位移大，在小变形阶段仅提供刚度和承载力而无法消能的缺点，将墙式摩擦阻尼器与防屈曲钢板墙在厚度方向进行并联布置，构成新型摩擦-防屈曲钢板墙复合减震构件。小变形阶段，复合构件中的摩擦阻尼器滑动消能，随着变形增大，防屈曲钢板墙进入屈服状态，摩擦阻尼器和防屈曲钢板墙共同消能。基于防屈曲钢板墙、摩擦阻尼器以及摩擦-防屈曲钢板墙复合构件的试验结果以及复合构件构造特点，建立了弹簧束简化计算模型，用于模拟摩擦-防屈曲钢板墙复合减震构件的力学性能。简化模型的计算结果与试验结果基本吻合，可替代实体有限元分析，且可在结构整体分析中直接应用。基于简化模型，通过参数分析的方法，以最优附加阻尼比为控制指标，探讨了复合构件中摩擦阻尼器滑动摩擦力与防屈曲钢板墙屈服承载力的合理比值（滑屈比）、构件高宽比建议值。参数分析结果表明，高宽比建议小于1.5，而滑屈比合理比值范围为0.07~0.10。

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胡大柱（1980—），男，副教授，博士，主要从事结构抗震与减震研究。E-mail：

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胡大柱（1980—），男，副教授，博士，主要从事结构抗震与减震研究。E-mail：

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胡大柱（1980—），男，副教授，博士，主要从事结构抗震与减震研究。E-mail：

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Journal of Structural Engineering, 2007, 133(3): 378-388., articleTitle=Framed steel plate wall behavior under cyclic lateral loading, refAbstract=null), Reference(id=1245390401264267844, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, doi=null, pmid=null, pmcid=null, year=2017, volume=33, issue=4, pageStart=59, pageEnd=67, url=null, language=null, rfNumber=[19], rfOrder=33, authorNames=潘毅, 高宪, 易路行, journalName=世界地震工程, refType=null, unstructuredReference=潘毅，高宪，易路行，等. 基于剪力比和刚度比的防屈曲支撑-RC框架抗震设计方法分析[J]. 世界地震工程, 2017, 33(4): 59-67., articleTitle=基于剪力比和刚度比的防屈曲支撑-RC框架抗震设计方法分析, refAbstract=null), Reference(id=1245390401343959622, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, doi=null, pmid=null, pmcid=null, year=2017, volume=33, issue=4, pageStart=59, pageEnd=67, url=null, language=null, rfNumber=[19], rfOrder=34, authorNames=PAN Yi, GAO Xian, YI Luxing, journalName=World Earthquake Engineering, refType=null, unstructuredReference=PAN Yi, GAO Xian, YI Luxing, et al. 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(in Chinese), articleTitle=Investigation of the seismic design methods of buckling-restrained braced-reinforced concrete frame structures based on shear ratio and stiffness ratio, refAbstract=null), Reference(id=1245390401432040009, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, doi=null, pmid=null, pmcid=null, year=2016, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[20], rfOrder=35, authorNames=null, journalName=null, refType=null, unstructuredReference=GB 50011—2010建筑抗震设计规范[S]. 2016年版. 北京：中国建筑工业出版社，2016., articleTitle=null, refAbstract=null), Reference(id=1245390401528509006, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, doi=null, pmid=null, pmcid=null, year=2016, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[20], rfOrder=36, authorNames=null, journalName=null, refType=null, unstructuredReference=GB 50011—2010 Code for seismic design of buildings[S]. 2016 ed. 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(in Chinese), articleTitle=null, refAbstract=null), Reference(id=1245390401604006478, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, doi=null, pmid=null, pmcid=null, year=2017, volume=39, issue=1, pageStart=78, pageEnd=83, url=null, language=null, rfNumber=[21], rfOrder=37, authorNames=丁永君, 刘胜林, 李进军, journalName=工程抗震与加固改造, refType=null, unstructuredReference=丁永君，刘胜林，李进军. 粘滞阻尼结构小震附加阻尼比计算方法的对比分析[J]. 工程抗震与加固改造, 2017, 39(1): 78-83., articleTitle=粘滞阻尼结构小震附加阻尼比计算方法的对比分析, refAbstract=null), Reference(id=1245390401675309648, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, doi=null, pmid=null, pmcid=null, year=2017, volume=39, issue=1, pageStart=78, pageEnd=83, url=null, language=null, rfNumber=[21], rfOrder=38, authorNames=DING Yongjun, LIU Shenglin, LI Jinjun, journalName=Earthquake Resistant Engineering and Retrofitting, refType=null, unstructuredReference=DING Yongjun, LIU Shenglin, LI Jinjun. Analysis of additional damping ratio calculation methods of nonlinear viscous damping structure under frequent earthquake[J]. Earthquake Resistant Engineering and Retrofitting, 2017, 39(1): 78-83. (in Chinese), articleTitle=Analysis of additional damping ratio calculation methods of nonlinear viscous damping structure under frequent earthquake, refAbstract=null)], funds=[Fund(id=1245390398386975184, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, awardId=51408361, language=CN, fundingSource=国家自然科学基金青年基金项目(51408361), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1245390385053282317, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, xref=1., ext=[AuthorCompanyExt(id=1245390385061670926, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, companyId=1245390385053282317, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1.School of Urban Construction and Safety Engineering, Shanghai Institute of Technology, Shanghai 201418, China), AuthorCompanyExt(id=1245390385065865231, 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journalId=1241701559352995854, articleId=1245390363846881829, language=CN, label=图2, caption=试验构件图, figureFileSmall=1j0jNq82gE2eC59d5FnIUg==, figureFileBig=9z+eIOjtqOzNCH1mTgHyWw==, tableContent=null), ArticleFig(id=1245390394041676014, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=EN, label=Fig. 3, caption=Details of test equipment, figureFileSmall=JpKsb1eVfWxPpHbxILmiUQ==, figureFileBig=6H63UuCdPQ+qKSwGncbYcA==, tableContent=null), ArticleFig(id=1245390394125562099, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=CN, label=图3, caption=试验测试装置图, figureFileSmall=JpKsb1eVfWxPpHbxILmiUQ==, figureFileBig=6H63UuCdPQ+qKSwGncbYcA==, tableContent=null), ArticleFig(id=1245390394213642486, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=EN, label=Fig. 4, caption=Hysteretsis curves and skeleton curves of FD, BRW and FD-BRW, figureFileSmall=+MfIXbrZJoy5JpJ6fBVPOQ==, figureFileBig=IwXKq1qxn6fjcaF65vo99A==, tableContent=null), ArticleFig(id=1245390394305917178, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=CN, label=图4, caption=各构件试验滞回曲线和骨架曲线, figureFileSmall=+MfIXbrZJoy5JpJ6fBVPOQ==, figureFileBig=IwXKq1qxn6fjcaF65vo99A==, tableContent=null), ArticleFig(id=1245390394419163393, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=EN, label=Fig. 5, caption=Simplified calculation model for FD-BRW, figureFileSmall=nrRfbj3IxIC9fPLZzYl9Wg==, figureFileBig=HlvfUZ+fU/EOiTJYJQ6gww==, tableContent=null), ArticleFig(id=1245390394507243780, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=CN, label=图5, caption=FD-BRW简化计算模型, figureFileSmall=nrRfbj3IxIC9fPLZzYl9Wg==, figureFileBig=HlvfUZ+fU/EOiTJYJQ6gww==, tableContent=null), ArticleFig(id=1245390394637267214, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=EN, label=Fig. 6, caption=Schematic diagram of widened end of the core plate of BRW, figureFileSmall=4ld9UmX2VQsu2r4/AfL4Yw==, figureFileBig=R7YHR7hy0vyV4o9E9vM0jg==, tableContent=null), ArticleFig(id=1245390394725347605, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=CN, label=图6, caption=BRW芯板端部加宽示意图, figureFileSmall=4ld9UmX2VQsu2r4/AfL4Yw==, figureFileBig=R7YHR7hy0vyV4o9E9vM0jg==, tableContent=null), ArticleFig(id=1245390394826010907, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=EN, label=Fig. 7, caption=Hysteretic model, figureFileSmall=69D51poE4qGPF0RJdm7Auw==, figureFileBig=9M97YUvK4Xt0zNLgAQpVUA==, tableContent=null), ArticleFig(id=1245390394905702690, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=CN, label=图7, 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tableContent=null), ArticleFig(id=1245390395320938812, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=CN, label=图9, caption=简化模型与试验结果滞回曲线对比, figureFileSmall=Mg4Chp7pmd8vesv/Rq31Mg==, figureFileBig=bTy7Vkd1pknZD4NV4ptC2A==, tableContent=null), ArticleFig(id=1245390395417407809, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=EN, label=Fig. 10, caption=Comparison of skeleton curves between simplified model and test results, figureFileSmall=uFcHPi6gwLEFxIM32ktCFQ==, figureFileBig=KvMaFvrpC50lkAeAQd9Dnw==, tableContent=null), ArticleFig(id=1245390395526459719, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=CN, label=图10, caption=简化模型与试验结果骨架曲线对比, figureFileSmall=uFcHPi6gwLEFxIM32ktCFQ==, figureFileBig=KvMaFvrpC50lkAeAQd9Dnw==, tableContent=null), ArticleFig(id=1245390395635511631, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=EN, label=Fig. 11, caption=Structural arrangement diagram of frame structure and FD-BRW instrallation, figureFileSmall=Q0HRHhDEGnemhEmvU5Bq3A==, figureFileBig=hyfJ29looSN3S9vC8jMHcA==, tableContent=null), ArticleFig(id=1245390395740369237, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=CN, label=图11, caption=纯框架结构及设置FD-BRW的结构布置图, figureFileSmall=Q0HRHhDEGnemhEmvU5Bq3A==, figureFileBig=hyfJ29looSN3S9vC8jMHcA==, tableContent=null), ArticleFig(id=1245390395807478104, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=EN, label=Fig. 12, caption=Comparison of seismic wave spectral characteristics and response spectrum curves, figureFileSmall=YN0PzMWK4DDlxfWnT4CB5Q==, figureFileBig=nIjMwxNO/Waao1zLEtQyWg==, tableContent=null), ArticleFig(id=1245390395966861661, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=CN, label=图12, caption=地震波频谱特性及反应谱曲线对比, figureFileSmall=YN0PzMWK4DDlxfWnT4CB5Q==, figureFileBig=nIjMwxNO/Waao1zLEtQyWg==, tableContent=null), ArticleFig(id=1245390396105273701, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=EN, label=Fig. 13, caption=Variation curves of additional damping ratio with α under small magnitude earthquakes, figureFileSmall=2t+0acsbYr9oMXHZCRkMlQ==, figureFileBig=JBl4TnC+6KtTuIbP5ePcjQ==, tableContent=null), ArticleFig(id=1245390396218519915, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=CN, label=图13, caption=小震下附加阻尼比随α的变化规律曲线, figureFileSmall=2t+0acsbYr9oMXHZCRkMlQ==, figureFileBig=JBl4TnC+6KtTuIbP5ePcjQ==, tableContent=null), ArticleFig(id=1245390396306600305, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=EN, label=Fig. 14, caption=Variation curves of additional damping ratio with α under intermediate magnitude earthquakes, figureFileSmall=YVguVPJLnTwWkuNTyBBd1w==, figureFileBig=qBHa7e13vENTtp9Jg2lsVg==, tableContent=null), ArticleFig(id=1245390396411457911, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=CN, label=图14, caption=中震下附加阻尼比随α的变化规律曲线, figureFileSmall=YVguVPJLnTwWkuNTyBBd1w==, figureFileBig=qBHa7e13vENTtp9Jg2lsVg==, tableContent=null), ArticleFig(id=1245390396516315518, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=EN, label=Fig. 15, caption=Variation curves of additional damping ratio with α under large magnitude earthquake, figureFileSmall=4YAxjZqkxNj6ji3doxZmuQ==, figureFileBig=8ma5JRE6a2qfFJmP8bqv3A==, tableContent=null), ArticleFig(id=1245390396591812992, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=CN, label=图15, caption=大震下附加阻尼比随α的变化规律曲线, figureFileSmall=4YAxjZqkxNj6ji3doxZmuQ==, figureFileBig=8ma5JRE6a2qfFJmP8bqv3A==, tableContent=null), ArticleFig(id=1245390396671504773, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=EN, label=Fig. 16, caption=Comparison of seismic wave spectral characteristics and response spectrum curves under large magnitude earthquake, figureFileSmall=Rw8tY0th+YdAQQ3liy0Z3Q==, figureFileBig=kydA907pQ5jC+DQwhuyOUw==, tableContent=null), ArticleFig(id=1245390396751196553, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=CN, label=图16, caption=大震分析地震波频谱特性及反应谱曲线对比, figureFileSmall=Rw8tY0th+YdAQQ3liy0Z3Q==, figureFileBig=kydA907pQ5jC+DQwhuyOUw==, tableContent=null), ArticleFig(id=1245390396839276941, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=EN, label=Fig. 17, caption=Comparative analysis of the variation of additional damping ratio with α when the aspect ratio is 1.5, figureFileSmall=+ezSZF/HDCXQkludZmlv7Q==, figureFileBig=UMLuBZzRh9dJ2CErXqzvDw==, tableContent=null), ArticleFig(id=1245390396927357328, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=CN, label=图17, caption=高宽比为1.5时附加阻尼比随α的变化规律对比分析, figureFileSmall=+ezSZF/HDCXQkludZmlv7Q==, figureFileBig=UMLuBZzRh9dJ2CErXqzvDw==, tableContent=null), ArticleFig(id=1245390397019632020, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=EN, label=Fig. 18, caption=Variation curves of additional damping ratio with β′ under small earthquakes, figureFileSmall=69tgOuMttSp3YeL7QZ7W4g==, figureFileBig=h/HQux8m2s6INgTkUCH1xQ==, tableContent=null), ArticleFig(id=1245390397120295318, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=CN, label=图18, caption=小震下附加阻尼比随β′的变化规律曲线, 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Design parameters of core specimens

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试件核心板件高度/mm宽度/mm厚度/mm材料
FD摩擦副2154003铜板
BRW耗能芯板92580010Q235B
FD-BRW耗能芯板92580010Q235B
摩擦副2154003铜板
), ArticleFig(id=1245390397468422563, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=CN, label=表1, caption=

核心部件尺寸表

, figureFileSmall=null, figureFileBig=null, tableContent=
试件核心板件高度/mm宽度/mm厚度/mm材料
FD摩擦副2154003铜板
BRW耗能芯板92580010Q235B
FD-BRW耗能芯板92580010Q235B
摩擦副2154003铜板
), ArticleFig(id=1245390397535531434, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=EN, label=Table 2, caption=

Test loading history

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加载等级循环周次峰值加载位移/mm加载等级循环周次峰值加载位移/mm
130.5635
231736.16（1/150构件高度）
332839.25（1/100构件高度）
4339312.33（1/75构件高度）
53410318.5（1/50构件高度）
), ArticleFig(id=1245390397615223213, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=CN, label=表2, caption=

试验加载历程

, figureFileSmall=null, figureFileBig=null, tableContent=
加载等级循环周次峰值加载位移/mm加载等级循环周次峰值加载位移/mm
130.5635
231736.16（1/150构件高度）
332839.25（1/100构件高度）
4339312.33（1/75构件高度）
53410318.5（1/50构件高度）
), ArticleFig(id=1245390397699109295, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=EN, label=Table 3, caption=

Related parameters of spring bundle unit

, figureFileSmall=null, figureFileBig=null, tableContent=
弹簧单元初始刚度/（kN/mm）屈服承载力/kN屈服后刚度比偏心距e/mm
交叉弹簧134.37246.840.12150
水平弹簧175.00875.000—
), ArticleFig(id=1245390397812355506, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=CN, label=表3, caption=

弹簧束单元相关参数

, figureFileSmall=null, figureFileBig=null, tableContent=
弹簧单元初始刚度/（kN/mm）屈服承载力/kN屈服后刚度比偏心距e/mm
交叉弹簧134.37246.840.12150
水平弹簧175.00875.000—
), ArticleFig(id=1245390397921407416, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=EN, label=Table 4, caption=

Comparison of yield point values and the maximum hysteresis loop area

, figureFileSmall=null, figureFileBig=null, tableContent=
构件类型试件FD-BRW试件BRWFD
屈服点/kN滞回环最大面积屈服点/kN滞回环最大面积屈服点/kN滞回环最大面积
试验689.9363.126×107607.3382.398×107185.21.099×107
ETABS644.1853.287×107584.4812.134×107175.01.138×107
误差/%-6.635.17-3.76-10.99-5.513.54
), ArticleFig(id=1245390398038847933, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=CN, label=表4, caption=

屈服点数值及最大滞回环面积对比表

, figureFileSmall=null, figureFileBig=null, tableContent=
构件类型试件FD-BRW试件BRWFD
屈服点/kN滞回环最大面积屈服点/kN滞回环最大面积屈服点/kN滞回环最大面积
试验689.9363.126×107607.3382.398×107185.21.099×107
ETABS644.1853.287×107584.4812.134×107175.01.138×107
误差/%-6.635.17-3.76-10.99-5.513.54
), ArticleFig(id=1245390398118539713, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=EN, label=Table 5, caption=

Parameters of frame model

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楼层梁截面尺寸/mm柱截面尺寸/mm混凝土强度等级
1~2250×500500×500C30
3~6250×500400×400C30
), ArticleFig(id=1245390398244368837, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390363846881829, language=CN, label=表5, caption=

框架模型参数

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楼层梁截面尺寸/mm柱截面尺寸/mm混凝土强度等级
1~2250×500500×500C30
3~6250×500400×400C30
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摩擦-防屈曲钢板墙复合减震构件简化计算模型及应用
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胡大柱 1 , 占昆旺 1 , 吴志平 1 , 赵娟 1 , 徐春丽 2
地震工程与工程振动 | 2024,44(6): 72-83
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地震工程与工程振动 | 2024, 44(6): 72-83
摩擦-防屈曲钢板墙复合减震构件简化计算模型及应用
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胡大柱1 , 占昆旺1, 吴志平1, 赵娟1, 徐春丽2
作者信息
  • 1.上海应用技术大学 城市建设与安全工程学院，上海 201418
  • 2.上海宝冶集团有限公司，上海 200941

    • 胡大柱（1980—），男，副教授，博士，主要从事结构抗震与减震研究。E-mail：

Calculation model and application of buckling-restrained steel plate wall combined with friction damper
Dazhu HU1 , Kunwang ZHAN1, Zhiping WU1, Juan ZHAO1, Chunli XU2
Affiliations
  • 1.School of Urban Construction and Safety Engineering, Shanghai Institute of Technology, Shanghai 201418, China
  • 2.Shanghai Baoye Group Co., Ltd., Shanghai 200941, China
doi: 10.13197/j.eeed.2024.0607
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摘要
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为解决防屈曲钢板墙屈服位移大，在小变形阶段仅提供刚度和承载力而无法消能的缺点，将墙式摩擦阻尼器与防屈曲钢板墙在厚度方向进行并联布置，构成新型摩擦-防屈曲钢板墙复合减震构件。小变形阶段，复合构件中的摩擦阻尼器滑动消能，随着变形增大，防屈曲钢板墙进入屈服状态，摩擦阻尼器和防屈曲钢板墙共同消能。基于防屈曲钢板墙、摩擦阻尼器以及摩擦-防屈曲钢板墙复合构件的试验结果以及复合构件构造特点，建立了弹簧束简化计算模型，用于模拟摩擦-防屈曲钢板墙复合减震构件的力学性能。简化模型的计算结果与试验结果基本吻合，可替代实体有限元分析，且可在结构整体分析中直接应用。基于简化模型，通过参数分析的方法，以最优附加阻尼比为控制指标，探讨了复合构件中摩擦阻尼器滑动摩擦力与防屈曲钢板墙屈服承载力的合理比值（滑屈比）、构件高宽比建议值。参数分析结果表明，高宽比建议小于1.5，而滑屈比合理比值范围为0.07~0.10。

摩擦-防屈曲钢板墙复合减震构件  /  摩擦阻尼器  /  防屈曲钢板墙  /  弹簧模型  /  参数分析

For the large yield displacement of the buckling-restrained steel plate wall(BRW), only stiffness and bearing capacity can be provided in the small deformation stage. BRW can not dissipate energy in the small deformation stage. To solve this problem, the wall type friction damper (FD) and buckling-restrained steel plate wall are arranged in parallel in the thickness direction to form a new type of buckling-restrained steel plate wall combined with friction damper (FD-BRW). In the small deformation stage, the friction damper in the composite member slides to dissipate energy. As the deformation increases, the buckling-restrained steel plate wall yields, and the friction damper and the buckling-restrained steel plate wall dissipate energy together. Based on the test results of BRW, FD and FD-BRW, a simplified calculation model was established to simulate the mechanical properties of FD-BRW. The simplified calculation model consists of three springs. The calculation results of the simplified model were basically consistent with the experimental results, which can replace the solid finite element analysis and can be directly applied in the overall analysis of the structure. Based on the simplified model, taking the optimal additional damping as the control index, the reasonable ratio of the sliding friction force of friction damper to the yield bearing capacity of the buckling-restrained steel plate wall (slip-yield ratio) and the recommended value of the height-width ratio of the member were discussed through parametric analysis. The results showed that the height-width ratio is recommended to be less than 1.5, and the reasonable range of slip-yield ratio is 0.07~0.10.

buckling-restrained steel plate wall combined with friction damper  /  friction damper  /  buckling-restrained steel plate wall  /  spring model  /  parameter analysis
胡大柱, 占昆旺, 吴志平, 赵娟, 徐春丽. 摩擦-防屈曲钢板墙复合减震构件简化计算模型及应用. 地震工程与工程振动, 2024 , 44 (6) : 72 -83 . DOI: 10.13197/j.eeed.2024.0607
Dazhu HU, Kunwang ZHAN, Zhiping WU, Juan ZHAO, Chunli XU. Calculation model and application of buckling-restrained steel plate wall combined with friction damper[J]. Earthquake Engineering and Engineering Dynamics, 2024 , 44 (6) : 72 -83 . DOI: 10.13197/j.eeed.2024.0607
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0　引言
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防屈曲钢板墙（buckling-restrained steel plate wall，BRW）是一种十分有效的承载-消能构件[1-6]，具有承载力高，抗侧效果好，且对建筑功能影响较小的优点[5]，适用于多高层钢结构。防屈曲钢板墙的屈服位移与其芯板高度有关，在层高4~6 m的钢结构建筑中，防屈曲钢板墙的屈服位移通常在8~10 mm。因而在减震设计中，多遇地震下防屈曲钢板墙的设计目标通常为弹性，仅用于提供刚度。但是对于高烈度设防地震区的钢结构建筑，多遇地震下通常需要减震构件提供附加阻尼以减小地震作用，这导致防屈曲钢板墙的应用受到限制。在以往工程设计中，为提供多遇地震下结构的附加阻尼，通常在结构中混合布置防屈曲钢板墙与黏滞消能器、黏滞阻尼墙、黏弹性消能器或者屈服位移较小的金属消能器，使得建筑结构在多遇地震和罕遇地震下均具有良好的减震效果[7-10]。但在建筑结构中布置过多数量的消能构件，会导致消能子结构数量增多，连接节点用钢量变大，施工难度增加，且工程造价变高。
墙式摩擦阻尼器（friction damper，FD）也是一种消能效果良好的减震构件，起滑位移小、进入滑动变形状态后，阻尼力保持稳定状态，加载刚度接近于零。在减震设计中，摩擦阻尼器通常用于增加结构附加阻尼，从而降低地震力。
结合防屈曲钢板墙及摩擦阻尼器各自特点，构建摩擦-防屈曲钢板墙复合减震构件（buckling-restrained steel plate wall combined with friction damper，FD-BRW），其主要特征为墙式摩擦阻尼器与防屈曲钢板墙在厚度方向并联布置，小变形阶段，摩擦阻尼器滑动摩擦消能，而防屈曲钢板墙为结构提供刚度，大变形阶段，防屈曲钢板墙与摩擦阻尼器共同消能。
作为新型复合减震构件，需要合理的力学模型以便工程应用。为此，根据摩擦-防屈曲钢板墙复合减震构件的特点以及试验结果，本文提出了基于非线性弹簧束单元的简化力学模型，并对力学模型的各弹簧参数进行系统分析。
1　摩擦-防屈曲钢板墙复合减震构件试验
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摩擦-防屈曲钢板墙复合减震构件的构造如图1所示。摩擦阻尼器摩擦材料采用铜片，防屈曲钢板墙的耗能芯板可采用Q235低碳钢。
为验证该摩擦-防屈曲钢板墙复合减震构件的力学特性，分别对防屈曲钢板墙、摩擦阻尼器及摩擦-防屈曲钢板墙复合减震构件进行了试验研究。试验构件的设计图如图2所示，核心部件尺寸如表1所示。由于摩擦阻尼器弹性刚度小于防屈曲钢板墙，若二者在厚度方向居中布置，则防屈曲钢板墙侧的侧向刚度明显大于摩擦阻尼器，将使得与构件相连的梁受到偏心力作用。为此，在厚度方向，防屈曲钢板墙距离试件中心30 mm，而摩擦阻尼器距离试件中心100 mm。
试验测试装置如图3所示，作动器端部的移动横梁与加载盖梁组成传力机构，试验构件下部与自平衡反力架连接，上部与加载盖梁连接，作动器往复加载带动加载盖梁水平移动，驱动试件变形，模拟试验构件在水平地震作用下的往复变形。
由于摩擦阻尼器起滑位移较小，试验全过程均采用位移控制的方式进行水平往复加载。试验的加载历程分为预加载和正式加载两部分。预加载的主要目的是确保试件与加载装置良好接触。正式加载采用位移加载，为观察摩擦阻尼器的性能，第1级加载按照0.5 mm位移幅值进行加载，从第2级开始至第6级加载位移幅值分别为1、2、3、4、5 mm。从第7级开始，加载位移按照防屈曲钢板墙高度的1/150、1/100、1/75、1/50逐级增大，每级位移幅值循环往复3次。3个试件的加载制度完全一致，正式加载历程如表2所示。
试验测试得到的滞回曲线和骨架曲线如图4所示。由于设备影响，每级加载至±140 kN出力位置处时，加载油缸出现顿挫现象，导致滞回曲线在该位置处出现一个拐点。
试验测试得到的试件FD滞回曲线呈现理想弹塑性特征，由于摩擦材料固有特性，随着变形的增加，摩擦力略有增大，在分析中可保守采用屈服后刚度为0的弹塑性单元模拟其性能。BRW滞回曲线的形状呈现梭形，加载过程中未出现强度退化现象，但与金属屈服型阻尼器相比，BRW的屈服后刚度较大。由FD、BRW及FD-BRW这3个试件的实测滞回曲线及骨架曲线可知，FD-BRW的屈服承载力、刚度和极限承载力等关键参数为BRW和FD这2个试件对应参数之和。
2　简化弹簧束计算模型
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对于BRW比较成熟的简化分析模型是双斜杆模型[11-13]，而FD-BRW的简化模型目前暂未有相关的研究。根据构造特点及试验结果，FD-BRW由BRW和FD并联组合而成，因而在交叉弹簧基础上引入一根模拟墙式摩擦阻尼器的水平弹簧[14-16]，形成FD-BRW的简化弹簧束计算模型，如图5所示。
由于FD-BRW上下焊接在结构梁上，会进一步增大框架梁的抗弯刚度[11]，可假定与减震构件直接相连区域内的梁抗弯刚度EI为无穷大；水平弹簧由墙式摩擦阻尼器简化而来，连接杆件可设为刚性杆，剪切位置在阻尼器的中心位置，水平弹簧居中布置；B和H分别为FD-BRW立面尺寸的宽和高，α为交叉弹簧与梁的夹角，e为弹簧支撑点相对钢板墙边缘距离，称为交叉弹簧的偏心距。
2.1　偏心距e的确定
图5所示的简化计算模型，需要确定各几何尺寸的计算方法。对模拟BRW性能的交叉弹簧，最重要的一个指标便是交叉弹簧支撑点距钢板墙边缘的偏心距e。为更好地防止BRW端部发生撕裂破坏，试验构件进一步加宽了芯板的端部弹性段的宽度，与陆烨等[17]提出的构造有所差异，如图6所示。在已有研究的基础上，简化计算模型中的偏心距e及夹角α的计算，如式（1）~式（2）所示：
2.2　各弹簧承载力及刚度的确定
2.2.1　交叉弹簧
经有限元分析和试验验证，本文的芯板构造与陆烨等[17]提出的TJI型构造受力机理基本一致。在此研究基础上，根据刚度等效原则可推导出交叉弹簧初始刚度，计算方法如式（3）所示：
式中，β为宽度修正系数：
当H/B≥1时，
当H/B<1时，
交叉弹簧屈服承载力可按式（5）计算：
其中：
钢板墙芯板（不计端部放大区）的立面面积为
钢板端部截面放大区的面积As按式（10）计算：
式（3）~式（10）中：E为钢材的弹性模量（N/mm2）；G为钢材剪切变形模量（N/mm2）；υ为钢材泊松比；H为芯板高度（mm）；t为芯板厚度（mm）；B为芯板宽度（mm）；I为芯板屈服段横截面的截面惯性矩。
2.2.2　水平弹簧
水平弹簧用于模拟摩擦-防屈曲钢板墙复合减震构件的摩擦阻尼器。由于其滞回性能符合理想弹塑性的性能[14]，仅需定义其滑动摩擦力、起滑位移和极限位移，便可完成对摩擦阻尼器的定义。水平弹簧初始刚度和屈服承载力可按式（11）、式（12）求得：
式中：K3为初始刚度；δy为起滑位移；Ff为屈服承载力；Qyb为滑动摩擦力。
墙式摩擦阻尼器极限位移由其摩擦副的长椭圆孔的长轴尺寸决定，一般为200~400 mm。
2.3　恢复力模型
2.3.1　交叉弹簧
试验结果表明，防屈曲钢板墙的骨架曲线和滞回曲线与金属阻尼器特性基本一致，故等效交叉弹簧的滞回曲线模型采用Bouc-Wen模型，如图7（a）所示。其中，弹性刚度Kd及屈服力承载Fdy可由式（3）~式（5）求得，屈服指数α可取2，屈服后刚度比q可取0.05~0.15。
2.3.2　水平弹簧
摩擦阻尼器的往复试验结果表明，在各工况下阻尼器都呈现良好的耗能性能。由其滞回曲线可观察出，摩擦阻尼器初始刚度大、第2刚度接近于零，因而可采用理想弹塑性模型模拟其滞回性能，如图7（b）所示。其中初始刚度K3及屈服承载力Ff可由式（11）~式（12）求得，δy取摩擦阻尼器的起滑位移。
3　弹簧束模型的模拟验证
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为了验证第2节所提出计算模型的准确性和适用性，采用式（1）~式（12）计算试验构件的各项力学性能参数和几何参数，并采用Etabs软件建立弹簧束模型，采用往复加载，得到滞回曲线。计算得到弹簧束单元参数如表3所示，Etabs计算模型如图8所示。在有限元模型中，采用多段塑性中的Plastic（Wen）连接单元模拟交叉弹簧，Isotropic连接单元模拟水平弹簧。
简化模型与试验结果的滞回曲线与骨架曲线对比如图9和图10所示。由图中的对比结果可以看出，简化模型分析得到的滞回曲线与试验结果基本吻合，说明该模型可用于摩擦-防屈曲钢板墙的分析。
提取试验及有限元分析的具体数据，分解出其滞回环最大面积（loop energy），并采用PARK法[18]在荷载系数取0.75的情况下可求得各构件的屈服点，各数据如表4所示。由对比结果进一步看出，模型误差范围较小，采用简化弹簧束模型可以代替复杂的实体有限元分析。
4　参数分析
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经试验和有限元分析可知，摩擦-防屈曲钢板墙复合减震构件具有良好的多级消能特性，且所提出的简化计算模型和公式可以用于结构计算。但为了更为高效地发挥FD-BRW的性能，其组成构件（BRW及FD）的相互间出力比例还需进一步进行研究。在本文提出的简化力学模型的基础上，结合一幢六层三跨的平面框架结构，以附加阻尼比为评判标准进行最优化参数分析。
参考屈曲约束支撑结构相关研究成果[19]，在参数分析中考虑了：①BRW屈服承载力与纯框架基底剪力的比值，定义为名义剪力比α；②FD-BRW构件的高宽比λ；③FD滑动摩擦力与BRW屈服承载力比值β。
4.1　结构基本信息
设计一个三跨六层的框架结构，层高3.6 m，跨度6 m，楼面恒载为4.0 kN/m2，活载为2.5 kN/m2，梁上恒载（梁上的填充墙自重）为6 kN/m，抗震设防烈度为8度（0.2 g），场地类别为II类场地。主要构件截面尺寸如表5所示，结构布置图及设置FD-BRW的结构如图11所示。为更好地模拟消能构件与主体结构连接位置处框架梁抗弯刚度增大的这一特性，在FD-BRW对应位置设置厚为200 mm，高度为500 mm的墙构件。
按照GB 50011—2010《建筑抗震设计规范》[20]要求，选取了5条天然波和2条人工波，各地震波频谱特性与规范反应谱对比如图12所示，所选取的地震波满足规范要求。
4.2　基于名义剪力比的BRW参数
考虑框架中设置FD-BRW后，由于结构刚度的增大，基底剪力将发生变化[19]，因而基底剪力取未设置FD-BRW的纯框架结构计算值，采用式（13）所计算的名义剪力比作为参数分析中的变量。
式中：Fy为反应谱法求得的纯框架结构基底剪力；FBRW为防屈曲钢板墙的屈服承载力。
在高宽比及屈服承载力均确定的情况下，BRW的其他参数，包括芯板厚度及初始刚度等可由式（3）~式（10）计算得到。
4.3　基于滑屈比的FD参数
FD的立面尺寸同BRW，其滑动摩擦力由滑屈比β确定，滑屈比定义为摩擦阻尼器的滑动摩擦力与防屈曲钢板墙的屈服承载力的比值，如式（14）所示：
式中：FFD为摩擦阻尼器的滑动摩擦力；FBRW为防屈曲钢板墙的屈服承载力。
4.4　分析结果
根据本文所提出的简化计算模型，使用Etabs有限元软件，对名义剪力比α分别取0.1、0.2、0.3、0.4、0.5、0.6，高宽比λ分别取1.0、1.5、2.0，滑屈比β分别取0.1、0.2、0.3、0.4、0.5、0.6，共计108个计算模型进行时程分析，小震及中震工况下采用快速非线性（fast nonlinear analysis method，FNA）方法，大震采用直接积分法。采用能量比法[21]计算附加阻尼比，取7条地震波计算结果的平均值，得到设置不同高宽比FD-BRW结构的附加阻尼比随名义剪力比α的变化规律，详细结果如图13~图15所示。
由图13、图15的分析结果可知：
1）在小震工况下，结构附加阻尼比随着滑屈比β和名义剪力比a的增加逐步增大，但增大的幅度随滑屈比β增大而逐渐减小。滑屈比较大时，当名义剪力比大于0.5时，附加阻尼比出现降低的趋势。
2）在中、大震工况下，随着滑屈比β和名义剪力比a的增加，结构附加阻尼比逐步提升，且提升幅度与滑屈比β的增幅近似呈线性关系。
3）FD-BRW高宽比λ越大，附加阻尼比越小，FD-BRW耗能能力越弱，故不建议摩擦-防屈曲钢板墙复合减震构件的高宽比过大。因为随着FD-BRW高宽比增大，BRW抗弯刚度对构件整体刚度的影响变大。对于没有侧向耗能部件的BRW，其弯曲耗能能力微弱，对于大高宽比BRW剪切耗能也不充分。因此，为保证较好的耗能能力，建议高宽比不大于1.5。
考虑到大震下结构等效周期延长，按照大震反应谱重新选用2条人工波，进行补充分析。其地震波频谱特性与规范反应谱对比如图16所示。对比分析7条地震波平均值与2条人工波所得到的附加阻尼比，如图17所示。由图可知，考虑结构周期延长后所选人工波的附加阻尼比计算结果基本规律与图15所得到的规律基本一致。
4.4.1　摩擦阻尼器对附加阻尼比的影响
由于FD-BRW的多级消能特性，为更加清晰地观察其组成部件对附加阻尼比的影响规律，以图13中高宽比为1的模型为例，进一步分析摩擦阻尼器对附加阻尼比的影响。
在小震工况下，FD-BRW主要由摩擦阻尼器耗能。为研究由摩擦阻尼器滑动摩擦力变化所引起的结构附加阻尼比的变化，定义FD的名义滑屈比β′为
小震工况下的名义滑屈比β′与结构附加阻尼比的关系如图18所示。从关系曲线可以看出，随着FD名义滑屈比β′的增加，结构附加阻尼比呈现出先增大后减小的抛物线状变化；且附加阻尼比的增加幅度逐渐减小。名义滑屈比β′在0.04左右时，结构所获得的附加阻尼比最大。
4.4.2　防屈曲钢板墙对附加阻尼比的影响
在大震下，FD-BRW中摩擦阻尼器和防屈曲钢板墙共同耗能。将高宽比为1的构件在大震下附加阻尼比与名义剪力比α关系曲线做进一步分析，见图19。图中的上部填充部分为FD的耗能，下部填充部分主要为BRW的耗能。通过对FD耗能的分析可知，随着其滑屈比β增加，其耗能能力逐渐增强。由BRW耗能分析可知，随名义剪力比α增大，BRW耗能能力逐渐增强，且在α为0.5左右时耗能能力放缓。故建议BRW的名义剪力比α取0.4~0.6之间为宜。
由名义剪力比α及名义滑屈比β′的建议比值可计算得到复合构件中摩擦阻尼器滑动摩擦力与防屈曲钢板墙屈服承载力的建议比值（滑屈比β）。当名义滑屈比β′=0.04，名义剪力比α=0.4~0.6，由式（13）~式（15）可得到滑屈比β建议值为0.07~0.10。
5　结论
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通过对摩擦-防屈曲钢板墙复合减震构件的试验、理论模型建立及参数分析，可得到以下结论：
1）基于摩擦-防屈曲钢板墙复合减震构件的特点，提出了简化弹簧束计算模型，模型计算结果与试验结果基本吻合。
2）通过参数分析，基于附加阻尼比最大的原则，给出了摩擦-防屈曲钢板墙构件中FD滑动摩擦力与BRW屈服承载力的建议比值，其取值范围为0.07~0.10。
3）结合参数分析结果，建议摩擦-防屈曲钢板墙复合减震构件中的BRW高宽比不大于1.5，在结构中设置该类型减震构件时，名义剪力比α取0.4~0.6能够取得较高的附加阻尼比。
基金
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  • 国家自然科学基金青年基金项目(51408361)
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2024年第44卷第6期
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doi: 10.13197/j.eeed.2024.0607
  • 接收时间：2023-10-22
  • 首发时间：2026-03-30
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  • 收稿日期：2023-10-22
  • 修回日期：2023-12-06
基金
国家自然科学基金青年基金项目(51408361)
作者信息
    1.上海应用技术大学 城市建设与安全工程学院，上海 201418
    2.上海宝冶集团有限公司，上海 200941
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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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