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Article(id=1245390259270303943, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245390255516397762, articleNumber=null, orderNo=null, doi=10.13197/j.eeed.2024.0519, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1689868800000, receivedDateStr=2023-07-21, revisedDate=1693238400000, revisedDateStr=2023-08-29, acceptedDate=null, acceptedDateStr=null, onlineDate=1774853776042, onlineDateStr=2026-03-30, pubDate=null, pubDateStr=null, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774853776042, onlineIssueDateStr=2026-03-30, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774853776042, creator=13701087609, updateTime=1774853776042, updator=13701087609, issue=Issue{id=1245390255516397762, tenantId=1146029695717560320, journalId=1241701559352995854, year='2024', volume='44', issue='5', pageStart='1', pageEnd='231', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774853775147, creator=13701087609, updateTime=1774854426342, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1245392986884911753, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245390255516397762, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1245392986889106058, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245390255516397762, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=199, endPage=209, ext={EN=ArticleExt(id=1245390259475824849, articleId=1245390259270303943, tenantId=1146029695717560320, journalId=1241701559352995854, language=EN, title=Hysteresis performance and simplified mechanical model of a novel partial self-centering shear link, columnId=null, journalTitle=Earthquake Engineering and Engineering Dynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

By combining the partial self-centering shape memory alloy(SMA) braces (SCB) with the shear slotted bolted connection-very short shear link (SSBC-VSSL), an innovative self-centering shear link (SC-SL) used in the eccentrically braced frame (EBFs) that has an advantage of good energy dissipation capacity and self-centering capacity, low damage and excellent seismic resilience capacity is developed. Cyclic tests were carried on SC-SL specimens designed by the proposed method, so the deformation modes and hysteresis curves can be obtained. Based on the test results, ten SC-SL models with the effect of SMA areas, high-strength bolt pretensions and shim friction coefficients were designed and analyzed by the validated finite analysis (FE) method. The results show that the VSSL is in the relative static during the slip stage, then the development process of very short shear link (VSSL) in SSCB-VSSL including yield, bearing, energy dissipation and inelastic deformation are appeared sequentially during the non-slip stage, while the SMAs in SCB are always subjected to elongation, thus increasing the energy dissipating capacity and self-centering capacity. Finally, the simplified mechanical models of SC-SL in the slip stage and non-slip stage are proposed by using the FE results, which can provide a new way to give important seismic design reference for EBFs.

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提出一种用于偏心支撑结构中的部分自复位耗能段，主要包括自复位形状记忆合金（shape memory alloy，SMA）支撑和扩孔螺栓连接型耗能段，具有耗能能力和自复位能力强、构件损伤小、震后功能可恢复等特点。基于部分自复位耗能段的设计方法，合理设计其试验模型，由此得到变形模式和滞回曲线等。随后采用校正的有限元法对部分自复位耗能段力学性能进行研究，主要考虑SMA面积、高强螺栓预拉力和垫片滑移系数的影响。研究结果表明：滑移阶段自复位耗能段中耗能段处于滑移并保持相对静止状态；随后非滑移阶段耗能段开始承载、耗能和非弹性变形等，整个过程中自复位SMA支撑提供耗能和复位能力，以及减小构件残余变形。基于不同因素下的分析结果，提出滑移阶段和非滑移阶段下自复位耗能段简化的力学模型，为偏心支撑结构的抗震设计与分析提供新的思路和理论基础。

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胡淑军（1985—），男，副教授，博士，主要从事可恢复功能结构体系研究。E-mail：
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刘俊（1985—），男，高级工程师，硕士，主要从事自复位结构研究。E-mail：

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刘俊（1985—），男，高级工程师，硕士，主要从事自复位结构研究。E-mail：

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刘俊（1985—），男，高级工程师，硕士，主要从事自复位结构研究。E-mail：

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figureFileBig=dHWUfkHYFlbL1szewMYGMg==, tableContent=null), ArticleFig(id=1245390269244359566, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390259270303943, language=CN, label=图2, caption=部分自复位耗能段试件尺寸图, figureFileSmall=qoT2KsW6BNQTpu3xpilk1g==, figureFileBig=dHWUfkHYFlbL1szewMYGMg==, tableContent=null), ArticleFig(id=1245390269349217173, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390259270303943, language=EN, label=Fig. 3, caption=Loading device, figureFileSmall=BgQAdL0AonfvZEhlEfRI0g==, figureFileBig=0WRPJZXgfqeiC0tuLofmlw==, tableContent=null), ArticleFig(id=1245390269483434907, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390259270303943, language=CN, label=图3, caption=加载装置, figureFileSmall=BgQAdL0AonfvZEhlEfRI0g==, figureFileBig=0WRPJZXgfqeiC0tuLofmlw==, tableContent=null), ArticleFig(id=1245390269579903906, tenantId=1146029695717560320, journalId=1241701559352995854, 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caption=试件SC-SL-1耗能段的破坏模式图, figureFileSmall=BYHmAneT9hgKG6NzgslP6A==, figureFileBig=pe9bRCW2bOFPObs/yQg3Ig==, tableContent=null), ArticleFig(id=1245390269957391290, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390259270303943, language=EN, label=Fig. 6, caption=Hysteresis curves of specimens SC-SL-1, figureFileSmall=ui6Ami0ucoR6AK/H0N/cjA==, figureFileBig=0G5lx5AbrtbdxoTUgJNmaA==, tableContent=null), ArticleFig(id=1245390270045471679, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390259270303943, language=CN, label=图6, caption=试件SC-SL-1的滞回曲线图, figureFileSmall=ui6Ami0ucoR6AK/H0N/cjA==, figureFileBig=0G5lx5AbrtbdxoTUgJNmaA==, tableContent=null), ArticleFig(id=1245390270158717893, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390259270303943, language=EN, label=Fig. 7, caption=Finite element analysis model of partial self-centering shear links, figureFileSmall=kE8UXx29gDF3UMCMW3pZuA==, figureFileBig=dXSOdVK2pL2nrC0vWs8+0g==, tableContent=null), ArticleFig(id=1245390270246798283, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390259270303943, language=CN, label=图7, caption=部分自复位耗能段的有限元分析模型, figureFileSmall=kE8UXx29gDF3UMCMW3pZuA==, figureFileBig=dXSOdVK2pL2nrC0vWs8+0g==, tableContent=null), ArticleFig(id=1245390270322295761, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390259270303943, language=EN, label=Fig. 8, caption=Comparison of hysteresis curve for SC-SL-1, figureFileSmall=Cm/g6U2hF2kq0oR0JdWn0g==, figureFileBig=R14Ec28yvHdJmyYojqxxvQ==, tableContent=null), ArticleFig(id=1245390270418764761, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390259270303943, language=CN, label=图8, caption=试件SC-SL-1的滞回曲线对比, figureFileSmall=Cm/g6U2hF2kq0oR0JdWn0g==, figureFileBig=R14Ec28yvHdJmyYojqxxvQ==, tableContent=null), ArticleFig(id=1245390270498456542, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390259270303943, language=EN, label=Fig. 9, caption=Deformation mode for specimen SCB-VS-3, figureFileSmall=9aZsUkC1sjuD6yXej0Hc1g==, figureFileBig=lWWtgfBhubf+mhJClCgLBQ==, tableContent=null), ArticleFig(id=1245390270607508450, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390259270303943, language=CN, label=图9, caption=模型SCB-VS-3的变形模式图, figureFileSmall=9aZsUkC1sjuD6yXej0Hc1g==, figureFileBig=lWWtgfBhubf+mhJClCgLBQ==, tableContent=null), ArticleFig(id=1245390270699783142, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390259270303943, language=EN, label=Fig. 10, caption=Influence of SMA area, figureFileSmall=wQfbmSoNEXp3E3PbEdcYFg==, figureFileBig=xk5DYommLktYWwQyZpZxBA==, tableContent=null), ArticleFig(id=1245390270796252137, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390259270303943, language=CN, label=图10, caption=SMA面积的影响, 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ArticleFig(id=1245390271240848383, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390259270303943, language=CN, label=图12, caption=垫片摩擦系数的影响, figureFileSmall=tnpGpYHhhavH1WDydqpdlQ==, figureFileBig=MS6AnMii84JasMyXxkZg8w==, tableContent=null), ArticleFig(id=1245390271379259397, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390259270303943, language=EN, label=Fig. 13, caption=Hysteresis curves of partial self-centering SMA brace during slip stage, figureFileSmall=Mh8dNmdwoVyvVaDgQGXOnQ==, figureFileBig=XR9vVhXQgkSs7svvPNen3A==, tableContent=null), ArticleFig(id=1245390271463145480, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390259270303943, language=CN, label=图13, caption=滑移阶段下部分自复位耗能段的滞回曲线, figureFileSmall=Mh8dNmdwoVyvVaDgQGXOnQ==, figureFileBig=XR9vVhXQgkSs7svvPNen3A==, tableContent=null), ArticleFig(id=1245390271609946125, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390259270303943, language=EN, label=Fig. 14, caption=Mechanical curves of partial self-centering SMA brace during slip stage, figureFileSmall=lT9imOAbh4t5+vwfjEdpMg==, figureFileBig=gv2SIOnlJtaDjmpN2+8cFg==, tableContent=null), ArticleFig(id=1245390271731580948, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390259270303943, language=CN, label=图14, caption=滑移阶段部分自复位耗能段的力学曲线, figureFileSmall=lT9imOAbh4t5+vwfjEdpMg==, figureFileBig=gv2SIOnlJtaDjmpN2+8cFg==, tableContent=null), ArticleFig(id=1245390271849021461, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390259270303943, language=EN, label=Fig. 15, caption=Hysteresis curves of partial self-centering SMA brace during non-slip stage, figureFileSmall=ZLLfRUg4i9DbiWysPZeX1w==, figureFileBig=N+5SGvI+7CQayJOXSHQYuw==, tableContent=null), ArticleFig(id=1245390271937101850, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390259270303943, language=CN, label=图15, caption=非滑移阶段下部分自复位耗能段的滞回曲线, figureFileSmall=ZLLfRUg4i9DbiWysPZeX1w==, figureFileBig=N+5SGvI+7CQayJOXSHQYuw==, tableContent=null), ArticleFig(id=1245390272037765152, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390259270303943, language=EN, label=Fig. 16, caption=Mechanical models of partial self-centering SMA brace during non-slip stage, figureFileSmall=XD/dtJUdGwNlKw7xXBKHBw==, figureFileBig=bhuzrXdZan8fUHIE2i6W7A==, tableContent=null), ArticleFig(id=1245390272134234147, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390259270303943, language=CN, label=图16, caption=非滑移阶段部分自复位耗能段的力学模型, figureFileSmall=XD/dtJUdGwNlKw7xXBKHBw==, figureFileBig=bhuzrXdZan8fUHIE2i6W7A==, tableContent=null), ArticleFig(id=1245390272251674663, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390259270303943, language=EN, label=Table 1, caption=

Mechanical parameters of steel plates

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厚度/mm屈服强度fy/MPa抗拉强度fu/MPa弹性模量E/MPa伸长率δ/%
635653520321.7
836154720622.2
1036855220823.3
1537255620923.2
), ArticleFig(id=1245390272385892399, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390259270303943, language=CN, label=表1, caption=

钢板的力学参数

, figureFileSmall=null, figureFileBig=null, tableContent=
厚度/mm屈服强度fy/MPa抗拉强度fu/MPa弹性模量E/MPa伸长率δ/%
635653520321.7
836154720622.2
1036855220823.3
1537255620923.2
), ArticleFig(id=1245390272490750003, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390259270303943, language=EN, label=Table 2, caption=

Analysis models of partial self-centering shear links

, figureFileSmall=null, figureFileBig=null, tableContent=
模型影响因素扩孔螺栓连接型耗能段自复位SMA支撑
P/kNμ1耗能段截面/mmSMA面积/mm2μ2Tb/kN
SCB-VS-F1SMA面积300.20210×110×6×894.200.07510
SCB-VS-F2300.20210×110×6×8125.600.07510
SCB-VS-F3300.20210×110×6×8141.300.07510
SCB-VS-F4300.20210×110×6×8157.000.07510
SCB-VS-F5滑移螺栓预拉力200.20210×110×6×8141.300.07510
SCB-VS-F6400.20210×110×6×8141.300.07510
SCB-VS-F7500.20210×110×6×8141.300.07510
SCB-VS-F8摩擦系数300.15210×110×6×8141.300.07510
SCB-VS-F9300.25210×110×6×8141.300.07510
SCB-VS-F10300.30210×110×6×8141.300.07510
), ArticleFig(id=1245390272578830389, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390259270303943, language=CN, label=表2, caption=

部分自复位耗能段的分析模型

, figureFileSmall=null, figureFileBig=null, tableContent=
模型影响因素扩孔螺栓连接型耗能段自复位SMA支撑
P/kNμ1耗能段截面/mmSMA面积/mm2μ2Tb/kN
SCB-VS-F1SMA面积300.20210×110×6×894.200.07510
SCB-VS-F2300.20210×110×6×8125.600.07510
SCB-VS-F3300.20210×110×6×8141.300.07510
SCB-VS-F4300.20210×110×6×8157.000.07510
SCB-VS-F5滑移螺栓预拉力200.20210×110×6×8141.300.07510
SCB-VS-F6400.20210×110×6×8141.300.07510
SCB-VS-F7500.20210×110×6×8141.300.07510
SCB-VS-F8摩擦系数300.15210×110×6×8141.300.07510
SCB-VS-F9300.25210×110×6×8141.300.07510
SCB-VS-F10300.30210×110×6×8141.300.07510
), ArticleFig(id=1245390272696270907, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390259270303943, language=EN, label=Table 3, caption=

Comparison of finite element and theoretical analysis

, figureFileSmall=null, figureFileBig=null, tableContent=
模型编号滑移阶段非滑移阶段模型编号滑移阶段非滑移阶段
FN/kNFS/kN误差/%FN/kNFS/kN误差/%FN/kNFS/kN误差/%FN/kNFS/kN误差/%
SCB-VS-F1143.41156.658.45520.92546.524.68SCB-VS-F6201.82213.455.45572.35590.573.09
SCB-VS-F2162.37175.497.48543.98570.374.63SCB-VS-F7224.68239.126.04574.48591.222.83
SCB-VS-F3181.50192.975.94570.16588.263.08SCB-VS-F8165.56181.928.99568.63590.223.66
SCB-VS-F4197.37214.157.84587.70605.112.88SCB-VS-F9199.02215.557.67572.76592.553.34
SCB-VS-F5156.35167.596.71565.33588.223.89SCB-VS-F10216.68232.816.93574.12591.622.96
), ArticleFig(id=1245390272775962687, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390259270303943, language=CN, label=表3, caption=

有限元及理论分析结果对比

, figureFileSmall=null, figureFileBig=null, tableContent=
模型编号滑移阶段非滑移阶段模型编号滑移阶段非滑移阶段
FN/kNFS/kN误差/%FN/kNFS/kN误差/%FN/kNFS/kN误差/%FN/kNFS/kN误差/%
SCB-VS-F1143.41156.658.45520.92546.524.68SCB-VS-F6201.82213.455.45572.35590.573.09
SCB-VS-F2162.37175.497.48543.98570.374.63SCB-VS-F7224.68239.126.04574.48591.222.83
SCB-VS-F3181.50192.975.94570.16588.263.08SCB-VS-F8165.56181.928.99568.63590.223.66
SCB-VS-F4197.37214.157.84587.70605.112.88SCB-VS-F9199.02215.557.67572.76592.553.34
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新型部分自复位耗能段的滞回性能与简化力学模型研究
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刘俊 1 , 王秋慧 1 , 张波 2, 3 , 胡淑军 3
地震工程与工程振动 | 2024,44(5): 199-209
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地震工程与工程振动 | 2024, 44(5): 199-209
新型部分自复位耗能段的滞回性能与简化力学模型研究
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刘俊1 , 王秋慧1, 张波2, 3, 胡淑军3
作者信息
  • 1.中国电建集团江西省电力设计院有限公司，江西 南昌 330096
  • 2.中国瑞林工程技术股份有限公司，江西 南昌 330031
  • 3.南昌大学 工程建设学院，江西 南昌 330031

    • 刘俊（1985—），男，高级工程师，硕士，主要从事自复位结构研究。E-mail：

通讯作者:

胡淑军（1985—），男，副教授，博士，主要从事可恢复功能结构体系研究。E-mail：
Hysteresis performance and simplified mechanical model of a novel partial self-centering shear link
Jun LIU1 , Qiuhui WANG1, Bo ZHANG2, 3, Shujun HU3
Affiliations
  • 1.Power China Jiangxi Electric Power Engineering Co., Ltd., Nanchang 330096, China
  • 2.China Nerin Engineering Co., Ltd., Nanchang 330031, China
  • 3.School of Infrastructure Engineering, Nanchang University, Nanchang 330031, China
doi: 10.13197/j.eeed.2024.0519
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摘要
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提出一种用于偏心支撑结构中的部分自复位耗能段，主要包括自复位形状记忆合金（shape memory alloy，SMA）支撑和扩孔螺栓连接型耗能段，具有耗能能力和自复位能力强、构件损伤小、震后功能可恢复等特点。基于部分自复位耗能段的设计方法，合理设计其试验模型，由此得到变形模式和滞回曲线等。随后采用校正的有限元法对部分自复位耗能段力学性能进行研究，主要考虑SMA面积、高强螺栓预拉力和垫片滑移系数的影响。研究结果表明：滑移阶段自复位耗能段中耗能段处于滑移并保持相对静止状态；随后非滑移阶段耗能段开始承载、耗能和非弹性变形等，整个过程中自复位SMA支撑提供耗能和复位能力，以及减小构件残余变形。基于不同因素下的分析结果，提出滑移阶段和非滑移阶段下自复位耗能段简化的力学模型，为偏心支撑结构的抗震设计与分析提供新的思路和理论基础。

自复位耗能段  /  扩孔螺栓连接型耗能段  /  自复位SMA支撑  /  滞回曲线  /  力学模型

By combining the partial self-centering shape memory alloy(SMA) braces (SCB) with the shear slotted bolted connection-very short shear link (SSBC-VSSL), an innovative self-centering shear link (SC-SL) used in the eccentrically braced frame (EBFs) that has an advantage of good energy dissipation capacity and self-centering capacity, low damage and excellent seismic resilience capacity is developed. Cyclic tests were carried on SC-SL specimens designed by the proposed method, so the deformation modes and hysteresis curves can be obtained. Based on the test results, ten SC-SL models with the effect of SMA areas, high-strength bolt pretensions and shim friction coefficients were designed and analyzed by the validated finite analysis (FE) method. The results show that the VSSL is in the relative static during the slip stage, then the development process of very short shear link (VSSL) in SSCB-VSSL including yield, bearing, energy dissipation and inelastic deformation are appeared sequentially during the non-slip stage, while the SMAs in SCB are always subjected to elongation, thus increasing the energy dissipating capacity and self-centering capacity. Finally, the simplified mechanical models of SC-SL in the slip stage and non-slip stage are proposed by using the FE results, which can provide a new way to give important seismic design reference for EBFs.

self-centering shear link(SC-SL)  /  shear slotted bolted connection with very short shear link (SSBC-VSSL)  /  self-centering SMA braces (SCB)  /  hysteresis curve  /  mechanical model
刘俊, 王秋慧, 张波, 胡淑军. 新型部分自复位耗能段的滞回性能与简化力学模型研究. 地震工程与工程振动, 2024 , 44 (5) : 199 -209 . DOI: 10.13197/j.eeed.2024.0519
Jun LIU, Qiuhui WANG, Bo ZHANG, Shujun HU. Hysteresis performance and simplified mechanical model of a novel partial self-centering shear link[J]. Earthquake Engineering and Engineering Dynamics, 2024 , 44 (5) : 199 -209 . DOI: 10.13197/j.eeed.2024.0519
正文
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0　引言
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地震作用下，兼具良好抗侧刚度和耗能能力的偏心支撑结构中耗能段率先发生塑性变形，并耗散输入结构中的能量，保护结构安全[1-3]。然而，小震、中震无损伤，大震后损伤较小和快速恢复结构功能的抗震设防目标被提出[4-5]，耗能段需进一步提高其耗能和自复位能力[5-6]，以使偏心支撑结构适应当前更高抗震要求。耗能段根据长度比ρ可分为剪切型（ρ≤1.6）、弯剪型（1.6<ρ<2.6）和弯曲型（ρ≥2.6）[7]。对于长度比小于1.0的短剪切型耗能段，其超强系数和塑性转角可达到1.90和0.13，明显高于规范允许值1.50和0.08[8]，承载能力和变形能力明显优于上述3种耗能段，有利于提高偏心支撑结构的抗震性能[9-11]。
扩孔型螺栓连接主要通过高强螺栓在长圆孔中摩擦滑移实现延性和耗能[12-14]。例如，KHOO等[12]对于带调质钢、低碳钢、耐磨钢垫片的扩孔型螺栓连接开展试验研究，指出不同垫片的性能与特点；赵俊贤等[11]基于在滑移节点板间设置丁基橡胶垫片，形成了摩擦力较小的扩孔型螺栓连接。刘超等[14]对采用铜、钢和铝垫片的扩孔型螺栓连接研究，得到了各垫片摩擦系数，以及连接的耗能能力和承载能力等。将扩孔螺栓连接型设置在偏心支撑结构中的短剪切型耗能段与钢支撑之间，可形成一种扩孔螺栓连接型耗能段[15]，具有高延性、强耗能、低损伤等特点，但震后残余变形较大，影响了结构震后修复和更换效率[16]。
形状记忆合金（shape memory alloy，SMA）是一种具有自复位、超弹性的智能材料，其最大恢复应变可达8%[17-18]。例如，QIU等[19]设计一种基于SMA的自复位支撑构件，其残余变形接近零，具有良好复位和耗能能力。钱辉等[20]将SMA应用于梁柱节点中，所得自复位节点的耗能和自复位能力得到明显提高。SUN等[21]提出采用SMA丝材的自复位钢支撑，具有捏缩特性明显、残余变形极小和耗能能力强等特点。胡淑军等[22]基于板件间长圆孔、滑移螺杆和SMA等构件的合理设置，提出一种在拉、压作用下SMA始终受拉且具有良好耗能和复位能力的自复位SMA支撑。
为进一步提高偏心支撑结构的抗震性能和震后功能恢复能力，本文在扩孔螺栓连接型耗能段两侧分别设置1个自复位SMA支撑，可得到一种新型部分自复位耗能段。开展部分自复位耗能段的试验研究，得到其变形模式和滞回曲线等。随后采用校正的有限元法对部分自复位耗能段开展参数化研究，详细分析SMA面积、高强螺栓预拉力和垫片滑移系数对滞回性能的影响，并得到滑移阶段和非滑移阶段自复位耗能段的简化力学模型，为偏心支撑结构的抗震设计与分析提供新的思路和理论基础。
1　试验研究
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1.1　模型设计
1.1.1　设计方法
1）扩孔螺栓连接型耗能段
为实现自复位耗能段预期耗能与复位能力，需保证扩孔螺栓连接型耗能段中扩孔型螺栓连接滑移荷载Fslip小于耗能段屈服剪力Vy，且扩孔型螺栓连接极限承载力Fu大于耗能段极限剪力Vu[15]，具体表示为
式（1）中，各承载力可通过式（2）~式（5）计算：
式中：ns、nb、P、μ分别为摩擦面数、滑移螺杆数、螺杆预拉力、摩擦系数；fyw、hw、tw分别为腹板屈服剪应力、高度、厚度；fuw、bf、tf、ts、e分别为腹板极限剪应力、翼缘宽度、翼缘厚度、加劲肋厚度、耗能段长度；d、fvb分别为高强螺栓直径和抗剪强度。
2）自复位SMA支撑
自复位SMA支撑的承载力FSCB主要由SMA承载力FSMA和扩孔型螺栓连接Ffs组成，可表示为
式中：As为SMA面积；σSMA为SMA应力，可根据Graesser模型计算[23]；ns1为摩擦面数，等于6；nb1为滑移螺杆数，等于2；Tb1为滑移螺杆预拉力；μ1为丁基橡胶摩擦系数，等于0.075[13]。
3）预期破坏模式
由于自复位耗能段主要由扩孔螺栓连接型耗能段和自复位SMA支撑组成，在达到极限状态时，2种构件均有可能发生破坏，具体表示为：①当自复位SMA支撑的变形超过SMA的变形，且扩孔螺栓连接型耗能段中的耗能段未达到极限状态时，自复位耗能段的破坏主要发生在自复位SMA支撑上，此时SMA丝材出现断裂现象；②自复位SMA支撑中SMA始终处于超弹性状态并提供耗能与复位能力，耗能段在达到极限位移后出现破坏现象，自复位耗能段达到极限状态。
1.1.2　试件模型
基于上述设计方法可得到部分自复位耗能段SC-SL-1模型，如图1所示。试件尺寸图如图2所示。自复位SMA支撑中，右端板尺寸是590 mm×90 mm×10 mm，侧向板1、2尺寸均为548 mm×90 mm×10 mm；SMA面积为94.20 mm2，滑移螺杆预拉力为10 kN；螺栓圆孔半径为14 mm，长圆孔尺寸为40 mm；固定板上圆孔半径为45 mm。扩孔螺栓连接型耗能段中，耗能段截面为H210 mm×110 mm×6 mm×8 mm，长度e、间距和厚度分别为300 mm、100 mm、10 mm，外伸端板为440 mm×250 mm×20 mm；端部下垫板中8个长圆孔尺寸L均为34 mm，所采用的M22高强滑移螺栓预拉力为50 kN，且下垫板与外伸端板间的铜垫片摩擦系数为0.30。竖向连接支撑的高度、宽度、厚度分别为644、260、10 mm；下端开有2个半径为14 mm的圆孔，上端沿竖向两侧分别设置有2块加劲肋，其屈服承载力远大于自复位SMA支撑的极限荷载值，可保证竖向连接支撑为自复位SMA支撑提供足够承载力。
1.1.3　材料性能
部分自复位耗能段中钢板厚度包括6、8、10、15 mm，材质均为Q355B，相应力学参数如表1所示。对自复位SMA支撑中所采用的直径为1.0 mm的镍钛形状记忆合金丝材开展单向拉伸试验研究，各主要参数结果分别是[21]：奥氏体向马氏体相变开始应力为550 MPa、奥氏体向马氏体相变结束应力为625 MPa、马氏体向奥氏体逆相变开始应力为265 MPa、马氏体向奥氏体逆相变结束应力为175 MPa、最大相变应变为0.08、初始弹性模量EA为59531 MPa。
1.1.4　加载装置与制度
加载装置：本次试验在南昌大学结构实验室内完成。为仅研究部分自复位耗能段的力学性能，假设钢支撑为自复位耗能段形成刚性约束，并忽略钢柱的影响，其加载装置主要包括作动器、部分自复位耗能段、加载钢梁、上垫梁、下垫梁、立柱、地梁和地锚等，其中部分自复位耗能段包括扩孔螺栓连接型耗能段（shear slotted bolted connection with very short shear link，SSBC-VSSL）和自复位SMA支撑，加载装置如图3所示。其中，作动器为自复位施加往复荷载；SSBC-VSSL上端通过8个高强螺栓与上垫梁连接，下端与下垫梁之间也通过8个高强滑移螺栓相连。自复位SMA支撑与竖向连接支撑通过高强螺栓相连，另一端与下垫梁通过轴销连接。另外，竖向连接支撑上端与上垫梁通过高强螺栓连接。
加载制度：试件SC-SL-1采用往复位移加载方式，每级位移加载3次。滑移阶段指扩孔螺栓连接型耗能段中高强螺栓仅在扩孔型螺栓连接中摩擦滑移，故分3次加载至长圆孔端部，位移分别为6、10、16 mm；非滑移阶段指高强螺栓滑移至扩孔型螺栓连接端部后，耗能段开始承载和发生非弹性变形，其加载位移分别为0.5L+0.01e、0.5L+0.03e、0.5L+0.05e、0.5L+0.07e、0.5L+0.08e，L为长圆孔尺寸，e为耗能段长度，0.08为剪切型耗能段的预期塑性转角[7]。
1.2　试验结果
1.2.1　变形模式
试件SC-SL-1自复位SMA支撑的变形和破坏模式如图4所示，试验过程中自复位SMA支撑始终处于滑移耗能和提供恢复力等状态。当试件位移为16 mm时，耗能段处于滑移阶段，自复位SMA支撑中右端板滑移且SMA受拉，如图4（b）所示；随着试件位移增大至25.25 mm，SMA为构件提供更大的承载和耗能能力，如图4（c）所示；当试件位移为40.45 mm（约为0.5L+0.08e）时，竖向连接支撑具有足够承载力，使得自复位SMA支撑右端板变形持续增大且为构件提供更大恢复力，如图4（d）所示。
耗能段主要发生了滑移、腹板屈服、翼缘屈曲和腹板屈曲等现象，如图5所示。耗能段处于初始滑移阶段，无明显相对变形，如图5（a）所示；随着试件位移增大至25.25 mm，自复位SMA支撑中右端板滑移距离也增大至加载位移，此时耗能段也发生明显屈服，如图5（b）所示；当试件位移为40.45 mm（约为0.5L+0.08e）时，耗能段的腹板和翼缘均进入屈曲状态，与普通短剪切型耗能段的破坏模式相同，如图5（c）所示。此时，由于SMA丝材变形能力达到极限状态并发生了丝材断裂现象，试件停止加载。
1.2.2　滞回曲线
试件SC-SL-1的滞回曲线整个过程试件的承载力随位移的增大逐渐增大，如图6所示。当加载位移不大于16 mm的滑移阶段时，耗能段仅处于滑移阶段且未发生屈服，滞回曲线主要由扩孔型螺栓连接和自复位SMA支撑组成。当加载位移达到极限值40.45 mm时，耗能段处于耗能和承载的非滑移阶段，滞回曲线由短剪切型耗能段和自复位SMA支撑组成，残余变形主要由短剪切型耗能段引起。在滑移阶段和非滑移阶段，试件的残余变形均由扩孔螺栓连接型耗能段[15]引起的，且采用残余变形极小的自复位SMA支撑可有效减小试件的残余变形，使其具有更强的承载、耗能和自复位能力。
2　有限元分析
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2.1　分析方法
2.1.1　模型描述
在部分自复位耗能段中，当自复位SMA支撑和扩孔螺栓连接型耗能段各板件截面和材料性能相同时，影响因素主要包括自复位SMA支撑中的SMA面积、扩孔螺栓连接型耗能段中的高强螺栓预拉力P和摩擦系数μ1。因此，设计SCB-VS-F1，SCB-VS-F2，SCB-VS-F3，SCB-VS-F4、SCB-VS-F5，SCB-VS-F6，SCB-VS-F7，SCB-VS-F8，SCB-VS-F9，SCB-VS-F10模型，具体参数值如表2所示。
1）SMA面积。模型SCB-VS-F1、SCB-VS-F2、SCB-VS-F3、SCB-VS-F4中自复位SMA支撑总面积分别为94.20、125.60、141.30、157.00 mm2，其它参数均相同。
2）高强螺栓预拉力P。以模型SCB-VS-F3为基础，模型SCB-VS-F5、SCB-VS-F6、SCB-VS-F7中高强螺栓预拉力P分别为30、40、60 kN，其它参数均相同。
3）摩擦系数μ1。以模型SCB-VS-F3为基础，SCB-VS-F8、SCB-VS-F9、SCB-VS-F10中垫片摩擦系数μ1分别为0.15、0.25和0.30，其它参数均相同。
2.1.2　分析方法
1）单元选取。部分自复位耗能段中自复位SMA支撑和扩孔螺栓连接型耗能段的各构件，均采用ABAQUS软件中的C3D8R单元进行模拟。该种单元具有8个节点，且每个节点有3个自由度等特点。
2）材料性能。部分自复位耗能段中，各构件材料性能见1.1.3节。
3）边界条件。部分自复位耗能段中，约束2个自复位SMA支撑中截面1和截面2所有节点各方向位移，同时约束扩孔螺栓连接型耗能段中间板两侧截面3、截面4上所有节点各方向的位移，如图7所示。另外，所有构件均需约束XY平面外的侧移。
4）加载方式。在部分自复位耗能段加载梁左侧截面上施加X方向往复位移，各加载步位移与1.1.4节所述相同。基于合理的单元、材料性能、边界条件和加载方式等，可对其进行有限元模拟分析。
2.2　模型校正
2.2.1　滞回曲线
建立试件SC-SL-1的有限元模型并进行分析，将所得滞回曲线与试验结果进行对比，如图8所示。滑移和非滑移阶段，各加载步的加载位移、构件刚度和承载力值均基本相等。当SC-SL-1达到最大加载位移40.45 mm时，有限元和试验研究所得极限荷载值分别为535.23、519.28 kN，两者误差仅为3.07%，即可验证自复位耗能段有限元分析方法可准确预测其承载力。
2.2.2　变形模式
1）滑移阶段。如图9（a）所示，自复位SMA支撑一侧被固定，往复荷载下通过竖向支撑带动SMA和滑移板移动，为自复位耗能段提供滑移和耗能；扩孔螺栓连接型耗能段中耗能段整体处于平行滑移状态，构件仅通过扩孔型螺栓连接摩擦滑移和耗能，与2.2.1节变形模式一致。
2）非滑移阶段。如图9（b）所示，自复位SMA支撑在竖向支撑的带动下，滑移板和SMA发生移动和超弹性变形，SMA的承载力和复位力随位移持续增大，同样为自复位耗能段提供耗能和复位能力等；扩孔螺栓连接型耗能段的中间板被固定，往复荷载下耗能段发生非弹性变形、承载和耗能，且扩孔螺栓连接型耗能段位移与自复位耗能段位移相等，与1.2.1节变形模式一致。
2.3　参数化分析
2.3.1　SMA面积的影响
模型SCB-VS-F1、SCB-VS-F2、SCB-VS-F3、SCB-VS-F4在滑称阶段和非滑移阶段的滞回曲线如图10所示。
滞回曲线具体表示如下：
1）滑移阶段。部分自复位耗能段在滑移阶段的滞回曲线如图10（a）所示。各模型的承载力随着SMA面积的增大而增大，且模型SCB-VS-F1、SCB-VS-F2、SCB-VS-F3、SCB-VS-F4的最大残余变形值分别为14.74、12.72、10.81、9.26 mm，即可明显提高构件的复位能力。
2）非滑移阶段。部分自复位耗能段在非滑移阶段的滞回曲线如图10（b）所示，各曲线变形趋势基本相同。SMA面积的增大可提高模型的承载力，且使其残余变形值由最大值32.52 mm减小至15.09 mm，即对构件的复位能力提升有明显效果。
2.3.2　高强螺栓预拉力的影响
模型SCB-VS-F3、SCB-VS-F5、SCB-VS-F6、SCB-VS-F7的滞回曲线如图11所示。
1）滑移阶段。随着模型SCB-VS-F3、SCB-VS-F5、SCB-VS-F6、SCB-VS-F7中剪切扩孔型螺栓连接的高强螺栓预拉力由20 kN增大至50 kN时，各模型的承载力、残余变形和耗能能力均逐渐增大，这主要是由于抗滑移承载力增大所引起的，如图11（a）所示。
2）非滑移阶段。当耗能段由滑移转入承载阶段后，各模型滞回曲线如图11（b）所示。各模型承载力不随螺栓预拉力的增大而不变，这主要是该阶段模型承载力由耗能段和自复位SMA支撑组成，与抗滑移承载力无关。然而，卸载过程中，预拉力的增大会提高构件的残余变形，并降低其复位能力。
2.3.3　垫片滑移系数的影响
模型SCB-VS-F3、SCB-VS-F8、SCB-VS-F9、SCB-VS-F10在滑称阶段和非滑移阶段的滞回曲线，如图12所示。
1）滑移阶段。模型SCB-VS-F3、SCB-VS-F8、SCB-VS-F9、SCB-VS-F10的滞回曲线如图12（a）所示。初始滑移阶段，随着扩孔型螺栓连接中垫片摩擦系数由0.15增大至0.30时，各模型的承载力和残余变形值呈增大趋势，且不利于构件的自复位。
2）非滑移阶段。当如图12（b）所示，随着摩擦系数增大，模型SCB-VS-F3、SCB-VS-F8、SCB-VS-F9、SCB-VS-F10的承载力基本不变，此时构件通过自复位SMA支撑和耗能段共同承载。另外，各模型残余变形值呈明显增大趋势，这主要由加载过程中扩孔型螺栓连接的摩擦滑移所引起的。
3　自复位耗能段的简化力学模型
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3.1　滑移阶段
以模型SCB-VS-F3为例，提取模型中扩孔型螺栓连接（shear slotted bolted connection，SSBC）的滞回曲线，两者曲线如图13所示。部分自复位耗能段的力学模型主要由扩孔型螺栓连接的力学模型和自复位SMA支撑的力学模型组成，如图14所示。此时，自复位耗能段各加载步承载力FSCB-VS由扩孔型螺栓连接的抗滑移承载力Fslip（式（2））和自复位SMA支撑承载力FSCB式（6）和式（7）叠加而成，如式（8）所示：
因此，滑移阶段，相比于扩孔型螺栓连接，部分自复位耗能段的残余位移值明显下降，且其承载能力、耗能能力和复位能力均得到明显改善。
3.2　非滑移阶段
非滑移阶段，以模型SCB-VS-F3为例，提取模型中扩孔螺栓连接型耗能段（SSBC-VSSL）的滞回曲线，两者曲线如图15所示。极限位移下，部分自复位耗能段的承载力FSCB-VS由扩孔螺栓连接型耗能段承载力VS式（3）和自复位SMA支撑承载力FSCB式（6）和式（7）组成，且相应力学模型如图16所示。因此，该阶段自复位耗能段的承载力如式（9）所示：
另外，基于图15可知，部分自复位耗能段和扩孔螺栓连接型耗能段的承载力差值为183.65 kN，近似于自复位SMA支撑承载力值187.82 kN。另外，2种构件的残余变形值分别等于17.39、37.80 mm，即相比于扩孔螺栓连接型耗能段，自复位耗能段残余变形值降低约54.03%，具有强耗能、高承载和高自复位等特点。
3.3　有限元与理论值对比验证
基于式（8）和式（9）中，可分别得到不同因素下各模型在滑移阶段和非滑移阶段的有限元承载力FN和理论承载力FS计算结果，如表3所示。各模型在达到预期最大位移时，滑移阶段两者最大误差为8.99%，非滑移阶段最大误差值为4.68%，即表明式（8）和式（9）能较准确地反映自复位耗能段的承载力。
4　结论
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本文提出了一种新型部分自复位耗能段并对其进行了试验研究、数值模拟和参数分析，研究其滞回性能和简化力学模型，主要结论如下：
1）部分自复位耗能段中，耗能段主要发生了滑移、腹板屈服、翼缘屈曲、腹板屈曲等现象，自复位SMA支撑始终处于滑移耗能和提供恢复力等状态。
2）滑移阶段，部分自复位耗能段中耗能段整体处于滑移状态，未有构件发生屈服；非滑移阶段，耗能段开始承载、耗能和非弹性变形。自复位SMA支撑始终提供耗能和复位能力，并减小其残余变形。
3）增大SMA面积可有效减小部分自复位耗能段全过程的残余变形，并提高构件的自复位能力和承载能力；增大高强螺栓预拉力和垫片摩擦系数会提高构件的残余变形值，但对极限承载力无明显影响。
4）基于不同因素下部分自复位耗能段的滞回曲线，提出了部分自复位耗能段在滑移阶段和非滑移阶段的简化力学模型，为相应结构的抗震设计与分析提供新的思路和理论基础。
5）本文主要针对新型部分自复位耗能段的滞回性能和简化力学模型进行了研究，滑移阶段和非滑移阶段承载力最大误差仅为8.99%和4.68%，即可较准确地预测自复位耗能段的承载力。
基金
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  • 国家自然科学基金项目(52468025; 51908268)
  • 江西省自然科学基金项目(20224BAB204062)
文献
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2024年第44卷第5期
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doi: 10.13197/j.eeed.2024.0519
  • 接收时间：2023-07-21
  • 首发时间：2026-03-30
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  • 收稿日期：2023-07-21
  • 修回日期：2023-08-29
基金
国家自然科学基金项目(52468025; 51908268)
江西省自然科学基金项目(20224BAB204062)
作者信息
    1.中国电建集团江西省电力设计院有限公司，江西 南昌 330096
    2.中国瑞林工程技术股份有限公司，江西 南昌 330031
    3.南昌大学 工程建设学院，江西 南昌 330031

通讯作者:

胡淑军（1985—），男，副教授，博士，主要从事可恢复功能结构体系研究。E-mail：
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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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