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Article(id=1245390364236952106, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245390357958082790, articleNumber=null, orderNo=null, doi=10.13197/j.eeed.2024.0609, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1694361600000, receivedDateStr=2023-09-11, revisedDate=1699977600000, revisedDateStr=2023-11-15, acceptedDate=null, acceptedDateStr=null, onlineDate=1774853801068, onlineDateStr=2026-03-30, pubDate=null, pubDateStr=null, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774853801068, onlineIssueDateStr=2026-03-30, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774853801068, creator=13701087609, updateTime=1774853801068, 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=93, endPage=101, ext={EN=ArticleExt(id=1245390364559913520, articleId=1245390364236952106, tenantId=1146029695717560320, journalId=1241701559352995854, language=EN, title=Static performance of high-strength steel composite Y-shaped eccentrically braced steel frames, columnId=null, journalTitle=Earthquake Engineering and Engineering Dynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

To study the bearing capacity, lateral stiffness, ductility, and failure mode of high-strength steel composite Y-shaped eccentrically braced steel frames under horizontal loads, pushover tests were conducted on a half-scale three-story specimen. The test adopted three-mass inverted triangle proportional loading, and used OpenSees software to establish a corresponding numerical model for simulation. The results show that under the action of horizontal load, the link begins to yield, and the stiffness of the structure gradually decreases as the load gradually increases. During the test, the plasticity of the link on the second floor of the structure is the most obvious, the inter-story drift is the largest, and the inter-story drift ratio reaches 0.0433 rad. When the structure is finally damaged, it is manifested as the failure of the joints between frame beam and link, and the frame beams and columns are still in an elastic state.When modeling in OpenSees, the connection between the link and the frame beam is adopted using the method of rigid link and rigid section. The pushover curve simulation results obtained by this modeling method are in good agreement with the test results, indicating that the numerical model can be used for the simulation analysis of the seismic performance of the global structure. The parametric analysis results show that the lateral stiffness and bearing capacity of the shear link are better than those of the shear-flexural link.

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为研究高强钢组合Y形偏心支撑钢框架在水平荷载作用下的承载能力、抗侧刚度、延性和破坏模式，对一个1/2缩尺的3层结构试件进行了静力推覆试验，试验采用三质点倒三角比例加载，并采用OpenSees软件建立了相应的数值模型进行模拟。研究结果表明：试件在水平荷载作用下，随着顶点位移的逐渐增大，耗能梁段开始屈服，结构的刚度逐渐降低；试验过程中，结构2层的耗能梁段塑性变形最为明显，层间位移最大，层间侧移角达到了0.0433 rad；结构在最终破坏时，表现为框架梁与耗能梁段连接处节点的破坏，框架梁柱仍处于弹性状态；OpenSees建模时耗能梁段与框架梁连接处采用刚性连接加刚性段的方式，该建模方法得到的推覆曲线模拟结果与试验结果吻合较好，表明数值模型可用于整体结构的抗震性能模拟分析；参数分析结果表明，剪切屈服型耗能梁段抗侧刚度和承载力均优于弯剪屈服型耗能梁段。

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李腾飞（1993—），男，助理研究员，博士，主要从事新型钢结构体系及子结构混合试验方法研究。E-mail：
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王泽（1998—），男，硕士，主要从事新型钢结构体系研究。E-mail：

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王泽（1998—），男，硕士，主要从事新型钢结构体系研究。E-mail：

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王泽（1998—），男，硕士，主要从事新型钢结构体系研究。E-mail：

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figureFileBig=6zTaVVK5NiGAtrbxLfaUbw==, tableContent=null), ArticleFig(id=1245390378917016447, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390364236952106, language=CN, label=图2, caption=试验加载装置示意图, figureFileSmall=0U1DvJFZE2Z7yvWtbLE3TQ==, figureFileBig=6zTaVVK5NiGAtrbxLfaUbw==, tableContent=null), ArticleFig(id=1245390379118343046, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390364236952106, language=EN, label=Fig. 3, caption=Instrumentation arrangement of specimen, figureFileSmall=+HF51wZaRpXPb+yKnN5CRQ==, figureFileBig=boCkUpJ+w734j/ID6C80Ww==, tableContent=null), ArticleFig(id=1245390379420332939, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390364236952106, language=CN, label=图3, caption=试件测点布置, figureFileSmall=+HF51wZaRpXPb+yKnN5CRQ==, figureFileBig=boCkUpJ+w734j/ID6C80Ww==, tableContent=null), ArticleFig(id=1245390379655213970, tenantId=1146029695717560320, journalId=1241701559352995854, 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curves, figureFileSmall=Jx7pkqZAg++BgHldoZxanA==, figureFileBig=+jckB8FcVcp47FcAiK7Llw==, tableContent=null), ArticleFig(id=1245390384088593371, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390364236952106, language=CN, label=图9, caption=曲线对比, figureFileSmall=Jx7pkqZAg++BgHldoZxanA==, figureFileBig=+jckB8FcVcp47FcAiK7Llw==, tableContent=null), ArticleFig(id=1245390384264754149, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390364236952106, language=EN, label=Fig. 10, caption=Comparison of curve of base shear force and drift, figureFileSmall=hIf5/1AO+xLJzESges0sRw==, figureFileBig=MOkCes4XYLe3TcdR+LgsyQ==, tableContent=null), ArticleFig(id=1245390384428332014, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390364236952106, language=CN, label=图10, caption=基底剪力-顶点侧移曲线对比, figureFileSmall=hIf5/1AO+xLJzESges0sRw==, figureFileBig=MOkCes4XYLe3TcdR+LgsyQ==, tableContent=null), ArticleFig(id=1245390384608687094, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390364236952106, language=EN, label=Table 1, caption=

Sectional dimension of specimens

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构件类型钢材牌号构件截面尺寸/mm
框架柱Q460H145×145×8×10
框架梁Q460H140×100×8×10
支撑Q355H100×100×6×10
1层耗能梁段Q235H125×70×4×8
2层耗能梁段Q235H100×70×4×8
3层耗能梁段Q235H80×70×3×8
), ArticleFig(id=1245390384738710525, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390364236952106, language=CN, label=表1, caption=

试件截面尺寸

, figureFileSmall=null, figureFileBig=null, tableContent=
构件类型钢材牌号构件截面尺寸/mm
框架柱Q460H145×145×8×10
框架梁Q460H140×100×8×10
支撑Q355H100×100×6×10
1层耗能梁段Q235H125×70×4×8
2层耗能梁段Q235H100×70×4×8
3层耗能梁段Q235H80×70×3×8
), ArticleFig(id=1245390384877121537, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390364236952106, language=EN, label=Table 2, caption=

Mechanical properties of steel

, figureFileSmall=null, figureFileBig=null, tableContent=
试样/mm弹性模量E/（×105 MPa）屈服强度fy/MPa极限抗拉强度fu/MPa延伸率δ/%
Q460-82.120473.500635.10025.360
Q460-102.060516.000691.97023.510
Q355-62.110414.700542.03028.290
Q355-102.010363.800545.80028.740
Q235-32.140283.100397.10031.570
Q235-42.170271.900402.10031.830
Q235-82.180276.700421.10032.180
), ArticleFig(id=1245390384961007624, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390364236952106, language=CN, label=表2, caption=

钢材力学特性

, figureFileSmall=null, figureFileBig=null, tableContent=
试样/mm弹性模量E/（×105 MPa）屈服强度fy/MPa极限抗拉强度fu/MPa延伸率δ/%
Q460-82.120473.500635.10025.360
Q460-102.060516.000691.97023.510
Q355-62.110414.700542.03028.290
Q355-102.010363.800545.80028.740
Q235-32.140283.100397.10031.570
Q235-42.170271.900402.10031.830
Q235-82.180276.700421.10032.180
), ArticleFig(id=1245390385145557012, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390364236952106, language=EN, label=Table 3, caption=

Parameter of the spring

, figureFileSmall=null, figureFileBig=null, tableContent=
耗能梁段长度/mm弹簧类型Steel02对应取值
1层2层3层
350剪切弹簧屈服强度fy/kN78.66761.32837.373
弹性模量E/（kN/mm）208.418160.61691.148
弯曲弹簧弹性模量E/（kN•mm）2647753.4001595545.200939927.085
), ArticleFig(id=1245390385304940572, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390364236952106, language=CN, label=表3, caption=

弹簧参数

, figureFileSmall=null, figureFileBig=null, tableContent=
耗能梁段长度/mm弹簧类型Steel02对应取值
1层2层3层
350剪切弹簧屈服强度fy/kN78.66761.32837.373
弹性模量E/（kN/mm）208.418160.61691.148
弯曲弹簧弹性模量E/（kN•mm）2647753.4001595545.200939927.085
), ArticleFig(id=1245390385460129827, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390364236952106, language=EN, label=Table 4, caption=

Comparison of performance indicators

, figureFileSmall=null, figureFileBig=null, tableContent=
类别屈服点极限点抗侧刚度K0/（kN/mm）延性μ
Δy/mmFy/kNΔu/mmFu/kN
试验42.208323.96792.017468.78911.1812.180
有限元43.200298.07887.500445.01610.2132.025
误差/%2.350-7.990-4.910-5.070-8.670-6.880
), ArticleFig(id=1245390385602736171, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390364236952106, language=CN, label=表4, caption=

性能指标比较

, figureFileSmall=null, figureFileBig=null, tableContent=
类别屈服点极限点抗侧刚度K0/（kN/mm）延性μ
Δy/mmFy/kNΔu/mmFu/kN
试验42.208323.96792.017468.78911.1812.180
有限元43.200298.07887.500445.01610.2132.025
误差/%2.350-7.990-4.910-5.070-8.670-6.880
), ArticleFig(id=1245390385736953905, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390364236952106, language=EN, label=Table 5, caption=

Parameters of the spring of energy dissipation link

, figureFileSmall=null, figureFileBig=null, tableContent=
耗能梁段长度/mm弹簧类型Steel02对应取值
1层2层3层
300耗能梁段类型剪切型剪切型剪切型
剪切弹簧屈服强度fy/kN78.81861.46938.580
弹性模量E/（kN/mm）232.532179.200102.400
弯曲弹簧弹性模量E/（kN•mm）3089045.6331861469.4001096581.600
400耗能梁段类型剪切型剪切型剪切型
剪切弹簧屈服强度fy/kN77.27559.92437.165
弹性模量E/（kN/mm）174.400134.40076.800
弯曲弹簧弹性模量E/（kN•mm）2316784.2251396102.050822436.200
450耗能梁段类型剪切型弯剪型剪切型
剪切弹簧屈服强度fy/kN76.68959.34236.652
弹性模量E/（kN/mm）155.022119.46668.266
弯曲弹簧屈服强度fy/（kN/mm）—13994.475—
弹性模量E/（kN•mm）2059363.7561240979.600731054.400
500耗能梁段类型弯剪型弯剪型剪切型
剪切弹簧屈服强度fy/kN76.17858.82936.218
弹性模量E/（kN/mm）139.520107.52061.40
弯曲弹簧屈服强度fy/（kN/mm）18578.68713994.475—
弹性模量E/（kN•mm）1827803.9601116881.640657948.960
550耗能梁段类型弯剪型弯剪型剪切型
剪切弹簧屈服强度fy/kN75.72558.37435.840
弹性模量E/（kN/mm）126.83697.74655.854
弯曲弹簧屈服强度fy/（kN/mm）18578.68713994.475—
弹性模量E（kN•mm）1684933.9821015346.945598135.418
), ArticleFig(id=1245390385829228601, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390364236952106, language=CN, label=表5, caption=

耗能梁段弹簧参数

, figureFileSmall=null, figureFileBig=null, tableContent=
耗能梁段长度/mm弹簧类型Steel02对应取值
1层2层3层
300耗能梁段类型剪切型剪切型剪切型
剪切弹簧屈服强度fy/kN78.81861.46938.580
弹性模量E/（kN/mm）232.532179.200102.400
弯曲弹簧弹性模量E/（kN•mm）3089045.6331861469.4001096581.600
400耗能梁段类型剪切型剪切型剪切型
剪切弹簧屈服强度fy/kN77.27559.92437.165
弹性模量E/（kN/mm）174.400134.40076.800
弯曲弹簧弹性模量E/（kN•mm）2316784.2251396102.050822436.200
450耗能梁段类型剪切型弯剪型剪切型
剪切弹簧屈服强度fy/kN76.68959.34236.652
弹性模量E/（kN/mm）155.022119.46668.266
弯曲弹簧屈服强度fy/（kN/mm）—13994.475—
弹性模量E/（kN•mm）2059363.7561240979.600731054.400
500耗能梁段类型弯剪型弯剪型剪切型
剪切弹簧屈服强度fy/kN76.17858.82936.218
弹性模量E/（kN/mm）139.520107.52061.40
弯曲弹簧屈服强度fy/（kN/mm）18578.68713994.475—
弹性模量E/（kN•mm）1827803.9601116881.640657948.960
550耗能梁段类型弯剪型弯剪型剪切型
剪切弹簧屈服强度fy/kN75.72558.37435.840
弹性模量E/（kN/mm）126.83697.74655.854
弯曲弹簧屈服强度fy/（kN/mm）18578.68713994.475—
弹性模量E（kN•mm）1684933.9821015346.945598135.418
), ArticleFig(id=1245390385950863426, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390364236952106, language=EN, label=Table 6, caption=

Comparison of performance indicators of parameter analysis

, figureFileSmall=null, figureFileBig=null, tableContent=
耗能梁段长度/mm屈服点极限点抗侧刚度K0/（kN/mm）延性μ
Δy/mmFy/kNΔu/mmFu/kN
30034.000272.34087.500455.83313.1522.574
40052.400320.18587.000429.8338.1611.660
45053.200277.75081.500360.5546.7741.532
50056.200242.97783.500324.7335.8331.486
55061.000246.87184.000316.1565.1621.377
0（抗弯框架）95.600254.172119.600304.7182.6731.251
), ArticleFig(id=1245390387938963532, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390364236952106, language=CN, label=表6, caption=

参数分析性能指标比较

, figureFileSmall=null, figureFileBig=null, tableContent=
耗能梁段长度/mm屈服点极限点抗侧刚度K0/（kN/mm）延性μ
Δy/mmFy/kNΔu/mmFu/kN
30034.000272.34087.500455.83313.1522.574
40052.400320.18587.000429.8338.1611.660
45053.200277.75081.500360.5546.7741.532
50056.200242.97783.500324.7335.8331.486
55061.000246.87184.000316.1565.1621.377
0（抗弯框架）95.600254.172119.600304.7182.6731.251
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高强钢组合Y形偏心支撑钢框架静力性能
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王泽 1 , 李腾飞 2 , 苏明周 1
地震工程与工程振动 | 2024,44(6): 93-101
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地震工程与工程振动 | 2024, 44(6): 93-101
高强钢组合Y形偏心支撑钢框架静力性能
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王泽1 , 李腾飞2 , 苏明周1
作者信息
  • 1.西安建筑科技大学 土木工程学院，陕西 西安 710055
  • 2.清华大学 土木工程系，北京 100084

    • 王泽（1998—），男，硕士，主要从事新型钢结构体系研究。E-mail：

通讯作者:

李腾飞（1993—），男，助理研究员，博士，主要从事新型钢结构体系及子结构混合试验方法研究。E-mail：
Static performance of high-strength steel composite Y-shaped eccentrically braced steel frames
Ze WANG1 , Tengfei LI2 , Mingzhou SU1
Affiliations
  • 1.School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, China
  • 2.Department of Civil Engineering, Tsinghua University, Beijing 100084, China
doi: 10.13197/j.eeed.2024.0609
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摘要
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为研究高强钢组合Y形偏心支撑钢框架在水平荷载作用下的承载能力、抗侧刚度、延性和破坏模式，对一个1/2缩尺的3层结构试件进行了静力推覆试验，试验采用三质点倒三角比例加载，并采用OpenSees软件建立了相应的数值模型进行模拟。研究结果表明：试件在水平荷载作用下，随着顶点位移的逐渐增大，耗能梁段开始屈服，结构的刚度逐渐降低；试验过程中，结构2层的耗能梁段塑性变形最为明显，层间位移最大，层间侧移角达到了0.0433 rad；结构在最终破坏时，表现为框架梁与耗能梁段连接处节点的破坏，框架梁柱仍处于弹性状态；OpenSees建模时耗能梁段与框架梁连接处采用刚性连接加刚性段的方式，该建模方法得到的推覆曲线模拟结果与试验结果吻合较好，表明数值模型可用于整体结构的抗震性能模拟分析；参数分析结果表明，剪切屈服型耗能梁段抗侧刚度和承载力均优于弯剪屈服型耗能梁段。

Y形偏心支撑钢框架  /  高强钢  /  静力推覆试验  /  OpenSees  /  刚性连接

To study the bearing capacity, lateral stiffness, ductility, and failure mode of high-strength steel composite Y-shaped eccentrically braced steel frames under horizontal loads, pushover tests were conducted on a half-scale three-story specimen. The test adopted three-mass inverted triangle proportional loading, and used OpenSees software to establish a corresponding numerical model for simulation. The results show that under the action of horizontal load, the link begins to yield, and the stiffness of the structure gradually decreases as the load gradually increases. During the test, the plasticity of the link on the second floor of the structure is the most obvious, the inter-story drift is the largest, and the inter-story drift ratio reaches 0.0433 rad. When the structure is finally damaged, it is manifested as the failure of the joints between frame beam and link, and the frame beams and columns are still in an elastic state.When modeling in OpenSees, the connection between the link and the frame beam is adopted using the method of rigid link and rigid section. The pushover curve simulation results obtained by this modeling method are in good agreement with the test results, indicating that the numerical model can be used for the simulation analysis of the seismic performance of the global structure. The parametric analysis results show that the lateral stiffness and bearing capacity of the shear link are better than those of the shear-flexural link.

Y-shaped eccentrically braced steel frame  /  high-strength steel  /  static pushover test  /  OpenSees  /  rigid link
王泽, 李腾飞, 苏明周. 高强钢组合Y形偏心支撑钢框架静力性能. 地震工程与工程振动, 2024 , 44 (6) : 93 -101 . DOI: 10.13197/j.eeed.2024.0609
Ze WANG, Tengfei LI, Mingzhou SU. Static performance of high-strength steel composite Y-shaped eccentrically braced steel frames[J]. Earthquake Engineering and Engineering Dynamics, 2024 , 44 (6) : 93 -101 . DOI: 10.13197/j.eeed.2024.0609
正文
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0　引言
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偏心支撑钢框架结构是一种良好的抗震结构体系，在遭遇地震作用时，主要表现为耗能梁段进入屈服进行耗能，结构主体基本保持弹性[1-3]。本文提出了高强钢组合偏心支撑钢框架结构，将高强钢应用于偏心支撑框架体系，即框架梁柱采用高强度钢材（屈服点在460 MPa及以上），其余构件采用强度较低的钢材，这样的设计不仅提高了结构的抗震性能，同时由于钢材强度的提高，构件截面可以适当的减小，达到节约钢材的目的。
高强钢组合Y形偏心支撑钢框架充分发挥了高强度钢材强度高、节约材料和偏心支撑框架具有良好耗能机制的优点，是一种良好的抗震结构体系，具有广泛的应用前景。段留省等[4]对单层高强钢组合Y形偏心支撑钢框架进行了单调加载和循环加载，对该结构进行了初步的抗震性能研究。连鸣等[5]、王凤等[6]对多层高强钢组合Y形偏心支撑钢框架进行了振动台试验和低周往复加载试验，随后连鸣等[7]对该结构的恢复力模型进行了研究。李腾飞等[8]、张琦等[9]对多层高强钢组合偏心支撑钢框架进行了混合试验研究。DUBINA等[10]进行了高强钢组合Y形偏心支撑钢框架的拟静力试验研究。为了研究结构在水平荷载下的性能，研究者对人字形中心支撑框架、钢板剪力墙结构和板式连接中心支撑框架结构进行了静力推覆试验[11-13]。程满等[14]建立了抗弯框架、偏心支撑钢框架和钢板剪力墙模型，分析了钢结构抗侧力体系在水平荷载下的性能。上述研究者对高强钢组合Y形偏心支撑钢框架进行了静力试验和振动台试验，分析研究了该结构的抗震性能，并对多种结构进行了静力推覆试验，但尚未对多层高强钢组合Y形偏心支撑钢框架在水平荷载作用下结构的性能指标展开试验研究。
为了研究高强钢组合Y形偏心支撑钢框架在水平荷载作用下的承载能力、抗侧刚度、延性和破坏模式，观察结构中耗能梁段的屈服和屈曲现象，对一个3层高强钢组合Y形偏心支撑钢框架结构进行了静力推覆试验，并采用OpenSees软件建立了相应的数值模型进行模拟，得到了结构在水平荷载作用下的性能指标。
1　试验概况
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1.1　试件设计
如图1所示，试件为一个1/2缩尺的两榀三层单跨结构模型，沿推覆加载方向两榀设置Y形偏心支撑，为保证结构平面外稳定，非加载方向设置K形偏心支撑。模型层高为1800 mm，总高为5400 mm，纵向和横向跨度均为2825 mm，耗能梁段长度为350 mm，混凝土楼板厚度为80 mm。采用C30细石混凝土，内置双层双向钢筋，间距为100 mm，钢筋采用HRB 335级，直径为6 mm。构件截面尺寸如表1所示。
试验中，框架柱和框架梁选用的是Q460级钢材，而支撑部分则采用了Q355级钢材，对于耗能梁段，选择Q235级钢材。为了确定钢材的材性，在各构件的特定部位取样，并加工了7组材性试件，每组包含3个试样。根据GB/T 228.1—2021《金属材料拉伸试验第1部分：室温试验方法》[15]中的相关规定对制备好的试样进行材性试验，得到不同钢材的力学性能指标，平均值见表2。
1.2　试验装置和加载制度
试验在西安建筑科技大学草堂校区结构实验室进行，试验加载装置示意图如图2所示。根据JGJ/T 101—2015《建筑抗震试验规程》[16]，采用位移控制单向静力加载，实际加载方式为采用2个1000 kN、1个500 kN的MTS作动器进行水平加载，按倒三角形式进行荷载分配，即1、2、3层的水平集中荷载分配比例为1∶2∶3。每层框架设一个加载系统，作用于分配梁中间，3套加载系统施加同步荷载，通过控制顶层作动器的位移来控制试件整体加载过程。在试件屈服之前，作动器加载的每级增量为0.2 mm；试件屈服之后，每级增量为0.5 mm，直至试件破坏。根据GB 50009—2012《建筑结构荷载规范》[17]，取试件的屋面配重为4.85 kN/m2，楼面配重为5.96 kN/m2，采用混凝土配重块来模拟竖向荷载，配重块与楼板和屋面连接处均采用M52螺栓进行连接固定，保证其稳定性。
1.3　测点布置
为了测量框架试件的侧移变形，在框架每层钢梁的水平轴线上布置位移计，每个耗能梁段处布置2个水平位移计来测量耗能梁段的转角，具体布置如图3所示。图中3-1，3-2等，第1个数字表示位移计所处楼层，第2个数字表示将各楼层位移计自下而上进行顺序编号。
1.4　试验过程及破坏特征
通过控制结构顶层侧移来对结构进行推覆试验，作动器所在方位为西侧，施加推力荷载。在顶层位移达到30 mm之前结构无明显现象，结构保持完全弹性；当位移加载到40 mm时结构1层北侧梁与耗能梁段连接处东侧翼缘出现裂缝，腹板连接处出现轻微裂缝，见图4（a），同时耗能梁段腹板开始进入屈服状态，3层南侧梁与耗能梁段翼缘连接处焊缝掉渣；位移达到50 mm时，1层北侧耗能梁段腹板与梁连接处裂缝继续开展，西侧翼缘与梁连接处也出现裂缝，2层耗能梁段腹板开始屈服，1层耗能梁段翼缘开始屈服；加载位移达到60 mm时，1层北侧耗能梁段西侧裂缝继续开展，2层南侧耗能梁段与支撑连接处出现细微裂缝，北侧梁与耗能梁段连接翼缘处出现裂缝，见图4（b）。1层和2层耗能梁段腹板应变逐渐增大，2层耗能梁段翼缘开始屈服。
在位移达到90 mm之后，结构1层北侧耗能梁段腹板段撕裂，2层南侧腹板最上面区格屈曲，北侧梁与耗能梁段连接处翼缘完全断裂，与梁连接腹板开裂，见图4（c），试验曲线进入平台段；达到110 mm时，结构1层南侧最上区格屈曲，北侧耗能梁段与支撑连接处翼缘焊缝开裂，见图4（d），2层南侧梁与耗能梁段连接处东边焊缝开裂；达到120 mm时，1层北侧耗能梁段与支撑连接处翼缘断裂，梁段处楼板出现明显横向裂缝，见图4（e）；达到140 mm时，1层北侧耗能梁段与支撑连接处腹板撕裂，见图4（f），试验曲线荷载出现明显下降；达到160 mm时2层南侧耗能梁段上下翼缘均断裂，北侧下翼缘完全断裂，至此试验结束，结构最终破坏图见图4（g）。
1.5　试验结果分析
根据作动器所记录数据作出试验结构的试验曲线如图5所示。结构极限水平承载力为501.2 kN。在试验过程中，首先第1层耗能梁段进入屈服状态，紧接着第2层耗能梁段屈服，由试验现象可以得到1、2层耗能梁段屈服时首先是腹板屈服，其次是翼缘屈服，这表明耗能梁段以剪切变形为主；在结构顶点侧移达到90 mm时试验曲线进入平台段；结构在顶点侧移达到140 mm时荷载出现明显下降，但结构仍有一定的承载能力；在试验结束时，3层耗能梁段尚未屈服，框架梁柱均处于弹性状态。
图6是楼层剪力与层间位移的关系曲线，分别记录了1、2、3层楼层剪力随层间侧移的变化。从图6中曲线的平台段可以看出，各个楼层的塑性发展程度从高到低为：2层、1层、3层。1层的塑性发展程度低于2层是由于在试件设计时为了保证结构在加载过程中不发生滑动，在试件的柱脚处设置了加劲肋板，并通过螺栓将柱脚底板与地槽连接，导致1层的整体刚度大于2层。
2　有限元模拟
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利用OpenSees软件建立与试件相同的模型进行Pushover分析，采用文献[18]中高强钢组合K形偏心支撑钢框架的建模方法，混凝土楼板采用刚性楼板假定，柱脚及梁柱采用刚接，支撑采用铰接。
2.1　材料本构模型
在进行OpenSees建模时首先要对材料的本构模型进行选择，由于所建立模型为纯钢结构，不用考虑混凝土材料的影响，楼板通过刚性楼板假定，对楼板平面内各个点的位移进行控制，起到简化模型的作用。材料本构选择Steel02钢材本构模型，该模型可以充分考虑材料的各向同性应变硬化和包辛格效应，材料的屈服强度和弹性模量选用表2材性试验实测值，应变硬化比取0.01，其余参数参考OpenSees用户手册[19]取默认值。
2.2　截面划分
为了考虑构件截面轴力与弯矩之间的耦合关系，选用纤维截面去建立模型的截面。由于所建立的模型仅使用了钢材这一种材料，因此在划分截面时不需要考虑多种材料之间的相互作用。通过OpenSees中纤维截面划分的fiber命令将工字钢截面划分为15个截面纤维，划分规则参考文献[20]，其中2个翼缘和1个腹板分别划分为5个纤维，划分示意图如图7所示，在对截面纤维赋予材料属性时，截面的翼缘和腹板分别采用相应的实测值，以保证模拟与试验对比的一致性。
2.3　单元选择
采用基于力的梁柱单元（Force-Based Beam-Column Element）来模拟框架梁柱，采用两端铰接的桁架单元（Truss）来模拟支撑，耗能梁段采用弹性梁柱单元（Elastic Beam Column Element）与零长度单元（ZeroLength Element）的组合来进行模拟，耗能梁段的具体建模方式在后文详细介绍。
2.4　耗能梁段建模
通过OpenSees对结构进行模拟时，最重要的就是对耗能梁段的建模。文献[18]的建模方法，将耗能梁段划分为3个单元，中间为弹性梁柱单元，在弹性梁柱单元两端设置零长度单元，零长度单元6个方向中剪切方向和平面内弯曲方向进行计算取值，其余4个方向设置为无限刚性。当耗能梁段为剪切屈服型时，考虑其在两端形成剪切弹簧。当耗能梁段为弯剪屈服型时，考虑其在两端形成剪切和弯曲弹簧。弹簧材料选用Steel02，其余材料选用弹性材料，其中Steel02材料中定义的屈服强度fy对应剪切材料的屈服剪力Vy和弯曲材料的屈服弯矩Mp，弹性模量E对应剪切材料的剪切刚度Ks和弯曲材料的弯曲刚度Kb。剪切弹簧材料参数计算参考文献[18]中的计算公式，弯曲弹簧材料参数按式（1）、式（2）计算：
屈服弯矩Mp计算如式（1）所示：
式中：Wp为消能梁段的塑性截面模量；fy为钢材屈服强度。
弯曲刚度Kb计算如式（2）所示：
式中：E为耗能梁段的弹性模量；I为截面惯性矩；e为耗能梁段长度。
由于OpenSees建模时构件长度采用的是截面之间轴线距离，而Y形偏心支撑钢框架中的耗能梁段与框架梁连接，在耗能梁段建模时应考虑框架梁高度的影响。在实际建模时，为了考虑框架梁高度的影响，在OpenSees中将框架梁高度的一半设置为刚性段（杆件刚度设置为无穷大）并通过RigidLink命令将单元的2个节点进行约束，建模示意图如图8所示。
在对试验进行模拟时，试验模型耗能梁段长度为350 mm，为剪切屈服型耗能梁段，因此在设置弯曲弹簧时选用弹性材料，仅需设置材料的弹性模量即可，弹簧参数见表3。
2.5　曲线对比
利用OpenSees软件建立与试件相同的模型进行Pushover分析，并与试验结果进行比较，对比结果如图9所示。该曲线与试验曲线的性能指标对比如表4所示，按GB 50011—2010《建筑抗震设计规范》[21]取最大层间位移角为2%的位移值作为极限位移，由表中数据可以看出有限元的屈服荷载比试验小7.990%，极限荷载比试验小5.070%，抗侧刚度比试验小8.670%，延性比试验小6.880%，总体而言，有限元模拟结果与试验结果吻合较为良好。
3　参数分析
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为进一步验证本文所提出的耗能梁段刚性连接的建模方法，假设耗能梁段长度分别为300、400、450、500、550 mm对结构进行参数分析，耗能梁段的屈服类型由耗能梁段长度比ρ来进行确定，ρ小于1.6时为剪切屈服型，介于1.6和2.6之间时为弯剪屈服型，大于2.6时为弯曲屈服型，耗能梁段长度比公式见式（3），并建立了相应的抗弯钢框架数值模型，以进一步对比分析结构的性能指标。
对于弯剪型耗能梁段需考虑其形成弯曲塑性铰，在建模时，弯曲方向选用Steel02材料，弯曲弹簧的相关参数根据2.4节中的式（1）、式（2）进行计算。采用刚性连接建模时，耗能梁段长度为450 mm时结构2层耗能梁段为弯剪屈服型，耗能梁段长度为500、550 mm时结构1层和2层耗能梁段为弯剪屈服型，其余各层以及各个参数的框架耗能梁段仍为剪切屈服型。建模弹簧参数见表5，数值模型的参数分析结果对比如图10所示，各参数性能指标见表6。
式中：e为耗能梁段长度；Mp为耗能梁段的塑性抗弯承载力；Vp为耗能梁段的塑性抗剪承载力。
由图10和表5可知，结构耗能梁段由剪切屈服型变为弯剪屈服型时，曲线变化明显。通过表6的性能指标对比可以看出，偏心支撑结构与抗弯框架相比，前者的承载力、抗侧刚度以及延性均优于后者，随着偏心支撑结构中耗能梁段长度增加，结构的屈服位移和极限荷载逐渐增大，抗侧刚度和延性逐渐降低。当结构中有耗能梁段由剪切屈服型变为弯剪屈服型时结构的承载力变化较大，随着弯剪型耗能梁段数量的增多，结构性能指标变化明显。
通过各项性能指标可以看出，剪切屈服型耗能梁段的承载力和抗侧刚度相比于弯剪屈服型优异，在设计结构时宜优先采用剪切屈服型耗能梁段。但在实际设计时，难以保证将耗能梁段设计成剪切屈服型，若为弯剪屈服型，耗能梁段会在两端发展塑性，可能会形成塑性铰，建模时框架梁高会对结果造成一定影响，采用文中的建模方式可以在一定程度上减小框架梁高的影响。
4　结论
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本文通过对一个两榀三层单跨的高强钢组合Y形偏心支撑框架进行静力推覆试验和有限元模拟，主要得到以下结论：
1）高强钢组合Y形偏心支撑钢框架在水平荷载作用下有较高的抗侧刚度和承载能力，且延性较好，具有较好的塑性变形能力，在达到极限位移后仍具有一定的承载能力。
2）OpenSees数值模型的推覆曲线模拟结果与试验结果吻合较好，表明数值模型可用于整体结构的数值模拟分析。
3）提出的在耗能梁段与框架梁连接处采用刚性连接加刚性段的方式，考虑了建模时框架梁高度的影响，并使建模耗能梁段长度与实际长度一致，更符合实际结果。
4）参数分析表明，剪切屈服型耗能梁段的承载力和抗侧刚度相比于弯剪屈服型优异，在结构设计时宜优先采用剪切屈服型耗能梁段。
基金
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  • 国家自然科学基金项目(51178382)
  • 中国博士后科学基金项目(2022M723005)
文献
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2024年第44卷第6期
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文章信息
doi: 10.13197/j.eeed.2024.0609
  • 接收时间：2023-09-11
  • 首发时间：2026-03-30
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  • 收稿日期：2023-09-11
  • 修回日期：2023-11-15
基金
国家自然科学基金项目(51178382)
中国博士后科学基金项目(2022M723005)
作者信息
    1.西安建筑科技大学 土木工程学院，陕西 西安 710055
    2.清华大学 土木工程系，北京 100084

通讯作者:

李腾飞（1993—），男，助理研究员，博士，主要从事新型钢结构体系及子结构混合试验方法研究。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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