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Article(id=1245390366434767462, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245390357958082790, articleNumber=null, orderNo=null, doi=10.13197/j.eeed.2024.0605, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1695052800000, receivedDateStr=2023-09-19, revisedDate=1702742400000, revisedDateStr=2023-12-17, acceptedDate=null, acceptedDateStr=null, onlineDate=1774853801592, onlineDateStr=2026-03-30, pubDate=null, pubDateStr=null, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774853801592, onlineIssueDateStr=2026-03-30, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774853801592, creator=13701087609, updateTime=1774853801592, 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=46, endPage=58, ext={EN=ArticleExt(id=1245390366782894707, articleId=1245390366434767462, tenantId=1146029695717560320, journalId=1241701559352995854, language=EN, title=Research on the torsional effect and control of RC frame structure with multiple different elevations, columnId=null, journalTitle=Earthquake Engineering and Engineering Dynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

Considering factors such as slope excavation quantity and slope stability, RC frame structures supported by foundations with different elevations (FSSFDEs) often occur, resulting in irregular structures and significant torsion. To study the torsional effects and corresponding control measures for FSSFDEs, the reliability of the finite element model was verified using pseudo-static tests and shaking table tests. Sixteen finite element models with varying structural parameters were analyzed using both elastic and elastoplastic dynamic finite element analysis. The study examined the influence of factors such as the total number of dropped stories, the number of spans and the number of dropped stories at the intermediate ground embedding end, and the number of spans at the upper ground end on the torsional effects of the structures. Additionally, the effectiveness of different torsional control measures was compared through case analysis. The main conclusions are as follows: In the elastic state, the torsional effect of RC frame structures with three different ground elevations is significant in the stories at the intermediate and upper ground ends, and it is smaller than that of structures with two different ground elevations. In the plastic state, it is beneficial to improve the torsional effect of the structure by decreasing the size ratio of the part under upper embedding end corresponding to the overall structure. Setting up horizontal grounding components, steel support or viscosity damping in the RC FSSFDEs can improve the torsion resistance. Setting up horizontal grounding components provides the best improvement on torsion effects for structures on rock slope.

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山地掉层结构考虑坡地开挖工程量、边坡稳定性等因素，常需设置多个接地端，导致结构平面和立面不规则，扭转效应显著。为研究3个不等高接地端的多台地掉层钢筋混凝土（reinforced concrete，RC）框架结构的扭转效应及控制措施，通过拟静力试验和振动台试验结果验证了有限元模型的可靠性，对建立的16个不同结构参数的有限元算例模型进行了弹性和弹塑性动力有限元分析，研究了此类框架结构扭转效应受接地端跨数、总掉层数、中接地端掉层数等因素的影响程度；通过算例分析对比了不同扭转控制措施的效果。研究结果表明：弹性状态下，3台地掉层RC框架结构在中接地层和上接地层处扭转效应显著，总体扭转效应小于对应的2台地掉层RC框架结构；而当结构进入弹塑性状态后，通过降低结构掉层部分长度在顺坡向总长度上的占比，可有效缓解结构的扭转效应；在3台地掉层RC框架结构中设置水平接地构件、钢支撑和黏滞阻尼器均能改善扭转效应，对于岩质边坡，设置水平接地构件对各扭转效应指标的改善最好。

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韩军（1978—），男，副教授，博士，主要从事结构抗震研究。E-mail：

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韩军（1978—），男，副教授，博士，主要从事结构抗震研究。E-mail：

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韩军（1978—），男，副教授，博士，主要从事结构抗震研究。E-mail：

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Seismic evaluation and retrofit of concrete buildings, refAbstract=null)], funds=[Fund(id=1245390397430673826, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, awardId=51638002, language=CN, fundingSource=国家自然科学基金项目(51638002), fundOrder=null, country=null), Fund(id=1245390397506171301, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, awardId=城科字2021第1-5, language=CN, fundingSource=重庆市建设科技项目(城科字2021第1-5), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1245390379848151962, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, xref=1., ext=[AuthorCompanyExt(id=1245390379860734876, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, companyId=1245390379848151962, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1.School of Civil Engineering, 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articleId=1245390366434767462, language=CN, label=图5, caption=掉层RC框架结构命名规则, figureFileSmall=pWO7kTsXzUtHo8N1mTMcnQ==, figureFileBig=YZFGOtxOdaIO4J/GYtqwTA==, tableContent=null), ArticleFig(id=1245390392380731584, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=EN, label=Fig. 6, caption=Response spectrum of the seismic waves, figureFileSmall=1sv2QqsZpfy9zrS6IWAfXg==, figureFileBig=2muFncamQa3cwtZlgVVhGg==, tableContent=null), ArticleFig(id=1245390392607224006, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=CN, label=图6, caption=地震波反应谱, figureFileSmall=1sv2QqsZpfy9zrS6IWAfXg==, figureFileBig=2muFncamQa3cwtZlgVVhGg==, tableContent=null), ArticleFig(id=1245390392871465163, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=EN, label=Fig. 7, caption=Torsional effect of structures with 6 floors under upper embedding end, figureFileSmall=1lgXPwNpZqXaeNDuZi7DUQ==, figureFileBig=ZM+I8FoRQBJeVNppxLJYOQ==, tableContent=null), ArticleFig(id=1245390393081180368, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=CN, label=图7, caption=掉6层结构的扭转效应, figureFileSmall=1lgXPwNpZqXaeNDuZi7DUQ==, figureFileBig=ZM+I8FoRQBJeVNppxLJYOQ==, tableContent=null), ArticleFig(id=1245390393416724693, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=EN, label=Fig. 8, caption=Inter-story torsional angle of different models, figureFileSmall=Fid/e7KZ1Umjur6QOUTBVw==, figureFileBig=+up+Wg+Irltwx6XDSkcBdA==, tableContent=null), ArticleFig(id=1245390393664188637, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=CN, label=图8, caption=不同模型层间扭转角, figureFileSmall=Fid/e7KZ1Umjur6QOUTBVw==, figureFileBig=+up+Wg+Irltwx6XDSkcBdA==, tableContent=null), ArticleFig(id=1245390393840349410, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=EN, label=Fig. 9, caption=Inter-story drift angles of different models, figureFileSmall=gIoQ1njuLjaQKAmypQYIuQ==, figureFileBig=F/G8dH6SL09FAhKf2NCRyQ==, tableContent=null), ArticleFig(id=1245390393928429799, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=CN, label=图9, caption=不同模型层间位移角, figureFileSmall=gIoQ1njuLjaQKAmypQYIuQ==, figureFileBig=F/G8dH6SL09FAhKf2NCRyQ==, tableContent=null), ArticleFig(id=1245390394045870318, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=EN, label=Fig. 10, caption=Inter-story torsional angle of the rigid side of the embedding story, figureFileSmall=Bk6a3jVFCHnLxKU2sGMbgg==, figureFileBig=re3fpNVkLeidEC5rqraDzg==, tableContent=null), ArticleFig(id=1245390394125562101, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=CN, label=图10, caption=接地层刚性边层间扭转角, figureFileSmall=Bk6a3jVFCHnLxKU2sGMbgg==, figureFileBig=re3fpNVkLeidEC5rqraDzg==, tableContent=null), ArticleFig(id=1245390394213642488, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=EN, label=Fig. 11, caption=The maximum inter-story torsional angle and inter-story drift angle of the part under upper embedding end, figureFileSmall=sZaXXt+dyOEzWcjLoKRM3w==, figureFileBig=c33ZJ4Q06qbSKlf1URgI0g==, tableContent=null), ArticleFig(id=1245390394305917179, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=CN, label=图11, caption=掉层部分最大层间扭转角、层间位移角, figureFileSmall=sZaXXt+dyOEzWcjLoKRM3w==, figureFileBig=c33ZJ4Q06qbSKlf1URgI0g==, tableContent=null), ArticleFig(id=1245390394419163391, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=EN, label=Fig. 12, caption=Torsional effect of D Group RC FSSFDE, figureFileSmall=jgMAMJChukvsHyletsKlzg==, figureFileBig=pucazGQUdyMnaqwP3cRM4A==, tableContent=null), ArticleFig(id=1245390394511438085, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=CN, label=图12, caption=D组掉层结构的扭转效应, figureFileSmall=jgMAMJChukvsHyletsKlzg==, figureFileBig=pucazGQUdyMnaqwP3cRM4A==, tableContent=null), ArticleFig(id=1245390394637267215, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=EN, label=Fig. 13, caption=Torsional effect of E Group RC FSSFDE, figureFileSmall=QKuAaSXwImQ2eYq6Xeez0A==, figureFileBig=0mYaCF7DMIu+KwdwAKU2Jw==, tableContent=null), ArticleFig(id=1245390394725347606, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=CN, label=图13, caption=E组掉层结构的扭转效应, figureFileSmall=QKuAaSXwImQ2eYq6Xeez0A==, figureFileBig=0mYaCF7DMIu+KwdwAKU2Jw==, tableContent=null), ArticleFig(id=1245390394826010908, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=EN, label=Fig. 14, caption=Torsional effect of RC frame structure with infill wall supported by different elevations foundations, figureFileSmall=86nGZLJpkQRcNsQBOwll9A==, figureFileBig=t4sK4Jefz9Urg1WxD6UpIQ==, tableContent=null), ArticleFig(id=1245390394905702689, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=CN, label=图14, caption=布置填充墙的掉层结构的扭转效应, figureFileSmall=86nGZLJpkQRcNsQBOwll9A==, figureFileBig=t4sK4Jefz9Urg1WxD6UpIQ==, tableContent=null), ArticleFig(id=1245390395023143209, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=EN, label=Fig. 15, caption=Diagram of model B3-1, figureFileSmall=8f6QFyWOLNv3dusJlc0glQ==, figureFileBig=4BA9DWOMJUNtglqXZoSrQw==, tableContent=null), ArticleFig(id=1245390395128000813, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=CN, label=图15, caption=模型B3-1简图, figureFileSmall=8f6QFyWOLNv3dusJlc0glQ==, figureFileBig=4BA9DWOMJUNtglqXZoSrQw==, tableContent=null), ArticleFig(id=1245390395190915378, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=EN, label=Fig. 16, caption=Elevation view of model B3-3, figureFileSmall=+2nJ4g2zBU9rPIb+laiqEQ==, figureFileBig=dCrEM/eDcauvXDRACx+ifw==, tableContent=null), ArticleFig(id=1245390395274801464, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=CN, label=图16, caption=模型B3-3立面图, figureFileSmall=+2nJ4g2zBU9rPIb+laiqEQ==, figureFileBig=dCrEM/eDcauvXDRACx+ifw==, tableContent=null), ArticleFig(id=1245390395379659071, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=EN, label=Fig. 17, caption=Structural torsional effects obtained from Pushover analysis, figureFileSmall=JVe2om5Y4if96/rqozTHwQ==, figureFileBig=meuQHRv8VirdpiGgxPY4pA==, tableContent=null), ArticleFig(id=1245390395455156548, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=CN, label=图17, caption=Pushover分析得到的掉层结构扭转效应, figureFileSmall=JVe2om5Y4if96/rqozTHwQ==, figureFileBig=meuQHRv8VirdpiGgxPY4pA==, tableContent=null), ArticleFig(id=1245390395560014157, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=EN, label=Fig. 18, caption=Structural torsional effects obtained from time-history analysis, figureFileSmall=6siVhK8C9uUovJ9lXacmQw==, figureFileBig=/zQCLdgqzLaHyv4kJF9EMg==, tableContent=null), ArticleFig(id=1245390395681648979, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=CN, label=图18, caption=时程分析得到的掉层结构扭转效应, figureFileSmall=6siVhK8C9uUovJ9lXacmQw==, figureFileBig=/zQCLdgqzLaHyv4kJF9EMg==, tableContent=null), ArticleFig(id=1245390395786506583, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=EN, label=Table 1, caption=

Information of earthquake waves

, figureFileSmall=null, figureFileBig=null, tableContent=
地震时间地震发生地点震级台站信息PGA/（cm/s2）
2008年5月Wenchuan8.0051CXQ167
2008年6月Iwate-Miyagi Nairiku6.9Kami Miyagi Miyazaki City153
1994年1月Northridge6.7Fairview Ave，El Monte123
1952年7月Kern County7.3Taft Lincoln School Tunnel176
), ArticleFig(id=1245390395929112923, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=CN, label=表1, caption=

地震波信息

, figureFileSmall=null, figureFileBig=null, tableContent=
地震时间地震发生地点震级台站信息PGA/（cm/s2）
2008年5月Wenchuan8.0051CXQ167
2008年6月Iwate-Miyagi Nairiku6.9Kami Miyagi Miyazaki City153
1994年1月Northridge6.7Fairview Ave，El Monte123
1952年7月Kern County7.3Taft Lincoln School Tunnel176
), ArticleFig(id=1245390396017193314, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=EN, label=Table 2, caption=

Comparison of torsional angles of FSSFDE

, figureFileSmall=null, figureFileBig=null, tableContent=
地震强度最大层扭转角/（×10-3 rad）楼层
0.12 g计算值2.126
实验值2.385
0.33 g计算值5.356
实验值6.946
), ArticleFig(id=1245390396172382567, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=CN, label=表2, caption=

掉层框架结构扭转角对比

, figureFileSmall=null, figureFileBig=null, tableContent=
地震强度最大层扭转角/（×10-3 rad）楼层
0.12 g计算值2.126
实验值2.385
0.33 g计算值5.356
实验值6.946
), ArticleFig(id=1245390396277240175, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=EN, label=Table 3, caption=

Comparison of top floor displacements of FSSFDE

, figureFileSmall=null, figureFileBig=null, tableContent=
工况天然波2x向顶层位移y向顶层位移
加载方向计算值/mm试验值/mm误差/%计算值/mm试验值/mm误差/%
10x单向1.301.342.9———
11y单向———1.992.031.9
12xy双向1.461.6410.91.691.732.3
13yx双向1.281.5718.51.672.1622.7
24xyz三向1.491.564.51.652.1723.9
25yxz三向1.301.321.51.701.690.6
33xyz三向4.715.2224.35.216.8323.7
), ArticleFig(id=1245390396369514871, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=CN, label=表3, caption=

掉层框架顶层位移对比

, figureFileSmall=null, figureFileBig=null, tableContent=
工况天然波2x向顶层位移y向顶层位移
加载方向计算值/mm试验值/mm误差/%计算值/mm试验值/mm误差/%
10x单向1.301.342.9———
11y单向———1.992.031.9
12xy双向1.461.6410.91.691.732.3
13yx双向1.281.5718.51.672.1622.7
24xyz三向1.491.564.51.652.1723.9
25yxz三向1.301.321.51.701.690.6
33xyz三向4.715.2224.35.216.8323.7
), ArticleFig(id=1245390396453400956, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=EN, label=Table 4, caption=

Naming and cross-sectional dimensions of models

, figureFileSmall=null, figureFileBig=null, tableContent=
算例编号命名柱截面尺寸/mm
A1D4K6-F4K4550（1）/600（1）
A2D4K4-D2K2-F4K4550（1）/500（1）/550（1）
A3D4K3-D2K3-F4K4550（1）/500（1）/550（1）
A4D4K2-D2K4-F4K4550（1）/500（1）/550（1）
B1D6K6-F4K4600（1~3）/500（1）/700（1）、600（2）
B2D6K4-D3K2-F4K4600（1~3）/600（1）/700（1）、600（2）
B3D6K3-D3K3-F4K4600（1~3）/600（1）/700（1）、600（2）
B4D6K2-D3K4-F4K4600（1~3）/600（1）/700（1）、600（2）
C1D8K6-F4K4650（1）、600（2~5）/500（1）/700（1）、600（2）
C2D8K4-D4K2-F4K4650（1）、600（2~4）/600（1）/700（1）、600（2）
C3D8K3-D4K3-F4K4650（1）、600（2~4）/600（1）/700（1）、600（2）
C4D8K2-D4K4-F4K4650（1）、600（2~4）/600（1）/700（1）、600（2）
D1D6K3-D2K3-F4K4600（1~3）/600（1）/700（1）、600（2）
D2D6K3-D3K3-F4K4600（1~3）/600（1）/700（1）、600（2）
D3D6K3-D4K3-F4K4600（1~3）/600（1）/700（1）、600（2）
E1D6K3-D3K3-F4K2600（1~3）/600（1）/700（1）、600（2）
E2D6K3-D3K3-F4K3600（1~3）/600（1）/700（1）、600（2）
E3D6K3-D3K3-F4K4600（1~3）/600（1）/700（1）、600（2）
), ArticleFig(id=1245390396533092734, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=CN, label=表4, caption=

模型命名及截面尺寸

, figureFileSmall=null, figureFileBig=null, tableContent=
算例编号命名柱截面尺寸/mm
A1D4K6-F4K4550（1）/600（1）
A2D4K4-D2K2-F4K4550（1）/500（1）/550（1）
A3D4K3-D2K3-F4K4550（1）/500（1）/550（1）
A4D4K2-D2K4-F4K4550（1）/500（1）/550（1）
B1D6K6-F4K4600（1~3）/500（1）/700（1）、600（2）
B2D6K4-D3K2-F4K4600（1~3）/600（1）/700（1）、600（2）
B3D6K3-D3K3-F4K4600（1~3）/600（1）/700（1）、600（2）
B4D6K2-D3K4-F4K4600（1~3）/600（1）/700（1）、600（2）
C1D8K6-F4K4650（1）、600（2~5）/500（1）/700（1）、600（2）
C2D8K4-D4K2-F4K4650（1）、600（2~4）/600（1）/700（1）、600（2）
C3D8K3-D4K3-F4K4650（1）、600（2~4）/600（1）/700（1）、600（2）
C4D8K2-D4K4-F4K4650（1）、600（2~4）/600（1）/700（1）、600（2）
D1D6K3-D2K3-F4K4600（1~3）/600（1）/700（1）、600（2）
D2D6K3-D3K3-F4K4600（1~3）/600（1）/700（1）、600（2）
D3D6K3-D4K3-F4K4600（1~3）/600（1）/700（1）、600（2）
E1D6K3-D3K3-F4K2600（1~3）/600（1）/700（1）、600（2）
E2D6K3-D3K3-F4K3600（1~3）/600（1）/700（1）、600（2）
E3D6K3-D3K3-F4K4600（1~3）/600（1）/700（1）、600（2）
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Seismic wave information

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编号台站信息方向PGA/（cm/s2）持时/s
USA00707洛杉矶比弗利大道N31W107.738.92
USA00721洛杉矶威尔榭大道NORTH153.641.92
USA01975索尔顿湖野生动物保护区UP473.639.12
USA02593加州布劳雷机场315216.537.89
USA02619埃尔森特罗布罗克曼路140138.639.07
ACC1310.040.00
ACC2310.040.00
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地震波信息

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编号台站信息方向PGA/（cm/s2）持时/s
USA00707洛杉矶比弗利大道N31W107.738.92
USA00721洛杉矶威尔榭大道NORTH153.641.92
USA01975索尔顿湖野生动物保护区UP473.639.12
USA02593加州布劳雷机场315216.537.89
USA02619埃尔森特罗布罗克曼路140138.639.07
ACC1310.040.00
ACC2310.040.00
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Arrangement location of the structural infill wall

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模型编号填充墙布置位置布置数量/道
B3未布置0
B3-S2顺坡向最外侧2
B3-H2横坡向最外侧2
B3-H4横坡向均匀布置4
B3-SH6顺坡向最外侧2
横坡向均匀布置4
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结构填充墙布置位置

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模型编号填充墙布置位置布置数量/道
B3未布置0
B3-S2顺坡向最外侧2
B3-H2横坡向最外侧2
B3-H4横坡向均匀布置4
B3-SH6顺坡向最外侧2
横坡向均匀布置4
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Proportion of plastic rotation at the beam end section

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模型梁端截面转角
结构所有梁端截面中接地端以上2层上接地端以上2层
0-BB-IOIO-LS0-BB-IOIO-LS0-BB-IOIO-LS
B319.679.70.719.280.80093.36.7
B3-150.249.20.675.025.0014.685.40
B3-220.179.50.522.577.50095.74.3
B3-321.378.30.423.376.70096.43.7
B3-421.677.90.623.376.70093.96.1
B3-521.178.40.624.275.80094.55.5
), ArticleFig(id=1245390397128683929, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=CN, label=表7, caption=

梁端截面塑性转角所占比例

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模型梁端截面转角
结构所有梁端截面中接地端以上2层上接地端以上2层
0-BB-IOIO-LS0-BB-IOIO-LS0-BB-IOIO-LS
B319.679.70.719.280.80093.36.7
B3-150.249.20.675.025.0014.685.40
B3-220.179.50.522.577.50095.74.3
B3-321.378.30.423.376.70096.43.7
B3-421.677.90.623.376.70093.96.1
B3-521.178.40.624.275.80094.55.5
), ArticleFig(id=1245390397216764315, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=EN, label=Table 8, caption=

Proportion of plastic rotation at the column end section

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模型柱端截面转角
结构所有柱端截面中接地端以上2层上接地端以上2层
0-BB-IOIO-LS0-BB-IOIO-LS0-BB-IOIO-LS
B374.422.92.763.925.011.152.130.217.7
B3-179.817.82.495.84.2057.342.70
B3-275.022.92.262.529.28.355.232.312.5
B3-377.021.31.763.927.88.357.334.48.3
B3-477.320.02.762.529.28.353.129.217.7
B3-577.719.92.565.326.48.355.229.215.6
), ArticleFig(id=1245390397334204831, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390366434767462, language=CN, label=表8, caption=

柱端截面塑性转角所占比例

, figureFileSmall=null, figureFileBig=null, tableContent=
模型柱端截面转角
结构所有柱端截面中接地端以上2层上接地端以上2层
0-BB-IOIO-LS0-BB-IOIO-LS0-BB-IOIO-LS
B374.422.92.763.925.011.152.130.217.7
B3-179.817.82.495.84.2057.342.70
B3-275.022.92.262.529.28.355.232.312.5
B3-377.021.31.763.927.88.357.334.48.3
B3-477.320.02.762.529.28.353.129.217.7
B3-577.719.92.565.326.48.355.229.215.6
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多台地掉层RC框架结构扭转效应及控制研究
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韩军 1, 2 , 徐雯燕 1 , 夏纯皇 1 , 刘立平 1, 2 , 李英民 1, 2
地震工程与工程振动 | 2024,44(6): 46-58
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地震工程与工程振动 | 2024, 44(6): 46-58
多台地掉层RC框架结构扭转效应及控制研究
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韩军1, 2 , 徐雯燕1, 夏纯皇1, 刘立平1, 2, 李英民1, 2
作者信息
  • 1.重庆大学 土木工程学院，重庆 400045
  • 2.山地城镇建设与新技术教育部重点实验室，重庆 400045

    • 韩军（1978—），男，副教授，博士，主要从事结构抗震研究。E-mail：

Research on the torsional effect and control of RC frame structure with multiple different elevations
Jun HAN1, 2 , Wenyan XU1, Chunhuang XIA1, Liping LIU1, 2, Yingmin LI1, 2
Affiliations
  • 1.School of Civil Engineering, Chongqing University, Chongqing 400045, China
  • 2.Key Laboratory of New Technology for Construction of Cities in Mountain Area, Ministry of Education, Chongqing 400045, China
doi: 10.13197/j.eeed.2024.0605
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摘要
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山地掉层结构考虑坡地开挖工程量、边坡稳定性等因素，常需设置多个接地端，导致结构平面和立面不规则，扭转效应显著。为研究3个不等高接地端的多台地掉层钢筋混凝土（reinforced concrete，RC）框架结构的扭转效应及控制措施，通过拟静力试验和振动台试验结果验证了有限元模型的可靠性，对建立的16个不同结构参数的有限元算例模型进行了弹性和弹塑性动力有限元分析，研究了此类框架结构扭转效应受接地端跨数、总掉层数、中接地端掉层数等因素的影响程度；通过算例分析对比了不同扭转控制措施的效果。研究结果表明：弹性状态下，3台地掉层RC框架结构在中接地层和上接地层处扭转效应显著，总体扭转效应小于对应的2台地掉层RC框架结构；而当结构进入弹塑性状态后，通过降低结构掉层部分长度在顺坡向总长度上的占比，可有效缓解结构的扭转效应；在3台地掉层RC框架结构中设置水平接地构件、钢支撑和黏滞阻尼器均能改善扭转效应，对于岩质边坡，设置水平接地构件对各扭转效应指标的改善最好。

掉层RC框架结构  /  多台地  /  有限元分析  /  扭转效应  /  抗扭设计

Considering factors such as slope excavation quantity and slope stability, RC frame structures supported by foundations with different elevations (FSSFDEs) often occur, resulting in irregular structures and significant torsion. To study the torsional effects and corresponding control measures for FSSFDEs, the reliability of the finite element model was verified using pseudo-static tests and shaking table tests. Sixteen finite element models with varying structural parameters were analyzed using both elastic and elastoplastic dynamic finite element analysis. The study examined the influence of factors such as the total number of dropped stories, the number of spans and the number of dropped stories at the intermediate ground embedding end, and the number of spans at the upper ground end on the torsional effects of the structures. Additionally, the effectiveness of different torsional control measures was compared through case analysis. The main conclusions are as follows: In the elastic state, the torsional effect of RC frame structures with three different ground elevations is significant in the stories at the intermediate and upper ground ends, and it is smaller than that of structures with two different ground elevations. In the plastic state, it is beneficial to improve the torsional effect of the structure by decreasing the size ratio of the part under upper embedding end corresponding to the overall structure. Setting up horizontal grounding components, steel support or viscosity damping in the RC FSSFDEs can improve the torsion resistance. Setting up horizontal grounding components provides the best improvement on torsion effects for structures on rock slope.

RC frame structure supported by foundations with different elevations (FSSFDE)  /  multiple different elevations  /  finite element analysis  /  torsional effect  /  torsion resistance design
韩军, 徐雯燕, 夏纯皇, 刘立平, 李英民. 多台地掉层RC框架结构扭转效应及控制研究. 地震工程与工程振动, 2024 , 44 (6) : 46 -58 . DOI: 10.13197/j.eeed.2024.0605
Jun HAN, Wenyan XU, Chunhuang XIA, Liping LIU, Yingmin LI. Research on the torsional effect and control of RC frame structure with multiple different elevations[J]. Earthquake Engineering and Engineering Dynamics, 2024 , 44 (6) : 46 -58 . DOI: 10.13197/j.eeed.2024.0605
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0　引言
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掉层结构是山地建筑中最广泛应用的结构类型。相较常规结构，掉层结构在结构上具有明显的不规则性，内力分布和形变特征也明显不同，这很大程度上是底部嵌入高度不同引起的。接地层的竖向构件具有较大的抗侧刚度，引发了结构偏心现象，显著增强了结构在地震作用下的扭转效应。同时上接地构件分配的地震剪力大导致破坏严重，需对山地掉层结构的扭转效应及抗震性能进行研究。
目前已有学者对2台地掉层结构的扭转效应、抗震性能和控制措施等进行了研究。李英民等[1]对扭转效应的研究发现结构的扭转非线性反应受弹性最大层间位移角的控制最为明显。刘立平等[2]指出位移比适用于不等高接地框架结构扭转效应的判别。唐洋洋等[3]建议，掉层结构的扭转效应可用单一楼层刚度中心的偏心率量化。相关研究表明，山地掉层结构与普通框架结构相比，由于上接地层柱具有更大的侧向刚度，承担更大的水平地震作用，掉层框架结构的破坏模式通常表现为上接地端柱率先发生破坏，成为结构的薄弱部位。这种破坏模式也是掉层框架结构在地震作用下的主要破坏模式[4-7]。为改善上接地端震害严重的问题，韩军等[8]指出当掉层部分跨数较多，上接地柱采用隔震支座或滑动支座时，掉层结构表现出良好的抗震性能；刘流等[9]采用了一种基于割集理论的失效模式评估方法，进行了偏于安全的掉层结构抗倒易损性分析。在山地掉层结构的实际设计中，现有研究[10-18]表明，设置水平接地构件、合理布置钢支撑和金属阻尼器、对竖向构件加强配筋等措施能提高掉层框架的总体抗震性能。此外，因山地结构和边坡存在复杂的相互作用，王一功等[19]研究了岩质场地和土质场地对多层接地框架的受力情况和破坏形式的不同影响；陈欣等[20]针对山地结构桩基与土质边坡的相互作用，认为底部在滑动面下的桩基对边坡抗滑移有利。
上述研究均针对2个不等高接地端的掉层结构。在实际工程中，场地内可能存在较大高差，受开挖工程量、边坡稳定性和其他因素影响，通常会存在3个或更多不等高的接地端，而此类框架结构的扭转效应可能与2接地端框架结构显著不同。因此，研究具有3个不等接地端的多台地掉层钢筋混凝土（reinforced concrete，RC）框架结构的扭转效应变得尤为重要，并基于研究提出改进措施，为设计提供参考。
基于有限元模型实验验证，本文设计了不同的多台地掉层RC框架结构算例模型进行有限元分析，比较了掉层RC框架在不同结构状态（弹性、弹塑性阶段）下的扭转效应，阐明了不同结构参数（如掉层总数和接地端跨数）对结构扭转效应的影响，并提出了一系列抗扭措施。
1　有限元模型及验证
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1.1　有限元模型建立
本文使用SAP2000分析软件建立掉层框架结构算例模型，框架混凝土采用Mander本构模型，钢筋采用三折线本构模型[21]。为研究框架结构屈服及屈服后的行为，在梁和柱两端分别设置塑性铰，位置设置在构件总长度10%和90%的位置上。此外，采用Hilber-Hughes-Taylor数值积分方法进行弹塑性时程分析，隐式求解结构的运动微分方程。
选取在重庆大学土木工程学院结构实验楼完成的1∶4缩尺掉层框架结构拟静力试验[22]和1∶8缩尺掉层框架结构振动台试验[17]进行有限元模型验证。通过对拟静力试验的对比，验证模型能否准确地模拟结构在低周往复荷载下的受力行为，同时对数值模型的材料本构、单元和参数设置等合理性进行验证；并与振动台试验进行对比，验证有限元模型的动力响应，进一步说明有限元建模的合理性与准确性。
1.2　拟静力试验模拟
采用5层3跨、掉层为2层1跨的拟静力试验对有限元模型进行验证，如图1所示。模型各层高度为750 mm，跨度均为1500 mm，梁截面尺寸为100 mm×150 mm，柱截面尺寸为150 mm×150 mm。混凝土强度C30，纵筋为HRB400，箍筋为HRB335。试验过程中，模型在恒定轴压力下，采用位移控制的水平低周往复加载制度。框架柱所承受的荷载分别为P1 = 5 kN，P2 = 10 kN，P3 = 9.3 kN和P4 = 4.7 kN。水平载荷的加载过程中，顶层和第3层始终保持2∶1的位移比。通过对比掉层RC框架结构低周往复加载的试验结果与模拟结果，得到了滞回曲线的对比图，如图2所示。对比试验和模拟中低周往复载荷作用下掉层RC框架结构的滞回曲线可知，其水平推力峰值为100 kN左右。在模拟中，滞回曲线的捏缩效应更不显著，但与试验结果整体吻合得较好，验证了有限元模拟方法的可靠性。
1.3　振动台试验模拟
振动台试验中的掉层结构模型共6层，沿顺坡向设置3跨、横坡向设置2跨，掉层设计为2层1跨，如图3所示。模型每层高375 mm，每跨750 mm，采用混凝土整体浇筑方法，立方体抗压强度8.9 MPa，弹性模量9900 MPa，引入镀锌铁丝以代替HRB400钢筋。
试验中共选取4条地震波加载，如表1所示。加载方向以顺坡向为主方向，顺坡向、横坡向按1∶0.85的比例双向加载，过程中逐级增大峰值加速度。
掉层RC框架结构振动台试验实测结构横坡向、顺坡向一阶自振周期分别为0.177 s和0.148 s，数值模拟结果分别为0.185 s和0.159 s，模拟与试验结果基本吻合，动力特性相似。有限元模型在地震波作用下部分工况的层扭转角、顶层位移与试验模型数据见表2与表3。在弹性阶段单向加载时误差在3%以内，双向地震动输入时误差为2.3% ~ 10.9%。工况33下结构的位移角约为1/72，已经进入了较强的非线性，误差最大在25%以内。天然波2加载（工况24）有限元模型顶层位移时程曲线与试验值对比结果见图4。由图可知，对于顺坡向与横坡向，模拟与试验得到的时程曲线的趋势和幅值相近，因此可以认为，有限元分析模型能够有效模拟掉层结构在地震作用下的响应特性。
2　算例设计
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2.1　模型概况
为研究3台地掉层RC框架在不同结构状态（弹性、弹塑性阶段）下的扭转效应及对应控制方法，分析上接地端跨数、中接地端跨数、中接地端掉层数以及总掉层层数等多个设计参数对该类结构扭转效应的影响规律，设计了16个不同算例模型进行动力时程分析。
各个算例的命名规则为DxKy-DxKy-FxKy，其中，D为掉层数，K为跨数，F为上接地端以上楼层数。以3台地掉层框架结构D6K3-D3K3-F4K4为例，表示上接地端以上部分为4层4跨、第1台和第2台均掉3层3跨的三接地端结构，如图5所示。
算例模型的抗震设防烈度为7度（0.15 g），场地类别为II类，设计地震分组为第2组，结构阻尼比为0.05，特征周期为0.40 s，为标准抗震设防类建筑。模型框架混凝土强度等级为C30，主筋HRB400，箍筋HPB300，沿X向10跨，Y向5跨，柱距6 m×6 m，层高3.3 m，板厚100 mm，梁截面尺寸250 mm×600 mm。模型柱截面尺寸见表4。
2.2　地震波选取
按双频段选波法选择7条地震波，包括5条天然波，2条人工波，所选地震波信息见表5，反应谱平均值与设计反应谱对比如图6所示。输入多遇地震和罕遇地震时，将7条地震波的PGA按GB 50011—2010《建筑抗震设计规范》[23]分别调幅至55、310 cm/s2。文中给出的结果为7条地震波取平均值后的结果。对三维掉层框架结构进行双向地震动输入动力时程分析。
3　多台地掉层RC框架结构扭转效应
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3.1　多台地掉层RC框架结构弹性扭转效应
限于篇幅，图7仅列出了掉层为6层的算例模型B1和B3在多遇地震作用下各层的扭转效应。掉层为4层、8层时其扭转效应规律与掉层为6层时规律相似。
在量化结构扭转特性时，常用层间扭转角指标。对于掉层框架结构，接地层包含了柔性边和刚性边层间扭转角，分别对应非接地部分和接地部分，其中，柔性边层间扭转角可由某层与下一层的扭转角之差来表示，刚性边层间扭转角等同于接地层扭转角。考虑到楼板视为刚体，除中、上接地层外，其余各楼层的层间扭转角均保持一致。
3台地掉层RC框架结构的层间扭转角在上接地层、中接地层处达到最大值，扭转效应在中接地层、上接地层处最为显著。接地层刚性边层间扭转角明显大于柔性边层间扭转角。相较于2台地掉层框架结构，3台地掉层框架结构上接地层刚性边、柔性边层间扭转角分别减小了19.9%、3.6%，3台地掉层框架结构的掉层部分占总结构的比例较小，结构偏心率减小，扭转效应减小。
3.2　多台地掉层RC框架结构弹塑性扭转效应
3.2.1　中接地端跨数对掉层结构扭转效应的影响
选用A1、A2、A3、A4（总掉层数为4层）；B1、B2、B3、B4（总掉层数为6层）；C1、C2、C3、C4（总掉层数为8层）共3组12个算例模型。每组的模型掉层部分总跨数与上接地端跨数不变，改变中接地端跨数。
图8给出了罕遇地震作用下不同算例模型的层间扭转角。2台地掉层框架结构与3台地掉层框架结构的层间扭转角变化趋势基本相同，柔性边最大层间扭转角大都出现在下接地层上一层。相较于2台地掉层框架结构，掉4层、6层、8层的3台地掉层框架结构上接地层刚性边层间扭转角分别减小了28.4%、3.8%、26.4%。当总跨数一定时，中接地端跨数设置越多，掉层结构的偏心率减小，使得中接地层及以下楼层的柔性边层间扭转角和上、下接地层刚性边层间扭转角均会减小，扭转效应得到改善。
图9给出了在罕遇地震作用下不同算例模型的层间位移角。3台地掉层框架结构相较于2台地掉层框架结构，随中接地端跨数增加，下接地层至中接地层的楼层层间位移角减小，中接地层至上接地层上一层的楼层层间位移角增大，其余楼层层间位移角变化趋势基本不受中接地端跨数的影响。中接地端跨数越多，中接地层部分刚度变大，分配的剪力进一步增加，导致在罕遇地震作用下塑性发展程度较大，层间位移角增大。相较规范中结构在弹塑性状态下的层间位移角限值（0.02）相比，各算例模型均有一定安全冗余。
3.2.2　总掉层数对掉层结构扭转效应的影响
本节对比了不同总掉层数的掉层框架结构在弹塑性状态下的扭转效应，在中接地端跨数相同的情况下，选用了4组共12个模型：A1-B1-C1、A2-B2-C2、A3-B3-C3和A4-B4-C4，分别对应不同的中接地端跨数（0、2、3、4），分析了总掉层数为4层、6层、8层时的3台地掉层框架结构的地震响应。
由图10可知，随总掉层数的改变，对于接地层刚性边层间扭转角。大部分模型呈先减小后增大的趋势。而2台地掉层结构的研究结果表明[24-25]，结构扭转效应随掉层数的增加而增大。对于4层掉层结构，其所掉的层数相对较少，故上接地端所受的地震作用相对较小。因此，在设计时上接地端柱的截面尺寸和配筋也相应较小，在一定程度上减弱了结构的扭转效应。
对原设计掉4层框架结构的接地端柱，采取增大截面尺寸并调整配筋与掉6层框架结构的相同。改进后的模型层间扭转角和层间位移角如图11所示。此时，随着总掉层数的逐步增加，掉层部分的层间扭转角和层间位移角也呈现出逐渐增大的趋势。扭转指标在掉层部分明显减小。当框架结构柱截面及配筋相同时，掉层结构扭转效应随掉层数的增加而增大。
3.2.3　中接地端掉层数对掉层结构扭转效应的影响
选取D1、D2、D3共3个模型，在掉层部分和上接地部分跨数不变时，研究中接地端掉层数对3台地掉层框架结构弹塑性扭转效应的影响。图12给出了D1~D3模型的层间扭转角和位移角，对于不同的中接地端掉层数，层间扭转角均有相近的变化趋势，接地层刚性边的层间扭转角最大。当掉层框架结构的总层数与上接地部分的层数一定时，中接地端掉层数由掉2层增加至掉4层时，掉层部分在总体结构中占比增大，上接地层偏心率增大，上接地层刚性边层间扭转角分别为0.00083、0.00101、0.00113，中接地层刚性边层间扭转角分别为0.00083、0.00084、0.00087，刚性边层间扭转角增大，掉层部分的扭转效应没有明显的变化。
3.2.4　上接地端跨数对掉层结构扭转效应的影响
选取E1、E2、E3共3个模型，当结构掉层部分相同时，研究上接地端跨数对3台地掉层RC框架结构弹塑性扭转效应的影响。图13给出了E1~E3算例模型的层间扭转角和层间位移角。当上接地端跨数由2跨增加至4跨时，上接地层处刚性边层间扭转角减小了35.3%。柔性边扭转角在中接地层上一层差距最大，E3仅为E1的29.8%。上接地层及以下部分的扭转指标呈减小趋势；上接地层以上楼层的各指标略微增加。当掉层部分跨数不变，随上接地端跨数的增加，结构的顺坡向掉层部分尺寸与总尺寸的比值减小，结构偏心率减小，有利于改善结构的扭转效应。
3.2.5　填充墙对掉层框架扭转效应的影响
在抗震分析中，填充墙通常被视为非结构构件，其对结构抗震性能的影响经常被忽视。然而，填充墙的存在可能改变结构体系的质量、刚度分布等，也可能对主体结构构件的局部约束条件产生不利影响。为探讨填充墙对多台地掉层框架结构扭转效应的影响，选取B3模型，沿其顺坡向与横坡向设置填充墙（表6），填充墙采用等效斜压杆模型[26]。
模型层间位移角与层间扭转角见图14。沿顺坡向设置填充墙会增大上接地层及以上楼层的层间扭转角，但上接地层以下楼层扭转效应减小。沿横向布置填充墙会降低上接地层及以上楼层的层间扭转角和层间位移角，中接地掉层部分的层间扭转角会略微增大，但层间位移角仍小于未布置填充墙的框架结构。总的来说，在实际工程中有横向均布布置填充墙约束的多台地掉层框架结构较未考虑填充墙影响时扭转效应减弱。
4　多台地掉层框架结构扭转控制措施
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4.1　扭转控制措施
1）设置水平接地构件
为增加掉层结构横坡向的侧向刚度，限制其在地震作用下的扭转响应，在掉层的上、中接地端的水平位置设置了和岩质边坡固接的接地构件，模型B3-1见图15。
2）设置钢支撑
在结构的适当位置设置钢支撑，以提升其整体刚度，并使刚度分布更均衡，从而减小结构整体的扭转效应。在模型B3中采用了两种钢支撑布置方案：模型B3-2采用自底层至上接地层上一层的双向支撑布置，模型B3-3则采用自底层至顶层的双向支撑布置。钢支撑均采用方管截面设计，选用Q235钢，截面外边长180 mm、壁厚为5 mm。模型B3-3的钢支撑布置立面图见图16，模型B3-2的支撑布置方式与图16相同，仅在布置层数上有差异。
3）设置黏滞阻尼器
黏滞阻尼器是一种速度相关的能量耗散装置，可在不增加结构刚度的情况下提供附加阻尼，显著降低地震作用。在地震作用下，掉层结构的柔性边可能产生显著的位移，而刚性边则因其接地端的刚度较高而位移较小。通过在柔性边安装黏滞阻尼器，可以有效耗散能量、减少振动，并缩小柔性边与刚性边之间的位移差，进而达到限制掉层结构扭转效应的目的。在模型B3上布置基于Maxwell模型的黏滞阻尼单元，非线性连接属性设定为amper-Exponential。经初步计算，确定阻尼系数C = 2 000 kN•（s/m），刚度K = 106 kN/m，阻尼指数α = 0.4。设计了2种模型方案：B3-4模型采用自底层至上接地层上一层的黏滞阻尼器双向布置，而B3-5型则从底层至顶层双向布置黏滞阻尼器。B3-4和B3-5模型的阻尼器布置位置与B3-2和B3-3模型的相同。
4.2　扭转效应控制效果对比
对模型结构分别进行Pushover弹塑性静力分析[27]和时程分析，图17、图18给出了设置抗扭措施的算例模型层间扭转角及层间位移角在罕遇地震作用下随楼层变化规律。3种扭转控制措施均能有效限制结构的扭转，其中，中接地层的刚性边层间扭转角减小了21.0%~82.5%不等，上接地层刚性边扭转角减小了11.1%~70.1%，其中设置水平接地构件对各扭转效应指标的改善最好，尤其是对接地层刚性边和掉层部分的影响效果显著。表7和表8为地震作用下，模型B3至B3-5的各类构件转角变形中，塑性转角所占比例。由统计结果可知，设置水平接地构件、钢支撑、黏滞阻尼器可以降低梁、柱截面进入塑性的程度，相较于自底层至上接地层上一层布置的方案，采用自底层至顶层方式布置的钢支撑与阻尼器在扭转控制方面展现出略微更优的性能。
5　结论
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本文通过对3台地掉层RC框架结构在弹性及弹塑性状态下的扭转效应进行研究，得到以下结论：
1）弹性状态下，3台地掉层RC框架结构在中接地层和上接地层处扭转效应显著，总体扭转效应小于对应的2台地掉层RC框架结构，上接地层刚性边、柔性边层间扭转角分别减小了19.9%、3.6%。
2）弹塑性状态下，当结构横坡向布置不变时，通过改变总掉层层数、中接地端跨数、中接地端掉层层数及上地端跨数，减小顺坡向结构的掉层部分尺寸与相应方向上总尺寸的比值，使得结构质心与刚心的偏心率减小，有利于改善3台地掉层RC框架结构的扭转效应。
3）当3台地掉层RC框架结构柱截面及配筋相同时，其扭转效应随掉层数的增加而增大；但当掉层框架结构跨数较多时，按现行规范设计的掉层框架结构，随总掉层数增加，结构接地端柱尺寸和配筋都会相应增大较多。
4）3台地掉层框架结构的扭转效应可通过设置水平接地构件、设置钢支撑和黏滞阻尼器等措施予以改善。3种扭转控制措施均能有效限制结构的扭转，其中，中接地层的刚性边层间扭转角减小了21.0% ~ 82.5%不等，上接地层刚性边扭转角减小了11.1% ~ 70.1%，其中设置水平接地构件对各扭转效应指标的改善最好。对于岩质边坡，建议优先选择设置水平接地构件，减小掉层结构的扭转效应。若采用设置钢支撑或阻尼器控制掉层RC框架结构扭转，综合考虑经济性等因素，宜从结构底部开始连续布置至上接地层上一层处。
基金
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  • 国家自然科学基金项目(51638002)
  • 重庆市建设科技项目(城科字2021第1-5)
文献
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2024年第44卷第6期
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doi: 10.13197/j.eeed.2024.0605
  • 接收时间：2023-09-19
  • 首发时间：2026-03-30
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  • 收稿日期：2023-09-19
  • 修回日期：2023-12-17
基金
国家自然科学基金项目(51638002)
重庆市建设科技项目(城科字2021第1-5)
作者信息
    1.重庆大学 土木工程学院，重庆 400045
    2.山地城镇建设与新技术教育部重点实验室，重庆 400045
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