无粘结内藏钢板支撑剪力墙滞回性能试验及工作性能研究
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摘要
无粘结内藏钢板支撑剪力墙是多高层建筑支撑体系中的一种形式(简称无粘结支撑墙板),它是指使用内藏钢板支撑作为水平抗侧力构件,外包钢筋混凝土墙板只为内藏钢板支撑提供侧向约束,支撑与墙板之间采用无粘结工艺加工而成的新型抗侧力构件,是一种墙板形式的不失稳支撑(防屈曲支撑)。由于隔离了支撑与混凝土之间的粘结力,内藏钢板支撑几乎承担了所有的水平力,在风荷载和小震作用下,无粘结支撑墙板相当于弹性阶段不失稳的中心支撑,在中震和罕遇地震作用下,支撑受拉受压均能屈服耗能,保护主体结构不受损伤,解决了震后修复困难的问题。对于隔墙比较多的公共与民用建筑,无粘结支撑墙板又可兼作隔墙使用,不影响建筑使用功能,具有很好的经济性。根据内藏钢板支撑的布置形式,无粘结支撑墙板可以分为单斜支撑墙板和人字形支撑墙板等。
虽然近年来不失稳支撑已经在国内外受到越来越多学者的关注,但是关于无粘结支撑墙板的研究很少,还存在研究空白。针对目前研究的不足,本文着重开展了下述工作,并得到了一些有用的结论。
首先,进行了七块单斜支撑墙板和六块人字形支撑墙板的拟静力试验研究,主要考察了内藏钢板支撑的布置形式、支撑的宽厚比、墙板的厚度、墙板的整体双层双向钢筋网间距、墙板端部与中间的加强构造方式和无粘结材料的变化对支撑墙板滞回性能的影响。试验表明,墙板以端部冲剪破坏和中间区域的局部受弯破坏为主;墙板的钢筋构造和支撑表面的无粘结材料是影响支撑墙板滞回性能的关键因素,当墙板端部和墙板中间设置带拉结筋的加密钢筋网构造时,墙板对支撑的约束效果最好,无粘结材料表面越光滑平整,厚度越小,支撑墙板的滞回性能越好;支撑端部采用带加劲肋板的加强方式时,能够有效防止支撑端部外伸段的局部屈曲;墙板端部采用的角钢和锚板加强件均能够有效防止墙板端部边缘的劈裂破坏;对试验破坏机理的分析表明,墙板的局部破坏是由支撑屈服段所发生的多波弯曲失稳引起的。
对试验曲线与试验数据的分析表明,试验所选用的无粘结材料能够很好地隔离支撑与墙板之间的粘结力;在弹性阶段,支撑墙板的水平抗侧刚度近似等于不失稳的内藏钢板支撑的理论水平抗侧刚度,证明无粘结材料能够较好地减少支撑与墙板之间的摩擦力;在破坏之前,滞回曲线始终饱满稳定,没有出现强度和刚度的退化现象,具有较好的耗能能力;滞回曲线可以用双线性模型进行简化,两者吻合较好;骨架曲线呈明显的双线性。
通过试验与理论推导相结合的方法,探讨了支撑墙板的工作性能,给出了修正后的整体稳定设计公式;根据抗弯承载力相等原则推导了墙板的有效宽度公式;针对支撑屈曲的特点和墙板的两种破坏模式,推导了支撑对墙板的局部挤压力公式,通过试验回归得到了防止墙板端部冲剪破坏的承载力公式;对支撑端部外伸段的局部屈曲和支撑与梁的连接节点受力性能作了简要分析;最后,给出了合理的墙板钢筋构造和支撑墙板的制作与施工方法建议,给实际工程应用提供借鉴。
Unbonded steel plate brace encased in reinforced concrete panel is one of the bracing members being used in multi-story and high-rise buildings. The unbonded material is painted onto the steel plate brace to remove the bond stress between the brace and the panel, so the axial load is only applied on the brace. The panel is only designed to prevent the encased brace from buckling so that the brace can dissipate seismic energy through axial yielding under both tensile and compressive forces. With the excellent energy dissipating capacity provided by this panel type of buckling-restrained brace which acts as a hysteretic damper, the damage to the main structure can be greatly alleviated under the strong motion earthquakes, however the encased braces will perform as the concectrical steel braces under the smaller earthquakes or wind load. As for the layout of the encased braces, it can be divided into diagonal-shaped braces and chevron-shaped braces, which are mainly used in the structures with many partition walls.
Recently, buckling-restrained braces have been attached much importance to by many scholars and engineers, but there are few papers dealing with the panel type of buckling-restrained brace(BRB) in which some questions such as the interaction between the braces and the panel are still unclear. So the main work and conclusions on the panel type of BRB are listed as follows.
Pseudo-static tests including seven pieces of panel type of diagonal-shaped buckling-restrained braces(DBRB) and six pieces of chevron-shaped buckling-restained braces(CBRB) have been carried out to investigate the hysteretic performance, in which the layout and width to thickness ratio of the encased steel plate brace, the thickness and reinforcement ratio of the panel, the edge reinforcement of the panel and the unbonded materials are considered. The tests indicate that the punching shear failure near the edge of panel and the local bending failure near the middle of panel are two major failure modes. The constructional reinforcement of panel and unbonded material are two important factors influencing the hysteretic performance of panel type of BRB. With smaller grids of mat reinforcement near the edge of braces and in the middle of panel and with smoother and thinner unbonded materials painted onto the steel plate braces, the panel type of BRB exhibit more stable hysteretic performance. Local buckling is prevented with the ribs welded at the end of braces. The split failure at the edge of panel is also prevented by the angle reinforcement or anchored slab reinforcement. It is found that local failure of the panel is due to the buckling in higher order mode in the yielding portion of brace.
The analysis results reveal that the unbonded materials do well in removing the bond stress between the brace and the panel. During elastic stage, the horizontal stiffness of the panel type of BRB almost amounts to that of the encased brace without buckling which suggests that the unbonded materials can also diminish the friction force in between. The panel type of BRB exhibit good ductility and stable performance with well energy dissipating capacity before failure. The hysteretic curves can be simplified by the bilinear hysteretic model which agrees well with the real curves. The skeleton curves also exhibit bilinear performance.
The working performance, the buckling behavior at the end of brace and the brace-beam connection design are also analyzed. The design formula on the overall stiffening requirement of the panel type of BRB is modified. The effective width of panel is derived from the principle of equal bending capacity. According to the failure mode, the stiffening force between the brace and the panel and the stiffening requirement preventing the edge of panel from punching shear failure are also obtained. Finally, in order to supply a reference for engineering application, the reasonable construction method and suggestion of the panel type of BRB are also summarized.
虽然近年来不失稳支撑已经在国内外受到越来越多学者的关注,但是关于无粘结支撑墙板的研究很少,还存在研究空白。针对目前研究的不足,本文着重开展了下述工作,并得到了一些有用的结论。
首先,进行了七块单斜支撑墙板和六块人字形支撑墙板的拟静力试验研究,主要考察了内藏钢板支撑的布置形式、支撑的宽厚比、墙板的厚度、墙板的整体双层双向钢筋网间距、墙板端部与中间的加强构造方式和无粘结材料的变化对支撑墙板滞回性能的影响。试验表明,墙板以端部冲剪破坏和中间区域的局部受弯破坏为主;墙板的钢筋构造和支撑表面的无粘结材料是影响支撑墙板滞回性能的关键因素,当墙板端部和墙板中间设置带拉结筋的加密钢筋网构造时,墙板对支撑的约束效果最好,无粘结材料表面越光滑平整,厚度越小,支撑墙板的滞回性能越好;支撑端部采用带加劲肋板的加强方式时,能够有效防止支撑端部外伸段的局部屈曲;墙板端部采用的角钢和锚板加强件均能够有效防止墙板端部边缘的劈裂破坏;对试验破坏机理的分析表明,墙板的局部破坏是由支撑屈服段所发生的多波弯曲失稳引起的。
对试验曲线与试验数据的分析表明,试验所选用的无粘结材料能够很好地隔离支撑与墙板之间的粘结力;在弹性阶段,支撑墙板的水平抗侧刚度近似等于不失稳的内藏钢板支撑的理论水平抗侧刚度,证明无粘结材料能够较好地减少支撑与墙板之间的摩擦力;在破坏之前,滞回曲线始终饱满稳定,没有出现强度和刚度的退化现象,具有较好的耗能能力;滞回曲线可以用双线性模型进行简化,两者吻合较好;骨架曲线呈明显的双线性。
通过试验与理论推导相结合的方法,探讨了支撑墙板的工作性能,给出了修正后的整体稳定设计公式;根据抗弯承载力相等原则推导了墙板的有效宽度公式;针对支撑屈曲的特点和墙板的两种破坏模式,推导了支撑对墙板的局部挤压力公式,通过试验回归得到了防止墙板端部冲剪破坏的承载力公式;对支撑端部外伸段的局部屈曲和支撑与梁的连接节点受力性能作了简要分析;最后,给出了合理的墙板钢筋构造和支撑墙板的制作与施工方法建议,给实际工程应用提供借鉴。
Unbonded steel plate brace encased in reinforced concrete panel is one of the bracing members being used in multi-story and high-rise buildings. The unbonded material is painted onto the steel plate brace to remove the bond stress between the brace and the panel, so the axial load is only applied on the brace. The panel is only designed to prevent the encased brace from buckling so that the brace can dissipate seismic energy through axial yielding under both tensile and compressive forces. With the excellent energy dissipating capacity provided by this panel type of buckling-restrained brace which acts as a hysteretic damper, the damage to the main structure can be greatly alleviated under the strong motion earthquakes, however the encased braces will perform as the concectrical steel braces under the smaller earthquakes or wind load. As for the layout of the encased braces, it can be divided into diagonal-shaped braces and chevron-shaped braces, which are mainly used in the structures with many partition walls.
Recently, buckling-restrained braces have been attached much importance to by many scholars and engineers, but there are few papers dealing with the panel type of buckling-restrained brace(BRB) in which some questions such as the interaction between the braces and the panel are still unclear. So the main work and conclusions on the panel type of BRB are listed as follows.
Pseudo-static tests including seven pieces of panel type of diagonal-shaped buckling-restrained braces(DBRB) and six pieces of chevron-shaped buckling-restained braces(CBRB) have been carried out to investigate the hysteretic performance, in which the layout and width to thickness ratio of the encased steel plate brace, the thickness and reinforcement ratio of the panel, the edge reinforcement of the panel and the unbonded materials are considered. The tests indicate that the punching shear failure near the edge of panel and the local bending failure near the middle of panel are two major failure modes. The constructional reinforcement of panel and unbonded material are two important factors influencing the hysteretic performance of panel type of BRB. With smaller grids of mat reinforcement near the edge of braces and in the middle of panel and with smoother and thinner unbonded materials painted onto the steel plate braces, the panel type of BRB exhibit more stable hysteretic performance. Local buckling is prevented with the ribs welded at the end of braces. The split failure at the edge of panel is also prevented by the angle reinforcement or anchored slab reinforcement. It is found that local failure of the panel is due to the buckling in higher order mode in the yielding portion of brace.
The analysis results reveal that the unbonded materials do well in removing the bond stress between the brace and the panel. During elastic stage, the horizontal stiffness of the panel type of BRB almost amounts to that of the encased brace without buckling which suggests that the unbonded materials can also diminish the friction force in between. The panel type of BRB exhibit good ductility and stable performance with well energy dissipating capacity before failure. The hysteretic curves can be simplified by the bilinear hysteretic model which agrees well with the real curves. The skeleton curves also exhibit bilinear performance.
The working performance, the buckling behavior at the end of brace and the brace-beam connection design are also analyzed. The design formula on the overall stiffening requirement of the panel type of BRB is modified. The effective width of panel is derived from the principle of equal bending capacity. According to the failure mode, the stiffening force between the brace and the panel and the stiffening requirement preventing the edge of panel from punching shear failure are also obtained. Finally, in order to supply a reference for engineering application, the reasonable construction method and suggestion of the panel type of BRB are also summarized.
引文
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53 Kazuo Inoue, Shinichi Sawaizumi, Yasuo Higashibata and Kazuhiro Inoue. Bracing Design Criteria of The Reinforced Concrete Panel Including Unbonded Steel Diagonal Braces. Journal of Structural and Construction Engineering, Architectural Institute of Japan. 1992,432(2):41~49
54 Kazuo Inoue, Shinichi Sawaizumi and Yasuo Higashibata. Stiffening Requirements for Unbonded Braces Encased in Concrete Panels. Journal of Structural Engineering, ASCE. 2001,127(6):712~719
55 Kazuo Inoue, Shinichi Sawaizumi, Yasuo Higashibata and Kazuhiro Inoue. Stiffening Design at The Edge of The Reinforced Concrete Panel Including Unbonded Steel Diagonal Braces. Journal of Structural and Construction Engineering, Architectural Institute of Japan. 1993,433(1):137~146
56 Tokinoya Hiroyoshi, Asai Hidekatsu and Eto Hiroaki. Structural Capacity ofThe Sandwich Type of Precast Seismic Controlling Walls: (Part 1) Compression Tests of Elements. Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan. 2002,(8):1065~1066
57 Asai Hidekatsu, Tokinoya Hiroyoshi and Eto Hiroaki. Structural Capacity of The Sandwich Type of Precast Seismic Controlling Walls: (Part 2) Horizontally Loading Tests in Frame. Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan. 2002,(8):1067~1068
58 Hidekatsu Asai, Hiroyoshi Tokinoya and Hiroaki Eto. Development of Compact Seismic Controlling System“Slim Damper”. Technical Research Institute, Obayashi Corporation. 2003,(66):15~22
59张新中.内藏钢板支撑剪力墙工作性能及恢复力特性试验研究.哈尔滨建筑工程学院硕士学位论文. 1989
60李清志.无粘结内藏钢板支撑剪力墙的受力特性及构造措施的试验研究.哈尔滨建筑工程学院硕士学位论文. 1993
61李国强,张晓光,沈祖炎.钢板外包混凝土剪力墙板抗剪滞回性能试验研究.工业建筑. 1995,25(6):32~35
62蔡崇兴.无耗材的消能支撑装置.中国专利: 2004200659294, 2004-07-09
63谢强.槽钢无屈曲消能支撑.中国专利: 2004201099707, 2004-12-09
64谢强.角钢无屈曲消能支撑.中国专利: 2004201099694, 2004-12-09
65 AISC. Seismic Provisions for Structural Steel Buildings. American Institute of Steel Construction. Chicago, Illinois, 2005
66 Federal Emergency Management Agency. NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures(FEMA450). Washington, D.C., 2003
67姚谦峰,陈平.土木工程结构试验.中国建筑工业出版社, 2001
68湖南大学,太原工业大学,福州大学.建筑结构试验.中国建筑工业出版社, 2003
69中华人民共和国行业标准.高层民用建筑钢结构技术规程(JGJ 99-98).北京: 1998
70赵熙元.钢结构材料手册.中国建筑工业出版社, 1994
71 GB/T228-2002.金属材料-室温拉伸试验方法. 2002
72中华人民共和国国家标准.普通混凝土力学性能试验方法(GBJ 81-85).北京: 1998
73中华人民共和国国家标准.混凝土结构设计规范(GB 50010-2002).北京: 2002
74中华人民共和国国家标准.建筑抗震设计规范(GB 50011-2001).北京: 2001
75过镇海.钢筋混凝土原理.清华大学出版社, 1999:29~39
76曹双寅.工程结构设计原理.东南大学出版社, 2002:50~51
77中华人民共和国国家标准.钢结构设计规范(GB 50017-2003).北京: 2003
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13 Kobayashi Fumioki, Murai Masatoshi and Iwata Mamoru. Experiments of Lightened Buckling-Restrained Braces. Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan. 2002,(8):549~550
14 Masatoshi Murai, Fumioki Kobayashi, Takahiro Noda and Mamoru Iwata. Experimental Study on Buckling-Restrained Braces using Steel Mortar Planks. Journal of Structural and Construction Engineering, Architectural Institute of Japan. 2003,569(7):105~110
15 Murai Masatoshi, Kobayashi Fumioki and Iwata Mamoru. Buckling-Restrained Braces Considering Fabricating Simplification and Lightening Weight. Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan. 2003,(9):769~770
16 Kobayashi Fumioki, Murai Masatoshi, Izumita Yohji and Iwata Mamoru. Experimental Study on Buckling-Restrained Braces Changing Width-Thickness Ratio of The Core Plate. Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan. 2004,(8):869~870
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18 Mamoru Iwata and Masatoshi Murai. Buckling-Restrained Brace using Steel Mortar Planks(Performance Evaluation as A Hysteretic Damper). Earthquake Engineering and Structural Dynamics. 2006,35(14):1807~1826
19 Izumita Yohji, Kobayashi Humioki, Murai Masatoshi and Iwata Mamoru. Buckling Behavior of The Core Plate on Buckling-Restrained Braces. Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan. 2004,(8):871~872
20 Izumita Yohji, Murai Masatoshi and Iwata Mamoru. Buckling Behavior ofThe Core Plate on Buckling-Restrained Braces using Steel Mortar Planks. Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan. 2005,(9):993~994
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24 Murai Masatoshi and Iwata Mamoru. Buckling-Restrained Braces using High Performance Hard Polyurethane. Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan. 2004,(8):865~866
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32 Toshiro Suzuki, Toshiyuki Ogawa and Tomotaka Ogasawara. A Study on Inelastic Buckling of Circular Tubes Under Axial Compression With Outer Constraints. Journal of Structural and Construction Engineering, Architectural Institute of Japan. 1994,458(4):137~143
33 Toru Takeuchi, Kazuaki Suzuki, Tomoki Marukawa, Yoshihiro Kimura, Toshiyuki Ogawa, Takeshi Sugiyama and Shiro Kato. Performances of Compressive Tube Members With Buckling Restrainer Composed of Mortal In-Filled Steel Tube. Journal of Structural and Construction Engineering, Architectural Institute of Japan. 2005,590(4):71~78
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35 Takeita Kazunari, Nagao Tadaharu, Taguchi Takashi and Haginoya Manabu. Studies on Buckling-Restrained Bracing using Triple Steel Tubes: (Part 2) Consideration on Experimental Results and FEM Analysis. Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan. 2005,(9):1013~1014
36 Matsushima Naoki, Nagao Tadaharu, Taguchi Takashi, Haginoya Manabu, Takeita Kazunari and Sawano Masashi. Studies on Buckling-Restrained Bracing using Triple Steel Tubes: (Part 3) Outline of Full Scale Elemental Tests and Experimental Results. Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan. 2006,(9):869~870
37 Haginoya Manabu, Nagao Tadaharu, Kamiya Takashi, Taguchi Takashi, Takeita Kazunari and Matsushima Naoki. Studies on Buckling-Restrained Bracing using Triple Steel Tubes: (Part 4) Consideration on Experimental Results of Full Scale Elemental Tests. Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan. 2006,(9):871~872
38 Hirota Minoru, Morino Shosuke, Shimokawa Hiroumi, Kamura Hisaya, Ito Shigeki and Kawaguchi Jun. Elasto-Plastic Behavior of Flat-Bar Brace Stiffened by Square Steel Tube: (Part 9) Affect of Clearance. Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan. 2002,(8):561~562
39李研,吴斌,王倩颖,欧进萍.防屈曲钢支撑阻尼器的试验研究.土木工程学报. 2006,39(7):9~14
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42 Usami Tetsu and Kaneko Hirofumi. Plastic Deformation Capacity of H-shaped Brace Constrained Flexural Buckling. Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan. 2005,(9):1021~1022
43 Iwata, M., Kato, T. and Wada, A. Buckling-Restrained Braces as Hysteretic Dampers. Proceeding, STESSA, Quebec, Canada. 2000:33~38
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45 Suzuki Yumi, et al. Study on Aseismatic Retrofit for RC Frame using Steel Bracing: (Part 3) Experiment on Steel Frames with Bracing Protected against Lateral Buckling. Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan. 2005,(9):1027~1028
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47刘建彬.防屈曲支撑及防屈曲支撑钢框架设计理论研究.清华大学工学硕士学位论文. 2005
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51 Wakabayashi, M., Nakamura, T., et al. Experimental Study on The Elasto-Plastic Behavior of Braces Enclosed by Precast Concrete Panels Under Horizontal Cyclic Loading: Part 1 and 2. Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan, Structural Engineering Section. 1973,(10):1041~1044
52慳原章雄,宮井清忠,宮井一雄,乙部秋良,小野徹夫.フリブレ一ス方式の可撓耐震壁その開発と応用設計例.建築技術. 1974,271(3):139~150
53 Kazuo Inoue, Shinichi Sawaizumi, Yasuo Higashibata and Kazuhiro Inoue. Bracing Design Criteria of The Reinforced Concrete Panel Including Unbonded Steel Diagonal Braces. Journal of Structural and Construction Engineering, Architectural Institute of Japan. 1992,432(2):41~49
54 Kazuo Inoue, Shinichi Sawaizumi and Yasuo Higashibata. Stiffening Requirements for Unbonded Braces Encased in Concrete Panels. Journal of Structural Engineering, ASCE. 2001,127(6):712~719
55 Kazuo Inoue, Shinichi Sawaizumi, Yasuo Higashibata and Kazuhiro Inoue. Stiffening Design at The Edge of The Reinforced Concrete Panel Including Unbonded Steel Diagonal Braces. Journal of Structural and Construction Engineering, Architectural Institute of Japan. 1993,433(1):137~146
56 Tokinoya Hiroyoshi, Asai Hidekatsu and Eto Hiroaki. Structural Capacity ofThe Sandwich Type of Precast Seismic Controlling Walls: (Part 1) Compression Tests of Elements. Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan. 2002,(8):1065~1066
57 Asai Hidekatsu, Tokinoya Hiroyoshi and Eto Hiroaki. Structural Capacity of The Sandwich Type of Precast Seismic Controlling Walls: (Part 2) Horizontally Loading Tests in Frame. Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan. 2002,(8):1067~1068
58 Hidekatsu Asai, Hiroyoshi Tokinoya and Hiroaki Eto. Development of Compact Seismic Controlling System“Slim Damper”. Technical Research Institute, Obayashi Corporation. 2003,(66):15~22
59张新中.内藏钢板支撑剪力墙工作性能及恢复力特性试验研究.哈尔滨建筑工程学院硕士学位论文. 1989
60李清志.无粘结内藏钢板支撑剪力墙的受力特性及构造措施的试验研究.哈尔滨建筑工程学院硕士学位论文. 1993
61李国强,张晓光,沈祖炎.钢板外包混凝土剪力墙板抗剪滞回性能试验研究.工业建筑. 1995,25(6):32~35
62蔡崇兴.无耗材的消能支撑装置.中国专利: 2004200659294, 2004-07-09
63谢强.槽钢无屈曲消能支撑.中国专利: 2004201099707, 2004-12-09
64谢强.角钢无屈曲消能支撑.中国专利: 2004201099694, 2004-12-09
65 AISC. Seismic Provisions for Structural Steel Buildings. American Institute of Steel Construction. Chicago, Illinois, 2005
66 Federal Emergency Management Agency. NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures(FEMA450). Washington, D.C., 2003
67姚谦峰,陈平.土木工程结构试验.中国建筑工业出版社, 2001
68湖南大学,太原工业大学,福州大学.建筑结构试验.中国建筑工业出版社, 2003
69中华人民共和国行业标准.高层民用建筑钢结构技术规程(JGJ 99-98).北京: 1998
70赵熙元.钢结构材料手册.中国建筑工业出版社, 1994
71 GB/T228-2002.金属材料-室温拉伸试验方法. 2002
72中华人民共和国国家标准.普通混凝土力学性能试验方法(GBJ 81-85).北京: 1998
73中华人民共和国国家标准.混凝土结构设计规范(GB 50010-2002).北京: 2002
74中华人民共和国国家标准.建筑抗震设计规范(GB 50011-2001).北京: 2001
75过镇海.钢筋混凝土原理.清华大学出版社, 1999:29~39
76曹双寅.工程结构设计原理.东南大学出版社, 2002:50~51
77中华人民共和国国家标准.钢结构设计规范(GB 50017-2003).北京: 2003