冷弯薄壁型钢组合楼盖整体承载性能理论与试验研究
|
摘要
由冷弯薄壁型钢桁架和OSB板组成的组合楼盖体系是轻钢结构住宅中一种富有特色的新型结构体系,对推动冷弯薄壁型钢结构住宅在我国的发展,具有十分重要的意义。为科学认识其整体承载性能并为其在我国的推广应用提供依据,论文对冷弯薄壁型钢组合楼盖的整体承载能力进行了理论及试验研究。
在试验研究方面,首先,对钢材和OSB板进行了材性试验,得到了材料的弹性模量和强度。其次,对单榀钢桁架,单榀组合桁架,三榀组合楼盖体系三组共9根试件进行了试验研究,试验取得了其极限荷载、变形曲线及破坏模式。最后,将试验与理论分析结果相对比,从而验证了理论分析模型的合理性、准确性和可靠性。
组合楼盖体系在理论分析时,可将其看作是一种组合桁架体系,OSB板视为桁架上弦的一部分,通过连接件的作用与钢桁架上弦一起,成为组合桁架刚度强度都较大的上弦,再与腹杆、下弦共同形成实际的组合桁架。本文按弹性理论及塑性理论分别进行了分析,得到其承载力计算公式。在考虑材料非线性和几何非线性的基础上,建立了冷弯薄壁型钢组合楼盖整体承载力ANSYS计算模型,并在试验验证其有限元分析模型的合理性、准确性和可靠性的基础上对可能影响冷弯薄壁型钢组合楼盖整体承载力的各种因素进行了分析。
通过理论分析及试验研究,得到以下主要结论:(1)冷弯薄壁型钢组合楼盖具有很大的刚度,在外部荷载作用下变形很小;(2)由于OSB板的连接作用,冷弯薄壁型钢组合楼盖不会发生平面外失稳现象;(3)当冷弯薄壁型钢组合楼盖的榀数达到三榀以上时,其力学性能的差别很小,可以用三榀组合楼盖作为整体组合楼盖的计算单元;(4)组合楼盖主要靠钢桁架来受力,钢桁架间距是影响组合楼盖受力性能的重要因素;(5)OSB板的厚度对组合楼盖受力性能影响较小;(6)组合楼盖的跨度是影响其受力性能的重要因素;(7)密排的自攻螺钉可以有效的防止钢梁与OSB板间的相对滑移。
Composite floor system is a new type of residential building system in light-gauge steel residence which is composed of cold-formed thin-wall steel truss and OSB board. It is very important to promote the development of cold-formed thin-wall steel residence in China. In order to realize the integral bearing behavior of cold-formed thin-wall steel composite floor and provide credibility basis of promotion in our country, theoretical and experimental researches are carried out.
Firstly, material tests of both steel and OSB board are taken to get the elastic modulus and ultimate strength. Secondly, nine specimens including single steel truss, single composite truss, three composite floor system are tested to get the ultimate load, deformation curve and failure mode. Lastly, it is showed that the theoretical analysis model is rational, exact and reliable by comparing the results of experiment and the theoretical analysis.
Composite floor can be simplified to composite trusses in the theoretical analysis. The composite truss is composed of top chord of composite truss, bottom chord of composite truss and web member. The top chord of composite truss is composed of top chord of truss and OSB board that’s attached to top chord of truss with self-drilling screws can be considered as a part of top chord of truss. The bearing capacity formula of composite trusses was presented by elastic and plastic theory analysis. Considering the nonlinearity of the material and geometry, nonlinear finite element model was set up for calculating the integral bearing capacity of cold-formed thin-wall steel composite floor, and then, based on the rational, exact and reliable theoretical analysis model validated by experimental results, some factors which may be affect integral bearing capacity of cold-formed thin-wall steel Composite floor have been taken account of in parameter analysis.
Though theoretical and experimental researches, the paper gives some conclusions as follows: (1) cold-formed thin-wall steel composite floor shows a large stiffness and small deformation under external loads; (2)out -of-plane instability phenomenon could not happen in cold-formed thin-wall steel composite floor because of the connective function of OSB board; (3) three Composite floor system can be considered as a calculating unit of integral composite floor because the difference of mechanical properties is very small when there are more than three composite floors; (4) The distance of steel truss is a important factor which affect the bearing capacity of composite floor because steel truss is the main bearing structure;(5) The thickness of OSB board has little influence on the mechanical properties of composite floor;(6)The span of composite floor has great influence on the mechanical properties of composite floor; (7) The relative slip between steel truss and OSB board can be prevented effectively by close-packed self-drilling screws.
在试验研究方面,首先,对钢材和OSB板进行了材性试验,得到了材料的弹性模量和强度。其次,对单榀钢桁架,单榀组合桁架,三榀组合楼盖体系三组共9根试件进行了试验研究,试验取得了其极限荷载、变形曲线及破坏模式。最后,将试验与理论分析结果相对比,从而验证了理论分析模型的合理性、准确性和可靠性。
组合楼盖体系在理论分析时,可将其看作是一种组合桁架体系,OSB板视为桁架上弦的一部分,通过连接件的作用与钢桁架上弦一起,成为组合桁架刚度强度都较大的上弦,再与腹杆、下弦共同形成实际的组合桁架。本文按弹性理论及塑性理论分别进行了分析,得到其承载力计算公式。在考虑材料非线性和几何非线性的基础上,建立了冷弯薄壁型钢组合楼盖整体承载力ANSYS计算模型,并在试验验证其有限元分析模型的合理性、准确性和可靠性的基础上对可能影响冷弯薄壁型钢组合楼盖整体承载力的各种因素进行了分析。
通过理论分析及试验研究,得到以下主要结论:(1)冷弯薄壁型钢组合楼盖具有很大的刚度,在外部荷载作用下变形很小;(2)由于OSB板的连接作用,冷弯薄壁型钢组合楼盖不会发生平面外失稳现象;(3)当冷弯薄壁型钢组合楼盖的榀数达到三榀以上时,其力学性能的差别很小,可以用三榀组合楼盖作为整体组合楼盖的计算单元;(4)组合楼盖主要靠钢桁架来受力,钢桁架间距是影响组合楼盖受力性能的重要因素;(5)OSB板的厚度对组合楼盖受力性能影响较小;(6)组合楼盖的跨度是影响其受力性能的重要因素;(7)密排的自攻螺钉可以有效的防止钢梁与OSB板间的相对滑移。
Composite floor system is a new type of residential building system in light-gauge steel residence which is composed of cold-formed thin-wall steel truss and OSB board. It is very important to promote the development of cold-formed thin-wall steel residence in China. In order to realize the integral bearing behavior of cold-formed thin-wall steel composite floor and provide credibility basis of promotion in our country, theoretical and experimental researches are carried out.
Firstly, material tests of both steel and OSB board are taken to get the elastic modulus and ultimate strength. Secondly, nine specimens including single steel truss, single composite truss, three composite floor system are tested to get the ultimate load, deformation curve and failure mode. Lastly, it is showed that the theoretical analysis model is rational, exact and reliable by comparing the results of experiment and the theoretical analysis.
Composite floor can be simplified to composite trusses in the theoretical analysis. The composite truss is composed of top chord of composite truss, bottom chord of composite truss and web member. The top chord of composite truss is composed of top chord of truss and OSB board that’s attached to top chord of truss with self-drilling screws can be considered as a part of top chord of truss. The bearing capacity formula of composite trusses was presented by elastic and plastic theory analysis. Considering the nonlinearity of the material and geometry, nonlinear finite element model was set up for calculating the integral bearing capacity of cold-formed thin-wall steel composite floor, and then, based on the rational, exact and reliable theoretical analysis model validated by experimental results, some factors which may be affect integral bearing capacity of cold-formed thin-wall steel Composite floor have been taken account of in parameter analysis.
Though theoretical and experimental researches, the paper gives some conclusions as follows: (1) cold-formed thin-wall steel composite floor shows a large stiffness and small deformation under external loads; (2)out -of-plane instability phenomenon could not happen in cold-formed thin-wall steel composite floor because of the connective function of OSB board; (3) three Composite floor system can be considered as a calculating unit of integral composite floor because the difference of mechanical properties is very small when there are more than three composite floors; (4) The distance of steel truss is a important factor which affect the bearing capacity of composite floor because steel truss is the main bearing structure;(5) The thickness of OSB board has little influence on the mechanical properties of composite floor;(6)The span of composite floor has great influence on the mechanical properties of composite floor; (7) The relative slip between steel truss and OSB board can be prevented effectively by close-packed self-drilling screws.
引文
[1] Reinhold M. Schuster,”Composite steel-deck concrete floor systems”. the Journal of Structural Division Proceeding of the America Society of Civil Engineers,1976,102 (STS):899-917.
[2] Max L.Porter, E. Ekberg,Jr. Design Recommendations for Steel Deck Floor Slabs,Journal of the Structural Division,Proceedings of ASCE,November 1976,Vol.102,No.ST11.
[3] Patrick Mark,Bridge Russell Q. Partial shear connection design of composite slabs. Engineering Structures,1994,16(5):348-362.
[4] Hamerlinck Ralph, Twilt Leen. Fire resistance of composite slabs. Journal of Constructional Steel Research, 1995, 33(l-2): 71-85.
[5] Bode Helmut, Sauerborn Ingeborg. Zur Berechnung durchlaufender Verbunddecken.Calculation of continuous composite slabs. Stahlbau, 1997, 66(7):416-426.
[6] Wendel M. Sebastian and Richard E. McConnel. Nonlinear FE Analysis of Steel- Concrete Composite Structures. Journal of Structural Engineering, 2001,126 (6):662-674.
[7]邓秀泰,聂建国.U-200压型钢板与混凝土组合楼板受力性能的试验研究[J].郑州工学院学报, 1989, 10(l).
[8]张培卿,刘文如.压型钢板-混凝土组合楼板正截面承载能力的实验研究[J].哈尔滨建筑大学学报,1994(8):62-68.
[9]孙荣华,陈世鸣.钢与混凝土组合楼板的纵向抗剪分析[J].华东工业大学学报,1997(3).
[10]詹建敏,吴炎海.压型钢板-混凝土组合楼板剪切粘结承载力试验研究[J].福建建筑,2002, (3):27-30.
[11]聂建国,易卫华,雷丽英.闭口型压型钢板-混凝土组合板的刚度计算[J].工业建筑,2003,33(12):19-2.
[12]吴炎海,黄英,邹飞杰.压型钢板-混凝土组合楼板受弯性能的试验研究.福建建筑,2003,82(2):27-30.
[13] Winter, G. Strength of Steel Compression Flanges. Transactions,ASME,Vol.112,1947,pp.527~576.
[14] Bijlard P.P.,and Fisher GP.,“Interaction of Column and Local Buckling in Compression Members”, NACA TN2640 1953.
[15] Timoshenko,S.P. and Gere,J.M.,Theory of Elastical Stability, McGraw-Hill,New York, 1959.
[16] Bleich,F.同济大学钢木结构教研室译.金属结构的屈曲强度(M).北京科学出版社,1965.
[17] Van der Neut, A,“The Interaction of Local Buckling and Column Failure of Thin-walled Compression Members”,Proceedings,12th International Congress Applied Mechanics,Springerverlag,Germany,1969.
[18] John T. DeWolf, Teoman Peokoz, and George winter. Local and overall buckling of cold- formed Steel members. Journal of the Structural Division,ASCE,Oct.,1974,2017-2036.
[19] V.Kalyanaraman,Teoman Peokoz,and George Winter. Unstiffened compression elements. Journal of the Structural Division,ASCE,Sept.,1977,1833-1848.
[20] Cheung,Y.K.,Finite Strip Method in Structural Analysis,Pergamon Press,Inc. New York,N.Y.,1976.
[21] Hancock. Local,Distortional and Lateral Buckling of I-Beams. J. of the Structural Div. Vol. 104,No. STll,November,1978,pp.1787-1798.
[22] Allen H.G. and Bulson P.S.: Background to Buckling [M] ,Maidenhead: McGraw-Hill,1980.
[23] Mulligan G.P. and Pekoz T.: Local Buckling Interaction Mulligan G.P. and Pekoz T.: Local Buckling Interaction in Cold-Formed Columns,Journal of Structural Engineering[J], Vol.113, No.3, March, 1987:604-620.
[24] Schafer,B.W.Local,Distortional,and Euler Buckling of Thin-Walled Columns.Journal of the Structural Engineering,ASCE,2002,128(3):289-299.
[25] Cheng Yu, and Benjamin W.Schafer, Local Buckling Tests on Cold-Formed Steel Beams. Journal of Structural Engineering. December 2003.
[26]郭彦林.用有限条法分析冷弯薄壁柱的弹塑性局部屈曲[J].钢结构,1988,3(2):14-16.
[27]郭彦林.冷弯薄壁型钢柱局部与整体屈曲[J].西安建筑科技大学学报(自然科学版),1989,21(2): 17-21.
[28]郭彦林,陈绍蕃.冷弯薄壁槽钢短柱局部屈曲后相关作用的弹塑性分析[J].土木工程学报, 1990,23(3):15-18.
[29]郭彦林.冷弯薄壁型钢柱局部与整体稳定相关作用的理论和试验研究.土木工程学报, 1991, 24(l):23-310.
[30]沈祖炎,张其林.受压方管钢柱的屈曲后极限承载力[J].土木工程学报,1991, 24(3): 15-26.
[31]陈绍蕃,惠颖.冷弯型钢局部屈曲的相关性和卷边板件的有效宽度[J].西安建筑科技大学学报, 1995, 27(l):240-246.
[32]张其林,沈祖炎.受压槽形截面的屈曲后极限强度[J].土木工程学报,1995, 28(2):11-19.
[33]陈剑,顾强,陈绍蕃.薄壁卷边槽钢梁板件相关屈曲分析及受压翼缘的有效宽厚比(I) [J].西安建筑科技大学学报,1996,28(l):14-18.
[34]朱慈勉,沈祖炎.薄壁柱相关屈曲分析的混合有限元模型[J].同济大学学报,1997,25(l): 11-16.
[35]习朱慈勉,沈祖炎,陈栋.薄壁箱形截面柱的承载力计算[J].同济大学学报, 1997,25(3): 268-273.
[36]张虎,顾强,杨应华.卷边槽形截面受弯构件翼缘板的有效宽度[J].西安建筑科技大学学报,1998, 30(2):107-111.
[37]谢文智,郝际平,何保康.用样条配点加权残值法分析冷弯薄壁型钢截面柱的局部相关屈曲[J].钢结构, 2000(3):34-46.
[38]郭兵,吴清波.卷边Z型钢的相关屈曲及有效宽度[J].钢结构.2001, 16(2):54-56.
[39]陈绍蕃.冷弯型钢板件相关屈曲的极限承载力.建筑钢结构进展[J],vol.4,No.1,2002.
[40]陈绍蕃,苏明周.冷弯型钢擦条的有效截面[J].建筑结构学报, 2003, 24(6):63-66.
[41]曾锋.冷弯薄壁矩形钢管板组相关屈曲性能研究[D].西安:西安建筑科技大学,2003.
[42]杨娜,支旭东,沈世钊.H型钢楔形薄壁构件的局部屈曲性能分析[J].土木工程学报, 2004, 37(8):11-15.
[43]蔺军,顾强,董石麟.梁腹板在弯、剪及局压复合应力作用下的屈曲分析[J].土木工程学报,2005,38(7):15-20.
[44]潘汉明,郭彦林,梁硕等.大直径薄壁钢管压弯构件的稳定分析[J] .土木工程学报,2007,40(3):11-17.
[45]朱聘儒.钢-混凝土组合梁设计原理[M].中国建筑工业出版社,1989
[46]唐进,叶梅新.混凝土桥面系-钢桁组合梁混凝土板有效宽度研究[J] .长沙铁道学院学报,No.2, Vol.16.
[47]金建新.钢—预应力混凝土叠合板组合桁架整体测试研究[D].上海:同济大学,1994.
[48]宋国涛.钢—混凝土组合桁架弹塑性抗弯强度分析[D].北京:北京交通大学,2005.
[49] GB/T 228-2002,金属材料室温拉伸试验方法[S].
[50]秦雅菲.冷弯薄壁型钢低层住宅墙柱体系轴压性能理论与试验研究[D].上海:同济大学,2005.
[51] GB/T 17657-1999,人造板及饰面人造板理化性能试验方法[S].
[52] LY/T 1580-2000,定向刨花板[S].
[53] GB50018-2002,冷弯薄壁型钢结构技术规范[S].
[54] Schafer B,Pekoz T.Geometric imperfections and residual stresses for use in the analytical modeling of cold-formed steel members.In Proceedings of Thirteenth International Specialty Conference on Cold-formed Steel Structures ,St.Louis, Missouri, USA,1996:649-664
[55] Young B,Rasmussen KJR,Tests of fixed-ended plain channel columns.Journal of Structural Engineering,ASCE 1998,124(2):131-9
[2] Max L.Porter, E. Ekberg,Jr. Design Recommendations for Steel Deck Floor Slabs,Journal of the Structural Division,Proceedings of ASCE,November 1976,Vol.102,No.ST11.
[3] Patrick Mark,Bridge Russell Q. Partial shear connection design of composite slabs. Engineering Structures,1994,16(5):348-362.
[4] Hamerlinck Ralph, Twilt Leen. Fire resistance of composite slabs. Journal of Constructional Steel Research, 1995, 33(l-2): 71-85.
[5] Bode Helmut, Sauerborn Ingeborg. Zur Berechnung durchlaufender Verbunddecken.Calculation of continuous composite slabs. Stahlbau, 1997, 66(7):416-426.
[6] Wendel M. Sebastian and Richard E. McConnel. Nonlinear FE Analysis of Steel- Concrete Composite Structures. Journal of Structural Engineering, 2001,126 (6):662-674.
[7]邓秀泰,聂建国.U-200压型钢板与混凝土组合楼板受力性能的试验研究[J].郑州工学院学报, 1989, 10(l).
[8]张培卿,刘文如.压型钢板-混凝土组合楼板正截面承载能力的实验研究[J].哈尔滨建筑大学学报,1994(8):62-68.
[9]孙荣华,陈世鸣.钢与混凝土组合楼板的纵向抗剪分析[J].华东工业大学学报,1997(3).
[10]詹建敏,吴炎海.压型钢板-混凝土组合楼板剪切粘结承载力试验研究[J].福建建筑,2002, (3):27-30.
[11]聂建国,易卫华,雷丽英.闭口型压型钢板-混凝土组合板的刚度计算[J].工业建筑,2003,33(12):19-2.
[12]吴炎海,黄英,邹飞杰.压型钢板-混凝土组合楼板受弯性能的试验研究.福建建筑,2003,82(2):27-30.
[13] Winter, G. Strength of Steel Compression Flanges. Transactions,ASME,Vol.112,1947,pp.527~576.
[14] Bijlard P.P.,and Fisher GP.,“Interaction of Column and Local Buckling in Compression Members”, NACA TN2640 1953.
[15] Timoshenko,S.P. and Gere,J.M.,Theory of Elastical Stability, McGraw-Hill,New York, 1959.
[16] Bleich,F.同济大学钢木结构教研室译.金属结构的屈曲强度(M).北京科学出版社,1965.
[17] Van der Neut, A,“The Interaction of Local Buckling and Column Failure of Thin-walled Compression Members”,Proceedings,12th International Congress Applied Mechanics,Springerverlag,Germany,1969.
[18] John T. DeWolf, Teoman Peokoz, and George winter. Local and overall buckling of cold- formed Steel members. Journal of the Structural Division,ASCE,Oct.,1974,2017-2036.
[19] V.Kalyanaraman,Teoman Peokoz,and George Winter. Unstiffened compression elements. Journal of the Structural Division,ASCE,Sept.,1977,1833-1848.
[20] Cheung,Y.K.,Finite Strip Method in Structural Analysis,Pergamon Press,Inc. New York,N.Y.,1976.
[21] Hancock. Local,Distortional and Lateral Buckling of I-Beams. J. of the Structural Div. Vol. 104,No. STll,November,1978,pp.1787-1798.
[22] Allen H.G. and Bulson P.S.: Background to Buckling [M] ,Maidenhead: McGraw-Hill,1980.
[23] Mulligan G.P. and Pekoz T.: Local Buckling Interaction Mulligan G.P. and Pekoz T.: Local Buckling Interaction in Cold-Formed Columns,Journal of Structural Engineering[J], Vol.113, No.3, March, 1987:604-620.
[24] Schafer,B.W.Local,Distortional,and Euler Buckling of Thin-Walled Columns.Journal of the Structural Engineering,ASCE,2002,128(3):289-299.
[25] Cheng Yu, and Benjamin W.Schafer, Local Buckling Tests on Cold-Formed Steel Beams. Journal of Structural Engineering. December 2003.
[26]郭彦林.用有限条法分析冷弯薄壁柱的弹塑性局部屈曲[J].钢结构,1988,3(2):14-16.
[27]郭彦林.冷弯薄壁型钢柱局部与整体屈曲[J].西安建筑科技大学学报(自然科学版),1989,21(2): 17-21.
[28]郭彦林,陈绍蕃.冷弯薄壁槽钢短柱局部屈曲后相关作用的弹塑性分析[J].土木工程学报, 1990,23(3):15-18.
[29]郭彦林.冷弯薄壁型钢柱局部与整体稳定相关作用的理论和试验研究.土木工程学报, 1991, 24(l):23-310.
[30]沈祖炎,张其林.受压方管钢柱的屈曲后极限承载力[J].土木工程学报,1991, 24(3): 15-26.
[31]陈绍蕃,惠颖.冷弯型钢局部屈曲的相关性和卷边板件的有效宽度[J].西安建筑科技大学学报, 1995, 27(l):240-246.
[32]张其林,沈祖炎.受压槽形截面的屈曲后极限强度[J].土木工程学报,1995, 28(2):11-19.
[33]陈剑,顾强,陈绍蕃.薄壁卷边槽钢梁板件相关屈曲分析及受压翼缘的有效宽厚比(I) [J].西安建筑科技大学学报,1996,28(l):14-18.
[34]朱慈勉,沈祖炎.薄壁柱相关屈曲分析的混合有限元模型[J].同济大学学报,1997,25(l): 11-16.
[35]习朱慈勉,沈祖炎,陈栋.薄壁箱形截面柱的承载力计算[J].同济大学学报, 1997,25(3): 268-273.
[36]张虎,顾强,杨应华.卷边槽形截面受弯构件翼缘板的有效宽度[J].西安建筑科技大学学报,1998, 30(2):107-111.
[37]谢文智,郝际平,何保康.用样条配点加权残值法分析冷弯薄壁型钢截面柱的局部相关屈曲[J].钢结构, 2000(3):34-46.
[38]郭兵,吴清波.卷边Z型钢的相关屈曲及有效宽度[J].钢结构.2001, 16(2):54-56.
[39]陈绍蕃.冷弯型钢板件相关屈曲的极限承载力.建筑钢结构进展[J],vol.4,No.1,2002.
[40]陈绍蕃,苏明周.冷弯型钢擦条的有效截面[J].建筑结构学报, 2003, 24(6):63-66.
[41]曾锋.冷弯薄壁矩形钢管板组相关屈曲性能研究[D].西安:西安建筑科技大学,2003.
[42]杨娜,支旭东,沈世钊.H型钢楔形薄壁构件的局部屈曲性能分析[J].土木工程学报, 2004, 37(8):11-15.
[43]蔺军,顾强,董石麟.梁腹板在弯、剪及局压复合应力作用下的屈曲分析[J].土木工程学报,2005,38(7):15-20.
[44]潘汉明,郭彦林,梁硕等.大直径薄壁钢管压弯构件的稳定分析[J] .土木工程学报,2007,40(3):11-17.
[45]朱聘儒.钢-混凝土组合梁设计原理[M].中国建筑工业出版社,1989
[46]唐进,叶梅新.混凝土桥面系-钢桁组合梁混凝土板有效宽度研究[J] .长沙铁道学院学报,No.2, Vol.16.
[47]金建新.钢—预应力混凝土叠合板组合桁架整体测试研究[D].上海:同济大学,1994.
[48]宋国涛.钢—混凝土组合桁架弹塑性抗弯强度分析[D].北京:北京交通大学,2005.
[49] GB/T 228-2002,金属材料室温拉伸试验方法[S].
[50]秦雅菲.冷弯薄壁型钢低层住宅墙柱体系轴压性能理论与试验研究[D].上海:同济大学,2005.
[51] GB/T 17657-1999,人造板及饰面人造板理化性能试验方法[S].
[52] LY/T 1580-2000,定向刨花板[S].
[53] GB50018-2002,冷弯薄壁型钢结构技术规范[S].
[54] Schafer B,Pekoz T.Geometric imperfections and residual stresses for use in the analytical modeling of cold-formed steel members.In Proceedings of Thirteenth International Specialty Conference on Cold-formed Steel Structures ,St.Louis, Missouri, USA,1996:649-664
[55] Young B,Rasmussen KJR,Tests of fixed-ended plain channel columns.Journal of Structural Engineering,ASCE 1998,124(2):131-9