简易柱脚转动约束对变截面门式刚架平面内稳定承载力影响研究
|
摘要
中国工程建设标准化协会2002年制定了《门式刚架轻型房屋钢结构技术规程》(CECS102:2002)。该《规程》在对门式刚架楔形柱进行稳定验算时,对门式刚架最经常采用的两种简易柱脚形式(1块底板加2或4枚锚栓的柱脚)一概视为铰接,这样就使得设计工作大大简化。然而,实验及相关分析表明,这两种柱脚形式(特别是4枚锚栓的简易柱脚)实际上具有相当程度的抗转动能力。柱脚实际存在的这种转动约束必然会增强楔形柱的稳定承载能力,那么这种约束究竟能在多大程度上增强楔形柱的稳定性能(实际上是门式刚架的整体稳定性能)?如何在设计中利用这一有利条件?
针对上述问题,本文对比了前人所做的关于柱脚转动约束刚度的研究。在借鉴实验资料及有关分析的基础上,引入了考虑不同的柱脚构造在柱子轴力、弯矩均随加载过程变化的变刚度柱脚约束力学模型,并采用考虑二阶非线性的有限元方法对门式刚架的整体稳定计算编制了程序,用计算机对单跨门式刚架在有代表性的荷载形式作用下进行了大量的计算。然后与不考虑柱脚约束的计算结果进行对比,研究了简易柱脚实际存在的抗转动约束能力能在多大程度上增强门式刚架的稳定承载力。发现柱脚配置4枚锚栓的柱脚具有很强的抗转动约束能力,该约束能力显著的提高门式刚架的平面内稳定承载力,可以在工程设计中考虑这种有利作用,更进一步节约材料,提高经济指标,并提出了具体的而且较为简单的措施。而柱脚仅配置2枚锚栓时,柱脚的抗转动约束能力表现的不太明显,而且当锚栓直径、底板厚度较小时,刚架的实际承载能力甚至低于《规程》的计算值,因此,建议当柱脚仅配置2枚锚栓时,不能过高的提高刚架的稳定承载力。但在保证一定的柱脚构造要求后,就可以较为安全使用《规程》的计算值。
The Standardization Institute of Chinese Construction enacted Technical specification for steel structure of light-weight buildings with gabled frames (CECS102:2002) in 2002. In the Specification, two kinds of column bases which have one plate and two or four anchor bolts are the most popular in portal frames and are considered as pinned bases when the stability for wedge-shaped column of portal frame is checked. It simplifies the design greatly. However, it has been proved that the two kinds of column bases (especially the base with four anchor bolts) actually have remarkable ability of rotational restrict with the deduction of theory and experiments. The rotational restrict of column base certainly improved the stability of the frame, but how much can the restrict increase the stability? And how to use the advantage in design?
On the above-mentioned issue, it is compared in the this paper that the research was made before on the rotational restricted stiffness of column base. With experimental information and relational analysis, it is introduced that the variational-stiffness column base modeling which is relative with axial force and moment. And the codes are made with second-order non-linear finite element methods for analyzing overall stability of portal frame. A lot of cases are computed with computer for stability of one-bay portal frame loaded by typical loads. After that, it is compared with the results of non-restrict column base. It is concluded that the column base with 4 anchor bolts has considerable anti-rotational ability, and the overall stability in plane of portal frame is remarkably strengthened by the ability. This advantage could be used in design, save lots of materials. And simple measures are introduced. And the anti-rotational ability of column base with 2 anchor bolts is neglectable. Moreover, the actual stability is less than Specification’s when the diameter of anchor bolts and the thickness of column base plate are too small. So it is suggested that no improving the overall stable capacity when column base is consisted of 2 anchor bolts. But when the structure of column base is ensured, the Specification’s stable capacity could be used safely.
针对上述问题,本文对比了前人所做的关于柱脚转动约束刚度的研究。在借鉴实验资料及有关分析的基础上,引入了考虑不同的柱脚构造在柱子轴力、弯矩均随加载过程变化的变刚度柱脚约束力学模型,并采用考虑二阶非线性的有限元方法对门式刚架的整体稳定计算编制了程序,用计算机对单跨门式刚架在有代表性的荷载形式作用下进行了大量的计算。然后与不考虑柱脚约束的计算结果进行对比,研究了简易柱脚实际存在的抗转动约束能力能在多大程度上增强门式刚架的稳定承载力。发现柱脚配置4枚锚栓的柱脚具有很强的抗转动约束能力,该约束能力显著的提高门式刚架的平面内稳定承载力,可以在工程设计中考虑这种有利作用,更进一步节约材料,提高经济指标,并提出了具体的而且较为简单的措施。而柱脚仅配置2枚锚栓时,柱脚的抗转动约束能力表现的不太明显,而且当锚栓直径、底板厚度较小时,刚架的实际承载能力甚至低于《规程》的计算值,因此,建议当柱脚仅配置2枚锚栓时,不能过高的提高刚架的稳定承载力。但在保证一定的柱脚构造要求后,就可以较为安全使用《规程》的计算值。
The Standardization Institute of Chinese Construction enacted Technical specification for steel structure of light-weight buildings with gabled frames (CECS102:2002) in 2002. In the Specification, two kinds of column bases which have one plate and two or four anchor bolts are the most popular in portal frames and are considered as pinned bases when the stability for wedge-shaped column of portal frame is checked. It simplifies the design greatly. However, it has been proved that the two kinds of column bases (especially the base with four anchor bolts) actually have remarkable ability of rotational restrict with the deduction of theory and experiments. The rotational restrict of column base certainly improved the stability of the frame, but how much can the restrict increase the stability? And how to use the advantage in design?
On the above-mentioned issue, it is compared in the this paper that the research was made before on the rotational restricted stiffness of column base. With experimental information and relational analysis, it is introduced that the variational-stiffness column base modeling which is relative with axial force and moment. And the codes are made with second-order non-linear finite element methods for analyzing overall stability of portal frame. A lot of cases are computed with computer for stability of one-bay portal frame loaded by typical loads. After that, it is compared with the results of non-restrict column base. It is concluded that the column base with 4 anchor bolts has considerable anti-rotational ability, and the overall stability in plane of portal frame is remarkably strengthened by the ability. This advantage could be used in design, save lots of materials. And simple measures are introduced. And the anti-rotational ability of column base with 2 anchor bolts is neglectable. Moreover, the actual stability is less than Specification’s when the diameter of anchor bolts and the thickness of column base plate are too small. So it is suggested that no improving the overall stable capacity when column base is consisted of 2 anchor bolts. But when the structure of column base is ensured, the Specification’s stable capacity could be used safely.
引文
[1] Lee, G.C., Morrell, L.M. and Ketter, R.L., Design of Tapered Members, Welding Research Council Bulletin, No.173, June, 1972.
[2] Foggel, C.M., and Ketter, R.L., Elastic Strength of Tapered Columns, Journal of the Structure Division, ASCE, Vol.88, No.ST5, Paper 3301, Oct., 1962.
[3] Charles, G..Culer and Stephen, M.Preg, Elastic Stability of Tapered Beam-Columns, Journal of the Structure Division, ASCE, Vol.94, No.ST2, Feb., 1968.
[4] Just, D.J., Just, Analysis of Plane Frame of Linearly Varying Rectangular Section, The Structural Engineer, Jan., 1975.
[5] Just, D.J., Just, Plane Frameworks of Tapering Box and I-section, Journal of the Structural Division, Vol.103, No.ST1.
[6] James, M. Gere, and Winfred, O. Cater, Critical Buckling Loads of Tapered Bars under Stepped Axial Loads, J. Struct. Eng., ASCE, Vol.112, No.6, June, 1986.
[7] Ermopulos, John C., Buckling of Tapered Bars under Stepped Axial Loads, J. Struct. Eng., ASCE, Vol.112, No.6, June, 1986.
[8] Davies, J. M., Inplane Stability in Portal Frame, The Structural Engineer, Vol.68, No.8/17, April, 1990.
[9] Balogh, J., Ivanyi Jr, M. and Varga, G., Analysi of Multi-interaction of Soil-Foundation-Steel Structure, J. Construct. Steel Res. , Vol.46, Nos.1-3, pp.117-118, paper number 323,1998.
[10] Silvestres, N., Mesquita, A., Camotim, D. and Silva, L., In-Plane Buckling Behavior of Pitched-Roof Steel Frames with Semi-Rigid Connections, Proceedings of the 1998 SSRC Annual Technical Session and Meeting(Theme Conference Workshop).
[11] Nogueiro, P., Silva, L., Silvestres, N. and Camotim, D., Proceedings of the 2000 SSRC Annual Technical Session and Meeting, pp. 104-116.
[12] Butler, D. J. and Anderson, G. B., the Elastic Buckling of Tapered Beam-column, Welding Research Supplement, 29-S, Jan., 1963.
[13] Hiroyaki Shiom and Maneaki Kurata, Strenth Formula for Tapered Beam-columns, Journal of Structural Engineering, Vol.110, No.7, July, 1984.
[14] J. M. Davies, P. Engel, T. T. C. Liu, and L. J. Morris, Realistic Modeling of Engineer, Vol.68, No.1/9, Jan., 1990.
[15] Melchers, R.E. and Maas, G., Column Base Restraint Effect for a Steel Portal Frame, the
Strutural Engineer, Vol.72, No. 4, 15 Feb.,1994.
[16] 刘安清,直线楔形杆件框架稳定性计算,建筑结构学报,1983, 4(2).
[17] 梁启智、曾令付,山形门式刚架的梁柱计算长度,土木工程学报,1987,20(1).
[18] 赵毅强,楔形杆件结构的弹性稳定分析,建筑结构学报,1990,11(6),58-68.
[19] 张振涛,薄壁变截面结构内力与构件稳定分析的有限元法,西安建筑科技大学硕士论文,1992.
[20] 顾强、周敏辉,楔形变截面门式刚架的设计(二),西安建筑科技大学学报, 1998,30(3),209-212.
[21] 陈绍蕃,门式钢框架轻型化的技术措施,建筑结构,1998,28(2),30-33.
[22] 陈绍蕃,轻型钢结构变截面门式刚架的稳定计算,建筑结构,1998,28(8),10-14.
[23] 王文明、郭彦林、赵熙元,变截面门式刚架结构的有限元分析,建筑结构,1999,29(10),57-60.
[24] 李峰,楔形变截面单跨门式刚架柱计算长度,西安建筑科技大学硕士论文,1999.
[25] 饶芝英、童根树,变截面门式刚架平面内弹性稳定计算,建筑结构,2000,30(4),8-11.
[26] 郭彦林、王文明、石永久,变截面门式刚架结构的非线性性能,工程力学,2000,17(4),29-36.
[27] 李峰、顾强,楔形变截面单跨门式刚架柱计算长度分析,西安建筑科技大学学报,2000,32(3),256-259.
[28] 卢林枫、顾强、解琦,门式刚架屋面坡度对二阶效应的影响及二阶弯矩计算公式,建筑结构,2001,32(2),26-56.
[29] 李国强、李进军,楔形压杆的非弹性稳定研究,土木工程学报,2001,34(6),34-37.
[30] 杨娜、沈世钊, 变截面门式刚架结构的几何非线性性能研究,哈尔滨建筑大学学报,2001,34(3),10-15.
[31] 申红侠、顾强,楔形变截面压弯构件平面内极限承载力,西安建筑科技大学学报,2002,34(4),400-406.
[32] 童骏、陈以一、伍益莹,柱脚弹性约束对门式刚架侧移和内力的影响,结构工程师,2003(2),25-35.
[33] 中国工程建设标准化协会,门式刚架轻型房屋钢结构技术规程(CECS102:2002),中国计划出版社,2003.
[34] Picard, A. and Beaulieu, D., Behaviour of a Simple Column Base Connection, Can. J. Civ. Eng., Vol.12, 1985, pp.126-136.
[35] Picard, A. and Beaulieu, D., Rotational Restraint of a Simple Column Base Connection, Can. J. Civ. Eng., Vol.14, 1987, pp.49-57.
[36] Hon, K.K. and Melchers, R.E., Experimental Behaviour of Steel Column Bases, J. Construct.
Steel Research, Vol.9, 1988, pp.35-50.
[37] 金涛,钢柱脚的抗滑移及转动约束作用,西安建筑科技大学硕士论文,1993.
[38] 戴贤阳,厂房钢结构露出型柱脚性能研究,西安建筑科技大学硕士论文,1990.
[39] 陈军,钢柱脚的转动约束,西安建筑科技大学硕士论文,1989.
[40] Thambiratnam,David P. and Paramasivam, P., Base Plates Under Axial Loads and Moments, Journal of Structural Engineering, Vol.112, No.5, May, 1986, pp.1166-1167.
[41] Penserini, Paul and Colson, Andre, Ultimate Limit Strength of Column-Base Connections, J. Construct. Steel Research, Vol.14, 1989, pp.301-320.
[42] Targowski, R., Lamblin, D. and Guerlement, G., Baseplate Column Connection Under Bending:Experimental and Numerical Study, J. Construct. Steel Research, Vol.27, 1993, pp.37-54.
[43] Ermopoulos, J. Ch. and Stamatopoulos, G. N., Analytical Modeling of Column-Base Plates Under Cyclic Loading, J. Construct. Steel Research, Vol.40, No.3,1996, pp.225-238.
[44] Stamatopoulos, G. N. and Ermopoulos, J. Ch., Interaction Curves for Column Base-Plate Connections, J. Construct. Steel Research, Vol.44, Nos.1-2,1997, pp.69-89.
[45] 于安麟、永毓栋、郭在田、戴贤阳,露出型钢柱脚抗剪性能的研究(I),工业建筑,22(3),1992,24-26.
[46] 于安麟、永毓栋、郭在田、戴贤阳,露出型钢柱脚抗剪性能的研究(II),工业建筑,22(5),1992,29-33.
[47] Hon, K.K. and Melchers, R.E., Mpment-Rotation Curves for ‘Pinned’ Column Bases, The Structural Engineer, 65B(3),1987, pp.54-58.
[48] Melchers, R. E., Column-Base Response Under Applied Moment, J. Construct. Steel Research, Vol.23, 1992, pp.127-143.
[49] Ermopoulos, John Ch. and Stamatopoulos, George N., Mathematical Modeling of Column Base Plate Connections, J. Construct. Steel Research, Vol.36, No.2,1996, pp.79-100.
[50] 九谷和秀、增田贯志,鉄骨柱脚の力学性状に関する実験的研究,日本建筑学会大会学术讲演梗概集(东北),1982,1815-1816.
[51] 增田贯志、九谷和秀、藤冈丰三雄,柱脚部の变形を考慮した鉄骨ラメンの实用计算法,日本建筑学会大会学术讲演梗概集(东北),1982,1817-1818.
[52] Chajes, A. and Churchill, J.E., Nonlinear frame analysis by finite element methods, Journal of Structural Engineering, ASCE, Vol. 113, No. 6, 1987, 1221-1235.
[53] 陈骥,钢结构稳定理论与设计,科学出版社,2001,pp.125.
[54] 陈绍蕃,钢结构设计原理(第二版),科学出版社,2000.
[55] 程睿,半刚性连接钢框架的有限元分析及近似计算方法,重庆大学硕士论文,2002,
pp.19-27.
[56] Chen, W. F. and Atsuta, T.,周绥平等译,梁柱分析与设计(第一卷),人民交通出版社,1997.
[57] 李国强、沈祖炎,钢结构框架体系弹性及弹塑性分析与计算理论,上海科学技术出版社,1998.
[58] 吕烈武、沈世钊、沈祖炎、胡学仁,钢结构构件稳定理论,中国建筑工业出版社,1983.
[59] 《冷弯薄壁型钢结构设计手册》编著组,冷弯薄壁型钢结构设计手册,中国建筑工业出版社,1996.
[60] 陈绍蕃,钢结构稳定设计指南,中国建筑工业出版社,1996.
[61] 朱伯芳,有限单元法原理与应用(第二版),中国水利水电出版社,1998.
[62] 王勖成、邵敏,有限单元法基本原理和数值方法(第二版),清华大学出版社,1997.
[63] 苏金明、阮沈勇,Matlab 6.1实用指南(上册),电子工业出版社,2002.
[64] 赵更新,杆系结构分析程序设计,电子科技大学出版社,1997.
[65] 何君毅、林祥都,工程结构非线性问题的数值解法,国防工业出版社,1994.
[66] 吴炎海,柱脚嵌固度对山形门式刚架结构分析的影响,福州大学学报,19(3),1991,87-94.
[67] 齐永胜,考虑柱脚约束楔形变截面门式刚架柱脚强度及平面内稳定承载力的研究,西安建筑科技大学硕士论文,2002.
[2] Foggel, C.M., and Ketter, R.L., Elastic Strength of Tapered Columns, Journal of the Structure Division, ASCE, Vol.88, No.ST5, Paper 3301, Oct., 1962.
[3] Charles, G..Culer and Stephen, M.Preg, Elastic Stability of Tapered Beam-Columns, Journal of the Structure Division, ASCE, Vol.94, No.ST2, Feb., 1968.
[4] Just, D.J., Just, Analysis of Plane Frame of Linearly Varying Rectangular Section, The Structural Engineer, Jan., 1975.
[5] Just, D.J., Just, Plane Frameworks of Tapering Box and I-section, Journal of the Structural Division, Vol.103, No.ST1.
[6] James, M. Gere, and Winfred, O. Cater, Critical Buckling Loads of Tapered Bars under Stepped Axial Loads, J. Struct. Eng., ASCE, Vol.112, No.6, June, 1986.
[7] Ermopulos, John C., Buckling of Tapered Bars under Stepped Axial Loads, J. Struct. Eng., ASCE, Vol.112, No.6, June, 1986.
[8] Davies, J. M., Inplane Stability in Portal Frame, The Structural Engineer, Vol.68, No.8/17, April, 1990.
[9] Balogh, J., Ivanyi Jr, M. and Varga, G., Analysi of Multi-interaction of Soil-Foundation-Steel Structure, J. Construct. Steel Res. , Vol.46, Nos.1-3, pp.117-118, paper number 323,1998.
[10] Silvestres, N., Mesquita, A., Camotim, D. and Silva, L., In-Plane Buckling Behavior of Pitched-Roof Steel Frames with Semi-Rigid Connections, Proceedings of the 1998 SSRC Annual Technical Session and Meeting(Theme Conference Workshop).
[11] Nogueiro, P., Silva, L., Silvestres, N. and Camotim, D., Proceedings of the 2000 SSRC Annual Technical Session and Meeting, pp. 104-116.
[12] Butler, D. J. and Anderson, G. B., the Elastic Buckling of Tapered Beam-column, Welding Research Supplement, 29-S, Jan., 1963.
[13] Hiroyaki Shiom and Maneaki Kurata, Strenth Formula for Tapered Beam-columns, Journal of Structural Engineering, Vol.110, No.7, July, 1984.
[14] J. M. Davies, P. Engel, T. T. C. Liu, and L. J. Morris, Realistic Modeling of Engineer, Vol.68, No.1/9, Jan., 1990.
[15] Melchers, R.E. and Maas, G., Column Base Restraint Effect for a Steel Portal Frame, the
Strutural Engineer, Vol.72, No. 4, 15 Feb.,1994.
[16] 刘安清,直线楔形杆件框架稳定性计算,建筑结构学报,1983, 4(2).
[17] 梁启智、曾令付,山形门式刚架的梁柱计算长度,土木工程学报,1987,20(1).
[18] 赵毅强,楔形杆件结构的弹性稳定分析,建筑结构学报,1990,11(6),58-68.
[19] 张振涛,薄壁变截面结构内力与构件稳定分析的有限元法,西安建筑科技大学硕士论文,1992.
[20] 顾强、周敏辉,楔形变截面门式刚架的设计(二),西安建筑科技大学学报, 1998,30(3),209-212.
[21] 陈绍蕃,门式钢框架轻型化的技术措施,建筑结构,1998,28(2),30-33.
[22] 陈绍蕃,轻型钢结构变截面门式刚架的稳定计算,建筑结构,1998,28(8),10-14.
[23] 王文明、郭彦林、赵熙元,变截面门式刚架结构的有限元分析,建筑结构,1999,29(10),57-60.
[24] 李峰,楔形变截面单跨门式刚架柱计算长度,西安建筑科技大学硕士论文,1999.
[25] 饶芝英、童根树,变截面门式刚架平面内弹性稳定计算,建筑结构,2000,30(4),8-11.
[26] 郭彦林、王文明、石永久,变截面门式刚架结构的非线性性能,工程力学,2000,17(4),29-36.
[27] 李峰、顾强,楔形变截面单跨门式刚架柱计算长度分析,西安建筑科技大学学报,2000,32(3),256-259.
[28] 卢林枫、顾强、解琦,门式刚架屋面坡度对二阶效应的影响及二阶弯矩计算公式,建筑结构,2001,32(2),26-56.
[29] 李国强、李进军,楔形压杆的非弹性稳定研究,土木工程学报,2001,34(6),34-37.
[30] 杨娜、沈世钊, 变截面门式刚架结构的几何非线性性能研究,哈尔滨建筑大学学报,2001,34(3),10-15.
[31] 申红侠、顾强,楔形变截面压弯构件平面内极限承载力,西安建筑科技大学学报,2002,34(4),400-406.
[32] 童骏、陈以一、伍益莹,柱脚弹性约束对门式刚架侧移和内力的影响,结构工程师,2003(2),25-35.
[33] 中国工程建设标准化协会,门式刚架轻型房屋钢结构技术规程(CECS102:2002),中国计划出版社,2003.
[34] Picard, A. and Beaulieu, D., Behaviour of a Simple Column Base Connection, Can. J. Civ. Eng., Vol.12, 1985, pp.126-136.
[35] Picard, A. and Beaulieu, D., Rotational Restraint of a Simple Column Base Connection, Can. J. Civ. Eng., Vol.14, 1987, pp.49-57.
[36] Hon, K.K. and Melchers, R.E., Experimental Behaviour of Steel Column Bases, J. Construct.
Steel Research, Vol.9, 1988, pp.35-50.
[37] 金涛,钢柱脚的抗滑移及转动约束作用,西安建筑科技大学硕士论文,1993.
[38] 戴贤阳,厂房钢结构露出型柱脚性能研究,西安建筑科技大学硕士论文,1990.
[39] 陈军,钢柱脚的转动约束,西安建筑科技大学硕士论文,1989.
[40] Thambiratnam,David P. and Paramasivam, P., Base Plates Under Axial Loads and Moments, Journal of Structural Engineering, Vol.112, No.5, May, 1986, pp.1166-1167.
[41] Penserini, Paul and Colson, Andre, Ultimate Limit Strength of Column-Base Connections, J. Construct. Steel Research, Vol.14, 1989, pp.301-320.
[42] Targowski, R., Lamblin, D. and Guerlement, G., Baseplate Column Connection Under Bending:Experimental and Numerical Study, J. Construct. Steel Research, Vol.27, 1993, pp.37-54.
[43] Ermopoulos, J. Ch. and Stamatopoulos, G. N., Analytical Modeling of Column-Base Plates Under Cyclic Loading, J. Construct. Steel Research, Vol.40, No.3,1996, pp.225-238.
[44] Stamatopoulos, G. N. and Ermopoulos, J. Ch., Interaction Curves for Column Base-Plate Connections, J. Construct. Steel Research, Vol.44, Nos.1-2,1997, pp.69-89.
[45] 于安麟、永毓栋、郭在田、戴贤阳,露出型钢柱脚抗剪性能的研究(I),工业建筑,22(3),1992,24-26.
[46] 于安麟、永毓栋、郭在田、戴贤阳,露出型钢柱脚抗剪性能的研究(II),工业建筑,22(5),1992,29-33.
[47] Hon, K.K. and Melchers, R.E., Mpment-Rotation Curves for ‘Pinned’ Column Bases, The Structural Engineer, 65B(3),1987, pp.54-58.
[48] Melchers, R. E., Column-Base Response Under Applied Moment, J. Construct. Steel Research, Vol.23, 1992, pp.127-143.
[49] Ermopoulos, John Ch. and Stamatopoulos, George N., Mathematical Modeling of Column Base Plate Connections, J. Construct. Steel Research, Vol.36, No.2,1996, pp.79-100.
[50] 九谷和秀、增田贯志,鉄骨柱脚の力学性状に関する実験的研究,日本建筑学会大会学术讲演梗概集(东北),1982,1815-1816.
[51] 增田贯志、九谷和秀、藤冈丰三雄,柱脚部の变形を考慮した鉄骨ラメンの实用计算法,日本建筑学会大会学术讲演梗概集(东北),1982,1817-1818.
[52] Chajes, A. and Churchill, J.E., Nonlinear frame analysis by finite element methods, Journal of Structural Engineering, ASCE, Vol. 113, No. 6, 1987, 1221-1235.
[53] 陈骥,钢结构稳定理论与设计,科学出版社,2001,pp.125.
[54] 陈绍蕃,钢结构设计原理(第二版),科学出版社,2000.
[55] 程睿,半刚性连接钢框架的有限元分析及近似计算方法,重庆大学硕士论文,2002,
pp.19-27.
[56] Chen, W. F. and Atsuta, T.,周绥平等译,梁柱分析与设计(第一卷),人民交通出版社,1997.
[57] 李国强、沈祖炎,钢结构框架体系弹性及弹塑性分析与计算理论,上海科学技术出版社,1998.
[58] 吕烈武、沈世钊、沈祖炎、胡学仁,钢结构构件稳定理论,中国建筑工业出版社,1983.
[59] 《冷弯薄壁型钢结构设计手册》编著组,冷弯薄壁型钢结构设计手册,中国建筑工业出版社,1996.
[60] 陈绍蕃,钢结构稳定设计指南,中国建筑工业出版社,1996.
[61] 朱伯芳,有限单元法原理与应用(第二版),中国水利水电出版社,1998.
[62] 王勖成、邵敏,有限单元法基本原理和数值方法(第二版),清华大学出版社,1997.
[63] 苏金明、阮沈勇,Matlab 6.1实用指南(上册),电子工业出版社,2002.
[64] 赵更新,杆系结构分析程序设计,电子科技大学出版社,1997.
[65] 何君毅、林祥都,工程结构非线性问题的数值解法,国防工业出版社,1994.
[66] 吴炎海,柱脚嵌固度对山形门式刚架结构分析的影响,福州大学学报,19(3),1991,87-94.
[67] 齐永胜,考虑柱脚约束楔形变截面门式刚架柱脚强度及平面内稳定承载力的研究,西安建筑科技大学硕士论文,2002.