带腹板开洞钢梁塑性承载力的计算
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摘要
本文解决的是带腹板开洞钢梁的破坏行为和塑性承载力问题。
首先，本文对带腹板开洞钢梁的塑性承载力的计算方法进行了阐述和推导，用一种巧妙的、扩展性很好的方法构造出承载力计算关键的一步——次弯矩函数，并且用该方法对带腹板开洞钢梁进行了计算，得出了其内力之间的相关曲线，这些计算结果能直观地反映出该类梁的一些受力特性，同时还可直接用于该类梁的设计和强度验算。
其次，用类似的方法，对洞口处有加劲肋的钢梁的承载力进行了推导和计算，其计算结果与无加劲肋时的情况对比，可以确定加劲肋对承载力的提高情况，同时也可以用于该类梁的设计和强度验算。
最后，采用数值分析方法，利用有限元分析软件ANSYS进行仿真计算，并将计算结果与理论计算结果对比，可以验证理论计算的正确性和适用性。同时，对影响带腹板开洞钢梁塑性承载力的几种因素进行了分析计算，这些因素包括：洞口的宽度、洞口的高度、洞口的面积、洞口的偏心距、洞口沿跨度的设置位置、钢梁的跨度以及加劲肋的布置形式。经分析知，这些参数对钢梁承载力的影响均是非线性的，且具有一定的变化规律。
The failure-behavior and the plastic capacity of steel beams with web openings are dealt with in this thesis.
Firstly, a calculation method of plastic capacity of steel beams with web openings is deduced and presented in this paper. With this ingenious and more expansible method, the secondary moment functions-the key stage for capacity calculation are formed. Steel beams with web openings are calculated with the method and some related curves of the internal forces are gained, too. According to the calculated results, some force-bearing characteristics of the beams are reflected. In the meanwhile, it can be used directly for design and strength checking of the beams.
Secondly, plastic capacity of steel beams with reinforced web openings is deduced and calculated with the similar method. Compared with the former results, that to what degree stiffening ribs improve the ultimate strength of the beams can be convinced. The calculated results can also be used directly for design and strength checking of the beams.
At last, with numerical simulations, the plastic capacity of steel beams with web openings are calculated by FEA software ANSYS. Compared the numerical results with the theoretical calculation results, the validity and applicability of the theoretical calculation can be verified. At the same time , some factors influencing the plastic capacity of steel beams with web openings are calculated and analyzed, including the breadth of openings, the height of openings, the area of openings, the eccentric distance of openings, the distance from openings to support, span of steel beams, stiffening ribs and so on. According to analysis, these parameters' effect on beams' plastic capacity is non-linear , which is in the state of being regular.
首先，本文对带腹板开洞钢梁的塑性承载力的计算方法进行了阐述和推导，用一种巧妙的、扩展性很好的方法构造出承载力计算关键的一步——次弯矩函数，并且用该方法对带腹板开洞钢梁进行了计算，得出了其内力之间的相关曲线，这些计算结果能直观地反映出该类梁的一些受力特性，同时还可直接用于该类梁的设计和强度验算。
其次，用类似的方法，对洞口处有加劲肋的钢梁的承载力进行了推导和计算，其计算结果与无加劲肋时的情况对比，可以确定加劲肋对承载力的提高情况，同时也可以用于该类梁的设计和强度验算。
最后，采用数值分析方法，利用有限元分析软件ANSYS进行仿真计算，并将计算结果与理论计算结果对比，可以验证理论计算的正确性和适用性。同时，对影响带腹板开洞钢梁塑性承载力的几种因素进行了分析计算，这些因素包括：洞口的宽度、洞口的高度、洞口的面积、洞口的偏心距、洞口沿跨度的设置位置、钢梁的跨度以及加劲肋的布置形式。经分析知，这些参数对钢梁承载力的影响均是非线性的，且具有一定的变化规律。
The failure-behavior and the plastic capacity of steel beams with web openings are dealt with in this thesis.
Firstly, a calculation method of plastic capacity of steel beams with web openings is deduced and presented in this paper. With this ingenious and more expansible method, the secondary moment functions-the key stage for capacity calculation are formed. Steel beams with web openings are calculated with the method and some related curves of the internal forces are gained, too. According to the calculated results, some force-bearing characteristics of the beams are reflected. In the meanwhile, it can be used directly for design and strength checking of the beams.
Secondly, plastic capacity of steel beams with reinforced web openings is deduced and calculated with the similar method. Compared with the former results, that to what degree stiffening ribs improve the ultimate strength of the beams can be convinced. The calculated results can also be used directly for design and strength checking of the beams.
At last, with numerical simulations, the plastic capacity of steel beams with web openings are calculated by FEA software ANSYS. Compared the numerical results with the theoretical calculation results, the validity and applicability of the theoretical calculation can be verified. At the same time , some factors influencing the plastic capacity of steel beams with web openings are calculated and analyzed, including the breadth of openings, the height of openings, the area of openings, the eccentric distance of openings, the distance from openings to support, span of steel beams, stiffening ribs and so on. According to analysis, these parameters' effect on beams' plastic capacity is non-linear , which is in the state of being regular.
引文
[1] Donghua Zhou. "Beitrag zur Rechenmodelle von Verbundtraegern mit Stegoeffnungen" Stahlbau 09/2003
[2] 周东华等．带腹板开洞组合梁的非线性计算．四川建筑科学研究，2004，(2)：21-24
[3] 白永生，蒋永生等．腹板开洞的钢与混凝土组合梁承载力计算方法综述和探讨．工业建筑，2004，(6)：68-70
[4] 王命平，李彬等．钢筋混凝土开洞短梁的受剪试验研究．建筑结构学报，2004，(6)：80-84
[5] Richard G. Redwood and John O. McCutcheon. Beam Tests with Unreinforced Web Openings[J]. Journal of Structural Division, ASCE, 1968, Vol. 94, No. STI: 1-17
[6] Richard G. Redwood. Plastic Behavior and Design of Beams with Web Openings[C]. Proceedings, First Canadian Structural Engineering Conference, Tronto, Canadian Steel Industries Construction Council, Toronto, Canada, 1968, 2: 127-138
[7] Judith G. Congdon and Richard G. Redwood. Plastic Behavior of Beams with Reinforced Holes. Journal of Structural Division, ASCE, 1970, Vol. 96, No. ST9: 1933-1955
[8] Peter B. Cooper and Robert R. Snell. Tests on Beams with Reinforced Web Openings. Journal of Structural Division, ASCE, 1972, Vol. 98, No. ST3: 611-632
[9] Tsong-Miin Wang. Strength of Beams with Eccentric Reinforced Holes. Journal of Structural Division, ASCE, 1975, Vol. 101, No. ST9: 1783-1800
[10] Roger Lupien and Richard G. Redwood. Steel Beams with Web Openings Reinforced on One Side. Canadian Journal of Civil Engineering, 1978, Vol.5, No.4: 451-461
[11] Ahmed Afifi Aglan and Samih Qaqish. Plastic Behavior of Beams with Mid-Depth Web Openings. Engineering Journal, AISC, 1982, Vol. 19, No. 1: 20-26
[12] 孙炳楠，洪滔等．工程弹塑性力学．杭州：浙江大学出版社，1998
[13] 陈惠发[美]．土木工程材料的本构方程(第二卷塑性与建模)．武汉：华中科技大学出版社，2001
[14] Bower, J. E. Elastic Stresses Around Holes in Wide-Flange Beams. Journal of Structural Division, ASCE, 1966, Vol. 92, No. ST2: 85-101
[15] Segner, E. P. Reinforced Requirements for Girder Web Openings. Journal of Structural Division, ASCE, 1964, Vol. 90, No. ST3: 147-164
[16] Bower, J. E. Experimental Stresses in Wide-Flange Beams with Holes. Journal of Structural Division, ASCE, 1966, Vol. 92, No. ST5: 167-186
[17] John E. Bower Ultimate Strength of Beams with Rectangular Holes. Journal of Structural Division, ASCE, 1968, Vol. 94, No. ST6: 1315-1337
[18] R. G. Redwood. Simplified Plastic Analysis for Reinforced Web Holes. Engineering Journal, AISC, 1971, Vol. 3, No. 3: 128-131
[19] Michael M. McCormick. Suggested Design Guides for Beams with Web Holes. Journal of Structural Division, ASCE, 1972, Vol. 98, No. ST12: 2814-2816
[20] Richard L. Kussman and Peter B. Cooper. Design Example for Beams with Web Openings. Engineering Journal, AISC, 1976, Vol. 13, No. 2: 48-56
[21] Harry D. Knostman, Peter B. Cooper and Robert R. Snell. Shear Force Distribution at Eccentric Web Openings. Journal of Structural Division, ASCE, 1977, Vol. 103 No. STG: 1207-1221
[22] Richard G. Redwood and Minoru Uenoya. Critical Loads for Webs with Holes. Journal of Structural Division, ASCE, 1979, Vol. 105, No. STIO: 2053-2076
[23] Brian K. Dougherty Elastic Deformation of Beams with Web Openings. Journal of Structural Division, ASCE, 1980, Vol.106, No. ST1: 301-312
[24] William C. Clawson and David Darwin. Tests of Composite Beams with Web Openings. Journal of Structural Division, ASCE, 1982, Vol. 108, No. ST1: 145-162
[25] William C. Clawson and David Darwin. Strength of Composite Beams at Web Openings. Journal of Structural Division, ASCE, 1982, Vol. 108, No. ST3: 623-64
[26] Redwood, R. G. and G. Poumbours. Analysis of Composite Beams with Web Openings. Journal of Structural Division, ASCE, 1984, Vol. 110, No. ST9
[27] Lawson, R. M. Design for Slabs and Beams with Steel decking. SCI/CIRIA publication, SCI-P-068, 1987
[28] Donahey, B. C. and Darwin, D. Web Openings in Composite Beams with Ribbed Slabs. Journal of Structural Division, ASCE, 1988, Vol. 114, No. ST3
[29] R. M. Lawson, K. F. Chung and A. M. Price. Tests on Composite Beams with Large Web Openings to Justify Existing Design Methods. The Structural Engineer, 1992, Vol. 70, No. 1/7
[30] E. H. Fahmy. Analysis of Composite Beams with Rectangular Web Openings. J. Construct. Steel Res., 1996, Vol. 37, No.1: 47-62
[31] 王勖成等．有限单元法基础原理和数值方法(第二版)．清华大学出版社，1996
[32] 任辉启．ANSYS 7.0工程分析实例详解．北京：人民邮电出版社，2003
[33] 任重．ANSYS实用分析教程．北京：北京大学出版社 2003
[34] 谭建国．使用ANSYS 6.0进行有限元分析．北京：北京大学出版社，2002
[35] 东方人华．ANSYS7.0入门与提高．北京：清华大学出版社，2004
[36] E. Hinton. NAFEMAS Introduction to Nonlinear Finite Element Analysis. British: Bell Ltd, 1992
[37] 徐秉业，刘信声．应用弹塑性力学．北京：清华大学出版社，1999
[38] 刘北辰．工程计算力学——理论与应用．机械工业出版社，1994
[39] [美]陈惠发等．Elasticity and Plasticity．北京：中国建筑工业出版社，2005
[40] 刘达，周东华等．钢与混凝土组合结构设计原理．北京：科学出版社，2005
[41] 钢结构设计规范，GB50017—2003
[42] 陈绍蕃．钢结构设计原理．北京：科学出版社，1987
[43] 沈祖炎等．钢结构基本原理．北京：中国建筑工业出版社，2000
[44] 胡海昌．弹性力学的变分原理及其应用．北京：科学出版社，1981
[45] 张洪明．Visual Basic 6.0程序设计基础教程．北京：科学出版社，2003
[2] 周东华等．带腹板开洞组合梁的非线性计算．四川建筑科学研究，2004，(2)：21-24
[3] 白永生，蒋永生等．腹板开洞的钢与混凝土组合梁承载力计算方法综述和探讨．工业建筑，2004，(6)：68-70
[4] 王命平，李彬等．钢筋混凝土开洞短梁的受剪试验研究．建筑结构学报，2004，(6)：80-84
[5] Richard G. Redwood and John O. McCutcheon. Beam Tests with Unreinforced Web Openings[J]. Journal of Structural Division, ASCE, 1968, Vol. 94, No. STI: 1-17
[6] Richard G. Redwood. Plastic Behavior and Design of Beams with Web Openings[C]. Proceedings, First Canadian Structural Engineering Conference, Tronto, Canadian Steel Industries Construction Council, Toronto, Canada, 1968, 2: 127-138
[7] Judith G. Congdon and Richard G. Redwood. Plastic Behavior of Beams with Reinforced Holes. Journal of Structural Division, ASCE, 1970, Vol. 96, No. ST9: 1933-1955
[8] Peter B. Cooper and Robert R. Snell. Tests on Beams with Reinforced Web Openings. Journal of Structural Division, ASCE, 1972, Vol. 98, No. ST3: 611-632
[9] Tsong-Miin Wang. Strength of Beams with Eccentric Reinforced Holes. Journal of Structural Division, ASCE, 1975, Vol. 101, No. ST9: 1783-1800
[10] Roger Lupien and Richard G. Redwood. Steel Beams with Web Openings Reinforced on One Side. Canadian Journal of Civil Engineering, 1978, Vol.5, No.4: 451-461
[11] Ahmed Afifi Aglan and Samih Qaqish. Plastic Behavior of Beams with Mid-Depth Web Openings. Engineering Journal, AISC, 1982, Vol. 19, No. 1: 20-26
[12] 孙炳楠，洪滔等．工程弹塑性力学．杭州：浙江大学出版社，1998
[13] 陈惠发[美]．土木工程材料的本构方程(第二卷塑性与建模)．武汉：华中科技大学出版社，2001
[14] Bower, J. E. Elastic Stresses Around Holes in Wide-Flange Beams. Journal of Structural Division, ASCE, 1966, Vol. 92, No. ST2: 85-101
[15] Segner, E. P. Reinforced Requirements for Girder Web Openings. Journal of Structural Division, ASCE, 1964, Vol. 90, No. ST3: 147-164
[16] Bower, J. E. Experimental Stresses in Wide-Flange Beams with Holes. Journal of Structural Division, ASCE, 1966, Vol. 92, No. ST5: 167-186
[17] John E. Bower Ultimate Strength of Beams with Rectangular Holes. Journal of Structural Division, ASCE, 1968, Vol. 94, No. ST6: 1315-1337
[18] R. G. Redwood. Simplified Plastic Analysis for Reinforced Web Holes. Engineering Journal, AISC, 1971, Vol. 3, No. 3: 128-131
[19] Michael M. McCormick. Suggested Design Guides for Beams with Web Holes. Journal of Structural Division, ASCE, 1972, Vol. 98, No. ST12: 2814-2816
[20] Richard L. Kussman and Peter B. Cooper. Design Example for Beams with Web Openings. Engineering Journal, AISC, 1976, Vol. 13, No. 2: 48-56
[21] Harry D. Knostman, Peter B. Cooper and Robert R. Snell. Shear Force Distribution at Eccentric Web Openings. Journal of Structural Division, ASCE, 1977, Vol. 103 No. STG: 1207-1221
[22] Richard G. Redwood and Minoru Uenoya. Critical Loads for Webs with Holes. Journal of Structural Division, ASCE, 1979, Vol. 105, No. STIO: 2053-2076
[23] Brian K. Dougherty Elastic Deformation of Beams with Web Openings. Journal of Structural Division, ASCE, 1980, Vol.106, No. ST1: 301-312
[24] William C. Clawson and David Darwin. Tests of Composite Beams with Web Openings. Journal of Structural Division, ASCE, 1982, Vol. 108, No. ST1: 145-162
[25] William C. Clawson and David Darwin. Strength of Composite Beams at Web Openings. Journal of Structural Division, ASCE, 1982, Vol. 108, No. ST3: 623-64
[26] Redwood, R. G. and G. Poumbours. Analysis of Composite Beams with Web Openings. Journal of Structural Division, ASCE, 1984, Vol. 110, No. ST9
[27] Lawson, R. M. Design for Slabs and Beams with Steel decking. SCI/CIRIA publication, SCI-P-068, 1987
[28] Donahey, B. C. and Darwin, D. Web Openings in Composite Beams with Ribbed Slabs. Journal of Structural Division, ASCE, 1988, Vol. 114, No. ST3
[29] R. M. Lawson, K. F. Chung and A. M. Price. Tests on Composite Beams with Large Web Openings to Justify Existing Design Methods. The Structural Engineer, 1992, Vol. 70, No. 1/7
[30] E. H. Fahmy. Analysis of Composite Beams with Rectangular Web Openings. J. Construct. Steel Res., 1996, Vol. 37, No.1: 47-62
[31] 王勖成等．有限单元法基础原理和数值方法(第二版)．清华大学出版社，1996
[32] 任辉启．ANSYS 7.0工程分析实例详解．北京：人民邮电出版社，2003
[33] 任重．ANSYS实用分析教程．北京：北京大学出版社 2003
[34] 谭建国．使用ANSYS 6.0进行有限元分析．北京：北京大学出版社，2002
[35] 东方人华．ANSYS7.0入门与提高．北京：清华大学出版社，2004
[36] E. Hinton. NAFEMAS Introduction to Nonlinear Finite Element Analysis. British: Bell Ltd, 1992
[37] 徐秉业，刘信声．应用弹塑性力学．北京：清华大学出版社，1999
[38] 刘北辰．工程计算力学——理论与应用．机械工业出版社，1994
[39] [美]陈惠发等．Elasticity and Plasticity．北京：中国建筑工业出版社，2005
[40] 刘达，周东华等．钢与混凝土组合结构设计原理．北京：科学出版社，2005
[41] 钢结构设计规范，GB50017—2003
[42] 陈绍蕃．钢结构设计原理．北京：科学出版社，1987
[43] 沈祖炎等．钢结构基本原理．北京：中国建筑工业出版社，2000
[44] 胡海昌．弹性力学的变分原理及其应用．北京：科学出版社，1981
[45] 张洪明．Visual Basic 6.0程序设计基础教程．北京：科学出版社，2003
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