轴压作用下钢管混凝土矩形柱的组合刚度研究
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摘要
钢管对核心混凝土的紧箍作用是钢管混凝土结构技术的关键力学问题之一,这一界面力学问题的准确描述是解决问题的关键,矩形截面的钢管混凝土结构尤其如此。本文基于连续介质力学方法,建立钢管混凝土小变形下的弹性分析理论,重点对矩形钢管混凝土柱的弹性本构关系、组合弹性模量、组合轴压刚度以及界面力学问题进行深入的理论研究、数值模拟。
主要工作和结论如下：
1、基于连续介质力学理论,结合弹性力学平面问题相关理论和结构力学位移求解方法,建立了钢管混凝土柱小变形条件下的界面力学问题的弹性分析理论,并借助matlab工具实现矩形钢管混凝土柱的弹性本构关系、组合弹性模量、组合轴压刚度以及界面力学问题数值求解。
2、获得了钢管混凝土组合柱的界面法向力(紧箍力)的分布函数表达式f1(x)和f2(y)。运用函数的图像能方便地描述界面紧箍力的分布规律。图像表明：方形截面和矩形截面的钢管混凝土界面法向力的分布很不均匀(呈类似二次曲线的形状),矩形截面比方形截面的紧箍力的分布更加的不均匀。在角点处都有应力集中的现象,角点的紧箍力最大,在中点处的紧箍力最小,方形截面的钢管混凝土紧箍作用比矩形截面的钢管混凝土要大。
3、研究了组合弹性模量的变化规律。随着含钢率的增大而明显增大；随着混凝土的强度等级的增高仅略有增大。研究也表明在相同的含钢率ρ下,截面的边长比在a／b≤2.4范围内,矩形钢管混凝土组合弹性模量比方形钢管混凝土组合弹性模量略小,差值在5%左右,故此范围矩形截面可以近似的等效为正方形的截面处理。此结论与文献[12]一致。
4、研究表明：钢管混凝土的组合弹性模量、组合轴压刚度要比目前采用的没有考虑紧箍作用的换算弹性模量、换算轴压刚度要高,在计算范围内,组合弹性模量比换算弹性模量提高约1.36%-15.3%,组合轴压刚度要比换算刚度提高约1.58%-20.1%。且随含钢率的增大而显著增大,随混凝土强度的提高而变化不大。
One of the key of mechanical problems of concrete-filled steel tube(CFT) structure is the confining effect between the steel tube and the core concrete. The key to solve the problem is to accurately describe the interfacial mechanics problems,especially to the rectangular section of CFT. The paper based on continuum mechanics theory, made a small-deformation elasticity theory analysis on rectangular concrete-filled steel tube column(CFTC). Focus on the elastic constitutive relation, compounding elastic modulus、compounding axis direction compressive stiffness and interfacial mechanics problems to rectangular CFTC of theoretical study deeply and numerical simulation.
The main conclusions of the paper as follows:
(1) Based on continuum mechanics theory and the method of elasticity theory and structural mechanics-related displacement solution.Be full advantage of this effective mathematical tool-MATLAB, it can obtain the compounding elastic constitutive relation、compounding elastic modulus、compounding axis direction compressive stiffness and the numerical solution of interfacial mechanics problems to the CFTC.
(2) It can obtain the distribution function expression f1(x) and f2(y) of the CFTC of the interfacial normal force. The images can conveniently describe the distribution of the confining force .The images show that the distribution of the rectangular section and square section CFTC of the interfacial normal force is uneven(it shows a shape of conic similarly), the distribution of rectangular section is more uneven than the square section.There is a phenomenon of stress concentration in the corner office.The confining force is maximum in the corner and least in the midpoint.The confining effect of square section CFTC is more than the rectangular section's.
(3) The paper study the variation of compounding elastic modulus, which increased obviously with the increase of steel ratio, increased slightly with the increase of strength grade of concrete.The study also shows that the compounding elastic modulus of rectangular section CFTC is slightly smaller than the square section's in the same steel ratioρwhen when a/b≤2.4,and the difference at 5%. This conclusion is consistent with the literature[12].
(4) The results show that the compounding elastic modulus and the ompounding axis direction compressive stiffnes of CFTC is higher than the conversion elastic modulus and the conversion axial stiffness without considering the confining effect,the compounding elastic modulus is higher than the conversion elastic modulus 1.36%-15.3% and the ompounding axis direction compressive stiffnes is higher than the conversion axial stiffness 1.55%-20.1% in the range of calculating.
主要工作和结论如下：
1、基于连续介质力学理论,结合弹性力学平面问题相关理论和结构力学位移求解方法,建立了钢管混凝土柱小变形条件下的界面力学问题的弹性分析理论,并借助matlab工具实现矩形钢管混凝土柱的弹性本构关系、组合弹性模量、组合轴压刚度以及界面力学问题数值求解。
2、获得了钢管混凝土组合柱的界面法向力(紧箍力)的分布函数表达式f1(x)和f2(y)。运用函数的图像能方便地描述界面紧箍力的分布规律。图像表明：方形截面和矩形截面的钢管混凝土界面法向力的分布很不均匀(呈类似二次曲线的形状),矩形截面比方形截面的紧箍力的分布更加的不均匀。在角点处都有应力集中的现象,角点的紧箍力最大,在中点处的紧箍力最小,方形截面的钢管混凝土紧箍作用比矩形截面的钢管混凝土要大。
3、研究了组合弹性模量的变化规律。随着含钢率的增大而明显增大；随着混凝土的强度等级的增高仅略有增大。研究也表明在相同的含钢率ρ下,截面的边长比在a／b≤2.4范围内,矩形钢管混凝土组合弹性模量比方形钢管混凝土组合弹性模量略小,差值在5%左右,故此范围矩形截面可以近似的等效为正方形的截面处理。此结论与文献[12]一致。
4、研究表明：钢管混凝土的组合弹性模量、组合轴压刚度要比目前采用的没有考虑紧箍作用的换算弹性模量、换算轴压刚度要高,在计算范围内,组合弹性模量比换算弹性模量提高约1.36%-15.3%,组合轴压刚度要比换算刚度提高约1.58%-20.1%。且随含钢率的增大而显著增大,随混凝土强度的提高而变化不大。
One of the key of mechanical problems of concrete-filled steel tube(CFT) structure is the confining effect between the steel tube and the core concrete. The key to solve the problem is to accurately describe the interfacial mechanics problems,especially to the rectangular section of CFT. The paper based on continuum mechanics theory, made a small-deformation elasticity theory analysis on rectangular concrete-filled steel tube column(CFTC). Focus on the elastic constitutive relation, compounding elastic modulus、compounding axis direction compressive stiffness and interfacial mechanics problems to rectangular CFTC of theoretical study deeply and numerical simulation.
The main conclusions of the paper as follows:
(1) Based on continuum mechanics theory and the method of elasticity theory and structural mechanics-related displacement solution.Be full advantage of this effective mathematical tool-MATLAB, it can obtain the compounding elastic constitutive relation、compounding elastic modulus、compounding axis direction compressive stiffness and the numerical solution of interfacial mechanics problems to the CFTC.
(2) It can obtain the distribution function expression f1(x) and f2(y) of the CFTC of the interfacial normal force. The images can conveniently describe the distribution of the confining force .The images show that the distribution of the rectangular section and square section CFTC of the interfacial normal force is uneven(it shows a shape of conic similarly), the distribution of rectangular section is more uneven than the square section.There is a phenomenon of stress concentration in the corner office.The confining force is maximum in the corner and least in the midpoint.The confining effect of square section CFTC is more than the rectangular section's.
(3) The paper study the variation of compounding elastic modulus, which increased obviously with the increase of steel ratio, increased slightly with the increase of strength grade of concrete.The study also shows that the compounding elastic modulus of rectangular section CFTC is slightly smaller than the square section's in the same steel ratioρwhen when a/b≤2.4,and the difference at 5%. This conclusion is consistent with the literature[12].
(4) The results show that the compounding elastic modulus and the ompounding axis direction compressive stiffnes of CFTC is higher than the conversion elastic modulus and the conversion axial stiffness without considering the confining effect,the compounding elastic modulus is higher than the conversion elastic modulus 1.36%-15.3% and the ompounding axis direction compressive stiffnes is higher than the conversion axial stiffness 1.55%-20.1% in the range of calculating.
引文
[1]姜维山,自国良.配复合箍、螺旋箍、x形筋钢筋砼短柱的抗震性能及抗震设计.建筑结构学报,1994.15(1)：2-16.
[2]Wang Q.X.,Zhao GFand Lin L.Y. Ductility of high strength reinforced concrete columns. Nuclear Engineering Design,1995.156 (2):75～81.
[3]Sen H.K.Triaxial stresses in short circular concrete filled tubular steel columns. international symposium, cames; Oct.4-6.1972.
[4]钟善桐.钢管混凝土中钢管与混凝土的共同工作.哈尔滨建筑大学学报,2001.34(1)：6-10.
[5]Candappa D. P. Setunge S. and Sanjayan J.G. Stress versus strain relationship of high strength concrete under high lateral confinement. Cement and Concrete Research,1999.29: 1977～1982.
[6]Xie J, Elwi A. E. and MacGregor J. G Mechanical properties of three high-strength concretes containing silica fume. ACI Material Journal,1995.92(2):135～145.
[7]韩林海,陶忠,刘威.钢管混凝士结构——理论与实践.福州大学学报(自然科学版),2001.29(6)：24-34.
[8]Chiaki Matsui, Jun'ichi Sakai, Toko Hitaka. SRC Standards and Test of CFT Frames CFT Structures in Japan,2001.
[9]郑永乾,韩林海.钢骨混凝土柱的耐火性能和抗火设计方法(Ⅱ).建筑钢结构进展,2006.8(3)：24～33.
[10]宋天诣,韩林海.组合结构耐火性能研究的部分新进展.工程力学,2008.25(2)：230～253.
[11]蔡益燕.对组合结构应用的几点思考.建筑钢结构进展,2002.4(3),32～35.
[12]钟善桐.钢管混凝土统一理论—研究与应用.北京：清华大学出版社,2006.20～60.
[13]贺锋,周绪红,唐昌辉.钢管高强混凝土轴压短柱承载力性能的试验研究.工程力学,2000.17(4)：61～66.
[14]Li Q. and Ansari F. Mechanics of damage and constitutive relationships for high strength concrete in triaxial compression. Journal of Engineering Mechanics, ASCE,1999.125(1): 1-10.
[15]Neoge P.K, Sen H.K and Chapman J.C. Concrete-filled tubular steel columns under eccentric loading/The Stuctural Engineer.1969,47(5):187-195.
[16]Knowles P.R. and Park R.Strength of concrete-filled steel tubular.Journal of the Structrual Division.1969,95(12):2565～2587.
[17]P.K.Gupta, S.M.Sarda, M.S.Kumar.Experimental and computational study on concrete filled steel tubular Columns under axial loads. Journal of Constructions Steel Research, 2005.61:1692～1712.
[18]Ehab Ellobody.Nonlinear behavior of concrete-filled stainless Steel stiffened slender tube columns.Thin-Walled Structure,2007.45:259～273.
[19]Hsuan-TehHua,Chiung-ShiannHuangb,Zhi-LiangChena.Finite element analysis of CFT columns subjected to anaxial compressive force and bending moment incombination. Journal of Constructions Steel Research,2005.61:1692～1712.
[20]European Committee for Standardization. Eurocode 4:Design of Composite Steel and Concrete Structures—Part 1.1:General rules and rules for buildings.1994.
[21]AISC (1999). Load and Resistance Factor Design Specification for Structural Steel Building.American Institute of Steel Construction.1999.
[22]Architectureal Institute of Japan(AIJ). Recommendations for Design and Concrete Filled Stell Tubular Structures.1997.
[23]蔡绍怀.现代钢管混凝土结构.北京：人民交通出版社,2003.12～46.
[24]蒋家奋,汤关柞.三向应力混凝土.北京：中国铁道出版社,1988.18～49.
[25]钟善桐.钢管混凝土结构.北京：清华人学出版社,2003.22～34.
[26]国家建筑材料工业局标准《钢管混凝土结构设计与施工规程》(JCJ 01-89).上海：同济大学出版社,1989.
[27]中国工程建设标准化协会标准《钢管混凝土结构设计与施工规程》，(CECS 28:90).北京：中国计划出版社,1990.
[28]中华人民共和国电力行业标准《钢-混凝土组合结构设计规程》(DL/T5085-1999).北京：中国电力出版社,1999.
[29]Zhong Shan tong, Zhang Sumei. Application and development of concrete-filled steel tubes in high rise buildings .Advances in Structural Engineering,1999.2(2):149～159.
[30]钟善桐.钢管混凝土的刚度分析.哈尔滨建筑大学学报,1999.32(3)：13～18.
[31]Zhong Shantong. The comparison of the composite rigidities with the conversion rigidities for CFST members [C]. Proc. of 6th ASCCS Conference, Los Angeles,2000.
[32]康希良,赵鸿铁,薛建阳,陈宗平.钢管混凝土柱组合轴压刚度的理论分析.工程力学,2007,1(2)：101～105.
[33]Shams, M.and Saadeghvaziri,M.A.(1997), State of the art of concrete -filled steel tubular columns, ACI Structural,1997.94(1):558～571.
[34]蔡绍怀.钢管混凝土结构的计算与应用.北京中国建筑工业出版社,1989.28～46.
[35]韩林海.钢管混凝土结构—理论与实践.北京：科学出版社,2004.17～32.
[36]韩林海,杨有福.矩形钢管混凝土轴心受压构件强度承载力的实验研究.土木工程学报,2001.34(4)：22～32.
[37]钟善桐.圆,八边,正方,与矩形钢管混凝土轴压性能的连续性.建筑钢结构进展,2004.6(4)14～22.
[38]陶忠,王志滨,韩林海.矩形冷弯型钢钢管混凝土柱的力学性能研究.工程力学,2006.23(3)：147～155.
[39]矩形钢管混凝土结构技术规程《CECS159:2004》.上海.同济大学出版社,2006.
[40]lmran 1. and Pantazopoulou S. J. Experimental study of concrete under triaxial stress. ACI Material Journal,1996.93(6):589～601.
[41]马欣伯,张素梅.各国规程关于圆钢管混凝土构件刚度计算方法的介绍和比较.工业建筑,2004.34(2)：75～78.
[42]吴家龙.弹性力学(Elasticity).北京：高等教育出版社,2001.38～45.
[2]Wang Q.X.,Zhao GFand Lin L.Y. Ductility of high strength reinforced concrete columns. Nuclear Engineering Design,1995.156 (2):75～81.
[3]Sen H.K.Triaxial stresses in short circular concrete filled tubular steel columns. international symposium, cames; Oct.4-6.1972.
[4]钟善桐.钢管混凝土中钢管与混凝土的共同工作.哈尔滨建筑大学学报,2001.34(1)：6-10.
[5]Candappa D. P. Setunge S. and Sanjayan J.G. Stress versus strain relationship of high strength concrete under high lateral confinement. Cement and Concrete Research,1999.29: 1977～1982.
[6]Xie J, Elwi A. E. and MacGregor J. G Mechanical properties of three high-strength concretes containing silica fume. ACI Material Journal,1995.92(2):135～145.
[7]韩林海,陶忠,刘威.钢管混凝士结构——理论与实践.福州大学学报(自然科学版),2001.29(6)：24-34.
[8]Chiaki Matsui, Jun'ichi Sakai, Toko Hitaka. SRC Standards and Test of CFT Frames CFT Structures in Japan,2001.
[9]郑永乾,韩林海.钢骨混凝土柱的耐火性能和抗火设计方法(Ⅱ).建筑钢结构进展,2006.8(3)：24～33.
[10]宋天诣,韩林海.组合结构耐火性能研究的部分新进展.工程力学,2008.25(2)：230～253.
[11]蔡益燕.对组合结构应用的几点思考.建筑钢结构进展,2002.4(3),32～35.
[12]钟善桐.钢管混凝土统一理论—研究与应用.北京：清华大学出版社,2006.20～60.
[13]贺锋,周绪红,唐昌辉.钢管高强混凝土轴压短柱承载力性能的试验研究.工程力学,2000.17(4)：61～66.
[14]Li Q. and Ansari F. Mechanics of damage and constitutive relationships for high strength concrete in triaxial compression. Journal of Engineering Mechanics, ASCE,1999.125(1): 1-10.
[15]Neoge P.K, Sen H.K and Chapman J.C. Concrete-filled tubular steel columns under eccentric loading/The Stuctural Engineer.1969,47(5):187-195.
[16]Knowles P.R. and Park R.Strength of concrete-filled steel tubular.Journal of the Structrual Division.1969,95(12):2565～2587.
[17]P.K.Gupta, S.M.Sarda, M.S.Kumar.Experimental and computational study on concrete filled steel tubular Columns under axial loads. Journal of Constructions Steel Research, 2005.61:1692～1712.
[18]Ehab Ellobody.Nonlinear behavior of concrete-filled stainless Steel stiffened slender tube columns.Thin-Walled Structure,2007.45:259～273.
[19]Hsuan-TehHua,Chiung-ShiannHuangb,Zhi-LiangChena.Finite element analysis of CFT columns subjected to anaxial compressive force and bending moment incombination. Journal of Constructions Steel Research,2005.61:1692～1712.
[20]European Committee for Standardization. Eurocode 4:Design of Composite Steel and Concrete Structures—Part 1.1:General rules and rules for buildings.1994.
[21]AISC (1999). Load and Resistance Factor Design Specification for Structural Steel Building.American Institute of Steel Construction.1999.
[22]Architectureal Institute of Japan(AIJ). Recommendations for Design and Concrete Filled Stell Tubular Structures.1997.
[23]蔡绍怀.现代钢管混凝土结构.北京：人民交通出版社,2003.12～46.
[24]蒋家奋,汤关柞.三向应力混凝土.北京：中国铁道出版社,1988.18～49.
[25]钟善桐.钢管混凝土结构.北京：清华人学出版社,2003.22～34.
[26]国家建筑材料工业局标准《钢管混凝土结构设计与施工规程》(JCJ 01-89).上海：同济大学出版社,1989.
[27]中国工程建设标准化协会标准《钢管混凝土结构设计与施工规程》，(CECS 28:90).北京：中国计划出版社,1990.
[28]中华人民共和国电力行业标准《钢-混凝土组合结构设计规程》(DL/T5085-1999).北京：中国电力出版社,1999.
[29]Zhong Shan tong, Zhang Sumei. Application and development of concrete-filled steel tubes in high rise buildings .Advances in Structural Engineering,1999.2(2):149～159.
[30]钟善桐.钢管混凝土的刚度分析.哈尔滨建筑大学学报,1999.32(3)：13～18.
[31]Zhong Shantong. The comparison of the composite rigidities with the conversion rigidities for CFST members [C]. Proc. of 6th ASCCS Conference, Los Angeles,2000.
[32]康希良,赵鸿铁,薛建阳,陈宗平.钢管混凝土柱组合轴压刚度的理论分析.工程力学,2007,1(2)：101～105.
[33]Shams, M.and Saadeghvaziri,M.A.(1997), State of the art of concrete -filled steel tubular columns, ACI Structural,1997.94(1):558～571.
[34]蔡绍怀.钢管混凝土结构的计算与应用.北京中国建筑工业出版社,1989.28～46.
[35]韩林海.钢管混凝土结构—理论与实践.北京：科学出版社,2004.17～32.
[36]韩林海,杨有福.矩形钢管混凝土轴心受压构件强度承载力的实验研究.土木工程学报,2001.34(4)：22～32.
[37]钟善桐.圆,八边,正方,与矩形钢管混凝土轴压性能的连续性.建筑钢结构进展,2004.6(4)14～22.
[38]陶忠,王志滨,韩林海.矩形冷弯型钢钢管混凝土柱的力学性能研究.工程力学,2006.23(3)：147～155.
[39]矩形钢管混凝土结构技术规程《CECS159:2004》.上海.同济大学出版社,2006.
[40]lmran 1. and Pantazopoulou S. J. Experimental study of concrete under triaxial stress. ACI Material Journal,1996.93(6):589～601.
[41]马欣伯,张素梅.各国规程关于圆钢管混凝土构件刚度计算方法的介绍和比较.工业建筑,2004.34(2)：75～78.
[42]吴家龙.弹性力学(Elasticity).北京：高等教育出版社,2001.38～45.