基于钢筋应变差的混凝土双向板极限状态分析方法
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摘要
为了合理确定混凝土双向板荷载-变形关系及极限状态,该文进行了一足尺混凝土双向板承载力试验研究,观察试验板裂缝开展及破坏模式,对荷载-变形关系、钢筋应变和板角约束力进行了测量。在此基础上,基于塑性铰线理论,考虑受拉薄膜效应,提出钢筋应变差概念、钢筋和混凝土应变破坏准则,结合板块内力平衡方程和弯矩平衡方程,建立混凝土双向板荷载-变形关系和极限荷载计算方法。同时,结合板壳有限元理论,编程计算混凝土板荷载-变形关系,分析薄膜效应机理及钢筋应变,并用于验证该文理论方法的合理性。最后,将该文理论方法计算结果与国内外试验结果以及其他理论结果进行对比。结果表明:与试验结果和其他理论计算结果相比,该文理论方法原理简单,计算容易,精度满足要求,可用于确定混凝土双向板的极限状态。
To reasonably determine the load-deflection and ultimate state of two-way concrete slabs,a test for a full-scale two-way concrete slab was conducted,including the cracks and failure mode,the load-deflection,steel strain and corners' restraint forces.Based on the test results,by solving the force and moment equilibrium equations and considering the tensile membrane action,one theoretical method was established according to the yield-line theory,the proposed steel strain difference,concrete and steel strain failure criteria to predict the slabs' load-deflection and the limit loads.Meanwhile,according to the shell finite element,the nonlinear procedure was developed to predict the load-deflection,the membrane mechanics and steel strains of the concrete slabs,and the rationality of the present theoretical method was verified.The comparison of the results predicted by the present method with other methods and the test results was conducted.The result shows that:compared with the test results and other methods,the present theoretical method is simple and easy to calculate,and it is capable of predicting the ultimate state of two-way concrete slabs with reasonable accuracy.
To reasonably determine the load-deflection and ultimate state of two-way concrete slabs,a test for a full-scale two-way concrete slab was conducted,including the cracks and failure mode,the load-deflection,steel strain and corners' restraint forces.Based on the test results,by solving the force and moment equilibrium equations and considering the tensile membrane action,one theoretical method was established according to the yield-line theory,the proposed steel strain difference,concrete and steel strain failure criteria to predict the slabs' load-deflection and the limit loads.Meanwhile,according to the shell finite element,the nonlinear procedure was developed to predict the load-deflection,the membrane mechanics and steel strains of the concrete slabs,and the rationality of the present theoretical method was verified.The comparison of the results predicted by the present method with other methods and the test results was conducted.The result shows that:compared with the test results and other methods,the present theoretical method is simple and easy to calculate,and it is capable of predicting the ultimate state of two-way concrete slabs with reasonable accuracy.
引文
[1]江见鲸,陆新征.混凝土结构有限元分析[M].北京:清华大学出版社,2013.Jiang Jianjing,Lu Xinzheng.Finite element analysis of concrete structures[M].Beijing:Tsinghua University Press,2013.(in Chinese)
[2]朱伯芳.有限单元法原理与应用[M].北京:中国水利水电出版社,2009.Zhu Bofang.The finite element method theory and applications[M].Beijing:China Water&Power Press,2009.(in Chinese)
[3]Wang Yong,Dong Yuli,Zhou Guangchun.Nonlinear numerical modeling of two-way reinforced concrete slabs subjected to fire[J].Computers and Structures,2013,119:23―36.
[4]Bailey C G,Toh W.Behaviour of concrete floor slabs at ambient and temperatures[J].Fire Safety Journal,2007,42(6):425―436.
[5]Bailey C G,Toh W.Small-scale concrete slab tests at ambient and elevated temperatures[J].Engineering Structures,2007,29(10):2775―2791.
[6]李国强,周昊圣,郭士雄.火灾下钢结构建筑楼板的薄膜效应机理及理论模型[J].建筑结构学报,2007,28(5):40―47.Li Guoqiang,Zhou Haosheng,Guo Shixiong.Mechanism and theoretical model of membrane action in slabs of steel buildings subjected to fire[J].Journal of Building Structures,2007,28(5):40―47.(in Chinese)
[7]张娜思,李国强.火灾下组合楼板薄膜效应分析的改进方法[J].土木工程学报,2009,42(3):29―35.Zhang Nasi,Li Guoqiang.An innovative analytical method for the membrane action of composite floor slabs in fire[J].China Civil Engineering Journal,2009,42(3):29―35.(in Chinese)
[8]董毓利.用变形和分解原理求混凝土板的受拉薄膜效应[J].力学学报,2010,42(6):1180―1187.Dong Yuli.Calculation of tensile membrane effects of concrete slabs using deformation additive decomposition theorem[J].Chinese Journal of Theoretical and Applied Mechanics,2010,42(6):1180―1187.(in Chinese)
[9]Yong Wang,Yuli Dong,Guanglin Yuan,Chaoying Zou.New failure criterion to determine the load carrying capacity of two-way reinforced concrete slabs[J].Advances in Structural Engineering,2015,18(2):221―236.
[10]Omer E,Izzuddin B A,Elghazouli A Y.Failure of unrestrained lightly reinforced concrete slabs under firePart I:Analytical models[J].Engineering Structures,2010,32(9):2631―2646.
[11]Omer E,Izzuddin B A,Elghazouli A Y.Failure of unrestrained lightly reinforced concrete slabs under fire-Part II:Verification and application[J].Engineering Structures,2010,32(9):2647―2657.
[12]Cashell K A,Elghazouli A Y,Izzuddin B A.Failure assessment of lightly reinforced floor slabs.I:Experimental investigation[J].Journal of Structural Engineering,2011,137(9):977―988.
[13]Cashell K A,Elghazouli A Y,Izzuddin B A.Failure assessment of lightly reinforced floor slabs.II:Analytical studies[J].Journal of Structural Engineering,2011,137(9):989―1001.
[14]Herraiz B,Vogel T.Novel design approach for the analysis of laterally unrestrained reinforced concrete slabs considering membrane action[J].Engineering Structures,2016,123:313―329.
[15]Burgess I.Yiled line plasticity and tensile membrane action in lightly-reinforced rectangular concrete slabs[J].Engineering Structures,2017,138:195―214.
[16]Ockleston A J.Load tests on a three storey reinforced concrete building in Johannesburg[J].The Structural Engineer,1955,33(10):304―322.
[17]Taylor R,Maher D,Hayes B.Effect of the arrangement of reinforcement on the behavior of reinforced concrete slabs[J].Magazine of Concrete Research,1965,18(55):85―94.
[18]Sawczuk A,Winnicki L.Plastic behavior of simply supported reinforced concrete plates at moderately large deflections[J].International Journal of Solids and Structures,1965,1(1):97―111.
[19]Hayes B.Allowing for membrane action in the plastic analysis of rectangular reinforced concrete slabs[J].Magazine of Concrete Research,1968,20(65):205―212.
[20]Cameron N J K,Usmani A S.New design method to determine the membrane capacity of laterally restrained composite floor slabs in fire Part 1:theory and method[J].The Structural Engineer,2005,83(19):1―6.
[21]JTG D62-2012,公路钢筋混凝土及预应力混凝土桥涵设计规范[S].北京:人民交通出版社,2012.JTG D62-2012,Code for design of highway reinforced concrete and prestressed concrete bridges and culverts[S].Beijing:China Communications Press,2012.(in Chinese)
[22]GB50010-2010,混凝土结构设计规范[S].北京:中国建筑工业出版社,2015.GB 50010-2010,Code for design of concrete structures[S].Beijing:China Architecture&Building Press,2015.(in Chinese)
[23]GB 50152-2012,混凝土结构试验方法标准[S].北京:中国建筑工业出版社,2012.GB 50152-2012,Standard for test method of concrete structures[S].Beijing:China Architecture and building Press,2012.(in Chinese)
[24]Ghoneim M G,Mcgregor J G.Tests of reinforced concrete plates under combined in-plane and lateral loads[J].ACI Structural Journal,1994,91(1):19―30.
[25]张大山,董毓利,房圆圆.考虑受拉薄膜效应的板块平衡法修正及在混凝土双向板中的应用[J].工程力学,2017,34(3):204―210.Zhang Dashan,Dong Yuli,Fang Yuanyuan.Modification of segment equilibrium method through considering tensile membrane effects and its application in two-way concrete slabs[J].Engineering Mechanics,2017,34(3):204―210,240.(in Chinese).
[26]郑颖人,王乐,孔亮,等.钢材破坏条件与极限分析法在钢结构中应用探索[J].工程力学,2018,35(1):55―65.Zheng Yingren,Wang Le,Kong Liang,et al.Steel damage condition and application of ultimate analysis method in steel structures[J].Engineering Mechanics,2018,35(1):55―65.(in Chinese).
[27]王勇,段亚昆,张亚军,等.单向面内约束混凝土双向板抗火性能试验研究及数值分析[J].工程力学,2018,35(3):65―78.Wang Yong,Duan Yakun,Zhang Yajun,et al.Experiment and numerical analysis on the fire-resistant performance of two-way concrete slabs with unilateral in-plane restraints[J].Engineering Mechanics,2018,35(3):65―78.(in Chinese)
[2]朱伯芳.有限单元法原理与应用[M].北京:中国水利水电出版社,2009.Zhu Bofang.The finite element method theory and applications[M].Beijing:China Water&Power Press,2009.(in Chinese)
[3]Wang Yong,Dong Yuli,Zhou Guangchun.Nonlinear numerical modeling of two-way reinforced concrete slabs subjected to fire[J].Computers and Structures,2013,119:23―36.
[4]Bailey C G,Toh W.Behaviour of concrete floor slabs at ambient and temperatures[J].Fire Safety Journal,2007,42(6):425―436.
[5]Bailey C G,Toh W.Small-scale concrete slab tests at ambient and elevated temperatures[J].Engineering Structures,2007,29(10):2775―2791.
[6]李国强,周昊圣,郭士雄.火灾下钢结构建筑楼板的薄膜效应机理及理论模型[J].建筑结构学报,2007,28(5):40―47.Li Guoqiang,Zhou Haosheng,Guo Shixiong.Mechanism and theoretical model of membrane action in slabs of steel buildings subjected to fire[J].Journal of Building Structures,2007,28(5):40―47.(in Chinese)
[7]张娜思,李国强.火灾下组合楼板薄膜效应分析的改进方法[J].土木工程学报,2009,42(3):29―35.Zhang Nasi,Li Guoqiang.An innovative analytical method for the membrane action of composite floor slabs in fire[J].China Civil Engineering Journal,2009,42(3):29―35.(in Chinese)
[8]董毓利.用变形和分解原理求混凝土板的受拉薄膜效应[J].力学学报,2010,42(6):1180―1187.Dong Yuli.Calculation of tensile membrane effects of concrete slabs using deformation additive decomposition theorem[J].Chinese Journal of Theoretical and Applied Mechanics,2010,42(6):1180―1187.(in Chinese)
[9]Yong Wang,Yuli Dong,Guanglin Yuan,Chaoying Zou.New failure criterion to determine the load carrying capacity of two-way reinforced concrete slabs[J].Advances in Structural Engineering,2015,18(2):221―236.
[10]Omer E,Izzuddin B A,Elghazouli A Y.Failure of unrestrained lightly reinforced concrete slabs under firePart I:Analytical models[J].Engineering Structures,2010,32(9):2631―2646.
[11]Omer E,Izzuddin B A,Elghazouli A Y.Failure of unrestrained lightly reinforced concrete slabs under fire-Part II:Verification and application[J].Engineering Structures,2010,32(9):2647―2657.
[12]Cashell K A,Elghazouli A Y,Izzuddin B A.Failure assessment of lightly reinforced floor slabs.I:Experimental investigation[J].Journal of Structural Engineering,2011,137(9):977―988.
[13]Cashell K A,Elghazouli A Y,Izzuddin B A.Failure assessment of lightly reinforced floor slabs.II:Analytical studies[J].Journal of Structural Engineering,2011,137(9):989―1001.
[14]Herraiz B,Vogel T.Novel design approach for the analysis of laterally unrestrained reinforced concrete slabs considering membrane action[J].Engineering Structures,2016,123:313―329.
[15]Burgess I.Yiled line plasticity and tensile membrane action in lightly-reinforced rectangular concrete slabs[J].Engineering Structures,2017,138:195―214.
[16]Ockleston A J.Load tests on a three storey reinforced concrete building in Johannesburg[J].The Structural Engineer,1955,33(10):304―322.
[17]Taylor R,Maher D,Hayes B.Effect of the arrangement of reinforcement on the behavior of reinforced concrete slabs[J].Magazine of Concrete Research,1965,18(55):85―94.
[18]Sawczuk A,Winnicki L.Plastic behavior of simply supported reinforced concrete plates at moderately large deflections[J].International Journal of Solids and Structures,1965,1(1):97―111.
[19]Hayes B.Allowing for membrane action in the plastic analysis of rectangular reinforced concrete slabs[J].Magazine of Concrete Research,1968,20(65):205―212.
[20]Cameron N J K,Usmani A S.New design method to determine the membrane capacity of laterally restrained composite floor slabs in fire Part 1:theory and method[J].The Structural Engineer,2005,83(19):1―6.
[21]JTG D62-2012,公路钢筋混凝土及预应力混凝土桥涵设计规范[S].北京:人民交通出版社,2012.JTG D62-2012,Code for design of highway reinforced concrete and prestressed concrete bridges and culverts[S].Beijing:China Communications Press,2012.(in Chinese)
[22]GB50010-2010,混凝土结构设计规范[S].北京:中国建筑工业出版社,2015.GB 50010-2010,Code for design of concrete structures[S].Beijing:China Architecture&Building Press,2015.(in Chinese)
[23]GB 50152-2012,混凝土结构试验方法标准[S].北京:中国建筑工业出版社,2012.GB 50152-2012,Standard for test method of concrete structures[S].Beijing:China Architecture and building Press,2012.(in Chinese)
[24]Ghoneim M G,Mcgregor J G.Tests of reinforced concrete plates under combined in-plane and lateral loads[J].ACI Structural Journal,1994,91(1):19―30.
[25]张大山,董毓利,房圆圆.考虑受拉薄膜效应的板块平衡法修正及在混凝土双向板中的应用[J].工程力学,2017,34(3):204―210.Zhang Dashan,Dong Yuli,Fang Yuanyuan.Modification of segment equilibrium method through considering tensile membrane effects and its application in two-way concrete slabs[J].Engineering Mechanics,2017,34(3):204―210,240.(in Chinese).
[26]郑颖人,王乐,孔亮,等.钢材破坏条件与极限分析法在钢结构中应用探索[J].工程力学,2018,35(1):55―65.Zheng Yingren,Wang Le,Kong Liang,et al.Steel damage condition and application of ultimate analysis method in steel structures[J].Engineering Mechanics,2018,35(1):55―65.(in Chinese).
[27]王勇,段亚昆,张亚军,等.单向面内约束混凝土双向板抗火性能试验研究及数值分析[J].工程力学,2018,35(3):65―78.Wang Yong,Duan Yakun,Zhang Yajun,et al.Experiment and numerical analysis on the fire-resistant performance of two-way concrete slabs with unilateral in-plane restraints[J].Engineering Mechanics,2018,35(3):65―78.(in Chinese)
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