纤维增强聚合物布加固裂纹木梁的稳定性
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摘要
梁中横向裂纹等效为无质量内部转动弹簧,假定纤维增强聚合物(FRP)布与梁表面紧密粘贴,建立了考虑轴向压力二阶效应FRP布加固裂纹梁线性弯曲的控制方程,并得到其显式解析通解.在此基础上,研究了FRP加固简支裂纹木梁的稳定性,通过数值求解方程,分析了纤维增强聚合物(CFRP)布含量、裂纹深度和位置以及数量等因素对CFRP布加固简支裂纹杉木梁临界载荷的影响,结果表明:CFRP加固可明显减小裂纹深度和数量等对裂纹杉木梁临界载荷的影响,且裂纹处弯矩较大或裂纹较深时加固效应愈加显著;CFRP加固裂纹木梁临界载荷随CFRP布加固层含量的增加而增加,但当CFRP布含量达到一定值后,进一步增加CFRP含量对CFRP加固裂纹梁临界载荷提高并不明显.
Regarding the transverse crack in beam as a massless inner rotation spring and assuming that tightly bonding between the beam surface and fiber reinforced polymer(FRP) sheet, the governing equation of linear bending of FRP-reinforced cracked beam with the effect of second-order axial pressure was established, and its general explicit analytical solution was derived. On this basis, stability of the simply-supported cracked beam reinforced with FRP-sheet is investigated, and influences of content of carbon fiber reinforced polymer(CFRP), crack depth, location and number on critical load of cracked fir timber beam were analyzed by solving equation numerically. It is shown from results that the influences of the crack depth and number on the critical load of cracked fir timber beam can be reduced evidently with the CFRP reinforcement, and the reinforcement effect is more remarkable when the bending moment at the crack location is larger or crack is deeper. And the critical load of the CFRP-reinforced cracked beam is increased with increase of the content of the CFRP reinforcement layer, but the critical load increase of the CFRP-reinforced cracked beam is not obvious when the content of the CFRP reinforcement layer reaches to some level.
Regarding the transverse crack in beam as a massless inner rotation spring and assuming that tightly bonding between the beam surface and fiber reinforced polymer(FRP) sheet, the governing equation of linear bending of FRP-reinforced cracked beam with the effect of second-order axial pressure was established, and its general explicit analytical solution was derived. On this basis, stability of the simply-supported cracked beam reinforced with FRP-sheet is investigated, and influences of content of carbon fiber reinforced polymer(CFRP), crack depth, location and number on critical load of cracked fir timber beam were analyzed by solving equation numerically. It is shown from results that the influences of the crack depth and number on the critical load of cracked fir timber beam can be reduced evidently with the CFRP reinforcement, and the reinforcement effect is more remarkable when the bending moment at the crack location is larger or crack is deeper. And the critical load of the CFRP-reinforced cracked beam is increased with increase of the content of the CFRP reinforcement layer, but the critical load increase of the CFRP-reinforced cracked beam is not obvious when the content of the CFRP reinforcement layer reaches to some level.
引文
[1]张青萍,陈军.中国现代木结构建筑发展之策略[J].中国科学:E辑,2009,39(5):874-877.
[2]庄荣忠,杨勇新.FRP加固木结构的研究和应用现状[J].四川建筑科学研究,2008,34(5):89-92.
[3]SPAUN F D.Reinforcement of wood with fiberglass[J].Forest Products Journal,1981,31(4):26-33.
[4]BUCHANAN A H.Bending strength of lumber[J].Journal of Structural Engineering,1990,116(5):1213-229.
[5]PLEVRIS N,TRIANTAFILLOU T C.FRP-reinforced wood as structural material[J].Journal of Material in Civil Engineering,ASCE,1992,4(3):300-317.
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[7]BORRI A,CORRADI M,GRAZINI A.A method for flexural reinforcement of old wood beams with CFRP materials[J].Composites Part B:Engineering,2005,36(2):143-153.
[8]马建勋,蒋湘闽,胡平,等.碳纤维布加固木梁抗弯性能的试验研究[J].工业建筑,2005,35(8):35-39.
[9]KIM Y J,HARRIES K A.Modeling of timber beams strengthened with various CFRP composites[J].Engineering Structures,2010,32(10):3225-3234.
[10]GóMEZ S,SVECOVA D.Behavior of split timber stringers reinforced with external GFRP sheets[J].Composites for Construction,2008,12(2):202-211.
[11]姜莹莹,杨骁.纤维增强聚合物加固带裂缝矩形截面木梁的弯曲[J].应用力学学报,2012,29(5):516-522.
[12]祝金标,王柏生,王建波.碳纤维布加固破损木梁的试验研究[J].工业建筑,2005,35(10):86-89.
[13]周钟宏,刘伟庆.碳纤维布加固木柱的轴心受压试验研究[J].工程抗震和加固改造,2006,28(3):44-48.
[14]邵劲松,刘伟庆.FRP约束木柱轴心抗压性能的弹塑性分析方法[J].建筑材料学报,2007,10(3):282-287.
[15]欧阳煜,龚勇.CFRP加固破损木柱偏心载荷作用下性能试验研究[J].上海大学学报,2012,18(2):209-212.
[16]ZHANG W,SONG X,GU X,et al.Compressive behavior of longitudinally cracked timber columns retrofitted using FRP Sheets[J].Journal of Structural Engineering,2012,138(1):90-98.
[17]TAHERI F,NAGARAJ M,KHOSRAVI P.Buckling response of glue-laminated columns reinforced with fiber-reinforced plastic sheets[J].Composite Structures,2009,88(3):481-490.
[18]OUYANG Y,YANG X,BAO R.Nonlinear stability of timber column strengthened with fiber reinforced polymer[J].Applied Mathematics and Mechanics,2011,32(7):903-916.
[19]BILELLO C.Theoretical and experimental investigation on damaged beams under moving systems[D].Italy:Universitàdegli Studi di Palermo,2001.
[20]FERNANDEZ-SAEZ J,RUBIO L,NAVARRO C,et al.Approximate calculation of the fundamental frequency for bending vibrations of cracked beams[J].Journal of Sound and Vibration,1999,225(2):345-352.
[21]KHAJI N,SHAFIEI M,JALALPOUR M,et al.Closed-form solutions for crack detection problem of Timoshenko beams with various boundary conditions[J].International Journal of Mechanical Sciences,2009,51(9-10):667-681.
[22]BAKHTIARI-NEJAD F,KHORRAM A,REZAEIAN M,et al.Analytical estimation of natural frequencies and mode shapes of a beam having two cracks[J].International Journal of Mechanical Sciences,2014,78(1):193-202.
[23]YANG X,HUANG J,OUYANG Y,et al.Bending of Timoshenko beam with effect of crack gap based on equivalent spring model[J].Applied Mathematics and Mechanics,2016,37(4):513-528.
[24]RUOTOLO R,SURACE C.Natural frequencies of a bar with multiple cracks[J].Journal of Sound and Vibration,2004,272(1-2):301-316.
[25]ATTAR M.A transfer matrix method for free vibration analysis and crack identification of stepped beams with multiple edge cracks and different boundary conditions[J].International Journal of Mechanical Sciences,2012,57(1):19-33.
[26]ZHANG Z G,CHEN F,ZHANG Z Y,et al.Vibration analysis of non-uniform Timoshenko beams coupled with flexible attachments and multiple discontinuities[J].International Journal of Mechanical Sciences,2014,80(1):131-143.
[27]PALMERI A,CICIRELLO A.Physically-based Dirac's delta functions in the static analysis of multi-cracked Euler-Bernoulli and Timoshenko beams[J].International Journal of Solids and Structures,2011,48(14-15):2184-2195.
[28]CIRELLO A,PALMERI A.Static analysis of Euler-Bernoulli beams with multiple unilateral cracks under combined axial and transverse loads[J].International Journal of Solids and Structures,2014,51(5):1020-1029.
[29]CADDEMI S,PALMERI A.Static analysis of Euler-Bernoulli beams with multiple unilateral cracks under combined axial and transverse loads[J].International Journal of Solids and Structures,2014,51(5):1020-1029.
[30]孙嘉琳,杨骁.基于等效弹簧模型的裂纹Euler-Bernoulli梁弯曲变形分析[J].力学季刊,2015,36(4):703-712.
[31]GB 50367-2006.混凝土结构加固设计规范[S].北京:中国建筑工业出版社,2006.
[32]KISA M.Vibration and stability of multi-cracked beams under compressive axial loading[J].International Journal of Physical Sciences,2011,6(11):2681-2696.
[2]庄荣忠,杨勇新.FRP加固木结构的研究和应用现状[J].四川建筑科学研究,2008,34(5):89-92.
[3]SPAUN F D.Reinforcement of wood with fiberglass[J].Forest Products Journal,1981,31(4):26-33.
[4]BUCHANAN A H.Bending strength of lumber[J].Journal of Structural Engineering,1990,116(5):1213-229.
[5]PLEVRIS N,TRIANTAFILLOU T C.FRP-reinforced wood as structural material[J].Journal of Material in Civil Engineering,ASCE,1992,4(3):300-317.
[6]JOHNS K C,LACROIX S.Composites reinforcement of timber in bending[J].Canadian Journal of Civil Engineering,2000,27(5):899-906.
[7]BORRI A,CORRADI M,GRAZINI A.A method for flexural reinforcement of old wood beams with CFRP materials[J].Composites Part B:Engineering,2005,36(2):143-153.
[8]马建勋,蒋湘闽,胡平,等.碳纤维布加固木梁抗弯性能的试验研究[J].工业建筑,2005,35(8):35-39.
[9]KIM Y J,HARRIES K A.Modeling of timber beams strengthened with various CFRP composites[J].Engineering Structures,2010,32(10):3225-3234.
[10]GóMEZ S,SVECOVA D.Behavior of split timber stringers reinforced with external GFRP sheets[J].Composites for Construction,2008,12(2):202-211.
[11]姜莹莹,杨骁.纤维增强聚合物加固带裂缝矩形截面木梁的弯曲[J].应用力学学报,2012,29(5):516-522.
[12]祝金标,王柏生,王建波.碳纤维布加固破损木梁的试验研究[J].工业建筑,2005,35(10):86-89.
[13]周钟宏,刘伟庆.碳纤维布加固木柱的轴心受压试验研究[J].工程抗震和加固改造,2006,28(3):44-48.
[14]邵劲松,刘伟庆.FRP约束木柱轴心抗压性能的弹塑性分析方法[J].建筑材料学报,2007,10(3):282-287.
[15]欧阳煜,龚勇.CFRP加固破损木柱偏心载荷作用下性能试验研究[J].上海大学学报,2012,18(2):209-212.
[16]ZHANG W,SONG X,GU X,et al.Compressive behavior of longitudinally cracked timber columns retrofitted using FRP Sheets[J].Journal of Structural Engineering,2012,138(1):90-98.
[17]TAHERI F,NAGARAJ M,KHOSRAVI P.Buckling response of glue-laminated columns reinforced with fiber-reinforced plastic sheets[J].Composite Structures,2009,88(3):481-490.
[18]OUYANG Y,YANG X,BAO R.Nonlinear stability of timber column strengthened with fiber reinforced polymer[J].Applied Mathematics and Mechanics,2011,32(7):903-916.
[19]BILELLO C.Theoretical and experimental investigation on damaged beams under moving systems[D].Italy:Universitàdegli Studi di Palermo,2001.
[20]FERNANDEZ-SAEZ J,RUBIO L,NAVARRO C,et al.Approximate calculation of the fundamental frequency for bending vibrations of cracked beams[J].Journal of Sound and Vibration,1999,225(2):345-352.
[21]KHAJI N,SHAFIEI M,JALALPOUR M,et al.Closed-form solutions for crack detection problem of Timoshenko beams with various boundary conditions[J].International Journal of Mechanical Sciences,2009,51(9-10):667-681.
[22]BAKHTIARI-NEJAD F,KHORRAM A,REZAEIAN M,et al.Analytical estimation of natural frequencies and mode shapes of a beam having two cracks[J].International Journal of Mechanical Sciences,2014,78(1):193-202.
[23]YANG X,HUANG J,OUYANG Y,et al.Bending of Timoshenko beam with effect of crack gap based on equivalent spring model[J].Applied Mathematics and Mechanics,2016,37(4):513-528.
[24]RUOTOLO R,SURACE C.Natural frequencies of a bar with multiple cracks[J].Journal of Sound and Vibration,2004,272(1-2):301-316.
[25]ATTAR M.A transfer matrix method for free vibration analysis and crack identification of stepped beams with multiple edge cracks and different boundary conditions[J].International Journal of Mechanical Sciences,2012,57(1):19-33.
[26]ZHANG Z G,CHEN F,ZHANG Z Y,et al.Vibration analysis of non-uniform Timoshenko beams coupled with flexible attachments and multiple discontinuities[J].International Journal of Mechanical Sciences,2014,80(1):131-143.
[27]PALMERI A,CICIRELLO A.Physically-based Dirac's delta functions in the static analysis of multi-cracked Euler-Bernoulli and Timoshenko beams[J].International Journal of Solids and Structures,2011,48(14-15):2184-2195.
[28]CIRELLO A,PALMERI A.Static analysis of Euler-Bernoulli beams with multiple unilateral cracks under combined axial and transverse loads[J].International Journal of Solids and Structures,2014,51(5):1020-1029.
[29]CADDEMI S,PALMERI A.Static analysis of Euler-Bernoulli beams with multiple unilateral cracks under combined axial and transverse loads[J].International Journal of Solids and Structures,2014,51(5):1020-1029.
[30]孙嘉琳,杨骁.基于等效弹簧模型的裂纹Euler-Bernoulli梁弯曲变形分析[J].力学季刊,2015,36(4):703-712.
[31]GB 50367-2006.混凝土结构加固设计规范[S].北京:中国建筑工业出版社,2006.
[32]KISA M.Vibration and stability of multi-cracked beams under compressive axial loading[J].International Journal of Physical Sciences,2011,6(11):2681-2696.