Experimental and theoretical analysis on the natural frequency of external prestressed concrete beams
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摘要
Analyses and computations of the natural frequencies of external prestressed concrete structures are the bases for studying the dynamic properties of such structures.We carried out dynamic tests on three types of external simply supported beams,pulling the beams gradually.Then vertical loads were applied to the beams while the frequencies and related coefficients were measured at every step.We calculated natural frequencies and the results indicate that natural frequencies increase as the prestressing force rises in the pre-crack stage,and decrease significantly during the post-crack stage.Substantial incoincidences exist between the calculated and experimental results for the frequency and its tendency to change.Based on the experimental results,we modified the stiffness and other parameters in the equations.The results calculated using the modified equations agree with experimental results well,so the modified equations can be used practically.
Analyses and computations of the natural frequencies of external prestressed concrete structures are the bases for studying the dynamic properties of such structures.We carried out dynamic tests on three types of external simply supported beams,pulling the beams gradually.Then vertical loads were applied to the beams while the frequencies and related coefficients were measured at every step.We calculated natural frequencies and the results indicate that natural frequencies increase as the prestressing force rises in the pre-crack stage,and decrease significantly during the post-crack stage.Substantial incoincidences exist between the calculated and experimental results for the frequency and its tendency to change.Based on the experimental results,we modified the stiffness and other parameters in the equations.The results calculated using the modified equations agree with experimental results well,so the modified equations can be used practically.
Analyses and computations of the natural frequencies of external prestressed concrete structures are the bases for studying the dynamic properties of such structures.We carried out dynamic tests on three types of external simply supported beams,pulling the beams gradually.Then vertical loads were applied to the beams while the frequencies and related coefficients were measured at every step.We calculated natural frequencies and the results indicate that natural frequencies increase as the prestressing force rises in the pre-crack stage,and decrease significantly during the post-crack stage.Substantial incoincidences exist between the calculated and experimental results for the frequency and its tendency to change.Based on the experimental results,we modified the stiffness and other parameters in the equations.The results calculated using the modified equations agree with experimental results well,so the modified equations can be used practically.
引文
[1] Harajli MH.Strengthening of concrete beams by external prestressing [J].PCI Journal,1993,38(6):76-88.
[2] Wang J,Zhang YX,Han L.Experimental study on strengthening beam by externally-prestressed-cable- offloading method [J].Journal of Wuhan University of Technology,2003,25(12):69-71.(In Chinese). 王佶,张迎霞,韩玲.体外预应力悬索分载法加固混凝土 梁试验研究[J].武汉理工大学学报,2003,25(12):69-71.
[3] Miyamoto A,Tei K,Nakamura H,et al.Behavior of prestressed beam strengthened with external tendons [J].Journal of Structure Engineering,2000,126(9): 1033-1044.
[4] Pisanit MA.A numerical model for externally prestressed beams [J].Structural Engineering and Mechanics,1996,4(2):177-190.
[5] Aparicio AC,Ramos G.Flexural strength of externally prestressed concrete bridges [J].ACI Structural Journal, 1996,93(5):512-523.
[6] Cao SQ,Zhang WD,Fei LX.Analysis of vibration modes: the theory,experiment and application [M]. Tianjin:Tianjin University Press,2001.(In Chinese). 曹树谦,张文德,萧龙翔.振动结构模态分析:理论,实验 与应用[M].天津:天津大学出版,2001.
[7] Ahlborn TM,Shield CK,French CW.Full-scale testing of prestressed concrete bridge girders [J].Experimental Techniques,1997,21(1):33-35.
[8] Xiong XY,Wang SS.Analysis and research of externally prestressed concrete beam vibration behavior [J].Earthquake Engineering and Engineering Vibration,2005,25(2):55-61.(In Chinese). 熊学玉,王寿生.体外预应力梁振动特性的分析与研 究[J].地震工程与工程振动,2005,25(2):55-61.
[9] Zhang YT,Wang XL,Li RG.Experimental and theoretical research on vibration frequency of full- prestressed concrete beam [J].Engineering Mechanics, 2007,24(8):116-120.(In Chinese). 张耀庭,汪霞利,李瑞鸽.全预应力梁振动频率的理论 分析与试验研究[J].工程力学,2007,24(8):116-120.
[10] Zhang YT,Wang XL,Li RG.Experimental research on nature frequency of prestressed concrete beams [J]. Journal of Huazhong University of Science and Technology:Nature Science Edition,2007,35(2):12- 15.(In Chinese). 张耀庭,汪霞利,李瑞鸽.预应力梁固有频率的试验研究[J].华中科技大学学报:自然科学版,2007,35(2):12- 15.
[11] Saiidi M,Douglas B,Feng S.Prestress force effect on vibration frequency of concrete bridge [J].Journal of Structure Engineering,1994,120(7):2233-2241.
[12] Liu LJ,He SH,Zhao XX.Effective prestress computation of existing PC simply-supported beam [J]. Journal of Transportation Engineering,2005,5(3):47- 51.(In Chinese). 刘龄嘉,贺拴海,赵小星.在役混凝土简支梁有效预应 力计算[J].交通运输工程学报,2005,5(3):47-51.
[13] Yu BC,Zhang Zh,Teng QJ.Influence of concrete differential aging time on the construction phases analysis of the Fenghua River Bridge [J].Journal of Chongqing University: Eng Ed [ISSN 1671-8224], 2004,3(2):34-37.
[14] Zhang QR.Practical regression analysis [M].Beijing: Geology Press,1988.(In Chinese). 张启锐.实用回归分析[M].北京:地质出版社,1988.
[15] Lu P.Dynamic analysis of axially prestressed micro/nanobeam structures based on nonlocal beam theory [J].Journal of Applied Physics,2007,101(7):1-10.
[2] Wang J,Zhang YX,Han L.Experimental study on strengthening beam by externally-prestressed-cable- offloading method [J].Journal of Wuhan University of Technology,2003,25(12):69-71.(In Chinese). 王佶,张迎霞,韩玲.体外预应力悬索分载法加固混凝土 梁试验研究[J].武汉理工大学学报,2003,25(12):69-71.
[3] Miyamoto A,Tei K,Nakamura H,et al.Behavior of prestressed beam strengthened with external tendons [J].Journal of Structure Engineering,2000,126(9): 1033-1044.
[4] Pisanit MA.A numerical model for externally prestressed beams [J].Structural Engineering and Mechanics,1996,4(2):177-190.
[5] Aparicio AC,Ramos G.Flexural strength of externally prestressed concrete bridges [J].ACI Structural Journal, 1996,93(5):512-523.
[6] Cao SQ,Zhang WD,Fei LX.Analysis of vibration modes: the theory,experiment and application [M]. Tianjin:Tianjin University Press,2001.(In Chinese). 曹树谦,张文德,萧龙翔.振动结构模态分析:理论,实验 与应用[M].天津:天津大学出版,2001.
[7] Ahlborn TM,Shield CK,French CW.Full-scale testing of prestressed concrete bridge girders [J].Experimental Techniques,1997,21(1):33-35.
[8] Xiong XY,Wang SS.Analysis and research of externally prestressed concrete beam vibration behavior [J].Earthquake Engineering and Engineering Vibration,2005,25(2):55-61.(In Chinese). 熊学玉,王寿生.体外预应力梁振动特性的分析与研 究[J].地震工程与工程振动,2005,25(2):55-61.
[9] Zhang YT,Wang XL,Li RG.Experimental and theoretical research on vibration frequency of full- prestressed concrete beam [J].Engineering Mechanics, 2007,24(8):116-120.(In Chinese). 张耀庭,汪霞利,李瑞鸽.全预应力梁振动频率的理论 分析与试验研究[J].工程力学,2007,24(8):116-120.
[10] Zhang YT,Wang XL,Li RG.Experimental research on nature frequency of prestressed concrete beams [J]. Journal of Huazhong University of Science and Technology:Nature Science Edition,2007,35(2):12- 15.(In Chinese). 张耀庭,汪霞利,李瑞鸽.预应力梁固有频率的试验研究[J].华中科技大学学报:自然科学版,2007,35(2):12- 15.
[11] Saiidi M,Douglas B,Feng S.Prestress force effect on vibration frequency of concrete bridge [J].Journal of Structure Engineering,1994,120(7):2233-2241.
[12] Liu LJ,He SH,Zhao XX.Effective prestress computation of existing PC simply-supported beam [J]. Journal of Transportation Engineering,2005,5(3):47- 51.(In Chinese). 刘龄嘉,贺拴海,赵小星.在役混凝土简支梁有效预应 力计算[J].交通运输工程学报,2005,5(3):47-51.
[13] Yu BC,Zhang Zh,Teng QJ.Influence of concrete differential aging time on the construction phases analysis of the Fenghua River Bridge [J].Journal of Chongqing University: Eng Ed [ISSN 1671-8224], 2004,3(2):34-37.
[14] Zhang QR.Practical regression analysis [M].Beijing: Geology Press,1988.(In Chinese). 张启锐.实用回归分析[M].北京:地质出版社,1988.
[15] Lu P.Dynamic analysis of axially prestressed micro/nanobeam structures based on nonlocal beam theory [J].Journal of Applied Physics,2007,101(7):1-10.
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