三塔两跨悬索桥中塔位移及跨中挠度简化计算方法
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摘要
为获得活载作用下三塔两跨悬索桥变形解析公式,首先通过微分与变分方法推导了均布荷载作用下单跨主缆挠度的解析计算公式,通过综合研究塔顶位移及主缆弹性伸长引起的主缆变形,推导了用于计算三塔两跨悬索桥中塔塔顶位移及加劲梁挠度的解析计算公式。研究发现,对单跨主缆施加均布荷载时,恒载大小对于主缆变形影响不大,主缆变形主要由缆的弹性伸长所引起,取决于主缆的轴向刚度及垂跨比;三塔两跨悬索桥的变形主要取决于中塔的变形以及主缆的伸长。建立三塔两跨悬索桥模型对本文公式进行验证,结果表明,公式能有效对塔顶位移及加劲梁挠度进行估算,可用于初步设计时对三塔悬索桥进行简化分析。
In order to obtain the analytic formula for deformation of suspension bridge with 3 pylons and 2main spans caused by live load,an analytic formula used for calculating the deflection of a main cable of single span under uniform live load is derived. Through study the deformation of main cable caused by pylon top displacement and cable elongation comprehensively,the analytic formulas for calculating the deformation of middle pylon top and deflection of stiffening girder in suspension bridge with 3 pylons and 2 main spans are derived. The research shows that( 1) the dead load has little effect on the deformation of the main cable when applying uniform live load along a single span,the deformation is mainly caused by the elastic elongation of the main cable and it depends on its sag-span ratio and the axial rigidity;( 2) the deformation of3-pylon and 2-span suspension bridges is mainly caused by the displacement of the middle pylon and the elongation of the cable. A finite element model of the suspension bridge is established to verify the proposed formula. It shows that the proposed formulas are effective for estimating the displacement of pylon top and the deflection of stiffening girder,which could be used for simplified analysis of a three-pylon suspension bridge in preliminary design stage.
In order to obtain the analytic formula for deformation of suspension bridge with 3 pylons and 2main spans caused by live load,an analytic formula used for calculating the deflection of a main cable of single span under uniform live load is derived. Through study the deformation of main cable caused by pylon top displacement and cable elongation comprehensively,the analytic formulas for calculating the deformation of middle pylon top and deflection of stiffening girder in suspension bridge with 3 pylons and 2 main spans are derived. The research shows that( 1) the dead load has little effect on the deformation of the main cable when applying uniform live load along a single span,the deformation is mainly caused by the elastic elongation of the main cable and it depends on its sag-span ratio and the axial rigidity;( 2) the deformation of3-pylon and 2-span suspension bridges is mainly caused by the displacement of the middle pylon and the elongation of the cable. A finite element model of the suspension bridge is established to verify the proposed formula. It shows that the proposed formulas are effective for estimating the displacement of pylon top and the deflection of stiffening girder,which could be used for simplified analysis of a three-pylon suspension bridge in preliminary design stage.
引文
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[10]CHOI D H,GWON S G,NA H S.Simplified Analysis for Preliminary Design of Towers in Suspension Bridge[J].Journal of Bridge Engineering,2014,19(3):165-184.
[12]杨进.多塔多跨悬索桥应用于海峡长桥建设的技术可行性与技术优势[J].桥梁建设,2009(2):36-39.YANG Jin.Technical Feasibility and Advantages of Applying Multi-tower and Multi-span Suspension Bridge to Construction of Long Bridge across Straits[J].Bridge Construction,2009(2):36-39.
[13]THAI H T,CHOI D H.Advanced Analysis of Multi-span Suspension Bridges[J].Journal of Constructional Steel Research,2013,90(5):29-41.
[14]CHOI D H,GWON S G,YOO H,et al.Nonlinear Static Analysis of Continuous Multi-span Suspension Bridges[J].International Journal of Steel Structure,2013,13(1):103-115.
[15]柴生波,肖汝诚,孙斌.活载下悬索桥主缆变形特性[J].同济大学学报:自然科学版,2012,40(10):1452-1457.CHAI Sheng-bo,XIAO Ru-cheng,SUN Bin.Deformation Characteristics of Main Cable in Suspension Bridge Caused by Live Load[J].Journal of Tongji University:Natural Science Edition,2012,40(10):1452-1457.
[2]JENNINGS A.Gravity Stiffness of Classical Suspension Bridges[J].Journal of Structure Engineering,1983,109(1):16-36.
[3]WOLLMANN G P.Preliminary Analysis of Suspension Bridge[J].Journal of Bridge Engineering,2005,6(4):227-233.
[4]GIMSING N J.Cable Supported Bridges:Concept and Design[M].2nd ed.New York:Wiley,1997.
[5]刘钊,刘厚军.悬索桥主缆变形及重力刚度新算法[J].工程力学,2009,26(6):127-132.LIU Zhao,LIU Hou-jun.New Arithmetic for Cable Deflection and Gravity Stiffness of Suspension Bridges[J].Engineering Mechanics,2009,26(6):127-132.
[6]IRVINE H M.Cable Structures[M].Cambridge:MIT University Press,1981.
[7]YOSHIDA O,OKUDA M,MORIYA T.Structural Characteristics and Applicability of Four-span Suspension Bridge[J].Journal of Bridge Engineering,2004,9(5):453-463.
[8]柴生波,肖汝诚,张学义,等.多跨悬索桥中塔纵向刚度研究[J].中国公路学报,2012,25(2):67-71.CHAI Sheng-bo,XIAO Ru-cheng,ZHANG Xue-yi,et al.Study of Longitudinal Stiffness of Middle Pylon in Multispan Suspension Bridge[J].China Journal of Highway and Transport,2012,25(2):67-71.
[9]KIUREGHIAN A D,SACKMAN J L.Tangent Geometric Stiffness of Inclined Cables Under Self-weight[J].Journal of Structural Engineering,2005,131(6):941-945.
[10]CHOI D H,GWON S G,NA H S.Simplified Analysis for Preliminary Design of Towers in Suspension Bridge[J].Journal of Bridge Engineering,2014,19(3):165-184.
[12]杨进.多塔多跨悬索桥应用于海峡长桥建设的技术可行性与技术优势[J].桥梁建设,2009(2):36-39.YANG Jin.Technical Feasibility and Advantages of Applying Multi-tower and Multi-span Suspension Bridge to Construction of Long Bridge across Straits[J].Bridge Construction,2009(2):36-39.
[13]THAI H T,CHOI D H.Advanced Analysis of Multi-span Suspension Bridges[J].Journal of Constructional Steel Research,2013,90(5):29-41.
[14]CHOI D H,GWON S G,YOO H,et al.Nonlinear Static Analysis of Continuous Multi-span Suspension Bridges[J].International Journal of Steel Structure,2013,13(1):103-115.
[15]柴生波,肖汝诚,孙斌.活载下悬索桥主缆变形特性[J].同济大学学报:自然科学版,2012,40(10):1452-1457.CHAI Sheng-bo,XIAO Ru-cheng,SUN Bin.Deformation Characteristics of Main Cable in Suspension Bridge Caused by Live Load[J].Journal of Tongji University:Natural Science Edition,2012,40(10):1452-1457.