集中冲击荷载作用下修正Timoshenko梁剪力动载系数研究
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摘要
推导了修正Timoshenko梁运动方程正交条件,并在此基础上得到了梁在跨中冲击荷载作用下的剪力响应计算方法。根据该方法计算的结果与经典Timoshenko梁理论计算结果对比,发现在梁长细比较小的情况下采用修正Timoshenko梁理论计算结果更精确。采用该方法得到了不同长细比固结梁和简支梁在跨中无增长时间三角形和有增长时间三角形集中力冲击荷载作用下的最大剪力动力荷载系数(DLF),并拟合出计算公式,可根据梁长细比和荷载持续时间与构件第一阶自振周期的比值来计算最大剪力动载系数,并用来确定墩柱等构件在冲击作用下的抗剪需求。
Orthogonality conditions of a modified Timoshenko beam were derived, and then its shear response calculation method under a concentrated impact load at its mid-span was deduced. The calculated results using this method were compared with those using the classical Timoshenko beam theory. It was shown that the calculation results using the modified Timoshenko beam theory are more accurate when the beam's slenderness ratio is smaller. Using this method, the maximum shear dynamic load factors(SDLFs) of a two-end fixed beam and a simply supported one with different slenderness ratios under a concentrated impact load impulse with and without a triangular time history at the beam mid-span were calculated, and the calculation formula was fitted. It was shown that the maximum SDLF can be calculated according to a beam's slenderness ratio and the ratio of the load duration to the beam's 1 st order natural vibration period, the maximum SDLF can be used to determine the anti-shear demand of a beam under impact load.
Orthogonality conditions of a modified Timoshenko beam were derived, and then its shear response calculation method under a concentrated impact load at its mid-span was deduced. The calculated results using this method were compared with those using the classical Timoshenko beam theory. It was shown that the calculation results using the modified Timoshenko beam theory are more accurate when the beam's slenderness ratio is smaller. Using this method, the maximum shear dynamic load factors(SDLFs) of a two-end fixed beam and a simply supported one with different slenderness ratios under a concentrated impact load impulse with and without a triangular time history at the beam mid-span were calculated, and the calculation formula was fitted. It was shown that the maximum SDLF can be calculated according to a beam's slenderness ratio and the ratio of the load duration to the beam's 1 st order natural vibration period, the maximum SDLF can be used to determine the anti-shear demand of a beam under impact load.
引文
[1] BUTH C E,WILLIAMS W F,BRACKIN M S,et al.Analysis of large truck collisions with bridge piers:phase 1[R].Report of guidelines for designing bridge piers and abutments for vehicle collisions.(No.FHWA/TX-10/9-4973-1).Texas:Texas Transportation Institute,The Texas A&M University,2010.
[2] 陈林,肖岩.桥墩防车辆撞击研究综述[J].公路交通科技:2012,29(8):78-86.CHEN Lin,XIAO Yan.Review of studies on vehicle anti-collision on bridge piers[J].Journal of Highway and Transportation Research and Development,2012,29(8):78-86.
[3] GOMEZ N L.Performance of circular reinforced concrete bridge piers subjected to vehicular collisions[D].Amherst,Mass.:Masters Theses.University of Massachusetts-Amherst,2014.
[4] SAATCI S,VECCHIO F J.Effects of shear mechanisms on impact behavior of reinforced concrete beams[J].ACI structural Journal,2009,106(1):78-86.
[5] KISHI N,MIKAMI H,MATSUOKA K G,et al.Impact behavior of shear-failure-type RC beams without shear rebar[J].International Journal of Impact Engineering,2002,27(9):955-968.
[6] PHAM T M,HAO H.Behavior of fiber-reinforced polymer-strengthened reinforced concrete beams under static and impact loads[J].International Journal of Protective Structures,2017,8(1):3-24.
[7] Bridge Design Specifications:AASHTO LRFD[S].American Association of State Highway and Transportation Officials.Washington,D.C.,2004.
[8] Eurocode1:Actions on structures-Part 1-7:General actions-Accidental actions:BS EN 1991-1-7—2006[S].The European Union Regulation.Brussels,2006.
[9] 公路桥涵设计通用规范:JTG D60—2015[S].北京:中华人民共和国交通运输部,2015.
[10] EL-TAWIL S,SEVERINO E,FONSECA P.Vehicle collision with bridge piers[J].Journal of Bridge Engineering,2005,10(3):345-353.
[11] BIGGS J M.Introduction to structural dynamics[M].New York:McGraw-Hill College,1964.
[12] 方秦,柳锦春.地下防护结构[M].北京:中国水利水电出版社,2010.
[13] MAGNUSSON J,HALLGREN M,ANSELL A.Shear in concrete structures subjected to dynamic loads[J].Structural Concrete,2014,15(1):55-65.
[14] JONES N.Structural impact[M].London:Cambridge university press,2011.
[15] ROSS T J,KRAWINKLER H.Impulsive direct shear failure in RC slabs[J].Journal of Structural Engineering,1985,111(8):1661-1677.
[16] 方秦,郭东,张亚栋,等.梁的剪力动力系数的确定[J].工程力学,2005,22(5):181-185.FANG Qin,GUO Dong,ZHANG Yadong,et al.Determination of shear dynamic factor in beams[J].Engineering Mechanics,2005,22(5):181-185.
[17] 钱七虎,王明洋.高等防护结构计算理论[M].南京:江苏科学技术出版社,2009.
[18] 万春风.Timoshenko梁运动方程的修正及其在结构冲击响应中的应用[D].上海:同济大学,2003.
[19] 吴晓,罗佑新.用Timoshenko梁修正理论研究功能梯度材料梁的动力响应[J].振动与冲击,2011,30(10):245-248.WU Xiao,LUO Youxin.Dynamic response of a beam with functionally graded materials with Timoshenko beam correction theory[J].Journal of Vibration and Shock,2011,30(10):245-248.
[20] 王乐,冷德新.剪切系数对 Timoshenko 梁模型影响研究[J].导弹与航天运载技术,2015 (3):57-59.WANG Le,LENG Dexin.Effects of shear coefficient on timoshenko beam[J].Missiles and Space Vehicles,2015(3):57-59.
[21] HUTCHINSON J R.Shear coefficients for Timoshenko beam theory[J].Journal of Applied Mechanics,2001,68(1):87-92.
[22] 曾翔.冲击和快速加载作用下钢筋混凝土梁柱构件性能试验与数值模拟研究[D].长沙:湖南大学,2014.
[23] THILAKARATHNA H M I,THAMBIRATNAM D P,DHANASEKAR M,et al.Numerical simulation of axially loaded concrete columns under transverse impact and vulnerability assessment[J].International Journal of Impact Engineering,2010,37(11):1100-1112.
[24] EL-TAWIL S,SEVERINO E,FONSECA P.Vehicle collision with bridge piers[J].Journal of Bridge Engineering,2005,10(3):345-353.
[25] BUTH C E,BRACKIN M S,WILLIAMS W F,et al.Collision loads on bridge piers:phase 2[R].Report of guidelines for designing bridge piers and abutments for vehicle collisions (No.FHWA/TX-11/9-4973-2).Texas:Texas Transportation Institute,The Texas A&M University,2011.
[26] AL-THAIRY H,WANG Y C.Simplified FE vehicle model for assessing the vulnerability of axially compressed steel columns against vehicle frontal impact[J].Journal of Constructional Steel Research,2014,102:190-203.
[2] 陈林,肖岩.桥墩防车辆撞击研究综述[J].公路交通科技:2012,29(8):78-86.CHEN Lin,XIAO Yan.Review of studies on vehicle anti-collision on bridge piers[J].Journal of Highway and Transportation Research and Development,2012,29(8):78-86.
[3] GOMEZ N L.Performance of circular reinforced concrete bridge piers subjected to vehicular collisions[D].Amherst,Mass.:Masters Theses.University of Massachusetts-Amherst,2014.
[4] SAATCI S,VECCHIO F J.Effects of shear mechanisms on impact behavior of reinforced concrete beams[J].ACI structural Journal,2009,106(1):78-86.
[5] KISHI N,MIKAMI H,MATSUOKA K G,et al.Impact behavior of shear-failure-type RC beams without shear rebar[J].International Journal of Impact Engineering,2002,27(9):955-968.
[6] PHAM T M,HAO H.Behavior of fiber-reinforced polymer-strengthened reinforced concrete beams under static and impact loads[J].International Journal of Protective Structures,2017,8(1):3-24.
[7] Bridge Design Specifications:AASHTO LRFD[S].American Association of State Highway and Transportation Officials.Washington,D.C.,2004.
[8] Eurocode1:Actions on structures-Part 1-7:General actions-Accidental actions:BS EN 1991-1-7—2006[S].The European Union Regulation.Brussels,2006.
[9] 公路桥涵设计通用规范:JTG D60—2015[S].北京:中华人民共和国交通运输部,2015.
[10] EL-TAWIL S,SEVERINO E,FONSECA P.Vehicle collision with bridge piers[J].Journal of Bridge Engineering,2005,10(3):345-353.
[11] BIGGS J M.Introduction to structural dynamics[M].New York:McGraw-Hill College,1964.
[12] 方秦,柳锦春.地下防护结构[M].北京:中国水利水电出版社,2010.
[13] MAGNUSSON J,HALLGREN M,ANSELL A.Shear in concrete structures subjected to dynamic loads[J].Structural Concrete,2014,15(1):55-65.
[14] JONES N.Structural impact[M].London:Cambridge university press,2011.
[15] ROSS T J,KRAWINKLER H.Impulsive direct shear failure in RC slabs[J].Journal of Structural Engineering,1985,111(8):1661-1677.
[16] 方秦,郭东,张亚栋,等.梁的剪力动力系数的确定[J].工程力学,2005,22(5):181-185.FANG Qin,GUO Dong,ZHANG Yadong,et al.Determination of shear dynamic factor in beams[J].Engineering Mechanics,2005,22(5):181-185.
[17] 钱七虎,王明洋.高等防护结构计算理论[M].南京:江苏科学技术出版社,2009.
[18] 万春风.Timoshenko梁运动方程的修正及其在结构冲击响应中的应用[D].上海:同济大学,2003.
[19] 吴晓,罗佑新.用Timoshenko梁修正理论研究功能梯度材料梁的动力响应[J].振动与冲击,2011,30(10):245-248.WU Xiao,LUO Youxin.Dynamic response of a beam with functionally graded materials with Timoshenko beam correction theory[J].Journal of Vibration and Shock,2011,30(10):245-248.
[20] 王乐,冷德新.剪切系数对 Timoshenko 梁模型影响研究[J].导弹与航天运载技术,2015 (3):57-59.WANG Le,LENG Dexin.Effects of shear coefficient on timoshenko beam[J].Missiles and Space Vehicles,2015(3):57-59.
[21] HUTCHINSON J R.Shear coefficients for Timoshenko beam theory[J].Journal of Applied Mechanics,2001,68(1):87-92.
[22] 曾翔.冲击和快速加载作用下钢筋混凝土梁柱构件性能试验与数值模拟研究[D].长沙:湖南大学,2014.
[23] THILAKARATHNA H M I,THAMBIRATNAM D P,DHANASEKAR M,et al.Numerical simulation of axially loaded concrete columns under transverse impact and vulnerability assessment[J].International Journal of Impact Engineering,2010,37(11):1100-1112.
[24] EL-TAWIL S,SEVERINO E,FONSECA P.Vehicle collision with bridge piers[J].Journal of Bridge Engineering,2005,10(3):345-353.
[25] BUTH C E,BRACKIN M S,WILLIAMS W F,et al.Collision loads on bridge piers:phase 2[R].Report of guidelines for designing bridge piers and abutments for vehicle collisions (No.FHWA/TX-11/9-4973-2).Texas:Texas Transportation Institute,The Texas A&M University,2011.
[26] AL-THAIRY H,WANG Y C.Simplified FE vehicle model for assessing the vulnerability of axially compressed steel columns against vehicle frontal impact[J].Journal of Constructional Steel Research,2014,102:190-203.