基于裂缝宽度的部分预应力混凝土梁设计方法
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摘要
为了简化部分预应力混凝土梁的设计过程,减少设计试算的次数,缩小预应力筋用量的取值范围,提出了基于裂缝宽度的部分预应力混凝土梁设计方法;从正常使用状态的裂缝宽度出发,根据《公路钢筋混凝土及预应力混凝土桥涵设计规范》(JTG D62—2004)(简称《公路规范》)中对裂缝宽度的规定,通过最大裂缝宽度求解受拉区普通钢筋的应力,并建立关于开裂截面中性轴高度的一元三次方程;根据预应力筋的有效应变要求,结合《公路规范》中最小配筋率的规定,得到了预应力筋用量的上、下限;给出了设计方法的主要步骤和具体验算过程,并设计了1根T形截面试验梁,以验证设计方法的合理性。研究结果表明:验算梁的抗弯承载力及预应力筋用量的上、下限满足规范要求;试验梁的荷载与挠度基本呈现三折线关系,在外荷载为50.0kN时,试验梁跨中出现裂缝,外荷载为128.5kN时,试验梁受拉普通钢筋屈服,外荷载为157.8kN时,试验梁跨中混凝土压碎破坏,试验梁总体呈延性破坏特征,满足承载性能要求;在受拉普通钢筋屈服前,试验梁实测最大裂缝宽度为0.18mm,未超过预估的最大裂缝宽度0.20mm,满足正常使用要求。可见,提出的设计方法合理、可行,能够简化部分预应力混凝土梁的设计过程。
In order to simplify the design process of partially prestressed concrete(PPC)beam and reduce the number of trial calculation and the range of prestressed reinforcement amount,a design method of partially prestressed concrete(PPC)beam based on crack width was proposed.Starting from the crack width under normal service condition and based on the regulations of crack width in Code for Design of Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts(JTG D62—2004)(Highway Code for short),the stress of non-prestressed reinforcement in tensile region was derived based on the maximum crack width.A cubic equation was established to calculate the neutral axis height of cracking section.Then based on the requirements of effective strain of prestressed reinforcement and the provisions of the minimum reinforcement ratio in Highway Code,the maximum and minimum amounts of prestressed reinforcement were obtained.Key design procedure and a detailed design example were also presented.Furthermore,a T-shaped test girder was designed to verify the design proposed method.Research result shows that the flexural bearing capacity and the maximum and minimumamount of prestressed reinforcement of designed girder can meet the code requirements.The load and deflection of test girder basically show a tri-line relationship.When the external load is50.0 kN,crack occurs in the midspan of test girder.When the external load is 128.5 kN,the tensile non-prestressed reinforcement yields.When the external load is 157.8 kN,the concrete is broken in the midspan of test girder.The test girder designed by the proposed method exhibits the characteristics of ductile failure and can meet the requirements of bearing performance.The measured maximum crack width of test girder is 0.18 mm before the non-prestressed reinforcement yielding and less than the predicted maximum crack width 0.20 mm,which means that it can meet the requirements of normal use.Obviously,the proposed design method is reasonable and feasible for practical design.It can simplify the design procedure of PPC beam.9 figs,25 refs.
In order to simplify the design process of partially prestressed concrete(PPC)beam and reduce the number of trial calculation and the range of prestressed reinforcement amount,a design method of partially prestressed concrete(PPC)beam based on crack width was proposed.Starting from the crack width under normal service condition and based on the regulations of crack width in Code for Design of Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts(JTG D62—2004)(Highway Code for short),the stress of non-prestressed reinforcement in tensile region was derived based on the maximum crack width.A cubic equation was established to calculate the neutral axis height of cracking section.Then based on the requirements of effective strain of prestressed reinforcement and the provisions of the minimum reinforcement ratio in Highway Code,the maximum and minimum amounts of prestressed reinforcement were obtained.Key design procedure and a detailed design example were also presented.Furthermore,a T-shaped test girder was designed to verify the design proposed method.Research result shows that the flexural bearing capacity and the maximum and minimumamount of prestressed reinforcement of designed girder can meet the code requirements.The load and deflection of test girder basically show a tri-line relationship.When the external load is50.0 kN,crack occurs in the midspan of test girder.When the external load is 128.5 kN,the tensile non-prestressed reinforcement yields.When the external load is 157.8 kN,the concrete is broken in the midspan of test girder.The test girder designed by the proposed method exhibits the characteristics of ductile failure and can meet the requirements of bearing performance.The measured maximum crack width of test girder is 0.18 mm before the non-prestressed reinforcement yielding and less than the predicted maximum crack width 0.20 mm,which means that it can meet the requirements of normal use.Obviously,the proposed design method is reasonable and feasible for practical design.It can simplify the design procedure of PPC beam.9 figs,25 refs.
引文
[1]AU F T K,SU R K L,TSO K,et al.Behaviour of partially prestressed beams with external tendons[J].Magazine of Concrete Research,2008,60(6):455-467.
[2]DU J S,AU F T K,CHAN E K H,et al.Deflection of unbonded partially prestressed concrete continuous beams[J].Engineering Structures,2016,118:89-96.
[3]NAAMAN A E.Partially prestressed concrete:review and recommendations[J].PCI Journal,1985,30(6):30-71.
[4]张耀庭,张江,杨力.预应力度对预应力混凝土框架结构抗震性能影响研究[J].工程力学,2017,34(2):129-136.ZHANG Yao-ting,ZHANG Jiang,YANG Li.Research on the effects of prestressing ratio on the seismic capacity of prestressed concrete frame structures[J].Engineering Mechanics,2017,34(2):129-136.(in Chinese)
[5]Joint ACI-ASCE Committee 423.State-of-the-art report on partially prestressed concrete(ACI 423.5R-99)[R].Farmington Hills:American Concrete Institute,2000.
[6]RAKA I G P,TAVIO,ASTAWA M D.State-of-the-art report on partially-prestressed concrete earthquake-resistant building structures for highly-seismic region[J].Procedia Engineering,2014,95:43-53.
[7]MOAWARD M,MAHMOND A,EL-KARMOTY H,et al.Behavior of corroded bonded partially prestressed concrete beams[J].HBRC Journal,2018,14(1):9-21.
[8]CHERN J C,YOU C M,BAZANT Z P.Deformation of progressively cracking partially prestressed concrete beams[J].PCI Journal,1992,37(1):74-84.
[9]SCHOLZ H.Simple deflection and cracking rules for partially prestressed members[J].ACI Structural Journal,1991,88(2):199-203.
[10]AU F T K,DU J S.Partially prestressed concrete[J].Progress in Structure Engineering and Materials,2004,2(6):127-135.
[11]NAAMAN A E,SIRIAKSOM A.Serviceability based design of partially prestressed beams,part 2—computerized design[J].PCI Journal,1979,24(2):68-89.
[12]KARAYANNIS C G,CHALIORIS C E.Design of partially prestressed concrete beams based on the cracking control provisions[J].Engineering Structures,2013,48:402-416.
[13]ABELES P W.Design of partially prestressed concrete beams[J].ACI Journal,1967,64(10):669-677.
[14]孙宝俊,郑文忠,吕志涛.部分预应力混凝土结构裂缝控制设计建议[J].中国公路学报,1995,8(2):61-64.SUN Bao-jun,ZHENG Wen-zhong,LU Zhi-tao.Crackcontrol design recommended for partially prestressed concrete structures[J].China Journal of Highway and Transport,1995,8(2):61-64.(in Chinese)
[15]王勇强,侯建国.部分预应力混凝土梁考虑裂缝闭合性能的裂缝控制设计方法的研究[J].武汉大学学报:工学版,2008,41(增):1-5.WANG Yong-qiang,HOU Jian-guo.Research on design methods of crack-controlling of partially prestressed concreted beams considering crack-closure[J].Engineering Journal of Wuhan University,2008,41(S):1-5.(in Chinese)
[16]张昊宇,郑文忠.对用名义拉应力控制预应力混凝土受弯构件裂缝宽度方法的2点改进[J].铁道科学与工程学报,2006,3(6):25-30.ZHANG Hao-yu,ZHENG Wen-zhong.Two pieces of improvement on the crack width control method using nominal tensile stress for prestressed concrete flexural member[J].Journal of Railway Science and Engineering,2006,3(6):25-30.(in Chinese)
[17]李子青,万振江.部分预应力混凝土桥梁设计方法的探讨[J].西安公路交通大学学报,1998,18(4):147-151.LI Zi-qing,WAN Zhen-jiang.Study on design method for partially prestressed concrete bridge[J].Journal of Xian Highway University,1998,18(4):147-151.(in Chinese)
[18]李忠诚,李唐宁.部分预应力(PPC)梁裂缝控制计算的探讨[J].建筑结构,2001,31(11):24-28,53.LI Zhong-cheng,LI Tang-ning.Discussion on calculation of PPC beam crack controlling[J].Building Structure,2001,31(11):24-28,53.(in Chinese)
[19]SHAHAWI M E,BATCHELOR B D.Design methods for partially prestressed concrete—a review[J].Canadian Journal of Civil Engineering,1987,14(2):269-277.
[20]蓝宗建,温峰.在使用荷载下出现裂缝的部分预应力砼梁裂缝宽度的计算[J].建筑结构学报,1993,14(5):19-27.LAN Zong-jian,WEN Feng.Calculation of crack width in partially prestressed concrete beams under service load[J].Journal of Building Structures,1993,14(5):19-27.(in Chinese)
[21]于琦,孟少平.部分预应力混凝土受弯构件裂缝宽度计算方法探讨[J].建筑结构,2009,39(3):31-33.YU Qi,MENG Shao-ping.Discussion on the method for calculating crack width of partial prestressed concrete beams[J].Building Structure,2009,39(3):31-33.(in Chinese)
[22]吴大宏,赵人达.基于神经网络的部分预应力混凝土梁荷载-裂缝模型研究[J].西南交通大学学报,2002,37(3):231-235.WU Da-hong,ZHAO Ren-da.The load and crack width model for partially prestressed concrete beams based on neural network[J].Journal of Southwest Jiaotong University,2002,37(3):231-235.(in Chinese)
[23]杜进生,刘西拉.无粘结部分预应力混凝土梁的挠度、裂缝宽度计算[J].中国公路学报,2000,13(4):70-73.DU Jin-sheng,LIU Xi-la.Calculation of deflection and crack width in unbounded partially prestressed concrete beams[J].China Journal of Highway and Transport,2000,13(4):70-73.(in Chinese)
[24]CHOWDHURY S H,LOO Y C.A new formula for prediction of crack widths in reinforced and partially prestressed concrete beams[J].Advances in Structural Engineering,2001,4(2):101-110.
[25]王军文,梁志广,李建中.部分预应力混凝土梁的应力和变形[J].工程力学,2002,19(5):108-113.WANG Jun-wen,LIANG Zhi-guang,LI Jian-zhong.The stress and deformation of partially prestressed concrete beams[J].Engineering Mechanics,2002,19(5):108-113.(in Chinese)
[2]DU J S,AU F T K,CHAN E K H,et al.Deflection of unbonded partially prestressed concrete continuous beams[J].Engineering Structures,2016,118:89-96.
[3]NAAMAN A E.Partially prestressed concrete:review and recommendations[J].PCI Journal,1985,30(6):30-71.
[4]张耀庭,张江,杨力.预应力度对预应力混凝土框架结构抗震性能影响研究[J].工程力学,2017,34(2):129-136.ZHANG Yao-ting,ZHANG Jiang,YANG Li.Research on the effects of prestressing ratio on the seismic capacity of prestressed concrete frame structures[J].Engineering Mechanics,2017,34(2):129-136.(in Chinese)
[5]Joint ACI-ASCE Committee 423.State-of-the-art report on partially prestressed concrete(ACI 423.5R-99)[R].Farmington Hills:American Concrete Institute,2000.
[6]RAKA I G P,TAVIO,ASTAWA M D.State-of-the-art report on partially-prestressed concrete earthquake-resistant building structures for highly-seismic region[J].Procedia Engineering,2014,95:43-53.
[7]MOAWARD M,MAHMOND A,EL-KARMOTY H,et al.Behavior of corroded bonded partially prestressed concrete beams[J].HBRC Journal,2018,14(1):9-21.
[8]CHERN J C,YOU C M,BAZANT Z P.Deformation of progressively cracking partially prestressed concrete beams[J].PCI Journal,1992,37(1):74-84.
[9]SCHOLZ H.Simple deflection and cracking rules for partially prestressed members[J].ACI Structural Journal,1991,88(2):199-203.
[10]AU F T K,DU J S.Partially prestressed concrete[J].Progress in Structure Engineering and Materials,2004,2(6):127-135.
[11]NAAMAN A E,SIRIAKSOM A.Serviceability based design of partially prestressed beams,part 2—computerized design[J].PCI Journal,1979,24(2):68-89.
[12]KARAYANNIS C G,CHALIORIS C E.Design of partially prestressed concrete beams based on the cracking control provisions[J].Engineering Structures,2013,48:402-416.
[13]ABELES P W.Design of partially prestressed concrete beams[J].ACI Journal,1967,64(10):669-677.
[14]孙宝俊,郑文忠,吕志涛.部分预应力混凝土结构裂缝控制设计建议[J].中国公路学报,1995,8(2):61-64.SUN Bao-jun,ZHENG Wen-zhong,LU Zhi-tao.Crackcontrol design recommended for partially prestressed concrete structures[J].China Journal of Highway and Transport,1995,8(2):61-64.(in Chinese)
[15]王勇强,侯建国.部分预应力混凝土梁考虑裂缝闭合性能的裂缝控制设计方法的研究[J].武汉大学学报:工学版,2008,41(增):1-5.WANG Yong-qiang,HOU Jian-guo.Research on design methods of crack-controlling of partially prestressed concreted beams considering crack-closure[J].Engineering Journal of Wuhan University,2008,41(S):1-5.(in Chinese)
[16]张昊宇,郑文忠.对用名义拉应力控制预应力混凝土受弯构件裂缝宽度方法的2点改进[J].铁道科学与工程学报,2006,3(6):25-30.ZHANG Hao-yu,ZHENG Wen-zhong.Two pieces of improvement on the crack width control method using nominal tensile stress for prestressed concrete flexural member[J].Journal of Railway Science and Engineering,2006,3(6):25-30.(in Chinese)
[17]李子青,万振江.部分预应力混凝土桥梁设计方法的探讨[J].西安公路交通大学学报,1998,18(4):147-151.LI Zi-qing,WAN Zhen-jiang.Study on design method for partially prestressed concrete bridge[J].Journal of Xian Highway University,1998,18(4):147-151.(in Chinese)
[18]李忠诚,李唐宁.部分预应力(PPC)梁裂缝控制计算的探讨[J].建筑结构,2001,31(11):24-28,53.LI Zhong-cheng,LI Tang-ning.Discussion on calculation of PPC beam crack controlling[J].Building Structure,2001,31(11):24-28,53.(in Chinese)
[19]SHAHAWI M E,BATCHELOR B D.Design methods for partially prestressed concrete—a review[J].Canadian Journal of Civil Engineering,1987,14(2):269-277.
[20]蓝宗建,温峰.在使用荷载下出现裂缝的部分预应力砼梁裂缝宽度的计算[J].建筑结构学报,1993,14(5):19-27.LAN Zong-jian,WEN Feng.Calculation of crack width in partially prestressed concrete beams under service load[J].Journal of Building Structures,1993,14(5):19-27.(in Chinese)
[21]于琦,孟少平.部分预应力混凝土受弯构件裂缝宽度计算方法探讨[J].建筑结构,2009,39(3):31-33.YU Qi,MENG Shao-ping.Discussion on the method for calculating crack width of partial prestressed concrete beams[J].Building Structure,2009,39(3):31-33.(in Chinese)
[22]吴大宏,赵人达.基于神经网络的部分预应力混凝土梁荷载-裂缝模型研究[J].西南交通大学学报,2002,37(3):231-235.WU Da-hong,ZHAO Ren-da.The load and crack width model for partially prestressed concrete beams based on neural network[J].Journal of Southwest Jiaotong University,2002,37(3):231-235.(in Chinese)
[23]杜进生,刘西拉.无粘结部分预应力混凝土梁的挠度、裂缝宽度计算[J].中国公路学报,2000,13(4):70-73.DU Jin-sheng,LIU Xi-la.Calculation of deflection and crack width in unbounded partially prestressed concrete beams[J].China Journal of Highway and Transport,2000,13(4):70-73.(in Chinese)
[24]CHOWDHURY S H,LOO Y C.A new formula for prediction of crack widths in reinforced and partially prestressed concrete beams[J].Advances in Structural Engineering,2001,4(2):101-110.
[25]王军文,梁志广,李建中.部分预应力混凝土梁的应力和变形[J].工程力学,2002,19(5):108-113.WANG Jun-wen,LIANG Zhi-guang,LI Jian-zhong.The stress and deformation of partially prestressed concrete beams[J].Engineering Mechanics,2002,19(5):108-113.(in Chinese)