【作者】 易云焜；

【导师】 肖汝诚；

【作者基本信息】 同济大学 ， 桥梁与隧道工程， 2007， 博士

【摘要】 梁拱组合体系是对传统拱桥的发展，是梁桥和拱桥的结合体，集合了两者的优点。在60～200m跨径范围内，梁拱组合体系造价低廉、施工难度小、对通航基本无阻碍，是最具有竞争力的桥型之一。常见的梁拱组合体系有平行式和内倾式(即提篮拱)两种；但近年来，将拱肋外倾，形成外倾式梁拱组合体系(即蝶形拱)的桥梁也屡见不鲜。本文对平行式梁拱组合体系的概念设计进行了归纳总结，对平行式梁拱组合体系的简化计算和梁拱协作机理进行了研究，对外倾式梁拱组合体系的拱肋倾角和吊杆夹角进行了参数分析以及提出了一种新的确定外倾式梁拱组合体系空间多索面吊杆张拉力的方法。1．平行式和外倾式梁拱组合体系的概念设计比较全面地归纳和总结了平面梁拱组合体系总体设计参数(矢跨比、拱肋高跨比、主梁高跨比、拱肋倾角、索面布置等)的一般确定原则以及结构截面尺寸(包括拱肋、主梁、吊杆)的常用取值；结合现有工程实例，总结了外倾式梁拱组合体系的结构布置规律。比较全面地总结了梁拱组合体系关键部位的试验和有限元分析结果，提出了梁拱组合体系关键部位钢筋的四个作用：拱肋的配筋要求；主梁的配筋要求、拱肋与主梁结合传力的配筋要求；局部应力集中的配筋要求。由此得出了关键部位钢筋布置的四个原则：拱肋的纵向钢筋和箍筋；主梁的纵向钢筋和箍筋；垂直于拱肋的斜拉筋；支座和角隅的加强钢筋网。2．梁拱组合体系的实用计算对均布荷载作用下，梁拱组合体系吊杆力的有限元结果进行分析、综合，作出了吊杆力大小相等的假定，并将吊杆力假定为膜张力，将梁拱组合体系分解成梁拱组合体和吊杆两种构件，由变形协调方程，通过结构力学方法求解出了均布荷载作用下梁拱组合体系的吊杆均布膜张力以及跨中拱肋、主梁挠度的简化公式。分析了简化公式误差产生的原因，即，用四次抛物线膜张力修正均布膜张力、余弦荷载修正膜张力产生的误差，分别提出了修正系数c1、c2，再将修正后的结果与有限元结果的比较，提出了综合修正系数c3。讨论了轴向变形的影响，给出了特例情况下的公式简化，并从动态变形协调角度得出了同样的计算公式。提出了集中荷载作用下的影响线求解思路。3．梁拱组合体系的梁拱协作机理研究由结构力学方法，给出了外荷载分别作用在拱肋、主梁以及均布膜张力作用下梁拱组合体的有关计算公式，并求解出了梁拱组合体的弹性中心公式。求解出了拱梁荷载比、拱梁弯矩比的计算公式，讨论了梁拱截面抗弯刚度比、吊杆拱肋等代弯矩刚度比、矢跨比、轴向变形影响系数对它们的影响曲线关系。由拱梁弯矩比、主梁轴力、主梁挠度、拱肋挠度四个指标，对刚拱柔梁、柔拱刚梁、刚拱刚梁进行了界定，得出了界定值，认为可将EI_b／EI_a≤1／50定义为刚拱柔梁；可将EI_b／EI_a≥20定义为柔拱刚梁，且必须将柔拱刚梁的计算模式取为朗格拱，不能仅将EI_a=20EI_b。4．外倾式梁拱组合体系的合理倾角确定根据拱肋、主梁、吊杆的夹角关系对外倾式梁拱组合体系进行了分类，由拱肋与竖直平面的夹角关系提出了基本体系Ⅰ、由拱肋和吊杆的夹角关系提出了基本体系Ⅱ。通过基本体系Ⅰ的位移、内力影响线分析，以及梁拱结构变形、结构内力、吊杆力、结构稳定性能等结构性能指标与拱肋倾角的关系的参数分析，得到了这些指标与拱肋倾角的变化关系，提出了合理的拱肋倾角值，即不超过30°；通过这些指标与吊杆夹角的关系的参数分析，得到了这些指标与吊杆夹角的变化关系，提出了合理的吊杆夹角值为零，即拱肋外力与拱肋同平面。5．空间多索面吊杆张拉力的确定探讨了桥梁结构的合理设计状态含义，并将其分为施工、成桥、运营等三个阶段，论述了三个阶段合理设计状态的定义和相互关系。提出运营阶段是桥梁合理设计状态的核心，但由于运营阶段的可变作用、收缩徐变等影响难于确定，实际中常常求解成桥时的合理设计状态。提出了一种新的、借助于大型通用有限元软件ANSYS的一阶优化算法的、能确保施工、成桥、营运设计受力和线型状态合理的、根据实际施工过程全仿真的、方便处理各种非线性因素影响的成桥合理设计状态索力(吊杆力)确定方法。这种方法简单可行，能建立成桥索力(设计变量)与合理设计状态指标(优化目标)的直接、正向联系。更多还原

【Abstract】 Beam-arch association bridge, which combined by beam and arch, is adevelopment to the traditional arch and integrate their merits. Between the span of60～200 meters, beam-arch association bridge is of competition for its strongpoints, such as low manufacturing cost, little difficulty to construct, nearly no-obstacle toships, etc. Usual styles for this kind of bridge are parallel one and inward one; recently, the outward one more and more comes into being. The paper summed up theregularities of concept design for the beam-arch association bridge, did researches onthe practical formula and cooperation mechanics between beam and arch, didparametric analysis on the arch slope angle and the suspender slope angle, and gave anew method on how to get the forces of multi spatial suspenders for the outwardbeam-arch association bridge.1. Concept design of parallel and outward beam-arch association bridgesThe popular rules that how to valuate general design parameters (such as ratio ofrise to span, ratios of height to span for arch and beam, slope angle of arch, layout ofcable plane, etc) and structural sectional dimensions (such as arch, beam, suspender)of parallel beam-arch association bridges were summed up. The actual layout rules foroutward beam-arch association were listed. Moreover, the paper generalized theresults of experiments and FEM analysis for the keypoints, and presented an ideal thatbars in the keypoints should have four functions: for the arch stress; for the beamstress; for the force transferring between arch and beam; and for the stress raisers.According to the ideal, the rule to arrange bars in the keypoints was presented: thelongitudinal and hoop reinforcements of arch; the longitudinal and hoopreinforcements of beam; the sloping bars normal to arch; the grid of reinforcements onthe bearings and the corners.2. Practical formula of the beam-arch association bridgesWith the FEM results of suspender forces under the uniform load, the paperassumed that all the suspender forces were equal, and the suspender forces could be regarded as filmy ones. The beam-arch association bridge was departed intobeam-arch body and filmy suspender. Through the deforming balance equation at themidpoint, the practical formulas of filmy suspender forces, deflections at the midpointwere acquired. Then, reasons of error between the FEM results and practical formulaswere discussed. Using quartic parabolic curve to replace uniform curve, cosine forceto filmy force, coefficients of correction—c1 and c2 were valuated; comparingbetween the FEM results and corrected formulas by c1 and c2, the third one—c3 wasvaluated. Effect of axial deformation, simplification of the formulas for special case, another way to the formulas of dynamic deformation balance equation were the nextwork. Finally, the influence line method, which is used to mechanically resolve thestructure under point force, was presented.3. Cooperation mechanic between beam and arch for beam-arch association bridgesWith the mechanical method, the formulas about beam-arch body were acquiredwhen it was individually loaded on arch, beam, arch and beam. The formula of elasticcenter was also got. Next, the paper presented the expressions on ratio of load sharingand ratio of moment sharing between beam and arch. Moreover, the influence curvesabout ratio of beam-arch sectional flexural rigidity, ratio of suspender-arch equivalentflexural rigidity, ratio of rise to span, influence coefficient of axial deformation weredealt with graph. Four performance indexes were used to defined the specificationbetween rigid arch and flexible beam, flexible arch and rigid beam, or rigid arch andrigid beam. The four indexes were beam-arch ratio of moment sharing, axial force ofbeam, arch deflection, and beam deflection. The author holds the ideal that thebeam-arch association bridge can be dealt into rigid arch and flexible beam whenEI_b/EI_a≤1/50; flexible arch and rigid beam when EI_b/EI_a≥20.4. Rational sloping angle of outward beam-arch association bridgesOutward beam-arch association bridges were classified according to therelationship of sloping angles between arch, beam, and suspender. From therelationship of sloping angle between arch plane and vertical plane, basic systemⅠwas defined; and relationship of sloping angle between arch plane and suspenderplane, basic systemⅡ. Through the influence line analyzing of displacement andinner force, and parametric analysis between structural performance indexes (such as) and arch sloping angle, the relation curves between those indexes and arch slopingangle were achieved, then the conclusion that rational arch sloping angle is less than30°was drawn; Through the parametric analysis between those indexes andsuspender sloping angle, the relation curves between those indexes and suspendersloping angle were achieved, then the conclusion that rational arch sloping angle is 0°was drawn. That is to say, when the external force is coplanar to arch plane, thesuspender angle is the most rational.5. Valuating of pushing forces for spatial multi suspendersThe meaning of rational design point for bridge was discussed, and it wasdivided into three stages—construction stage, completed bridge stage, and servicestage. Then, the meaning and relationship between the three rational design pointswas discussed. The core stage was service stage, but because of the uncertainty ofeffects by variable forces, shrinkage, and creep, the rational design point at the servicestage was usually solved. A new method to valuate the pushing forces for spatial multisuspenders was presented, which was based on the first-order algorithm in the popularFEM software—ANSYS, could ensure the rationality of internal force and line shapein all the three design points, was completely emulated from the actual construction, and was convenient to deal with all the nonlinear factors. The method is simple andfeasible, and can set up the direct and forward connection between the suspenderforces (design variables) and indexes of rational design point.更多还原