Key-problem Study For Design Theory Of Beam-arch Association Bridges

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.