Analytical Theory For Static And Dynamic Characteristics Of Suspension Bridges Stiffened By Truss Girders With Integral Orthotropic Deck

In terms of the steel truss with integral steel deck (ISDT), an equivalent continuummodel is established, and theoretical investigation together with parametric analyses arestudied in the dissertation, primaryly focusing on warping torsion and shear lag effectsof ISDT, static behavior and free vibration characteristics of suspension bridge stiffenedby ISDT. The main contribution in the dissertation is as follows:(1) The structural types and parameters of stiffening trusses of those in-servicesuspension bridges are summarized and statistically analyzed. The structural features ofthe types of different components are investigated, including the main truss, transversebracing, and lateral bracing. Based on statistic data, a criterion is proposed to determinethe key design parameters, such as the stiffening truss height. In addtition, the structuralcharacteristics and details of ISTD are described. Taken the Lishui Suspension Bridge asexample, an alternative scheme design using ISDT as stiffening girders is presentedcomparing with the original design using conventional stiffening truss with detachedreinforced concrete deck, and comparisons in terms of technology&economy are madebetween the reinforced concrete deck and the integral steel deck.(2) the ISDT bridge is a composite structure consisting of orthotropic steel deckand spatial truss. The basic idea of continuum model method in analyzing struss bridgeis to transform the web member systems into equivalently continuous distributed shearthin-walls. By extending this method to the application of ISDT, concept of theequivalent normal and shear thickness are proposed for the orthotropic steel deck,reflecting its different abilities in resisting the normal strains and the shear strains; whilethe equivalent normal thickness of web member systems is taken as zero. Consequently,both conventional truss and ISDT are converted into the analogy thin-walled girders inthe form of identical parameters. According to the basic principles of Umansky’s secondtheory, warping restrainted torsion of the analogy girder is theoretically studied, and itstorsional characteristics are explicitly derived.In addition, the influence of the variations in the geometrical dimensions of maintruss, lateral bracing and intergal steel deck on the torsional behavior of ISDT issubjected to parametric analysis. From the perspective of the torsional strain energy, thetorsional properties of thin-walled girder are revealed. The ratio of warping strainenergy to total strain energy is set as an estimate criteria. When this ratio is less than 0.05, the restrainted torsional behavior of the structure can be regarded as pure torsion.The correlations between this energy ratio with both the warping coefficient ofcross-section and the torsion coefficient of thin-walled girder are developed. Warpingcharacteristics and torsional properties of conventional truss, ISDT and flat box girderadopted in the suspension bridge, are revealed.(3) The integral steel deck, acting as a flange, participates in overall mechanicalbehavior of ISDT bridge. Therefore, when the ISDT is under the vertical load, shear lagphenomenon will appear on the deck, similar as a common thin-walled girder with wideflange. By transfoming the ISDT into equivalent thin-walled girder, the shear lag effectof ISDT is studied with energy variation method. Considering the structuralcharacteristics of ISDT girder, three independent generalized displacement functions areemployed in the analysis, including the deflection, rotation angle of the girder and themaximum difference of warp displacement on flange. In addtion, an uniform warpingdisplacement on the whole cross section is chosen to meet the axial self-equilibriumcondition for normal stresses on section. When calculating general potential energy,shear strain energy of the analogy web of main trusses is taken into consideration, thefeature of the steel deck as stiffened flange distinguished from flat flange is alsoconsidered. The fundamental equations concerning the three generalized displacementare derived by the principle of minimum potential energy.Furthmore, the reasonable order of shear lag warping function on flange isdiscussed. The correlations between the effective width coefficient and differentstructural parameters are developed, including deck span-width ratio, deck platethickness, stiffener thickness and the stiffener type. Based on the comparison of theeffective width coefficients of the stiffened flange among different specifications, therecommended method is presened.The concept of shear lag in panel truss is proposed for analyzing the stressconcentration on the integral deck near the main truss nodes.(4) Based on the linear deflection theory, vertical static analysis of suspensionbridge is studied using direct iteration solution, obtaining the distribution patters ofbending moments and shear forces of stiffening girders. Combined with the shear lagtheory, the characteristics of shear lag in the stiffening ISDT girder are presented undertypical disadvantageous load cases. Non-uniform stress distribution on the deck is stillconsiderable at the position where concentrated load acts on. The effective widthcoefficients of the stiffening ISDT girder is similar along longitudinal axis, which isdifferent from a single girder without cables supporting. In addition, the lateral membrane theory in analysising the lateral static behaveor ofsuspension bridge, is solved with the application of trigonometric series method, theanalysis and comparison of loading effect caused by lateral wind forces are madebetween the suspension bridges stiffened by ISDT, and those bridge stiffened byConventional steel truss or steel box girder.(5) The coupled vibration equations of the suspension bridge are deduced,involving the complete spacial displacements of the two cables and the stiffening girder,which reveals the multi-degree displacements coupling relationship on the cases ofin-plane vibration and spacial vibration of suspension bridge as a result.The practical simplified model is established for the in-plane vibration coupedlongitudinal and vertical motions, in which the effect of the cable’s longitudinal motionis considered. The frequency estimation formula to the lower-order antisymmetricvertical and longitudinal coupling mode is developed. The influence of the cables’ andthe stiffening girder’s geometric parameters on coupling effect is investigated. As tosuspension bridges without longitudinal constraint to stiffening girder, this kind ofcoupling vibration is generally common considering the practically-adopted parametersof cables and stiffeding girder of these existing bridges.For the suspension bridge with center ties, the cables are respectively employed foreach half bridge, to establish the compatibility equations considering the longitudinaldisplacement of the cable at mid-span. In addition, the compatibility condition betweenthe longitudinal displacements of cables and the deformation of both center ties andstiffening girder at mid-span is established. Based on the variation of additional cabletension caused by center ties, the effects of center tie to various mode cases are clarified.For the antisymmetric torsional vibration, the center tie’s restriction on the cable’slongitudinal movement causes an antisymmetric additional cable tensions at mid-span,which will enhance its natural frequency as a result. The torsional vibration differentialequation of the suspension bridge with center ties is derived theoretically, and thegeneral expressions of mode shapes and the implicit equations of frequencies arepresented. The dimensionless parameters controlling the vibration characteristics, suchas the ratio of cables’ elastic stiffness to the sum of cables’ gravity stiffness togetherwith girder’s stiffness, are defined and discussed, to reveal the effectes of themechanical parameters of cables, stiffening girder and center ties on the torsional modesand frequencies. The approximate estimates for torsional symmetric and antisymmetricfundamental frequencies are obtained by the Ritz approach.Finally, as to Lishui Suspension Bridge, the wind-induced stability assessment is evaluated for the proposed design scheme of the bridge stiffened by ISDT, based on thefree vibration analyse mentioned.