Innovative steel bridge girders with tubular flanges

I-shaped steel girders with tubular flanges have been studied for application in highway bridges because of their large torsional stiffness compared to conventional I-shaped steel plate girders (I-girders). For straight girder bridges, the large torsional stiffness of a tubular flange girder (TFG) results in significantly greater lateral–torsional buckling strength compared to a corresponding I-girder. For horizontally curved girder bridges, the large torsional stiffness of a TFG results in much less normal stress, vertical displacement and cross-sectional rotation compared to a corresponding I-girder. The paper presents experimental and finite element analysis results for straight and horizontally curved TFG bridges. The results show the advantages of TFGs in comparison to conventional I-girders. A TFG demonstration bridge constructed in the USA is described.     

Torsional stiffness requirements for diaphragm bracing of discretely braced I-girders

I-section girders are laterally interconnected by Torsional bracings that are discretely installed to increase resistance to lateral-torsional buckling. However, there are confusing discrepancies in the current design specifications for the stiffness of diaphragm-type bracings. The mathematical formula for determining the required torsional stiffness is still unclear. In this study, rigorous examinations were carried out to clarify the effects of the web distortional stiffness and the number of diaphragm bracings. To achieve the purpose of this study, the theoretical derivation of the stiffness equations was thoroughly examined. Three-dimensional finite-element analysis was used for the parametric numerical analyses of a series of feasible two-girder system models, and enhanced equations are proposed for achieving sufficient stiffness in the torsional bracings. The practical validity of the proposed equations are verified by statistical correlation analyses, which clearly prove their superiority compared to current design guidelines.     

单箱双室箱梁对称弯曲时的局部扭转效应

为研究单箱双室箱梁在对称竖向荷载作用下的受力特征,基于横截面的荷载等效原理与荷载分解,分析了单箱双室箱梁对称弯曲时的局部扭转效应。基于截面的剪力流平衡和箱室受力分解,得到了局部扭转的等效荷载及应力计算式。通过与有机玻璃模型试验和有限元模拟结果的对比,验证了局部扭转效应计算式的正确性,并获得了单箱双室简支箱梁的局部扭转效应下的应力分布规律。研究表明,单箱双室箱梁在仅中腹板作用竖向荷载及两边腹板作用相等竖向荷载时,均存在纵向弯曲和局部扭转的组合变形模式。局部扭转由约束扭转、畸变和横向弯曲效应组成,在截面引起纵向应力和横向应力。局部扭转效应的理论计算结果与模型试验和板壳有限元分析结果吻合良好,表明基于截面剪力流等效的局部扭转荷载求解方法对双室箱梁是适用的;单箱双室箱梁的局部扭转效应在荷载作用点附近截面最为突出,截面上、下缘纵向应力和横向应力以中腹板为拐点呈折线分布,其应力分布和大小与荷载在横截面上作用的部位紧密关联;对算例箱梁,局部扭转效应产生的纵向应力可达初等梁弯曲应力的25%。     

Study of horizontally curved bridge girders with tubular top flanges

A system of I-shaped steel plate girders [i.e., conventional I-girders (IGs)] with cross frames between girders is widely used in curved bridges in the USA. A conventional IG has low torsional stiffness and strength, so before it is braced by cross frames, it develops large deformations and stresses under its own weight if unsupported within the span; temporary shoring is usually required during erection of a curved conventional IG bridge. An I-shaped girder with a hollow tube as the top flange (i.e., a TFG1) has larger torsional stiffness and strength than a conventional IG, resulting in improved behaviour and simpler curved bridge erection. In this paper, curved TFG1 bridge systems are analysed and compared with corresponding conventional IG systems. The advantages of curved TFG1 systems are (1) individual curved TFG1s have smaller deformations and stresses than corresponding conventional IGs during erection, and can carry their weight across the span without temporary shoring or bracing within the span; (2) curved TFG1 systems have smaller second-order effects than corresponding conventional IG systems; (3) curved TFG1 systems require lighter cross sections or fewer interior cross frames than corresponding conventional IG systems.     

Consideration of the problem of shearing and torsion of thin-walled beams with arbitrary cross-section

In structural analysis it is often necessary to determine the geometrical properties of cross-sectional areas. The location of the shear center is of greater importance for a thin-walled cross-section. The purpose of this paper is the computation of the shear center of arbitrary thin-walled cross-sections using the finite element method. The coupling problem of shearing and torsional deformation of thin-walled beams based on Saint Venant's theory is considered. This problem of coupled shearing and torsional deformation was analyzed using the finite element method in which the matrix of shear rigidity and torsional rigidity were determined. The shear center can be obtained by determining the coordinate axes so as to eliminate the nondiagonal terms. Then, applying the stiffness matrix of shear rigidity and torsional rigidity obtained in the above, the stiffness matrix of the space framework elements in which the shear deformation is taken into consideration is developed.     

Improvement effects of bottom lateral bracings on dynamic performance of curved steel twin I-girder bridges under running vehicles

The torsional stiffness of curved twin I-girder bridges is very low, which may lead to a vulnerability to eccentric dynamic loads. This study is intended to investigate the improvement effect of bottom lateral bracings on dynamic performance of curved twin I-girder bridges under running vehicles, using a developed numerical approach. In this approach, to conduct the running vehicle-bridge interaction analysis, finite element method is used to create the detailed models of both the curved bridge and the running vehicle. Parametric studies are carried out using these numerical models to investigate the effect of bottom lateral bracings on the dynamic performance of the curved bridge under running vehicles. The numerical results indicate that the proposed bottom lateral bracing systems can increase the torsional stiffness of the bridge, whose increasing rate depends on the type of bracing configuration. The bottom lateral bracings can also distribute dynamic loads smoothly between the two main girders, which leads to a more stable structure.     

Biegedrillknicken von Trägern mit einfach‐symmetrischen Profilen

Lateral torsional buckling of girders with monosymmetric cross‐sections. The determination of the critical moment for lateral torsional buckling constitutes a main design issue for steel girders subjected to bending moments. This paper presents simple formulae for the estimation of the critical moment for simply supported girders subjected to end moments and transverse loading. The formulae cover a wide range of practical applications. They are derived by formulation of the relevant energy potential and solution by means of the Ritz method. For the angle of twisting one series terms are considered. The accuracy in comparison with more elaborated solutions by means of more series terms is examined. The comparison shows the adequacy of the proposed method.     

单索面斜拉桥薄壁钢箱梁受力研究

介绍了单索面斜拉桥薄壁钢箱梁体系剪力滞后效应的研究现状,并列举了剪力滞分析方法。结合一实际斜拉桥荷载试验,分析了单索面斜拉桥体系下薄壁钢箱梁的整体受力性能,通过实测数据与有限元计算结果对比分析,结果表明:塔端位置处截面剪力滞后效应不明显,而跨中截面处主梁剪力滞效应则非常突出;实测主梁抗扭性能满足要求。     

Design aid for moment strength of built-up crane runway girders

The evaluation of elastic moment for built-up crane runway girders is not an easy task as the difficulty involves the calculation of torsional properties including warping constant, the coefficient of monosymmetry, and torsion constant. To date, all AISC specifications offer no specific formulas for determining the elastic critical moment for WC (W-shape with Cap channel) or SC (S-shape with Cap Channel) girders. They provide only the approximate formulas which were derived from singly symmetric I-sections. Based on this study, the AISC approximate formulas would underestimate the elastic critical moment of WC/SC girders by 6?C25% depending upon the unbraced length. This paper first summarizes the theoretical and AISC formulas for WC/SC girders. Theoretical torsional properties and relevant design parameters for WC/SC girders are computed and arranged in tabular form for design purposes. With these design values made available, engineers can perform more rational evaluation of WC/SC girders more conveniently. Lastly, a simplified but rational design approach is proposed for all available WC and SC girders listed in the AISC design manuals.     

Nonuniform torsional analysis of variable and open cross-section bars

This work gives exact solutions for the torsional analysis of variable and open cross-section bars. An analytical method is derived to form the stiffness matrix of the bar, including the effect of warping. Only one element is needed for the exact solution in regions with continuous variation in section properties and loading. Several examples are given and compared to approximate results.     

变截面吊车梁直角突变式支座的构造

变截面吊车梁的疲劳破坏与变截面的支座构造紧密相关。根据变截面吊车梁两种直角突变式支座构造的疲劳性能研究结果,讨论变截面吊车梁直角突变式支座节点的合理构造,并推荐其中一种疲劳性能好、经历过工程实践检验而可广泛推广应用的支座节点构造。     

Torsional vibrations of open and variable crosssection bars

This work gives exact solutions for the torsional vibration frequencies of symmetric variable and open cross-section bars. An analytical method is derived to form the dynamic stiffness matrix of the bar, including the effect of warping. An example is given and compared to approximate results. The effect of warping is demonstrated.     

Finite strip elastic buckling solutions for thin-walled metal columns with perforation patterns

Approximate finite strip eigen-buckling solutions are introduced for local, distortional, flexural, and flexural-torsional elastic buckling of a thin-walled metal column with perforation patterns. These methods are developed to support a calculation-based strength prediction approach for steel pallet rack columns employing the American Iron and Steel Institute׳s Direct Strength Method, however they are generally posed and could also be useful in structural studies of thin-walled thermal or acoustical members made of steel, aluminum, or other metals. The critical elastic global buckling load including perforations is calculated by reducing the finite strip buckling load of the cross-section without perforations using the weighted average of the net and gross cross-sectional moment of inertia along the length of the member for flexural (Euler) buckling, and for flexural-torsional buckling, using the weighted average of both the torsional warping and St. Venant torsional constants. For local buckling, a Rayleigh–Ritz energy solution leads to a reduced thickness stiffened element equation that simulates the influence of decreased longitudinal and transverse plate bending stiffness caused by perforation patterns. The cross-section with these reduced thicknesses is input into a finite strip analysis program to calculate the critical elastic local buckling load. Local buckling at a perforation is also treated with a net section finite strip analysis. For distortional buckling, a reduced thickness equation is derived for the web of an open cross-section to simulate the reduction in its transverse bending stiffness caused by perforation patterns. The approximate elastic buckling methods are validated with a database of 1282 thin shell finite element eigen-buckling models considering five common pallet rack cross-sections featuring web perforations that include 36 perforation dimension combinations and twelve perforation spacing combinations.     

Sensitivity analysis of free torsional vibration frequencies of thin-walled i-beam resting on elastic foundation

The sensitivity analysis of natural frequencies of torsional vibration of thin-walled I-beams resting on a Winkler-type elastic foundation and subjected to axial static loads is discussed. The first-order variation of the frequencies due to the design variable variations is derived. The cross- ection dimensions, the beam material constants and the foundation stiffness are assumed to be the design variables. The considerations are based on the theory of thin-walled beams with nondeformable cross-section. The underintegral sensitivity coefficients of the flange width and the foundation stiffness variations for a simply supported I-beam are determined. An accuracy of approximation of the natural frequencies changes due to the design variable change, by means of their first-order variations, is also investigated.     

Sensitivity analysis of critical torsional buckling load of thin-walled I-columns resting on elastic foundation

The sensitivity analysis of the critical load of torsional buckling of thin-walled I-columns resting on a Winkler-type elastic foundation is presented. The column behaviour is described according to the theory of a thin-walled beam with non-deformable cross-section. The first-order variation of the critical load due to the design variable variations is derived. The cross-section dimensions, except for the web height, the column material constants and the foundation stiffness, are assumed to be the design variables. The single eigenvalues are only discussed. Finally, a numerical example dealing with a simply supported I-column is presented. The accuracy of the approximation of the critical load change, caused by the design variable variations by means of its first-order variation, is also investigated.     

三塔结合梁斜拉桥结合段刚度匹配研究

结合梁斜拉桥主跨结合梁和边跨混凝土梁因为材料以及截面形式不同,所以二者在刚度上存在较大的差异,为保证应力和变形沿桥纵向顺畅协调地传递,需使主梁刚度在结合段处平稳过渡。该文结合武汉二七路长江大桥,首先建立其结合段空间有限元模型,然后在此基础上增大、减小结合段钢梁板材厚度以及加劲肋密度建立结合段刚度匹配优化模型,通过对此5个模型在其最不利工况下的计算结果进行对比分析,得出结合段最佳的刚度匹配形式。结果表明,增大钢梁板材厚度以及加劲肋密度为结合段最佳的刚度匹配形式,可以改善结合段纵向正应力传递。     

Shear flow in thin-walled cellular sections

Frequently flexural members are made of single or multiple cellular sections due to a variety of reasons. Clearly, the superb torsional capacity of such sections is a major attraction for girders in horizontally curved alignments. However, the ease of maintenance and esthetic considerations favor the choice of such girders.     

Der Einfluss von Zwischenhölzern auf das Biegedrillknickverhalten zweiteiliger Brettschichtholzträger

The influence of intermediate links on the lateral torsional buckling of two‐part glued laminated girders. The lateral torsional buckling behaviour of two‐part laminated girders can be influenced very advantageously by means of intermediate links. The reason for it represents mainly the shearing connecting of the two elements in their longitudinal direction. Furthermore the intermediate links cause an elastic torsional coupling which is the reason why the lateral torsional buckling of the single parts of the girder also is determined by vertical displacements besides the usual torsions and horizontal displacements which require further deformation energy. In this paper the bifurcation loads are determined for a girder with different types of the intermediate links by means of a finite element analysis. In addition nonlinear elasticity calculations according to theory of second order are carried out to get the forces and moments of the links. The results of the investigations demonstrate that connections between the two parts of the girder are the reason that the buckling loads rise significantly. The arithmetical consideration of the connections at the supports alone shows already very positive consequences on the buckling behaviour of the girder.     

钢-混凝土组合梁的抗扭特点

钢-混凝土组合梁能充分发挥混凝土抗压强度高、钢材抗拉性能好的优势,近年来,在我国已得到了越来越广泛的应用。相比抗弯曲性能,目前对组合梁扭转性能的研究还很少。然而,在建筑及桥梁结构中,组合梁受扭转作用是不少的。本文介绍了开口截面组合梁和箱形组合梁的极限抗扭特点及已有的研究成果,并指出了需要进一步研究的问题。     

Influence of shear deformation on restrained torsional warping of pultruded FRP bars of open cross-section

Pultruded FRP bars of open cross-section possess relatively low transverse shear moduli in relation to their axial and flexural moduli. This can result in shear deformation constituting a significant proportion of the total deformation induced by non-uniform bending, and a reduction in the buckling loads of members subjected to axial compression and bending. Herein an approximate theory for quantifying the influence of shear deformation on the restrained torsional warping of pultruded FRP bars of open cross-section is presented. Contrary to expectations the theory indicates that the influence of shear deformation on the restrained warping torsional stiffness of such members is not significant. The theory is validated by a series of bending and torsion tests on three pultruded FRP I-beams.