Ho-Sung Na

Simplified Analysis for Preliminary Design of Towers in Suspension Bridges

This paper proposes an equivalent suspension bridge model for the preliminary design of support towers of suspension bridges. In this simplified model, the bridge is composed of its support towers, with equivalent springs replacing suspension cables and girders. An explicit formula for the spring stiffness was derived for the horizontal stiffness at the end of an inclined main cable and compared with Ernst’s formula as well as finite-element analysis results. For the analysis of the model, dead and live loads acting on the girders of each span were replaced with horizontal and vertical forces calculated using the deflection theory and placed on the tops of the support towers. Equilibrium equations were derived from free-body diagrams for each tower and their solutions were obtained from boundary conditions at the ends of the towers. This resulted in the formulation of nonlinear load-displacement equations in matrix form for the simplified bridge model. An example four-span suspension bridge was analyzed for displacements at the tops of the towers and moment reactions at the bottoms of the towers under six live-load cases. A comparison of the model predictions with a FEM analysis showed excellent agreement. The results prove that the proposed analysis method can be a useful alternative for the preliminary analysis and design of suspension bridge towers.

Stability evaluation of steel girder members in long-span cable-stayed bridges by member-based stability concept

The member-based design concept utilizing the buckling length of each structural member has been widely used to assess the buckling instability of steel structures. Since steel girder members in conventional cable-stayed bridges are generally exposed to large axial forces, the buckling instability of these members should be carefully investigated in the design stage. However, analytical approaches for obtaining the buckling lengths of steel members, such as the alignment chart, story-buckling and story-stiffness methods, may not be adopted to cable-stayed bridges because these approaches imply some theoretical assumptions that are adequate only for steel framed-structures. Furthermore, the boundary conditions of steel girder members supporting by cables are obscure to be prescribed in general terms. Numerical eigenvalue analysis may be one of the most excellent candidates for determining the buckling lengths of steel girder members in that this method can handle the interactions among members implicitly without any irrelevant assumptions for cable-stayed bridges. This paper discusses detailed procedures for obtaining buckling lengths of steel girder members in cable-stayed bridges by numerical eigenvalue analysis. In order to avoid the problem of generating excessively large buckling lengths in some girder members having small axial forces, a modified eigenvalue analysis is proposed by introducing the concept of a fictitious axial force. Practical application example for a real cable-stayed bridge is illustrated with some discussions on the effect of the proposed modification and stability evaluation by member-based stability concept.

Iterative eigenvalue analysis for stability design of three-dimensional frames considering a fictitious axial force factor

In design of steel frames, it is well known that the Euler buckling equation with eigenvalue analysis may lead to unexpectedly large effective lengths of members that have relatively small axial force. This paper illustrated the use of a fictitious axial force factor to overcome the problem mentioned above. Considering a fictitious axial force factor, the illustrated method determines the elastic and inelastic effective lengths of each member in three-dimensional steel frames based on iterative schemes and the stiffness reduction factors. To verify the validity of the illustrated method, the effective lengths of example frames by the proposed method were compared with those of previously established methods. The results show that the proposed method gives reasonable effective lengths of all members in space frames, and can be a good substitute for previously established methods.

Modification of moment equations in the CHBDC (2000) for soil-metal box structures

This paper evaluates the moment equations in the 2000 Canadian Highway Bridge Design Code (CHBDC) for soil-metal box structures, which are applicable to spans less than 8 m. Finite element analyses are carried out for soil-metal box structures having spans of 4-15 m using the deep corrugated metal plates under three construction stages: backfill up to the crown, backfill up to the cover depth, and live loading. The coefficients of moment equations are newly proposed based on the results of numerous finite element analyses considering various design variables, such as span length, soil depth, and backfill conditions. The validity of the proposed coefficients in the moment equations of the CHBDC (2000) is investigated and compared with the existing coefficients and numerical results of finite element analyses. The comparisons show that the moments of the CHBDC (2000) give good predictions for spans less than 8 m, but underestimate them for spans greater than 8m. In contrast, the proposed moments give good estimates of numerical results for the spans of 4–15 m.