On the Coupled Free Vibrations of a Suspension Bridge (II)

Following the previous investigation on the free vibrations of a suspension bridge, this paper presents the specific characteristic associated with the second class of (torsional) modes. Numerical works are carried out by use of the Rayleigh-Ritz method under the lower order of approximations

On the Coupled Free Vibrations of a Suspension Bridge-(I)

In Part I, a set of fundamental equations of motions of a suspension bridge is derived and classified into two classes of modes, the first of which can be termed as the deflectional modes, while the second can be termed as the torsional modes. Analytical solutions for the deflectional modes of free vibrations are discussed and determined by employing the Ritz method with and without a fix point at midspan of stiffening floor. Detailed informations for the torsional modes and some basic applications of the theory developed here will be described in Part II

Safety Analysis and Minimum-Weight Design of Rigid Frames Based on Reliability Concept

This paper deals with the safety analysis and the minimum-weight design of rigid frames based on reliability concepts. A safety analysis of redundant systems has difficult features, which are due to the fact that those systems generally have many various possible failure modes. As a rule, the approximations have been done on the assumptions of statistical independence and complete dependence among failure modes. However, the resulting solutions may be widely different as the number of failure modes increases. Also, usual structures have considerable dependence on their own failure mechanisms. A simple formula presenting a good upper bound is derived herein by using the correlations between every two modes. The discussion is done with respect to the lower bound. Its improvement is attempted by introducing a simple mathematical model, which is used for estimating the probability that any three events occur simultaneously. This paper also outlines the minimum-weight design with reliability constraints. The proposed method is employed in the safety analysis. The results are discussed and compared with those of the deterministic method. For large systems, an approximate design method is proposed, which decomposes the possible failure modes into basic and nonbasic modes

On Vortex Shedding Excitations of Cable-Stayed Bridge of Closed Polygonal Cross Sections

This paper presents a few fundamental instability characteristics of vortex shedding excitations for closed cross sections of bridge structures by means of wind tunnel and water flume tests. Experimental results indicate that the hexagonal form of a cross section with spoilers and flaps is a satisfactory stable cross section for aeolian oscillations. It is also noted that there are multiple synchronized regions of wind velocities for vortex shedding excitations of such cross sections treated here. As far as induced drag forces acting on obstacles and shedding frequencies are concerned, the results by water flume tests well coincide with those by wind tunnel tests

Experimental Studies on Free Vibrations of a long spanned Suspension Bridge

This paper presents the experimental results for static and dynamic characteristics of a suspension bridge with inclined hanger system comparing those with ordinary vertical hanger system by use of three spans suspension bridge model (3, 250+6, 500+3, 250). The discrepancy due to the inclination of hangers is studied by the model test on the natural frequencies, the frequency responses and the damping-amplitude relations for the above cases. The results indicate that the inclination of hanger system may increase the deflectional stiffness when the load acts asymmetrically and dynamically the damping effect in the free vibrations

On Geometry of Truss

It has been shown, by a number of examples, that it is possible to obtain rational designs by introducing a geometrical variation of trussed structures into the design process. To determine the effective geometrical configuration, two kinds of parameters, cross sectional areas and nodal coordinates, need to be taken into account in the optimization procedure. The treatment of nodal coordinates apparently results in the increase of the number of design variables, which often induces some difficulties in the application of mathematical programming. Large scale optimization problems generally have a poor convergency to require excessive computation time or memory capacity. For such problems, U. Kirsch proposed a decomposition approach and showed its efficiency by some design examples. In this paper, a search for least-weight geometry is carried out by a two-step treatment based on Kirsch's approach. The cross sectional areas are assumed to be completely dependent on and determined from the set of nodal coordinates. Then, two design approaches are considered. The first approach is the deterministic method based on the allowable stress criterion. The other is the probabilistic method, where the safety is examined by the system failure probability. Also, the influence of buckling constraints and the number of employed nodes on geometry are discussed through some numerical examples

On the Torsional Distorsions of Long-spanned, Four-walled Trussed Structures

In this paper the torsional deformation of four walled stiffening girders is investigated from the theoretical point of view and the results are compared with experimental results performed on the two types of models, namely the so-called plate-girder type model and the truss type model. The Torsion-box theory is applied for analysis of torsional behaviour of four trussed-walled box girder beams. However the truss type girder can resist torsion less compared with the ideal thin-walled girder and can be characterized by the modified form of the Two-spar theory rather than the Torsion-box theory

On Galloping Oscillation of Square Prism in Two Dimensional Uniform Flow

In the connection of frequently used structural members of longspanned bridges, the aeroelastic characteristics of a square prism are investigated, based on the quasi-steady theory. The experimental results of the wind tunnel tests are compared with the theoretical characteristics, using the theory given by G. V. Parkinson. In this paper, some considerations on the critical wind velocity for galloping phenomenon of square prism are presented. Also, the qualitataive method to determine the induced amplitude is discussed

A Study on the Bandwidth Reduction of the Stiffness Matrix of a Framed Structure

How to give the numerical number for joints of a framed structure in order to reduce the bandwidth of its stiffness matrix, has been studied and a number of methods have been proposed already. Though the minimum bandwidth is wholly governed by the connectivity relationship between joints, only a few studies have taken that fact into the consideration. The connectivity relationship of a framed structure can be sufficiently shown by the use of a linear graph, which is composed of nodes and lines. Its characteristics can be understood by introducing the concept of graph theory. In this paper, the authors propose a graphical method to obtain the minimum bandwidth of tree structures. This is a kind of statically determinate system including no closed path, by the application of some definitions in graph theory. By use of the this sequential file method, all the nodal sequences are efficiently filed along the longest nodal sequence among the graph. The number of rows of filed nodal sequences present the bandwidth of the original structure

A Network-Topological Study on Statical Analysis of Rigid Framed Structures

For the numerical analysis of complex structures with high redundancy by use of the digital computer, there arise a number of difficulties to solve the problems on an account of the fact that the increase of the rank of matrice involved requires much storage and time to obtain numerical results. A network-topological formulation of structural analysis leads effective algorithm to solve these problems. The alternative derivation of Spiller's formula and a memory-saving algorithm is considered in this paper