Curved Girder Bridge Research Articles

Shear Lag Analysis and Effective Width of Curved Girder Bridges

The effective width of curved girder bridges is formulated by substituting the flange stress derived from present theory into the equation of effective width definition for the curved girders. The required information in formulating the effective width rule for design of curved girder bridges are provided. The actual longitudinal stress distributions for the curved girders are evolved from the present theory for shear lag in order to determine the effective width. The thin-walled curved girders used in this investigation are based on box and channel cross sections, and are analyzed for a uniform lateral load and for a concentrated load. Numerical examples are shown for several problems to investigate the effect on the effective width of curved girder bridges. The values of the effective width obtained by the present theory are compared with those of the straight girder bridges. According to the results, the values of the effective width of curved girder bridges can be regarded as the values of the straight girder bridges approximately.

State-of-the-art of curved girder bridge programs

This paper will present information on the numerous computer programs that have been developed which may be used to analyze or design curved girder bridges. The material is limited to programs applicable to curved bridges loaded normal to the plane of curvature and does not consider arches or rings. Specifically, the capabilities of 27 software systems are examined.

Closure to “Theoretical Analysis of Curved Girder Bridges”

Closure to “Theoretical Analysis of Curved Girder Bridges”

Discussion of “Theoretical Analysis of Curved Girder Bridges”

Discussion of “Theoretical Analysis of Curved Girder Bridges”

Theoretical Analysis of Curved Girder Bridges

A method for predicting stress and deflection of horizontally curved girder highway bridges is presented which gives close agreement between predicted and measured values. Values obtained by use of this method are compared with values obtained using CUGAR 1 for both stress and deflection.

Curved girder bridge analysis

A Fourier Series Slope-Deflection Technique has been developed as a means of analyzing curved girder bridge systems, which may contain orthotropic decks. The technique incorporates both pure and warping torsional effects as well as bending effects. Girder deflections and internal forces are determined at any location along the respective girders. The resulting forces include bending moment, shear, pure torsion, warping torsion, and bimoment. The entire slope-deflection analyses has been programmed for use on an IBM 7094 computer, FORTRAN IV language. The three programs for a (1) single span analysis, (2) two-span continuous structure, and (3) three-span continuous structure may be obtained from the authors.

Analysis of Horizontally Curved Box Girder Bridges

A stiffness method for the analysis of simply supported curved girder bridges with horizontal sector plates and vertical cylindrical shell elements is outlined. Stiffness coefficients of sector plates are presented herein whereas stiffness coefficients of shell elements are based on Hoff’s solution of Donnell’s equations. A numerical example illustrating the application of the method is shown. Some interesting results, particularly those with respect to the effect of radius of curvature, were obtained. A comparison is made between the results of a curved twin box girder bridge obtained by the proposed method and Tung’s method.

Analysis of Curved Girder Bridges

The Fourier Series slope-deflection method has been developed as a means of analyzing curved orthotropic deck bridge systems. Bridge deflections and internal forces in the curved girders are determined at any location on the span. The method allows for the interaction of the curved orthotropic or isotropic plates with curved elastic girders. All deflections, slopes, and internal forces are assumed as a Fourier Series and are thus determined by a term-by-term solution. Equilibrium equations are developed at all girder-plate junctions as they are at member joints in the rigid frame slope-deflection method. The entire slope-deflection analysis has been programmed for use on an IBM 7094 computer. This program is applied to an existing straight beam and a number of hypothetical curved beam spans. The effects of slab thickness, warping and pure torsional stiffness, and radius of curvature are presented for a hypothetical curved bridge system.

Analysis of Curved Girder Bridges

Geometric, aesthetic, and economic considerations have led to the increased use of horizontally curved girders for highway bridges and interchange facilities which involve curved alignment. Despite the slightly higher fabrication costs associated with curving the girders, the net costs for such bridges, in certain cases, are lower than those for curved bridges with straight beams placed along the chords of the curved roadway. This overall economy is a result of the elimination of many substructure units (piers) and simplified form work necessary for the roadway slab. Since curved girders may be classified as linear elastic structures, all the various methods of linear structural analysis may be applied to the design of curved bridges. Although considerable analytical work has been done in this area, no attempt has been made to correlate the various methods of analysis or evaluate the degree of approximation inherent in several of the design procedures. The purpose of this paper is twofold. First, the fundamental differences between the behavior of individual straight girders and curved girders loaded normal to the plane of curvature will be established. Second, numerical results obtained from an approximate method of analysis widely used in the design of curved bridges3 will be compared with a rigorous analysis of curved grid systems.

Testing of a Model Curved Steel Girder Bridge

Tests of three 1/8-scale curved girder bridge models are being conducted in the Civil Engineering Department at the University of Rhode Island at Kingston, with the purpose of confirming analytical solutions. This is a report on one of these tests, a three-girder, two span model of a 160 ft long prototype bridge. The model actually simulates a highway ramp for a typical city interchange. Our objective as stated in the beginning was to try to prove that Professor Lavelles analysis is accurate. Results from testing this three-girder model bridge indicates that the analysis is conservative and accurate within limits tolerable to design.

STUDY ON FREE VIBRATION OF CURVED GIRDER BRIDGES

The studies on free vibration of a curved girder bridge are much complicated because the bending vibrations in orthogonal directions are generally coupled with the torsional one. The object of this paper is to present the fundamental equation for a freely vibrating curved girder bridge with an unsymmetrical cross-section and to obtain an approximate solution of the frequency equation. From these results, the practical formulae for determining the natural frequencies are proposed. Furthermore, the validity of this theory is verified by comparison with the results obtained from the experimental studies.

Discussion of “Moments and Free Vibrations in Curved Girder Bridges”

Discussion of “Moments and Free Vibrations in Curved Girder Bridges”

Closure to “Moments and Free Vibrations in Curved Girder Bridges”

Closure to “Moments and Free Vibrations in Curved Girder Bridges”

THREE DIMENSIONAL ANALYSIS OF SIMPLY SUPPORTED CURVED GIRDER BRIDGES

Whenever a curved girder bridge is loaded. transversely, the bending and torsion are generally bicoupled. Hence, it is much favorable to adopt such a structural type as box girder bridge or grillage one, which can resist effectively the torsion induced over the whole cross section of bridge.In this paper, the authors have obtained the solutions for the deformations and also for the strese resultants by means of the generalized torsion bending theory which they developed in the previous paper.

THREE DIMENSIONAL STRESS ANALYSIS FOR CONTINUOUS CURVED GIRDER BRIDGE

For the continuous curved girder bridge under the vertical loads, the three dimensional stress analysis is presented on the basis of the torsion bending theory.In a continuous curved girder bridge having a number of spans, the cross sectional quantities as well as the principal dimensions will generally differ from those in adjacent span and it is a statically indeterminate structure. For the sake of analysis, the simply supported system will be produced by cutting the structure at each intermediate supports m. Then both the bending moments Mm and the warping moments _??_m that must be applied at the cross sections in order to close the gaps and restore continuity are the statical redundancies of the problem. From the condition of continuity, the theorem of least work leads to a set of elastic equations (11) for the unknown stress resultants Mm and _??_m.The coefficients a, b and d contained in the equations can be easily determined by the formulas (12) to (49), and also the load terms Lm and Nm, are given by the formulas (50) to (98) for some typical loading conditions.Solving these equations to find the magnitudes of the unknown quantities and adding the contributions due to the end moments Mm, _??_mand due to the applied loading upon the imaginary simply supported system, the final stress resultants, namely, the bending moment Mym, the warping moment Mwm, the St. Venant's torsional moment Tsm the secondary torsional moment Twm, the shear force Qm due to bending and the total torsional moment Tm, of the mth span can be readily evaluated from the expressions (5) to (10). Hence stress distribution at any cross section can be clarified by means of the formulas (51) and (53) given in reference (3).Similarly the deformation, namely, the deflection δm of the shear center and the rotating angle βm about the same point at any cross section are given by (128) and (129) respectively.A three-equal-span continuous curved girder bridge with the same constant section as King County shown in Fig. 2 are treated as a numerical example of the foregoing analysis.From these results of the estimation, the influence lines of the stress resultants and the deformations at some selected cross section are illustrated in Fig. 3 to 21.Thus the effects of the curvature upon the basic characteristic in the continuous curved bridge can be explicitly seen by examining of all the data obtained in this paper.

Moments and Free Vibrations in Curved Girder Bridges

Solutions for orthotropic fan-shaped plates, which are simply supported at 2 opposite straight edges and rigidly attached to elastic beams at other curved edges, have been obtained for static case of uniformly distributed load and for case of free vibrations; these solutions applied to numerical analysis of curved girder bridges.