Girder Moments Research Articles

Fundamental Parameters Affecting Non Linearity of Suspension Bridges

In this research factors affecting the non-linearity of suspension bridges were studied. The fundamental parameters studied are the main and side span lengths, cable sag, tower height, cable x-section and the flexural rigidity of the stiffening girder .The effect of variation of each parameter on the cable tension and the girder moments is studied. A non-linear 2-dimensional mathematical model of a 3 span, continuous suspension bridge is considered . The solution is based on the second order deflection theory given in a computerized form. It has been found that the degree of effect of these parameters on the results of analysis in a descending order is: the main span length, side span length, cable sag, cable section and the stiffness of the bridge girder.

Long-Term Structural Health Monitoring of the San Ysidro Bridge

As part of the Lifecycle Innovative Financing Evaluation initiative, the San Ysidro Bridge along U.S. Route 550 will be monitored throughout a 10year warranty period to determine changes in deflection, stiffness, and load-carrying capacity. This paper discusses an initial live-load test on the San Ysidro Bridge as well as a subsequent load test on a full-scale single lane test bridge. The two load tests in conjunction with finite element modeling were used to determine the load rating for both shear and moment of the San Ysidro Bridge. This load rating was then compared with the load rating using the distribution factors from the American Association of State Highway and Transportation Officials (AASHTO) Standard and Load and Resistance Factor Design Specifications. According to both AASHTO specifications, the interior girder shear controlled the load rating of the San Ysidro Bridge. Using the finite element modeling scheme of frame and shell elements the interior girder moment was found to control the design. This load rating will be used as a baseline for comparison with future load ratings throughout the warranty period.

Evaluation of localised loading on suspension bridges

The deck girder moments and suspender-cable tensions caused by the application of localised loading to a conventionally articulated suspension bridge with a slender deck girder are expressed in a generalised and normalised form. Comparison with the analogous solutions for localised loading on cable-stayed bridges shows considerable similarity in practical numerical results, despite the disparity between the algebraic forms resulting from the differences of the basic mechanics of the suspension-cable and straight-stay structural systems.

Evaluation of localised loading on suspension bridges

The deck girder moments and suspender-cable tensions caused by the application of localised loading to a conventionally articulated suspension bridge with a slender deck girder are expressed in a generalised and normalised form. Comparison with the analogous solutions for localised loading on cable-stayed bridges shows considerable similarity in practical numerical results, despite the disparity between the algebraic forms resulting from the differences of the basic mechanics of the suspension-cable and straight-stay structural systems.

Finite strip analysis of multi-span box girder bridges by using non-periodic B-spline interpolation

A multi-span bridge has the peak value of resultant girder moment or membrane stress at the interior support. In this paper, the spline finite strip method (FSM) is modified to obtain the more appropriate solution at the interior support where the peak values of solution exist. The modification has been achieved by expressing the shape function with non-periodic B-splines which have multiple knots at the boundary. The modified B-splines have the useful feature for interpolating the curve with sudden change in curvature. Moreover, the modified spline FSM is very efficient in analyzing multi-span box girder bridges, since a bridge can be modeled by an assembly of strips extended along the entire bridge length. Numerical examples of the bridge analysis have been performed to verify the efficiency and accuracy of the new spline FSM.

Girder moments in simply supported skew composite bridges

The evaluation of girder moments in composite bridges becomes more urgent with the trend to increasing truck loads. The method specified by the American Association of State Highway and Transportation Officials for such an evaluation depends only on the centre-to-centre girder spacing. This method does not account for skew and therefore is extremely conservative for skew composite bridges, since the presence of skew reduces the longitudinal moments in the girders. The method proposed by the Ontario Highway Bridge Design Code (OHBDC) depends on the longitudinal and transverse rigidities of the bridge in addition to the girder spacing. However, this method is limited to bridges with skew parameters less than a certain value specified in the code. In this paper, the influence of skew on the moment distribution factor is investigated. Furthermore, the influences of other factors such as girder spacing, bridge aspect ratio, number of lanes, number of girders, and intermediate transverse diaphragms on the moment distribution factor are examined. An experimental program was conducted on six simply supported skew composite steel–concrete bridge models. The finite element method was used for the theoretical analysis. Good agreement is shown between the experimental results and the theoretical results. In addition, the finite element method was employed to conduct an extensive parametric study on more than 300 prototype composite bridge cases. The data generated from the parametric study were used to deduce expressions for the moment distribution factor for OHBDC truck loading and for dead load. An illustrative example is presented. Key words: bridges, codes of practice, composite, distribution, moment, reinforced concrete, skew, structural engineering, tests.

Girder Moments in Continuous Skew Composite Bridges

Simply supported structures are used efficiently for bridges up to a certain span limit, beyond which the use of continuous structures becomes more economical. As a result of continuity, support moments are developed and therefore span moments are significantly reduced. The design method specified by the American Association of State Highway Transportation Officials (AASHTO) does not account for the effect of skew and continuity and therefore is extremely conservative for skew continuous composite bridges since both skew and continuity influence the longitudinal moments in the girders. In the present paper, test results from three continuous composite steel-concrete bridge models are used to verify a finite-element analysis for such bridges. The finite-element analysis is then employed to conduct an extensive parametric study on more than 600 prototype continuous composite bridge cases. Several parameters are varied, such as girder spacing, angle of skew, bridge aspect ratio, spans ratio, number of lanes, number of girders, and intermediate transverse diaphragms. The data generated from the parametric study is used to deduce expressions for both span and support moment-distribution factors for AASHTO truck loading as well as for dead load. An illustrative design example is presented.

Longitudinal girder moments in simply supported bridges by the finite strip method

The finite strip method is used to analyze three different kinds of simply supported highway bridges: slab-on-girder, two-cell box-girder, and rectangular voided slab bridges. Deck width from two lanes to four lanes are considered. The Ontario highway bridge design (OHBD) truck load is applied at the most critical location of the bridge. A total of 12 design curves are developed, corresponding to different bridge sections and deck widths. From these design curves, one can obtain the ratio of the maximum longitudinal bending moment to the equivalent beam moment. Key words: bridge decks, design curves, concrete, steel, finite strip, OHBD truck load.

Nonlinear analysis of grid systems

A method is proposed for the nonlinear analysis of grid systems. The structure is loaded incrementally and the current stiffness matrices of each member are evaluated using a numerical procedure and the moment–curvature and torsion–twist relationships of the grid elements. The member stiffness matrices are used to develop the global stiffness matrix of the grid structure. In other respects, the method is very much similar to linear elastic analysis of grid framework. A bridge structure is analyzed using a computer program, developed by incorporating the proposed method. The program is able to predict the nonlinear characteristics of the structure such that it can reduce the girder moments and (or) the total material costs. Key words: bridges, nonlinear analysis, slab-on-girder bridges, grillage analysis, ultimate load capacity.

Dealing with varying moments of inertia of girders in bridge analysis

In many slab-on-girder bridges, especially those that are continuous over two or more spans, the moment of inertia of a girder varies significantly along the length of the bridge. This paper critically examines the practice of analyzing such bridges for load distribution by methods that make the assumption of constant longitudinal torsional and flexural rigidities. It is found that this practice may not be valid for those slab-on-girder bridges in which variations of the girder moments of inertia are very large.A recommended procedure is given for cases in which the variation in moment of inertia is not too severe. The procedure involves (a) the determination of total bending moments, treating the bridge as a beam of variable moment of inertia, and (b) the determination of an equivalent constant moment of inertia for beams of varying moment of inertia. Using this procedure the load distribution properties of the bridge can be realistically analyzed by those computer-based methods (e.g., orthotropic plate, finite strip, and semicontinuum methods) or manual methods (e.g., AASHTO and Ontario methods) that cannot directly take account of the variation of longitudinal flexural rigidity.The validity of the recommended procedure is established by comparing its results with those of the grillage analysis method that does take account of the variation of the girder moment of inertia. Key words: bridge analysis, girders, load distribution, slab-on-girder bridges.

Effect of Cable Stiffness on Cable‐Stayed Bridges

The effect of cable stiffness on the behavior of cable-stayed bridges is presented. Bridges of radiating arrangement, with 12, 20, 28, and 36 cables per plane were investigated. Three cases of side to main span ratios, 0.35, 0.40, and 0.45, were considered for which cable tensions, girder deflections and tower and girder moments were computed. The computational work was done on IBM 360. The stiffness matrix method, treating the bridge as a two-dimensional structure, was used.

Seismic Response of Reinforced Concrete Frames

Analytical studies of the elastic and inelastic response of reinforced concrete frames subjected to earthquake motion are presented. The effect of stiffness degradation on the seismic response and in particular on ductility demand is examined. Several single-story frames are analyzed; stiffness degradation significantly increases ductility demand in short period systems. Studies of multistory frames are also presented; stiffness degradation again increases ductility demand but the effect is pronounced only in the upper stories. The bending moments and forces induced in an inelastic multistory frame are smaller than those in a purely elastic frame. However, if the columns are designed to remain elastic while the girders yield, the reduction in the column moments and axial forces is not as large as that in the girder moments.

Seismic design of multistorey steel-frame buildings using dynamic analysis

A study is made of the feasibility and usefulness of a seismic design method for multistorey steel-frame buildings. The method employs a time-series elastic response analysis of the structure for a ground motion compatible with a design response spectrum. The correlation between the elastic and elasto-plastic response is investigated and it is suggested that the design forces in the members of an elasto-plastic structure can be obtained by applying appropriate reduction factors to the forces obtained in an elastic analysis.A design example is presented in which a multistorey steel-frame building with a rather large setback is designed for seismic forces by using the results of an elastic dynamic analysis for a selected ground motion and reducing the forces so obtained by applying one uniform force reduction factor to all girder moments and another, a smaller one, to all column moments and axial loads.

Computerized automatic design of concrete buildings

The salient features of the AMECO system of integrated computer programs are described. The entire structural design process, from geometry generation in 2- or 3-dimensional, load calculations, etc., to productionof construction documents is computerized in to one operation. Using English language commands, the engineer inputs basic parameters, such as name of the building code, number of stories, floor required to seismic factor, typical member lengths and their connectivities. As few as 16 commands are live loads, design a building of 2000 members. Optional commands are available to input predetermined data or to modify the automatic design procedures. The results of two analyses of a 30 storey frame are presented, one using AMECO with its automatic simulation of the construction sequence, and the second one, using a stiffness matrix program. The latter analysis shows substantial discrepancies in column axial strains and girder moments, demonstrating the potential dangers in use of stiffness matrix programs for structures with high dead loads, such as tall buildings. AMECO utilizes a relaxation method for frame analysis, which produces exact, in-core solutions of a 2000 member building in less than 30 sec on a CDC 6600 computer using 33,000 words of memory.

Preliminary Wind Analysis of Multistory Bents

Recent progress in computers has permitted rapid analysis of the multistory bent, including deformations due to horizontal forces. The first part of this paper presents an analysis of the girder and column forces and moments for an arbitrary story. Equilibrium equations are derived in general form, in terms of the external forces and bent geometry—an especially convenient approach for tabular work. The second part deals with the deformation of the multistory bent. An outline of the basic assumptions is followed by a proposed deformation curve, which yields the allowable deformation angle for any story, based on the allowable deflection index (drift limitation). Subsequently, equations are derived for the horizontal deflections due to each of the following factors: axial deformation of the columns, bending of the columns, and bending of the girders. The paper concludes with a numerical example.