George E. Ramey

Theoretical and numerical convergence rates for some conforming finite elements

Abstract One of the major requirements of an approximate solution method is to rapidly converge to the exact solution. This paper is concerned with the rapidity of solution convergence for many conforming finite element models. Convergence rates are determined by theoretical analyses and checked by numerical investigation. Solution error plots are made for each element and in most cases these plots indicate a numerical convergence rate which is in agreement with that predicted by theory. The investigation considers only discretization errors; and the solution quantities referred to are for the system energy quantities which correspond to the eigenvalues for eigenvalue problems. The convergence rates determined are applicable to eigenvalue and static problems devoid of stress singularities.

Error estimates for conforming finite element solutions

Abstract A method for determining realistic error estimates for conforming finite element solutions is presented. The method requires solution of the problem by at least two, and preferably three mesh schemes that yield monotonic solution covergence. This in turn will automatically yield one solution bound, upper or lower. The paper describes a simple and practical scheme for obtaining the other bound by utilizing the solutions from the multiple mesh schemes. These bounds bracket the exact solution within relatively narrow limits and provide the basis of the error estimate. The solution quantities considered are the system energy quantities; and for eigenvalue problems these correspond to the eigenvalues themselves. As in convergence proofs, it is expected that the displacement and stress quantities will follow the behavior of the energy quantities. The proposed bounding method is applicable to eigenvalue and static problems devoid of stress singularities, and considers only the discretization error of conforming finite element models. The validity of the proposed bounding method has not been proved mathematically; however, extensive numerical applications of the method indicate its workability in every case tested. Results of some applications are included in this article.

Screening Tool to Assess Adequacy of Bridge Timber Pile Bents during Extreme Scour Events

AbstractTimber substructure bridges supported by three, four, or five piles were commonly used in Alabama in the past for secondary and county highway bridges. Because of the large number of such bridges in the state, the Alabama DOT recently developed a screening tool to assist its engineers in assessing the adequacy of bridge pile bents for extreme flood and scour events. The evaluation procedure employed in the screening tool is presented in this paper through the following sequence: (1) preliminary or general checks; (2) possible kick-out or plunging failure; (3) bent pile buckling failure; (4) transverse pushover failure from combined vertical gravity and lateral floodwater loadings; and (5) bent upstream pile beam-column failure from combined vertical gravity and lateral debris raft loadings. This paper discusses the theoretical background for the equations used to evaluate each failure mode in the timber screening tool, in addition to describing the flow of the screening process.

Review of Current AASHTO Fatigue Design Specifications for Stud Shear Connectors

Fatigue design provisions for stud shear connectors in the current AASHTO LRFD Bridge Design Specifications are based on the research conducted in the mid 1960s by Slutter and Fisher, who tested 44 push-out specimens to determine the fatigue life of the shear connector. An analysis of test data produced by Slutter and Fisher and an examination of the current AASHTO design provisions in comparison with their European and Japanese counterparts suggest that the AASHTO may significantly underestimate the fatigue life of stud shear connectors, especially in the range of fatigue behavior where most bridges are designed. A design example is presented that demonstrates that the required number of studs according to the AASHTO can be more than twice the number required by other design codes in Europe and Japan. A possible reason for this discrepancy is discussed.

CRACKING DAMAGE/DETERIORATION AND REHABILITATION CONSIDERATIONS OF SOME BIRMINGHAM, ALABAMA, INTERSTATE BRIDGE DECKS

The Alabama Department of Transportation (ALDOT) has more than 4830 m of major Interstate bridges (three to five lanes wide) near downtown Birmingham, Alabama, that have significant levels of deck cracking and deterioration. The bridges are part of the Interstate 65 and Interstate 59 highway system through the city and are approximately 27 years old. It appears that deck cracking is primarily the result of (a) early drying and thermal shrinkage, (b) early concrete obstructed settlement, (c) thin and flexible decks, (d) light and flexible superstructures, and (e) heavy traffic volume and loadings. The deck condition versus age and the crack classification/width versus age curves are presented for three typical bridge decks, along with a photographic portrayal of the state of deck cracking and deterioration. Comparisons of experimental and theoretical load deflection behavior of two of the bridges are presented. The rehabilitation or replacement of the bridge decks that are approximately 55 740 M2 is a matter of great concern to ALDOT. Actions the agency is currently taking and actions it plans to take are also presented.

Some effects of system idealizations, singularities and mesh patterns on finite element solutions

Abstract Solution accuracy, convergence, and rate of convergence are of paramount importance in finite element analysis. Important variables affecting the solution, in addition to the particular finite element utilized are structural idealizations, singularities and mesh pattern. These are the variables considered in this article. Numerical examples are considered to demonstrate some of the effects of these variables on the solution convergence. The example problems indicate monotonie upper or lower bound solution convergence for conforming elements in the proper n - sequence when idealization and discretization errors are of the same sign. For singularity cases, solution convergence is usually well behaved for practical n values, but at a reduced rate of convergence. Various mesh patterns did affect solution accuracy, but did not affect convergence or convergence rate.

Full-Scale Implementation and Testing of Full-Depth Precast Bridge Deck Panels

A bridge deck panel system using nonprestressed full-depth precast concrete bridge deck panels with continuous shear pockets was investigated. First, the research team performed conceptual improvement, design, detailing, and fabrication studies on a specific deck replacement system (System CD-2) previously proposed by NCHRP Project 12-65 researchers. Key improvements to the CD-2 deck panel system included modifications to the transverse joint coupler for ease of construction and the addition of a longitudinal staged-construction joint to expedite bridge deck replacement projects. Next, an experimental program was carried out to construct and perform service-level load testing on a full-size precast deck panel assemblage that incorporated the refinements. On the basis of static and cyclic loading test results, it was found that the modified CD-2 deck panel system as a whole performed satisfactorily with regard to AASHTO serviceability requirements.