A model for the rigid body motions of skew bridges

This thesis investigates the rigid body motions of skew bridges, concentrating on the in-plane translational and rotational displacements of the bridge deck induced by impact between the deck and the abutments. Experience in the San Fernando Earthquake of February 9, 1971 demonstrates that this feature is particularly important for skew bridges. A simple model, in which the bridge deck is represented by a rigid rod restricted by column and abutment springs is examined first. This model illustrates the mechanism by which in-plane rotational vibrations is triggered after the closure of the gap between the bridge deck and the abutment. It also shows that the force-deflection relations of the columns and the abutments are particularly important features for the response of the bridge. methods for the exact and approximate estimation of the elastic stiffness of elastically founded, tapered bridge columns with octagonal cross section are presented next. The methods are applied to a bridge used later as an example. In addition, the yielding of the columns is examined and the force-deflection relations for bending about two orthogonal axes are estimated. The abutments are treated as rigid bodies and the soil embankments as Winkler Foundations with elastic spring constants increasing with depth. For the examination of the yielding of soil the Rankine theory is used. Based on these assumptions an approximate force-deflection relation for the abutments is constructed. The response of a more complicated bridge model applied to a bridge near Riverside, California is examined at the end of the thesis and examples of the results are given. This model, in which the bridge deck is still represented as a rigid rod, has three in-plane degrees of freedom: two orthogonal displacements and a rotation, and is capable of capturing many of the more important features of the nonlinear, yielding response of skew bridges during strong earthquake shaking

Full-Scale Field Resonance Tests of a Railway Bridge

Report No. CCEER-95-8Field dynamic resonance tests of the Strawberry Park Underpass, a two span simply supported railway bridge located in Los Angeles, were performed by using an eccentric mass dynamic shaker. The east span of the structure and the adjacent roadbed were instrumented with twenty four FBA-11 accelerometers. The bridge was shaken in both the longitudinal and the transverse directions. To identify the influence of the rails, the tests were performed initially with the rails in place and then with the rails cut at the abutments. The natural frequencies and the corresponding modal damping values of the first and second transverse, the first longitudinal and the first vertical modes were calculated. Significant participation of the adjacent roadbed, indicating a strong interaction between the structure and the soil, was also observed. A three dimensional finite element program was developed, in order to predict the experimentally developed results. These predictions were reasonably accurate. This model will be the first step towards further analytical studies, which are currently under development. This report describes the experimental procedures, the analysis of the data and its results and the development of the analytical model (Abstract by authors)

Nonlinear Seismic Response of Isolated Bridges and Effects of Pier Ductility Demand

Report No. CCEER-95-6A nonlinear computer program to predict the dynamic response of base isolated bridges to orthogonal, horizontal earthquake ground motions was developed. The computer program can model multi-span bridges with straight, continuous superstructures and multi-column bents. Hysteretic behavior of elastomeric or lead-rubber isolators, abutments, shear keys, and columns can be modeled. Nonlinear analysis of the six-span Verdi bridge near Reno, Nevada showed that column ductility demands can be eliminated using isolation. Contrary to linear elastic theory, the superstructure displacements were controlled. Studies were conducted to show that seismic isolation may not be effective in bridges with long columns and located on deep soil deposits. The AASHTO Guide Specifications for Seismic Isolation Design were evaluated. Results of the simplified linear methods compared well with nonlinear analysis in the longitudinal direction but were in error by 21% transversely (Abstract by authors)

Summary of Pretest Analysis of Cazenovia Creek Bridge

Report No. CCEER-94-3As part of a study to evaluate the basic dynamic characteristics of the southbound bridge of Cazenovia Creek, a detailed parametric study was carried out and is described in this report. A 3-dimensional analysis model was developed for the modal analysis of the bridge. Also a simple model was constructed for the analysis of the bridge. For the evaluation of the influence of the soil stiffness at the foundation, 8 soil stiffnesses were employed in the modal analyses for both the 3-D and the 2-D models. Finally, for considering the effect of the actual state of the bridge, two further modifications were made in the 3-dimensional model. The transverse frequencies of the 3-D model and the 2-D model were compared and the difference in frequencies of two models were less than 10 percent for all the comparisons. The influence of the soil stiffness on the dynamic behavior of the bridge should be considered when the soil stiffnesses are less than 10 times the standard value. In the pretest parameter study, the frequencies of both the cracked and uncracked structure were calculated. The properties in the cracked structure had more influence on the fundamental frequency than the other frequencies. Three loading cases were performed in the parameter study. In the first loading case, two concentrated loads of 150 kips each were horizontally applied to the 1/3 points of the bridge. In the second case, 150 kips were applied to one 1/3 point of the bridge. In the third case, a load of 150 kips was applied to the abutment. The participation factors, displacement and acceleration time histories corresponding to these three loading cases are discussed in the report (Abstract by authors)

Experimental and Analytical Investigation of Seismic Bridge-Abutment Interaction in a Curved Highway Bridge

Report No. CCEER-15-05Seat-type bridge abutments are most commonly used to support the end spans of curved highway bridges. This type of abutment is often selected to eliminate unbalanced stresses in the superstructure under service loads, in particular thermal expansion and contraction. However, depending on the width of the expansion gap, large earthquakes may cause the expansion gap to close which results in bridge-abutment interaction. This phenomenon was studied in a federally funded research project examining the seismic performance of curved highway bridges at the University of Nevada, Reno. As a part of this research a 2/5th scale model of a 3-span curved steel girder bridge was constructed on four multi-degree-of-freedom shake tables. Two configurations of the bridge one without bridge-abutment interaction and one with nonlinear bridge-abutment interaction were tested. The purpose of these tests was to: (i) identify the influence of bridge abutment interaction on the global seismic response of the bridge, (ii) characterize the force deformation characteristics of dynamic bridge-abutment interaction, and (iii) provide experimental data used to calibrate numerical models of bridges including bridge abutment interaction. Based on the experimental investigation it was concluded that bridge-abutment interaction shortens the effective period of vibration of the bridge, which results in decreased deck displacement and increased total base shear demands. However, the increase in base shear demand is resisted by the abutments which results in a net reduction in column shear demand. Though the deck displacement is reduced at the mid-span of the bridge, the active displacement of the deck at the abutments is increased due to the increased in-plane deck rotation generated as a result of the sudden changes in eccentricity between the center of mass and center of stiffness. The amount of in-plane rotation is shown to depend on the phasing and intensity of the ground motion. Interaction between the bridge and abutment backwall can generate significant radial shear forces through contact friction. These radial forces limit the radial displacement of the ii bridge while in contact with the backwall particularly after the radial shear keys have failed. However, depending on the details of the abutment backwall local damage may occur. In general, engaging the passive resistance of the backfill soil was able to improve the seismic response of the bridge by reducing damage to the columns and adding an additional form of energy dissipation. Both rigorous 3D finite element and simplified grillage models of the experimental model were validated using available software. Good agreement between the numerical models and the experimental data were obtained using both models however the computational effort was greatly reduced using the simplified grillage model. A grossly simplified 3DOF model of the bridge analyzed using the linear multi-modal response spectrum method was shown to give a prediction of the peak displacement response with minimal complexity. Finally, a parameter study determined that the degree of curvature, size of expansion gap,column diameter, and abutment backfill soil type all influence the response of the bridge. Based on the small scale parameter study conducted herein, bridge designers are encouraged to optimize the combination of expansion gap width with the selection of column diameter to minimize the column and/or abutment soil ductility demands

System Identification Studies on Cazenovia Creek Overpass

Report No. CCEER-95-9The actual system identification algorithms and programs for southbound Cazenovia Creek bridge are developed. These consist of the following: 1.A finite element software package used in the mathematical approximation of the bridge's soil and structural parameters 2.An error criterion function whose minimizing yields the best quality of fit between the computed and the measured data sets 3.A pattern search algorithm which leads to the optimum solution by minimizing the above error criterion function through modification of the model's parameters within a bounded multi-parameter domain 4.An algorithm for the numerical evaluation of the Hessian matrix and its eigenvalues to confirm the existence of any local minimum indicated by the convergence of the above pattern search algorithm. The verification of all the algorithms and the confirmation of the validity of the methodology above were performed in order to address questions on their efficiency and limitations for the southbound bridge. A "fictitious" problem was constructed by assigning to the bridge model a set of known input variable values and then determining the model's computed or "exact" response corresponding to these input values. In these tests, a zero error (or zero noise) is computed when using the error criterion function. The data set in the fictitious problem consists of an "exact" copy of the model's computed response used in the place of the corresponding measured data sets in the field. The data sets of six, five and four variables were tested and the data set of four variables showed the satisfactory results. The four variables were the soil spring stiffness of abutment, soil spring stiffness of the pier, moments of inertia of the superstructure in both the transverse and vertical directions. Finally, the system identification using the measured data from the field was carried out in this study (Abstract by authors)

Full-Scale Field Resonance Tests of a Railway Bridge

Report No. CCEER-97-1-BThis report presents the sensitivity analysis of fatigue evaluation for Nevada steel bridges. Parameters affecting applied stress ranges were studied and varied in a three-span four steel plate girder bridge to determine their effect on fatigue evaluation. The allowable stress range parameters were examined to determine their effect on the overall fatigue behavior. The current research and practice of other major state DOTs in dealing with fatigue cracks, evaluation procedures and repair methods were studied and examined. From the study, it was found that for closely spaced (S 17.5 ft.) bridges, the 3-D structural analysis gave approximately 50% and 25% higher stress range values than the 2-D analysis respectively. For normally spaced (10 < S < 14 ft.) bridges, the 2-D structural analysis gave 50% higher values. For the case of skewed bridges, the 2-D structural analysis gave approximately 50%, 75%, and 170% higher values of stress ranges than 3-D analysis for 0� , 30� , and 60� skewed bridges, respectively. It was also found that increasing the skew angle, girder spacing and depth will decrease the stress ranges. The applied stress ranges did not vary with the configuration and cross-sectional area of cross frame and lateral bracing. However, as skew angle increases, cross frame and lateral bracing members attracted more axial forces having these location prone to out-of-plane fatigue cracking. The single HS2O Truck was found to be the most damaging load in terms of fatigue life due to its high frequency of occurrence during the life span of a bridge. Over thirty states responded to the questionnaire about fatigue evaluation and repair methods. Many of these responses could be applicable to Nevada steel bridges (Abstract by authors)

An Evaluation of the Current Caltrans Seismic Restrainer Design Method

Report No. CCEER-92-8The primary objective of this study was to develop an understanding of the implications of the current Caltrans hinge restrainer design procedure. Two aspects of the problem were studied. One was the effects of changing (a) the cross sectional area of restrainers and (b) the restrainer gap on the nonlinear response of a bridge with several hinges. The other was the sensitivity of the number of required restrainers to changes in some of the simplifying assumptions which are made in the current Caltrans restrainer design method. Computer program NEABS-86 was used in the nonlinear analyses [3]. The focus of this part of the study was the relative displacements at the joints, restrainer forces, and restrainer stresses. Three earthquake records, the El Centro 1940, Eureka 1954, and Saratoga 1989. In addition to input earthquakes, the number of restrainers at each hinge, the restrainer gaps, and the hinge gaps were varied. It was found that when a restrainer gap of 0.75 in. is assumed, the number of restrainers does not affect the response significantly. It is recommended that the design should be based on cases with and without restrainer gaps to encompass all the critical forces, stresses, and displacements. To study the effects of design assumptions on the required number of cables, several manual calculations of the example in the Caltrans restrainer design guidelines were carried out. The deviations from the method included the treatment of mass and stiffness of bridge segments as different hinges closed. Another variable was the simultaneous reduction in the restrainer gap and increase in the hinge gap. The results indicated that slight variation in some of the assumptions can change the number of restrainers significantly. A more streamlined design method that incorporates the nonlinear response of bridge components needs to be developed (Abstract by authors)

Effect of Hinge Restrainers on the Response of the Madrone Drive Undercrossing During the Loma Prieta Earthquake

Report No. CCEER-92-9One of the most common seismic retrofitting techniques employed by the California Department of Transportation in recent years is the use of longitudinal restrainer cable systems. The Madrone Drive Undercrossing was retrofitted in 1985 with restrainer cables at the intermediate hinges and concrete shear keys at the abutments. The October 1989 Loma Prieta earthquake caused extensive damage in the San Francisco Bay Area. Ground acceleration at the Madrone Drive Undercrossing was estimated at 0.65-g. This report describes the computer earthquake analysis conducted to determine the effect of the restrainer cables on the bridge's response. Analysis cases examined include models with restrainer cables and without restrainer cables. Comparison of the results is made which provides an indication of the performance of the cables (Abstract by authors)