Cable-stayed bridges can exhibit large amplitude irregular stay cable oscillations under certain conditions of combined
traffic flow and rain-wind loads that can pose severe risks to structural integrity. To investigate the mechanisms causing
this behavior, a high fidelity nonlinear finite element model of a typical cable-stayed bridge has been developed using
LS-DYNA based on the design of the Bill Emerson Memorial Bridge at Cape Girardeau, MO. The model uses over
540,000 finite elements representing 1254 bridge components to fully describe the detailed real geometry of the bridge
tower, deck, stay cables, edge girders and floor-beam support girders. Traffic loads on the bridge deck are simulated by
a Poisson Distributed Pulse (PDP) stochastic process model involving multi-lane traffic flows of more than 300 vehicles
of various axle loads with varying arrival rates. The response data sets generated by the LS-DYNA simulations were
then analyzed for chaotic behavior with the software CTBR. This extracts the nonlinear system invariants, the Lyapunov
exponents, to identify the chaotic behavior from the dynamics of the structural system. The simulations showed positive
Lyapunov exponents at various locations of the bridge deck and the bridge stay cable network. The analysis of these
results revealed that even in the absence of strong rain-wind excitations the bridge deck vibration exhibits significant
chaotic behavior that could excite the stay cables into a stronger chaotic regime, especially at the upper portion of the
networked stay cables. This illustrates a phenomenon often ignored or unable to be captured by conventional linear
dynamics analysis. Analysis of actual data sets collected from a monitoring network on the bridge also confirmed this
chaotic behavior.
Long term structural health monitoring has become recognized as an important tool for ensuring the structural
performance of our nation's cable-stayed bridges. However, this depends upon the establishment of a reliable base-line
of structural condition at the early stage of the bridge's service life. The recent completion of the Bill Emerson Memorial
Bridge at Cape Girardeau, MO, which included the installation of a network of seismic motion sensors, provides an
opportunity to investigate the issues of creating such a base-line. Moreover, the availability of such a monitoring data
set enables the evaluation of the possibility of inherent chaotic behavior in cable-stayed structures. This study analyzed
the time series data sets collected from various locations along the bridge deck and tower of the Bill Emerson Bridge
using CTBR, a Windows-based software application developed by Turner-Fairbank Highway Research Center of FHWA. This software automates the process of extracting the Lyapunov exponents, which are used to characterize the nonlinear dynamics of a structure. The analysis found one or more positive Lyapunov exponents, the signature of chaotic behavior, at various locations on the bridge deck. This phenomenon, resulting from ambient traffic loading rather than
from wind and rain loading on the stays themselves, illustrates a mechanism that has been implicated in chaotic behavior
of other cable stayed bridges. The analysis has thus revealed a previously unknown effect of chaotic deck motions that
could couple into the stay cables. This research demonstrates that once the base-line chaotic systems have been identified it will be possible to track the values of the Lyapunov exponents over time to monitor the structural health of the bridge.
Cable-stayed bridges are a recent development in bridge structural design in which the cables meet the bridge deck at an acute angle rather than perpendicularly. Some early cable-stayed bridges have exhibited large amplitude stay cable oscillations. One such bridge, the Fred Hartman Bridge across the Houston Ship Channel in Texas displayed two different modes of vibration: a local mode involving independent motion of individual cables and a global mode, in which the cables vibrated collectively under certain wind and rain conditions. This abrupt shift in mode as a function of a change in environmental parameters suggests chaotic behavior. Analysis of the probability density function of maximum accelerations of the cables typically showed a fractal power law distribution at lower values, but also some sharp changes in the tails. The Lorentz Map plots of the data also indicated two regimes: a dissipative one at lower acceleration values and chaotic behavior beyond a critical acceleration value. The plots also imply that the chaotic system is nearly one-dimensional. The working hypothesis is that steady winds impose additional stresses on the stay cables that push them over the boundary into the chaotic regime where random impulses from falling raindrops become amplified into cable oscillations.
KEYWORDS: Fractal analysis, Bridges, Complex systems, Iterated function systems, Structural health monitoring, Molecular bridges, Data modeling, Associative arrays, Data analysis, Analytical research
Bridges and other civil structures can exhibit nonlinear and/or chaotic behavior under ambient traffic or wind loadings. The probability density function (pdf) of the observed structural responses thus plays an important role for long-term structural health monitoring, LRFR and fatigue life analysis. However, the actual pdf of such structural response data often has a very complicated shape due to its fractal nature. Various conventional methods to approximate it can often lead to biased estimates.
This paper presents recent research progress at the Turner-Fairbank Highway Research Center of the FHWA in applying a novel probabilistic scaling scheme for enhanced maximum entropy evaluation to find the most unbiased pdf. The maximum entropy method is applied with a fractal interpolation formulation based on contraction mappings through an iterated function system (IFS). Based on a fractal dimension determined from the entire response data set by an algorithm involving the information dimension, a characteristic uncertainty parameter, called the probabilistic scaling factor, can be introduced. This allows significantly enhanced maximum entropy evaluation through the added inferences about the fine scale fluctuations in the response data. Case studies using the dynamic response data sets collected from a real world bridge (Commodore Barry Bridge, PA) and from the simulation of a classical nonlinear chaotic system (the Lorenz system) are presented in this paper. The results illustrate the advantages of the probabilistic scaling method over conventional approaches for finding the unbiased pdf especially in the critical tail region that contains the larger structural responses.
This describes a research program to apply nonlinear analysis and chaos theory to structural health monitoring. Earlier approaches based on linear modal analysis typically examined fundamental frequencies of the structure. However, significant changes in the fundamental frequency were usually not detected until the structure was severely damaged. In chaos theory, the fundamental frequencies are not assumed to be fixed, instead they wander time in a characteristic pattern around a central value, called an attractor. In a chaotic system, a set of parameters called Lyapunov exponents play the role of fundamental frequencies in linear system analysis. The current FHWA research program involves the development of algorithms to extract these exponents from structural monitoring data. These algorithms are being evaluated against simulated data sets produced by an advanced 3D nonlinear dynamics finite element code using synthesized ambient traffic loadings. Chaotic behavior was observed in the modeled bridge.
As part of a program to apply stochastic system analysis to structural heath monitoring of highway structures, a detailed Finite Element (FE) model of a typical highway bridge has been developed. The model was created for use with the nonlinear explicit FE code, LS-DYNA, and consists of 144 parts and approximately 40,000 elements. The model represents a standard two-lane bridge with a span length of 40 meters. It consists of 4 girders and 21 cross frame sections. This paper discusses some important practical aspects involved in the modeling of such highway bridges including connections, material properties, boundary and dynamic loading conditions. Extensive simulations were conducted using a SGI supercomputer at the FHWA sponsored National Crash Analysis Center at the George Washington University to determine the bridge structural response under dynamic loadings. The resulting data sets from these simulations are used as the basis for chaotic system invariant spectrum analysis described in related papers in this conference.
KEYWORDS: Monte Carlo methods, Bridges, Stochastic processes, Computer simulations, Plasma display panels, Data modeling, Algorithm development, Finite element methods, Modeling and simulation, Systems modeling
Bridge dynamics data are usually collected as a function of excitations by ambient traffic loads. However, the stochastic aspects of the multi-lane, continuous traffic flows significantly complicate the loading conditions in dynamics analysis of highway bridges. Such ambient traffic loadings often cause incremental changes of structural shear or bending stresses in bridge structures and therefore result in fatigue damage. Most current approaches for modeling traffic loading rely on simple load spectra approximations and address only the maximum effect of the loading. Therefore, they have limited ability to take into account the effect of such multi-lane ambient traffic flow loadings. This paper presents a stochastic modeling and simulation approach to describe ambient traffic flows over the highway bridges.
Aging highway structures can display complicated nonlinear dynamics behavior due to degradation of structural properties or crack damage, as well as to variations in environmental and dynamic loading conditions. This paper explores the feasibility of utilizing the spatial distribution of the Lyapunov exponents for damage detection in nonlinear bridge structures. In particular, this approach considers the chaotic nature of the response of general nonlinear highway bridges due to ambient traffic loadings in the analysis of the observed bridge response data for each monitoring locations. A novel algorithm, based on the average mutual information from observed data and a stochastic orthogonalization using polynomial chaoses, is used to efficiently extract the nonlinear bridge system invariants consisting of a set of Lyapunov exponents.
Development smart systems for damage detection and health monitoring of highway bridges using measured response data has been an important research focus. However, difficulty often exists when bridges exhibit significant nonlinear behavior due to aging degradation of structural properties, inelastic deformation and fracture damage, as well as uncertain boundary, environmental and dynamic loading conditions. This paper presents an analysis of system invariant spectrum applied to smart systems in structural health monitoring of general highway bridge systems. In particular, the spatial distribution feature of the system invariant is used to explore changes in a general nonlinear highway bridge structure due to damages.
Effective detection of structural damages has been a challenging issue in the health monitoring of highway bridge structures. Most currently used nondestructive detecting techniques, though, rely heavily either on extensive measurements of local structural behavior or on analysis based on linear dynamics using simple structural models. Their applications, therefore, are often limited by the experimental costs and the complexity of real bridge structures. This research explores the possibility of applying an energy index approach in general nonlinear finite element analysis for damage detection in highway bridge structures. The nonlinear behaviors of the bridges under dynamical loading conditions due to material inelastic deformation and crack damages have been considered. It is shown that by utilizing the energy balance rule for a general, dynamically loaded nonlinear solid body a spatially indexed, scalar energy parameter can be formulated based on the generalized J integral used in fracture mechanics. The evaluation of such an energy index can be implemented into general 3-dimensional nonlinear finite element analysis procedures in computer simulations to detect and locate the structural damages within the highway bridge structures. The effectiveness and feasibility of the proposed energy index approach are illustrated in numerical simulation studies.
Sensors are currently available and used to monitor structural performance and loads incurred by bridges already in service. However, there has been limited research concerning the stresses that steel bridge girders endure during transport from the manufacturer to the job site and during the installation process. This paper reports the measured stresses on steel bridge girders during transportation from Lancaster, PA to Hanover, NH and during construction of the Ledyard Bridge on the New Hampshire - Vermont border. Two different monitoring system were developed for this data acquisition in a mobile environment. The first, a fiber optic strain monitoring system, utilizing Bragg grating technology. The second utilized an electrical- resistive foil strain gage network, in conjunction with wireless telemetry equipment. Together, these two systems formed a smart structure system for monitoring bridge girders while confirming the accuracy of data gathered through redundancy. Result conclusively demonstrated for the first time, that stresses in beams during transportation are significant and approach the factor of safety margin in girder design.
KEYWORDS: Sensors, Waveguides, Microwave radiation, Signal detection, Ka band, Wave propagation, Signal to noise ratio, Inspection, Nondestructive evaluation, Electrical engineering
The influence of the waveguide flange, frequency of operation and liftoff on crack detection sensitivity using the dominant mode as well as the higher-order mode approaches are presented. The results indicate that the optimal choice of these parameters can significantly enhance crack detection sensitivity in practical applications.
Quasi-elastic neutron scattering provides a direct measure of the amount of water bound during the hydration of tricalcium silicate, the principal component of Portland cement. This can be used to follow the progress of the reaction as a function of time. To examine the effect of temperature on the process measurements were made on samples held at fixed temperatures ranging from 5 to 40 degrees C. The results show at least three different stages of the hydration reaction. The early stage appears to be controlled by surface reactivity, the late stage by diffusion through the calcium silicate hydrate gel.
Sensors are now becoming available that can be embedded in concrete or asphalt, or attached to steel structures for monitoring structural performance over significant periods of time. For the most effective use of these sensors, a monitoring strategy has to be developed for each specific application, which can range from heavy impact detection to modal analysis to concrete shrinkage. Among the tradeoffs that must be considered is the type of sensor. Other factors include the frequency range, the number and location of the sensors and the duration of the data collection. Data collection, transmission and storage systems are also significant components of the overall system.
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