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## Feasibility Study on Dynamic Bridge Load Rating (2002)

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### BibTeX

@TECHREPORT{Chen02feasibilitystudy,

author = {Shen-En Chen and Patra Siswobusono and Norbert Delatte and B J Stephens and Shen-En Chen and Patra Siswobusono and Norbert Delatte and B J Stephens},

title = {Feasibility Study on Dynamic Bridge Load Rating},

institution = {},

year = {2002}

}

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### Abstract

Sponsoring Agency Code Supplementary Notes Abstract This project examined the feasibility of using ambient vibration measurements as a supplement to routine bridge inspection. The goal of this research was to develop a cost-effective testing methodology, which could be implemented easily on county highway bridges in Alabama. Preliminary study included conducting modal testing on a two-lane concrete deck/steel stringer bridge. Vibrations due to impact excitation and ambient traffic were used to extract the first bending mode. These data were used to determine the dynamic load impact factors of the bridge. Due to the relatively light weight of the bridge, the weight of an automobile significantly influenced the resonant frequencies. Numerical analysis using the Finite Element Method (FEM) was conducted to validate the experimental results. This research also included making and testing a miniature model of a skewed bridge to help understand the complex modal behaviors of a single-span, concrete deck/steel stringer bridge. Using modal testing, it was hoped to conduct focused and reproducible studies on the composite actions and boundary effects of this type of bridge. Like a real structure, the model was constructed with four girders and a deck. The miniature bridge had a span of 7.125 inches and a skewed width of 7.875 inches. The miniature model was tested under different boundary conditions. The model helped in determining optimal sensor locations and critical modes. The study also included static testing to determine possible load rating techniques on actual bridges. The results of this study showed that it might be possible to use vibration measurements to determine the remaining load capacity of a bridge. Key Words Executive Summary Heavy traffic volumes and larger vehicles on the nation's aging transportation system present an immediate and significant public safety issue. Recent statistics show that more than a third of the United States' half-million highway bridges are either "structurally deficient" or "functionally obsolete." Therefore, transportation professionals are faced with an increasingly difficult scenario for resource management. This issue is especially pressing at the county level. Bridges managed by county and local governments are predominantly short-span bridges, and are often located in remote areas. As a result, they are often given lower priority. The main goal of this research was to conduct a feasibility study on using ambient vibration measurements to quantify bridge load capacity, and to estimate the remaining useful life as an additional safety measure for bridges. The project included literature reviews, laboratory tests on bridge models and full-field vibration measurements on actual bridges. The intended outcome of this research was an effective testing methodology that could be used to accurately monitor bridge performance with minimal traffic interruption. This research studied how field measurements of bridge vibration under regular traffic may be used to retrieve useful information to complement existing load tests and analyses to improve bridge load ratings. In this research, a load capacity prediction technique using ambient vibration measurements has been proposed. This method assumed that the bridge behaves like an elastic spring, where the load capacity of the structure represented the spring stiffness. For a simple bridge with a predominantly bending deformation, the vibration frequency could be used to predict the bridge capacity via inversion. Theoretical studies of the correlation between measured vibrations and the remaining stiffness were conducted on a miniature bridge model as an additional analytical technique. 1 Section 1. Introduction Introduction Heavy use of the nation's aging transportation systems presents an immediate and significant public safety issue at both the national and state levels. Due to the lack of federal support, this issue is especially pressing for county LT20 bridges (bridges span less than 20 ft). Bridges managed by county and local governments are predominantly short-span bridges and are typically located in remote areas. A recent survey of 44 counties in Alabama notes that a total funding of approximately 120 million dollars would be needed to replace structurally deficient LT20 bridges Based on the conditions assessed from visual inspection, an appropriate reduction in capacity is applied to control traffic loading. For many reasons, these load ratings are not verified using deflection and strain measurements, but are derived from theoretical analyses. Sometimes, the assigned load rating may deem the bridge inadequate for anticipated vehicular usage requiring its replacement. Conservative rating procedures based on visual inspection makes it difficult to accurately determine the true load capacity of these structures. Unlike federal or state owned highway bridges, where static and dynamic load tests using standard truck loads may be applied to determine the actual load capacity of the bridge, LT20 bridges are rarely tested. Hence, the actual load capacity of the bridge is not usually included in the BMS database. Advanced instrumentation has been applied to nondestructively monitor highway bridges. Several in-situ instrumentation techniques, such as fatigue monitoring of structural members, have been proposed in the past. However, these techniques do not provide direct assessment of the global or system behaviors of the structure (Chase et al. 2000) and do not provide for the determination of the remaining capacity of the structure. A load capacity prediction technique using ambient vibration measurements has been proposed as part of this research effort. This new method assumes that the bridge behaves like an elastic spring, where the load capacity of the structure is directly related to the spring stiffness. Hence, for a simple bridge with a predominantly bending deformation, the fundamental vibration frequency together with the mass of the bridge can be used to determine the bridge capacity. 2 This report summarizes results of an attempt to validate the proposed methodology. The scope of study included testing of a miniature bridge model used for theoretical studies and actual field tests on a selected bridge. Since the primary focus of this research is on smaller bridges, the selected bridge was limited to a single span bridge. However, the methodology can be extended to more complicated bridges. Project Objectives The objectives of this research were to investigate the state-of-the-art of dynamic testing of bridges, conduct proof-of-concept tests on using ambient vibration measurements to quantify bridge load capacity, investigate field ambient vibrations of a selected bridge, and to propose a viable testing methodology for use in actual applications. In short, the goal of this research was to develop a testing technique that involves minimal instrumentation, does not interfere with traffic and can provide bridge engineers a reasonable estimate of the remaining capacity of a bridge. Approach and Work Plan There are several applications of vibration measurements for bridge monitoring Report Outline A comprehensive review of existing reports on the use of vibration measurements for bridge evaluation is presented in Section 2 of this report. Also presented are detailed treatises of the theoretical background of dynamic load rating determination and a brief summary of existing practices in bridge inspection. Section 3 describes the studies on the miniature bridge model used to validate the proposed methodology. Section 4 focuses on the actual testing of the selected bridge while Section 5 focuses on the finite element modeling of the actual bridge. Section 6 discusses and reviews the proposed testing methodology. (AASHTO, 1990, NYDOT, 1982. Specialized professional organizations such as the American Concrete Institute (ACI), also publish inspection procedures targeting specific structures or materials (ACI, 1992). Inspections are typically performed by experienced engineers, who are knowledgeable about structural and material behavior, and who are able to identify anomalies in critically damaged structures. Damage such as fatigue cracks, excessive rust on steel members, de-coloration and loss of mass on concrete structures give strong indications of the state of deterioration of the structure. Clearly, the reliability of an inspector's heuristic knowledge and practical experience is important. However, in order to make these necessary visual observations, the bridge inspectors are frequently exposed to dangerous, potentially life threatening environments. Advanced instrumentation techniques, i.e., non-destructive evaluation (NDE) techniques, have been used as supplements for visual inspection for more complex state-owned or federal-owned bridges. NDE techniques, such as acoustic emission, ultrasonic, and ground penetrating radars, focused on damage behavior studies of single members A more attractive technique to quantify structural behaviors for engineers and scientists is to measure the modal/dynamic behavior of a structure. Vibration measurement has been a standard procedure for evaluating structures for dynamic characterization and damage, and for understanding how a structure would behave under certain dynamic loading conditions. Understanding the vibratory behavior of a structure can reveal important information about the stiffness distribution within a structure. Due to the relationship between dynamic behavior and a structure's global mechanical characteristics, vibration testing has been an attractive NDE method for structural integrity evaluation (Chowdhury, 2000, Cioara and Inspection of LT20 Bridges Inspection of LT20 bridges and culverts is divided into two overall categories: integrity of the structural material supporting traffic loads is coded in the structural condition ratings; and condition of the channel associated with the structure is coded in the channel and channel protection rating. Structural condition ratings for LT20 bridges are separated into four categories: deck, superstructure, substructure, channel, and channel protection. The elements within each 4 condition rating are inspected using a 0-9 point scale in accordance with the guidelines. This data then is used to determine the sufficiency rating of the bridge. Sufficiency rating is used in the prioritization of bridges for replacement in the Roads Bridge Replacement Prioritization Database (BRPD) Load rating is obviously an important contributor to the sufficiency rating. The National Bridge Inventory System (NBIS) requires that all Federal and State bridges (20 feet or longer) be properly inspected and posted with respect to the remaining useful life and structural condition. Standard load tests are done to determine the load capacity of federal-owned and state-owned highway bridges. However, load tests are generally not applied to county bridges, which are mostly LT20 bridges. Current practice is to perform load rating calculations of LT20 bridges by hand, based on the results of regular visual inspections. Without load tests, it is difficult to sustain the same safety levels for LT 20 bridges as Federal and State bridges. Bridge Vibration Studies In recent years, significant interest has been shown in using frequency responses of structures for damage state assessment Several researchers have made more ambitious attempts to use the same responses for locating and quantifying damage (e.g. Furthermore, vibration mode shapes have also been studied as part of damage detection. Recently, modal curvature-based methods have gained attention from various researchers in damage detection. Using strain gage measurements, Dynamic Load Factor Rating a bridge requires the inspectors to quantify damages (both structural and non-structural) on various bridge components and subjectively assign relative scores for each item in consideration (FHWA, 1991). If structural deficiency is identified, engineers will then conduct a detailed stress analysis to determine the load capacity of the structure. Dynamic effects of traffic live load are accounted for using a dynamic load factor (DLF). The computed load capacity is then compared to the design load capacity of the bridge (AASHTO, 2000 Saadeghvaziri (1993) indirectly related the DLFA to the DLFM, the dynamic load factor for moment. The dynamic amplification factor for deflection (DAD) was determined by using a speed parameter α, defined as lf V 2 / = α and the exact solution for deflection of a simply supported beam traversed by a constant force. Finite element results yielded a DAD that was in agreement with the exact solution for a range of α from 0.1 to 0.6 (typical highway bridges). Saadeghvaziri then determined the dynamic amplification factor for the moment (DAM). The ratio of the DAM to the DAD FE was 0.822 for the particular range of the speed parameter. This work also indirectly defined the proportionality between the dynamic deflection and load factors. Biggs (1956) concluded that the most important factors influencing traffic-excited vibration of short span bridges were the vehicle characteristics, road surface roughness and vehicle speeds. For longer span bridges, the traffic pattern becomes more complicated, including multiple excitations and more complex signal processing techniques would be required to extract the actual bridge modal data In this report, DLFA is computed based on ambient traffic passing over a test bridge. Two DLFAs are investigated: one based on the first bending mode amplitude and the other on the amplitude of the acceleration in the frequency domain. The first bending mode was chosen for analysis since it was the fundamental mode in simple span, two-lane, LT20 bridges with assumed symmetric loading. Given these conditions it is usually the dominant mode, attracts the most energy, and can be more easily identified. Isolation of the first bending mode allows for singledegree-of-freedom (SDOF) simplifications and comparisons to bending stiffness to obtain remaining capacity. Dynamic Load Rating To facilitate the analysis of a complicated structure such as a bridge, certain assumptions and simplifications are necessary. Since the emphasis of this paper was placed on the analysis of a small-scale bridge model, a SDOF model was used to interpret the behavior of the bridge model The same stiffness k can be used in determining the static deflection through the Hooke's Law: where P is load capacity. Assuming the fundamental frequency mode (first bending mode) to be the most critical and dominant mode (which is a reasonable assumption for a simple span bridge), then the bending stiffness associated with this mode may be determined using Equation (2.4) once the fundamental frequency and mass are determined. The stiffness obtained may be compared to the stiffness from static tests utilizing a line load at its mid-span. Under this assumption, the bridge model behaves as a beam in pure bending. The stiffness of the bending beam can then be determined using elastic beam theory. To reduce the beam model to a SDOF system it is necessary to determine the effective values of the mass and stiffness. For the dynamic analysis, an assumed shape function for the deformed shape was derived given appropriate boundary conditions. The effective values were then calculated from: is the deflection shape function and x n denotes the normalized variable. If fixed boundary conditions are considered for the beam, the assumed normalized displacement function becomes ( ) It is known that a bridge lose stiffness either through age or damage. Assuming suc h a loss in stiffness occurs with no accompanying loss of mass, the new frequency for the SDOF model may be determined from Where k ' represents the reduced stiffness, If a limiting deflection, δ limit , is set, then the corresponding load, P,' can be determined as: This corresponding load can be used as the new load capacity for the model. For a full-scale bridge, the deflection δ is predetermined by AASHTO (1992) guidelines given standard truck loadings. If testing reveals a reduction in natural frequency, then the new stiffness ' k and the corresponding load capacity P' can be determined as described above. The new load rating would then be calculated as: The dynamic effect is expressed in terms of DLFA, which is essentially the ratio between the dynamic and static deflections (Chowdhury, 2000): This DLFA is typically used to factor out the dynamic effects on the load capacity to warrant a lower load posting. In AASHTO, the dynamic effects caused by the interaction of a moving live load on an actual bridge are accounted for by an impact factor (AASHTO, 1992). where l is the span of the bridge. For example, an LT20 would have the maximum IF of 1.30. Equation (2.12) can then be used to determine the posted load rating for the bridge. 10 Section 3. Miniature Bridge Model Introduction The construction and testing of a miniature model of a skewed bridge is reported herein. The goal of this section was to gain an understanding of the complex behavior of a single-span skewed bridge of the concrete slab on steel stringer type, and also to determine if vibration measurements could be used in load-capacity assessment of full-sized bridges. The skewness of such a bridge, coupled with the interaction between the concrete deck and the stiffening stringers, create complicated deformation patterns. It is proposed that, through focused and reproducible studies on miniature models, the composite actions and boundary effects of fullscale bridges may be understood. The miniature model is not a scaled-down copy of an actual bridge. The primary members and geometry of the real structure are simulated, enabling the representation of the behavior of the real structure. Both static and dynamic tests were conducted on the miniature model. Finite element (FE) modeling was then utilized to simulate the miniature model. The effective stiffness of the first bending mode was then compared with the stiffness as determined from the static tests. The validated stiffness was then incorporated into a single-degree-of-freedom model, which was utilized in new load capacity determinations. Miniature Bridge Model The miniature bridge model was constructed to simulate a concrete-slab/steel-girder bridge. Four plastic girders (d = 7/16 in, t w = 1/16 in, b f = 5/32 in and t f = 1/16 in) were bonded to a Plexiglas deck (3/32 in thickness) for the construction of the model bridge. The geometry of the miniature model consisted of a parallelogram-shaped deck (20-degree skew from the span direction) with length of 7 1/8 in and width of 7 3/4 in. Under the deck, four evenly spaced girders were attached using a strong epoxy. The overall weight of the model was determined as 0.28 lb. Dynamic and Static Testing The testing of the model consisted of both static and dynamic tests. The static load tests were carried out on a Structural Testing Analyzer 1000 (STA1000) system. 11 Figure 3.2 illustrates the static load test setup. Instead of overhead loading, the STA 1000 system uses a pull-down mechanism on the specimen. To accommodate the loading fixtures, a hole was drilled in the middle of the deck. Using the static test, a force-displacement relationship for the linear range of the deflection was obtained. The loading was applied directly at the midspan and parallel to the fixed-end boundaries. The stiffness was then determined from the forcedisplacement curve. Dynamic testing was carried out using a modally tuned hammer and an accelerometer. Timed-data for the vibrations were then collected using a Velleman Digital Oscilloscope PCS64i and were post-processed to determine the frequency information. To simulate loss of stiffness, the girders were completely cut through using a band saw. The cut was made at mid-span parallel to the end of the model. The static and dynamic tests were then repeated. Test results including fundamental vibration frequencies and the static deflection due to a 100-lb force have been tabulated in 12 Damage Scenarios To investigate the effects of damage, three scenarios were examined for the miniature bridge model 13 As the level of damage to the model was increased, the stiffness calculated from the static load test decreased, but not proportionally to the amount of damage 14 Finite Element Modeling To validate the test results, finite element modeling (FEM) was conducted using the commercial software ALGOR. Linear static stress and normal mode analyses were conducted to simulate the static and dynamic tests. There were 5928 solid elements in the model of the deck and girders. Material properties were obtained directly from the manufacturers of the respective materials and are presented in For the linear stress analysis, a static line load was applied on the centerline of the FE model, parallel to the ends of the model, in accordance with the actual test performed on the physical model. The load was evenly distributed based on the element length. The FEM deflection was then compared to the results obtained from the actual tests. As shown in 15 Boundary Effects and Effective Length To understand the boundary conditions experienced by the miniature bridge model, both simply supported and fixed conditions were applied to FE models and to the actual bridge. The fixed boundary conditions required matching actual static and dynamic data to FE results. Fixed boundary conditions for the actual model were very difficult to create, and it was accepted that perfectly fixed boundary conditions could not be achieved experimentally. The test setup required the bridge model to be clamped at both ends with aluminum L-brackets, which were then clamped to the abutments with C-clamps. The extent to which the brackets restricted rotation was limited by the amount of force that could be exerted on the model's cross-section without damaging the girders. For the static analysis, a correlation beam stiffness and deflection given a point load at centerspan and appropriate loading was obtained using elastic beam theory: 16 where ff δ is static displacement for fixed-fixed conditions. It is related to stiffness through Equation (2.5) from the static analysis. From dynamic analysis and assuming SDOF, where the effective mass was calculated from Equation (2.6) as m = 2.74 x 10 -4 lbf•sec 2 /in. The values for the stiffness obtained from the static analysis are presented in Load Capacities The goal of this initial research was to calculate the load capacity of the bridge model using vibration data. Given the geometry and boundary conditions for the model bridge, the load carrying capacity comes primarily from the bending stiffness. With specific loading and geometric simplifications, the model bridge was approximated as a beam. This allowed the strong-axis bending stiffness, as defined in Equation (2.7) to be compared to the effective stiffness of the first bending mode as defined in Equation (3.2). Equation (2.6) and Equation (2.11) were used to give the maximum allowable deflection as defined by the AASHTO Bridge Specification, Section 10.6.2 where l is the effective length. The load capacities for k , as determined from Equation (3.2), may be calculated. Given the effective length of the model of l = 6.50 in, Equation (3.3) mandates a maximum deflection of 0.008281 in. In determining the posted load rating (P posted ), Equation (2.13) was first used to determine the DLFA. For the given bridge model with an effective length of 6.50 in, the DLFA was 18 determined to be 1.30. In order to properly determine the load rating of the bridge, the remaining capacity was reduced in accordance with Equation (2.12). P posted for each damage case of the miniature model presented in Only the load capacities calculated from the undamaged static and dynamic cases were in agreement. Close correlation between the FE and actual load capacity calculations indicated that the method was useful, but in need of refinement. In all cases, the actual bridge model data indicated a lower remaining load capacity than did the FE model. Discrepancies in Results The FE model and the idealized SDOF model predicted a reduction in the bending stiffness and natural frequency of the first bending mode due to damage. Differences in the results become quite large, as the level of damage increased. The degree and pattern of the discrepancies may indicate: (1) deficiencies in the model test setup, (2) the level of damage for Case 2 was too severe, and (3) the need for a non-linear SDOF model (to account for large deflection due to damage). The k static for the undamaged case showed good correlation between the FE and actual models with only 0.12% difference. However, damage in Case 2 and Case 3 deviated by 34.50% and 39.09% respectively. This could have resulted from inadequate fixation of the boundary conditions or equipment precision, both of which would have been amplified by the extreme damage. This hypothesis was seemingly verified by comparing the k static to the k calculated 19 from the vibration measurements The original shape function for the model was derived using the undamaged case. As the damage increased, the geometry and behavior of the model changed, rendering the original shape function inaccurate. It should also be noted that the damage was applied to only one material, the plastic girders, thus changing the relative stiffness contributions of the two materials. If such large damage case scenarios were to be further investigated, the need for a nonlinear SDOF model may be necessary. If less severe damage is to be studied, a single shape function and a linear SDOF model should be adequate. Summary This study provided an insight into the proposed dynamic load rating from a theoretical standpoint. The effective stiffness of the model from dynamic testing was shown to be higher than the result of static testing -this was especially true for the damaged cases. The FE results were consistently higher than the experimental results. It was obvious that the model testing may have involved non-linear behavior for severe damage. The use of more brittle construction materials might better reflect the behavior of actual bridges. The bridge model did not provide insights into traffic-induced dynamic impacts and vehicle mass effects, which were later studied using actual bridge testing (Section 4).