Feasibility Study on Dynamic Bridge Load Rating

by

Shen-En Chen, Patra Siswobusono and Norbert Delatte Department of Civil and Environmental Engineering

University of Alabama at Birmingham Birmingham, Alabama

B.J. Stephens

Department of Mechanical Engineering University of Alabama at Birmingham

Birmingham, Alabama

Prepared by

UTCA

University Transportation Center for Alabama The University of Alabama, The University of Alabama at Birmingham, and

The University of Alabama in Huntsville

UTCA Report Number 01221 May 2002

ii

Technical Report Documentation Page 1. Report No FHWA/CA/OR-

2. Government Accession No. 3. Recipient Catalog No.

5. Report Date June 2002

4. Title and Subtitle Feasibility Study on Dynamic Bridge Load Rating 6. Performing Organization Code 7. Authors Shen-En Chen, Patra Siswobusono, Norbert Delatte and B.J. Stephens

8. Performing Organization Report No. UTCA Report 01221

10. Work Unit No.

9. Performing Organization Name and Address Department of Civil and Environmental Engineering The University of Alabama at Birmingham 1075 13th Street South, Suite 321 Birmingham, Alabama 35294-4440

11. Contract or Grant No. DTRS98-0028 13. Type of Report and Period Covered Final Report; January 1, 2001 – June 31, 2002

12. Sponsoring Agency Name and Address University Transportation Center for Alabama University of Alabama PO Box 870205 Tuscaloosa, Alabama 35487

14. Sponsoring Agency Code

15. Supplementary Notes 16. 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. 17. Key Words Dynamic load rating, vibration measurements, bridge testing, ambient vibration, modal testing county bridges

18. Distribution Statement

19. Security Classification (of this report)

20. Security Classification (of this page)

21. No of Pages

22. Price

Form DOT F 1700.7

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Contents

Contents ..............................................................................................................................iii List of Tables .......................................................................................................................v List of Figures ......................................................................................................................v Executive Summary............................................................................................................vi 1.0 Introduction....................................................................................................................1 Project Objectives ..........................................................................................................2 Approach and Work Plan...............................................................................................2 Report Outline................................................................................................................2 2.0 Background and Literature Review ...............................................................................3 Bridge Inspection Technology.......................................................................................3 Inspection of LT20 Bridges ..........................................................................................3 Bridge Vibration Studies ..............................................................................................4 Dynamic Load Factor.....................................................................................................6 Dynamic Load Rating ...................................................................................................7 3.0 Miniature Bridge Model ..............................................................................................10 Introduction..................................................................................................................10 Miniature Bridge Model ..............................................................................................10 Dynamic and Static Testing ..................................................................................11

Damage Scenarios........................................................................................................12 Boundary Effects and Effective Length ......................................................................15 Load Capacities ..........................................................................................................17 Discrepancies in Results ..............................................................................................18 Summary......................................................................................................................19 4.0 Testing of County Bridge No. 020-59-202Z................................................................20 Introduction .................................................................................................................20 Shelby County Bridge No. 020-59-2027 ....................................................................20 Single Impact Test .................................................................................................21 Full-Scale Modal Test ...........................................................................................22 Ambient Traffic Excitation .........................................................................................25

Dynamic Amplification..........................................................................................26 Effect of Vehicle Mass...........................................................................................27

Controlled Vehicle Excitation Testing ........................................................................29

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Bridge Remaining Capacity.........................................................................................29 Summary ......................................................................................................................29

5.0 Finite Element Simulation of Actual Bridge ..............................................................30 Introduction .................................................................................................................30 Full-Scale Bridge Model .............................................................................................30

Boundary Effects ...................................................................................................31 Summary .....................................................................................................................32 6.0 Discussion ...................................................................................................................33 Discussion on Bridge Monitoring Methodology ........................................................33

Summary of Bridge Model and Actual Bridge Study..................................................34 Proposed Dynamic Load Rating Algorithm ...............................................................35 Potential Benefits .........................................................................................................36 Limitations ..................................................................................................................36 7.0 Conclusions .................................................................................................................38 8.0 Recommendations for Future Studies .........................................................................40

Vibration Testing Methodology...................................................................................40 Wireless Networking....................................................................................................40

9.0 References ....................................................................................................................42 Appendix A: Acknowledgements .....................................................................................46 Appendix B: Lists of Acronyms and Symbols ..................................................................47

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List of Tables Number Page 3-1 Description and Frequencies of First Four Mode Shapes ....................................12 3-2 Damage Scenarios ................................................................................................12 3-3 Dynamic Test Results and Calculated Load Capacities ......................................14 3-4 Material Properties ...............................................................................................14 3-5 Static Load Test Results ......................................................................................17 4-1 Traffic Vibration Measurements with Single Car Passing .................................25 4-2 Controlled Vehicle Crossings with Measured First Vibration Mode ..................29 5-1 Summary of Material Properties used in FE Modeling .......................................30 5-2 FE Model Results for Full-Scale Bridge FEM Model .........................................31

List of Figures

Number Page 2-1 Single degree of freedom model ............................................................................7 3-1 Miniature bridge model .......................................................................................11 3-2 Static test setup .....................................................................................................11 3-3 Static load/deflection curve for undamaged bridge model .................................12 3-4 Static load/deflection curve for damaged bridge model ......................................13 3-5 First bending mode ..............................................................................................13 3-6 Percent frequency change for different damages .................................................15 3-7 Frequency shift versus stiffness reduction ...........................................................16 3-8 Load capacities (without impact factor reduction) ...............................................18 4-1 Shelby County Bridge .........................................................................................20 4-2 Posted load limit for structure no. 020-59-202z ..................................................21 4-3 Sensor setup underneath the bridge .....................................................................22 4-4 Impact grid for modal testing .............................................................................23 4-5 First bending mode from modal testing ...............................................................24 4-6 First torsion mode ................................................................................................24 4-7 Mass effect on frequency change .........................................................................28 5-1 Finite element models...........................................................................................32 6-1 Proposed SDOF spring model for load capacity determination ..........................33 6-2 Flowchart of the bridge dynamic load rating (Miller, 2001)................................36 8-1 A proposed wireless solution of the bridge sensing system (Fisher, 2001) .........41

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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.

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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 (Grimes, 2001). To maintain these bridges, engineers conduct regular visual inspections of these bridges. Currently, most bridges are required by federal mandate to be inspected no less than once every two years. Information from these inspections, along with existing data about the construction and modifications of the bridge, are maintained in a Bridge Management System (BMS) database. 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.

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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 (Cawley and Adams, 1979; Alampalli et. Al, 1997; and Chase and Laman, 2000). These approaches focused on measurements of the dominant vibration frequency of a bridge due to excitations from ambient traffic, to determine the remaining capacity of the bridge for a specified allowable deformation. To develop this methodology, proof-of-concept studies were first conducted on a miniature bridge model, including both static and dynamic tests to determine the model stiffness and finite element modeling to provide theoretical validation of the test results. Once the theoretical foundation of the method was established, field studies were conducted on a selected bridge. 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.

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Section 2. Background and Literature Review Bridge Inspection Technology Physical inspection of transportation facilities is the key to effective management of the state’s transportation infrastructure. The goals of inspection are to recognize potential danger of failures and to identify damaged locations for possible repair and rehabilitation. Federal agencies, the American Association of State Highway Transportation Officials (AASHTO), and state agencies such as New York State Highway Division, publish standard procedures for inspection of transportation structures (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 (Manning, 1985). Hence, they do not reflect accurately the behavior of a structure at the system level. These methods are also discouraging because of their dependency on expensive instrumentation. 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 Alampalli, 2000). 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

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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) (Grimes, 2001). They are attained through periodic field inspections. Factors contributing to a bridge’s sufficiency rating other than structural adequacy are average daily traffic (ADT), roadway classification, load rating, and serviceability. Sufficiency ratings are calculated based on ranking of bridge elements and the other factors mentioned above. The ratings range from 0-100, and those bridges with a rating below 50 may be eligible for replacement using Special Bridge Replacement Program (SBRP) funds. County and local governments use load ratings along with sufficiency rating and ADT to prioritize LT20 bridges for replacement. 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 (Adams et al., 1978; Cawley et al., 1979; Petroski, 1981, Gudmundson, 1983; Rizos et al., 1990; Hearn and Testa, 1991; Frswell et al. 1992; Chen et al. 1995, etc.). Several research efforts have been directed towards damage assessment in large civilian structures. Examples include the works reported by Dewolf et al. 1986; Mazurek and DeWolf, 1990; Aktan et al. 1994; Raghavendrachar, et al., 1992; Salane, et al., 1990; Toksoy et al. 1993; Samman et al. 1994; Williams et al., 1994; Aktan et al. 1997; and Alampalli et al. 1997. Since dynamic responses can be directly related to the global stiffness of a structure, this approach gives an excellent indication of the overall damaged state of the structure. An exhaustive survey on dynamic testing of civilian structures has been conducted by Farrar et al. (1995); and overviews of progress in this area of study have been presented by Hausner et al. (1997) and Venkatappa (1997). Several researchers have made more ambitious attempts to use the same responses for locating and quantifying damage (e.g. Gudmundson 1983; DiPasquale et al. 1990; and Pandey et al. 1995). Crack detection using vibration methods was investigated as early as the 1940s. For example, Thomson (1949) proposed a model to determine equivalent vibration frequencies of a slender beam with a narrow slot. Thomson recognized that the width of the slot had little influence on vibration frequencies compared to the depth and that minute cracks have little influence on frequency shifts of higher modes. Using multiple axial mode frequencies, Adams et al. (1978) was able to identify damage location on a straight bar. They noted that the frequency

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level was a function of location. Cawley et al. (1979) presented a method using the ratio of frequency changes in two modes obtained both experimentally and numerically to locate damage. Using a simple model, Petroski (1981) illustrated that cracking not only introduces higher vibration amplitudes, but also introduces higher frequency modes of vibration. Gudmundson (1983) pointed out that crack closing can considerably affect the dynamic behavior of a structure. Furthermore, vibration mode shapes have also been studied as part of damage detection. Salawu et al. (1994) studied the performance of damage detection methods based on mode shapes and found that the modal assurance criteria (MAC) and co-ordinate modal assurance criteria (COMAC) were influenced by the presence of damage, but neither could locate damage accurately. Salane et al. (1990) studied the variation of modal stiffness and damping, and concluded that the variations in viscous damping ratios could not be related to the deterioration of a structure. They stated that changes in selected mode shapes were the best indicators of damage location and also that the mode shapes with large displacements in the vicinity of damage were the most useful indicators. Recently, modal curvature-based methods have gained attention from various researchers in damage detection. Using strain gage measurements, Elkordy et al. (1994) constructed strain mode shape for damage detection. Salawu et al. (1994) also studied curvature effects and pointed out that, in order to correctly identify damage locations, a sufficient number of spatial data points and modes are needed. They also noted that multiple damage locations were generally difficult to identify for most methods, but curvature-based methods were able to give a better indication of multiple damage locations. Pandey et al. (1995) also investigated curvature mode shapes as a damage location parameter. The changes in the curvature mode shape were found to be more localized in the vicinity of damage as compared to the changes in the displacement mode shapes. It was also found that different modes gave different indications of damage level. Pandey et al. (1991) concluded that the higher the modes, the larger the curvature difference values. They showed that by increasing the damage level, the curvature value also increased. However, with only limited amount of spatial data, the effect of data density was not investigated. Park et al. (1995) proposed a damage index method based on modal strain energy. The technique was based on the fractional strain energy of a member, which was calculated by using the ratio of the modal strain energy contained in the member to the modal strain energy contained in the entire structure. The damage index was calculated considering all the measured modes (Park et al. 1995). A statistical approach was then used to identify the damage based on the variation of the damage index values along the structure. The authors recognized the need to use high quality mode shapes. Hence, they proposed using Shannon’s sampling theorem to reconstruct mode shapes. Cornwell et al. (1997) and Choi et al. (1997) extended the damage index method to two-dimensional problems. Using finite element analysis results, their studies showed that the strain energy approach worked equally well for 2-D plate structures. Choi et al. (1997) implied that the compliance-based approach gave better results than did the energy-based approach. Because in both studies only numerical results were used, the effect of experimental noise was not discussed. Ratcliffe (1997) indicated that for damage detection only, the

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curvature-based technique did not require a priori knowledge of the undamaged structure. In other words, undamaged information was not required by curvature-based techniques for damage detection. Further enhancement of the Laplacian method using a cubic function curve fit was also reported to identify damage as small as 0.5 % in a FE model (Ratcliffe, 1997). 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). Typically, a load test is conducted if actual load capacity is required. Dynamic load tests may involve determining DLF on the bridge and the load distribution on different girders. According to AASHTO, DLF is calculated as

3.0125

50<

+=

sDLF (2.1)

where S is the loaded length along the bridge assuming the truck load to be uniformly distributed. AASHTO limits design DLF to be less than 30% (2000). Using accelerometer measurements, Chowdhury (2000) computed the dynamic load factor for acceleration (DLFA) as

( )( ) 1−=ty

tyDLFA

slow

fast

&&

&& (2.2)

where fasty&& is acceleration amplitude for a vehicle at high speed and slowy&& is acceleration amplitude for a vehicle at low speed. This relationship defines the DLFA as a ratio of the dynamic response to the pseudo-static response and quantifies the dynamic effect as a function of travel speed. Using standard truckloads, he measured the DLFA for a continuous multi-span steel bridge and that of a single span concrete T-bridge. His test results indicated DLFA magnitudes of 1.33 and 1.84 for the steel girder and the concrete bridge, respectively. 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 lfV 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 DADFE 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.

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Latheef et al. (1991), on the other hand defined DLFA as:

static

staticdynamic

y

yyDLFA

&&

&&&& −= (2.3)

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 (Cioara and Alampalli, 2000). In the case of LT20 county bridges, the traffic is typically limited to a single car for each passing. Hence, the analysis is relatively simple. 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 single- degree-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 (Figure 2-1).

Figure 2-1. Single degree of freedom model.

The load capacity of a structure can be estimated if the stiffness of the structure can be accurately determined. This is accomplished by determining the vibration frequency of the structure. Given a mass, m, attached to a spring of stiffness, k, the natural frequency of the SDOF model can be determined as:

8

mk

fπ21

= (2.4)

The same stiffness k can be used in determining the static deflection through the Hooke’s Law:

kP

=δ (2.5)

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:

( ) ( )( )∫ Φ= nnn dxxxmm 2~ (2.6)

( ) ndxEIk 2~Φ ′′= (2.7)

Where ( )nxΦ is the deflection shape function and xn denotes the normalized variable. If fixed boundary conditions are considered for the beam, the assumed normalized displacement function becomes

( ) 234 163216 nnnn xxxx −+−=Φ (2.8) Equation (2.4) can then be used to determine the SDOF model vibration frequency using the effective modal values. It is known that a bridge lose stiffness either through age or damage. Assuming such a loss in stiffness occurs with no accompanying loss of mass, the new frequency for the SDOF model may be determined from

9

mk

f ~

~

21 ′

=′π

(2.9)

Where k

~' represents the reduced stiffness,

kkk ∆−=′ ~~

(2.10) If a limiting deflection, δ limit, is set, then the corresponding load, P,' can be determined as:

( ) itfmP lim22 δπ ′=′ (2.11)

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:

DLFAP

Pposted

′= (2.12)

The dynamic effect is expressed in terms of DLFA, which is essentially the ratio between the dynamic and static deflections (Chowdhury, 2000):

( )( )ty

tyDLFA

slow

fast

&&

&&= (2.13)

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).

30.1125

501 ≤

++=

lIF (2.14)

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.

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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 full-scale 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, tw = 1/16 in, bf = 5/32 in and tf = 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. Figure 3.1 shows the bottom view of the bridge model, including the girders. 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.

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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 mid-span and parallel to the fixed-end boundaries. The stiffness was then determined from the force-displacement 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.

Figure 3-2. Static test setup. 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 Table 3-1.

Figure 3-1. Miniature bridge model.

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Table 3-1. Description and frequencies for first four mode shapes

First Strong-Axis Bending Mode

First Torsion Mode

First Diagonal Bending Mode

Second Diagonal Bending Mode

474.8 Hz 506.9 Hz 559.9 Hz 685.1 Hz Damage Scenarios To investigate the effects of damage, three scenarios were examined for the miniature bridge model (Table 3-2): Damage was created by cutting each of the plastic I-beams at mid span. FE models were constructed for each of the damaged case scenarios through element elimination. Boundary conditions and loading conditions were assumed to be the same for all cases.

Table 3-2. Damage scenarios

Case Description 1 Undamaged

2 50% reduction in cross section to all girders

3 100% reduction in cross section to all girders

Static and dynamic analyses were performed on both the FE and actual models for all damage cases. For the static and dynamic cases, fixed-fixed boundary conditions were used. The stiffness values calculated from the force-displacement graphs of the static test are presented in Table 3-3. The equivalent stiffness values calculated from the dynamic test also are presented in the table. Figures 3-3 and 3-4 show the linear segment of the load deflection curves for the undamaged and damaged bridge models. It was shown that with the cut damage, the stiffness of the structure was obviously reduced. This was also reflected in the slopes of the curves:

• y= 2.010 x + 29.383 for undamaged model • y= 0.911 x + 21.086 for damaged model

Bridge Model 1: fixed-fixedy = 2.0099x + 29.383

0

50

100

150

200

0 20 40 60 80

Deflection ( .001 in)

Fo

rce

(lb

s)

Figure 3-3. Static load/deflection curve for undamaged 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 (Table 3-3). The miniature bridge model also experienced a reduction in the first bending mode frequency with each cut. As seen in Figure 3-5, the relationship between the amount of damage (or loss of stiffness) and the shift in frequency was not linear. From the new natural frequencies for Case 2 and Case 3, the reduced load capacity was calculated using Equation (2.11). The results of these calculations are presented in Table 3-3.

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00%

% Stiffness reduction

% F

req

uen

cy S

hif

t

FE ModelActual ModelSDOF Model

Figure 3-5. Frequency shift versus stiffness reduction.

Bridge Model 1: damaged

y = 0.9113x + 21.086

050

100150200250

0 50 100 150 200 250

Deflection (.001 in)

Fo

rce

(lb

s)

Figure 3-4. Static load/deflection curve for damaged bridge model.

14

Table 3-3. Dynamic test results and calculated load capacities

Boundary conditions

Frequency (Hz)

k~

(lbf/in) (Equation x)

Percent Difference Between Static and Dynamic

Assumed Max

Deflection (l/800) (in)

d

Load Capacity

(lbf) P

Percent Difference Between FE and Actual

New Load Capacity

(lbf), Given

DLFA=1.3 Fixed-fixed-FE 474.77 2436.47 -5.49 % 8.28 x 10-03 20.18

Damage Case 2 436.10 2055.75 0.30 % 8.28 x 10-03 17.02

Damage Case 3 402.04 1747.11 4.29 % 8.28 x 10-03 14.47

Fixed-fixed-actual 470 2387.75 -6.54 % 8.28 x 10-03 19.77 -2.00 % 15.21

Damage Case 2 416 1870.60 39.39 % 8.28 x 10-03 15.49 -9.01 % 11.92

Damage Case 3 373 1503.87 46.50 % 8.28 x 10-03 12.45 -13.92 % 9.58

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 Table 3-4.

Table 3-4. Material properties.

Material ρmass (lbfs 2/in) Elastic Modulus, E

(lbf/in2) Poisson’s Ratio, υ

Plastic I-Beams 9.909 x 10-5 377000 .40

Plexiglas Plate 11.13 x 10-5 406000 .41

Using eigen value analysis, the natural vibration frequencies of the model can be determined. The first bending mode is shown in Figure 3-6, which corresponds to a natural frequency of 474.77 Hz – comparable to experimental results that were verified at multiple locations. The first mode was found to be a bending mode when fixed-fixed boundary conditions were applied, thus confirming the assumption made in the method. Descriptions and frequencies for the first four mode shapes are presented in Table 3-1. 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 Table 3-3, the numerical and experimental results for the undamaged model are of the same order of magnitude. The deviation between the deflections of the FE model and actual static tests became larger as more severe damage was introduced. This was likely due to the nonlinear nature of the severely damaged model.

15

Figure 3-6. First bending mode.

To study the effects of damage on different girders and their impacts on the frequency shifts, through-cut in a single girder was induced in the finite element model. Figure 3-7 shows the changes in frequency for the first 20 vibration modes. The damage scenarios shown in each figure are damage on each individual girder. The plots indicate the different mode frequencies reflecting the effect of different damage locations. From these plots, it was observed that the induced damage may have different effects on the different mode frequencies. It can also be observed that the damage at the inner girders and outer girders produced different vibration frequencies. Hence, it can be concluded that the change is dependent upon the frequency mode as well as the damage location. Hence, careful study of frequency shifts can also reveal locations of damages. For practical purposes, the percent variation in the first mode frequency shift was adequate for dynamic load rating. 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.

16

Figure 3-7. Percent frequency change for different damage. Acknowledging this deficiency in the test setup required that the appropriate boundary conditions be applied to the FE model. Correlation was first established between the static test results for the actual model and the FE model. Manipulations of the FE model resulted in fixing the entire cross–section of the girders, with an effective length between fixed elements of 6.50 inches. This effective length matched the experimental test setup. Verification of the boundary conditions came from correlation of the FEM and actual results for the first bending mode. For the static analysis, a correlation beam stiffness and deflection given a point load at center-span and appropriate loading was obtained using elastic beam theory:

EIl

P

ff

= 3

192δ

(3.1)

17

where ffδ 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,

( )22~~fmk π= (3.2)

where the effective mass was calculated from Equation (2.6) as m~ = 2.74 x 10-4 lbf•sec2/in. The values for the stiffness obtained from the static analysis are presented in Table 3-5. These values were compared to the values obtained from the dynamic analysis in Table 3-3 to validate the model.

Table 3-5. Static load test results

Boundary Conditions Damage Case

Effective Length (in) Load (lbf) Deflection (in) kstatic (lbf/in)

Fixed-fixed-FE Case 1 6.50 100.00 0.03879 2577.98

Case 2 6.50 100.00 0.04879 2049.60

Case 3 6.50 100.00 0.05969 1675.32

Fixed-fixed-actual Case 1 6.50 100.00 0.03914 2554.90

Case 2 6.50 100.00 0.07452 1342.00

Case 3 6.50 100.00 0.09742 1026.50

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 (2000):

800maxl

=δ (3.3)

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. Figure 3-8 illustrates that as the stiffness of the model decreased with progressive damage, the load required to produce the maximum allowable deflection decreased from 19.77 lbf to 12.45 lbf (case 3). In determining the posted load rating (Pposted), 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). Pposted for each damage case of the miniature model presented in Table 3-3. 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.

Figure 3-8. Load capacities (without impact factor reduction).

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 kstatic 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 kstatic to the k

~ calculated

19

from the vibration measurements (Table 3-5). The deviation between the stiffness values increase as the level of damage increased, indicating problems with the experimental setup. 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).

20

Section 4. Testing of County Bridge No. 020-59-202Z Introduction This section reports the findings of dynamic testing of a selected county bridge in Shelby, Alabama. Among the 94 LT20 bridges in Shelby County, the bridge number 020-59-202Z was selected based on its accessibility. The vibration studies on the bridge included tests using ambient traffic excitation, single-point impact excitation and full-scale modal testing. The bridge bending stiffness was determined based on the first dominant vibration mode frequency. Dynamic load impact factors were found using the ratio between responses from different traffic excitations. Shelby County Bridge No. 020-59-202Z Vibration testing using ambient traffic vibration was attempted on the selected bridge. The subject bridge is located in southern Shelby County on Shelby Co. Road 20 (Figure 4-1). The bridge has a clear span of 18 ft 3 in. (travel length) and an actual span of 20 ft 10 in. (boundary to boundary). The deck is composed of 5 in. concrete (150 lb/yd3), five inches thick. A 16 in. thick soil aggregate (cherty) base (115 lb/yd3) and a 1½ in. thick bituminous concrete wearing surface (165 lb/yd3) were placed over the deck. The bridge also has standard flex beam guardrails (25 lb/ft/side). The girders are steel S12x31.8 beams (flange width, Bf=5 in., depth, d=12 in., flange thickness, tf=0.544 in. and web thickness, tw=0.35 in.). The bridge was constructed in 1959 with 5 stringers spaced at 58 in. on center. There are no cover plates. The bridge is skewed at a 20o angle, which is the same skew used in the laboratory model.

Figure 4-1. Shelby County bridge.

21

Inspections from County engineers resulted in the posting of maximum allowable traffic loads for different vehicle types (Figure 4-2). Single Impact Test Impact tests using a 20-lb sledgehammer were first conducted to determine the natural vibration modes of the bridge. The vibrations were picked up using 2 accelerometers- one placed near the center girder and the other placed near an outermost girder, so that the impact energy distribution could be determined (Chowdhury, 2000). The signals were collected using a 2-channel digital oscilloscope (Velleman, PC Scope PCS64i) and a laptop. The impact was applied at the center of the bridge. Using the hammer, multiple modes were then excited. A sampling frequency of 100 Hz was used. The first bending mode of the bridge was determined to be at 18 Hz. The natural vibration behaviors of the bridge were confirmed and further investigated using FEM modeling. Figure 4-3 shows the sensor setup underneath the bridge deck. Wood panels were constructed to support the charge amplifiers that connected to the sensors. A 100 ft cable then extended the signal wire to the PC Scope, which was connected to the RS232 port on the laptop.

Figure 4-2. Posted load limit for structure no. 020-59-202Z.

22

Full-Scale Modal Test Full-scale modal testing was conducted using an instrumented 20- lb sledgehammer to determine the natural vibration modes of the bridge. The goal of modal testing was to experimentally construct the mode shapes for system identification and mode validation. To conduct modal testing, multiple spatial data was collected. This could have been achieved either via a multi pick-up method or by using a single reference point with multiple excitations. In this case, the vibrations were detected using a single seismic piezoelectric accelerometer (PCB Piezotronics) with a magnetic base placed at the center of the outermost girder. The signals were collected using a four-channel data acquisition system (IOtech Wavebook/513, 12-bit MHz Data Acquisition System) and a laptop. A 4-Channel ICP Sensor Signal Conditioner (PCB) was used to enhance the signals. A grid of forty-two nodes was drawn on the bridge (Figure 4-4) and was impacted individually with the sledgehammer. Each node, depicted as Nxy, was excited five times using a sampling frequency of 1000 Hz for the first 12 nodes (nodes N11 through N26) and a sampling frequency of 500 Hz for nodes N31 through N76.

Figure 4-3. Sensor setup underneath the bridge.

23

Figure 4-4. Impact grid for modal testing.

Signal analysis software DADiSP (DADiSP 1999) was used to analyze the signals captured from the bridge to determine the natural frequency peaks. Linear regression was performed on the data to remove any noise acquired by the accelerometer and to eradicate any baseline shift. An average frequency of the first bending mode of each node was sought. The first bending mode of the bridge was determined to be 18 Hz. The transfer functions (eigen vectors) were determined by dividing the output responses with the corresponding input functions. Since the spatial data were complex, the imaginary part of the transfer functions provided the modal amplitudes. The result of the impact test on the first bending mode can be seen on Figure 4-5. The first torsion mode was also detected to be at 24 Hz (Figure 4-6).

24

Figure 4-5. First bending mode from modal testing.

Figure 4-6. First torsion mode.

25

Ambient Traffic Excitation To study the effects of different vehicles traveling on the bridge, the excitation of the bridge during regular traffic was monitored. To capture the first bending mode, two accelerometers were used. One was placed at the center of the bridge and the other was placed near the outermost girder. Table 4-1 shows 25 recorded vehicle passages including the vehicle type, estimated weight, first bending frequency and relative speed of the vehicle. From the table, it can be observed that added mass of a passing vehicle can significantly reduce the vibration frequency of the bridge. For example, the Kenworth dump truck of 22,000 lb reduced the frequency from 18.25 Hz to 14 Hz.

Table 4-1. Traffic Vibration Measurements With Single Car Passage

Record Type of vehicle Approx. weight (lbs)

First bending frequency

(Hz)

Amax,CH1(f) / Amax,CH2(f)

Amax,fast(f) / Amax,slow(f) [Amax,fast(t) / Amax,slow(t)]

Travel direction

Comments

01 Full-sized Chevy with boat 7500 18.1 0.11 E N

02 Chevy S-10 3300 17.3 0.17 W N

03 Toyota Tacoma, ext cab 3600 17.6 0.39 W MF (10

mph>limit)

04 Toyota Tacoma, reg cab 3400 - - E MF

05 Mid 80’s Ford Mustang ? 17.6 0.52 E MF

06 90’s mid-sized VW 3300 - - E F (< 10 mph over)

07 Geo Prism 2700 - - W MF

08 Kenworth dump truck 22000 14 0.48 W MF

09 Toyota Camry 3300 17.5 0.59 E N

10 Toyota Corolla 2700 17.3 0.53 W F

11 Pontiac Parisian 3800 16.8 0.50 1.22 [1.3] W MF

12 FS Chevy w/toolbox combo 4800 17.2 0.58 W N

13 Subaru Wagon 16.3 0.61 W VS (too slow)

14 Ford F-150 ? 17.7 0.53 W F

15 MS Chevy reg cab 4600 15.8 0.62 1.9 [1.7] W MF

16 Pontiac Parisian 3800 17.5 0.56 W N

17 MS Chevy reg cab 4600 17.6 0.50 W N

18 MS Ford reg cab ? 16.8 0.48 W N

19 MS Ford with toolboxes ? - - W N

20 Toyota Camry 3300 17.3 0.50 2.9 [1.9] W MF

22 FS Dodge truck 16.0 0.67 W N 23 Toyota Paseo 2800 17.6 0.62 W MF

24 Jeep Grand Cherokee

4600 16.0 0.67 E MF

25 Toyota Tacoma 3400 17.6 0.44 E MF Comments: W- west-ward, E- East-ward, N – normal speed, MF – Moderate fast speed, VS – very slow speed, F – fast speed

26

To determine the excitation of the first bending mode, the ratios between the modal magnitudes of the two accelerometers (Amax,CH1 and Amax,CH2) are also provided in Table 4-1. The distribution factor (DF) between the girders is defined as the ratio of the maximum responses between the two sensors. Given sensor one’s central location, sensor two’s location near the outside girder, and ideal first mode bending, then both sensors should have recorded equal amplitudes Amax(t). However, the location of the vehicle, the effects of damping, and the presence of the outside concrete stiffeners affected the ratio of the amplitudes. A car traveling directly in the center of the roadway would excite sensor 1 more than sensor 2:

( )( ) 1

1max,

2max, <fAfA

CH

CH

For example, the two vehicles with low ratios (0.11 for the full-size Chevrolet truck with a boat and 0.17 for the Chevrotlet S-10) may result from the vehicles traveling on the lane away from the sensors. The DF for the acceleration data should equal the DF for the moments, indicating the critical load carrying member (the one to focus upon when determining dynamic load capacity). Dynamic Amplification Since there was no traffic control, the dynamic amplification due to different vehicles at different speeds was studied. From the 26 recorded crossings, only three cars had repeated crossings: a Toyota Camry, a MS Chevrolet with regular cab and a Pontiac Parisian. The DLFAs listed in Table 4-1 are ratios of the fast passage response to the slow passage response for each duplicate vehicle crossing. For each vehicle type, two DLFA values were computed: the first value was the ratio of spectrum amplitudes of the first bending mode, and the second value (inside of bracket) was the amplitude ratio from the maximum time signal. Except for the Toyota Camry case, it is shown that the two DLFAs were very close in value – indicating that either approach can be used to determine the DLFA. The Pontiac Parisian, which weighed 3800 lb, had the lowest DLFA (0.22 and 0.30). The MS Chevrolet with regular cab, which weighed 4600 lbs, had higher DLFAs (0.90 and 0.70) than the Pontiac. The mass effect on the dynamic factor of the bridge was critical and was investigated further.

27

Effect of Vehicle Mass Due to the relatively light weight of the bridge, the mass of a passing vehicle becomes critical to the measured frequencies. From the measured frequencies in Table 4-1, it is obvious that the frequencies due to traffic loads are lower than the frequency from the hammer impact. To study the effect of the added mass, a SDOF model with a lumped mass and an elastic spring was used to model the bridge. To simplify the calculation of the effective mass, the bridge was assumed to be a beam in bending, with the deck acting as a portion of the girder (full-composite action). The effective flange area was transformed as an equivalent steel area. Assuming a deformed shape:

234

163216

−

+

−=

lx

lx

lx

lx

y (4.1)

The effective mass and stiffness are then calculated as:

∫

= dx

lx

ymm2

~ (4.2)

dxlx

yEIk2

~∫

= && (4.3)

The total weight of the bridge was 124,000 lb. The effective mass of the bridge was 112.96 lbfs2/in. and the effective stiffness of the bridge was 1.585 x 106 lbf/in. The vibration frequency was then:

mk

f ~

~

21π

= (4.4)

The frequency of the SDOF model was calculated to be 18.9 Hz. The frequency due to be added mass, ∆m, can be computed as:

mmk

f∆+

=′ ~

~

21π

(4.5)

28

Figure 4-7 shows the frequency ratio, f’/f, versus mass ratio mm ~/∆ . A 20% increase in mass was shown to reduce the frequency to 90% of its original value. For example, the Toyota Camry increased the mass by 7.79%. As a result, the frequency shifted to 17.337 Hz (3.7% shift). The Kenworth dump truck, which weighed 22,000 lb, reduced the vibration frequency about 22 %. The SDOF model confirmed the shifts in the natural frequency of the bridge resulting from the mass of the vehicles. Inversely, this model can also be used to determine the effect of stiffness reduction.

Figure 4-7. Mass effect on frequency change.

0.80

0.85

0.90

0.95

1.00

0.00 0.10 0.20 0.30 0.40 0.50

Ratio of Mass Reduction (dm/m)

Rat

io o

f Fre

qu

ency

sh

ift (f

'/f)

29

Controlled Vehicle Excitation Testing A study to determine the effect of different vehicle speeds on the bridge’s bending mode was also conducted. A vehicle weighing approximately 6400 lb was driven over the bridge at different speeds, and the excitation of the bridge was monitored (Table 4-2). It was observed that a speed ranging between 20 and 40 mph caused the first bending mode to be between 17.5 Hz and 19.1 Hz with a mean frequency 18.25 Hz and a standard deviation of 62 %. Thus, different vehicle speeds caused the vibration periods of the first bending mode to fluctuate. This indicated a significant impact of vehicle speeds on the bridge vibration behavior.

Table 4-2. Controlled vehicle crossings with measured first vibration mode.

Speeds (MPH) Amplitude (sec) Frequency (Hz)

20 0.00071 18.7

30 0.00077 17.85

30b 0.00127 17.5

40 0.00048 17.8

40b 0.00073 18.55

40c 0.00049 19.1

` Bridge Remaining Capacity Based on the dynamic testing results, it was possible to determine the existing remaining capacity for the bridge. Assuming the first bending mode, the bridge effective stiffness was calculated as 1.585 x 106 lbf/in. Using the previously defined AASHTO deflection limit of L/800 (AASHTO,1992), the limiting deflection for the 18 ft 3 inch long bridge would be approximately 0.27 inches. Assuming a single spring SDOF model, then the load capacity of the bridge in its existing condition was estimated as follows:

Compared to Figure 4-2, this estimated capacity is significantly larger than the maximum posted load limit. Hence, it can be concluded that the posted load is very conservative. Even using the highest impact factor (i.e. 1.9), the predicted load capacity would still be higher than the posted load limit. Summary The results of this study show that the DLFA and estimated load capacities from vibration data are consistent and may be used on short span bridges. The weights and traveling speeds of passing vehicles are critical to the dynamic behavior of the bridge. Using a deflection limit, it is possible to establish the remaining load capacity of the bridge - an invaluable piece of information for engineers. Finally, careful placement of the sensors was found to be critical.

tonKP effectiveit 9.196limmax =×= δ

30

Section 5. Finite Element Simulation of Actual Bridge Introduction The next step in this research was to validate the experimental observations reported in Section 4 for the purpose of demonstrating the effectiveness of the proposed technique. This was accomplished via FEM. FEM was ideal since the actual bridge could not be damaged, and the FE model also served as a tool for future parametric studies. However, the model needed to be validated with actual test data. It should be noted that FEA is not a required component in the proposed dynamic load rating technique. Full-Scale Bridge Model Full-scale FEM models of the bridge were constructed to study the vibration modes and make comparisons with the experimental results. Assuming full connection between different components, the bridge was modeled as a deck with a chert overlay and steel girders. The full connectivity assumption was thought to be reasonable, since the impact load from actual dynamic tests would be very small compared to the weight of the bridge. The material constants used in the FE model are listed in Table 5-1. Since the elastic modulus of the chert base layer was not known, an assumption had to be made. After several trials, an elastic modulus of 8 x 104 lbf/in2 appeared to be most reasonable. However, a modulus of 3 x 105 lbf/in2 is presented in Table 3 for comparison purposes. The bridge was modeled using a commercial FEM Software, Algor, with approximately 11,000 solid elements. Eigen value analysis was then conducted to determine the natural mode shapes and frequencies.

Table 5-1. Summary Of Material Properties Used In FE Modeling

ASTM A36 Steel Girders Concrete Deck Chert (10% Econcrete)

Mass Density (lbf*s 2/in/in3) 7.356x10-4 2.24819x10-4 2.24819x10-4 Modulus of Elasticity (lbf/in2) 29x106 3 x106 3 x105* Poisson’s Ratio .29 0.15 0.15 Thermal Coefficient of Expansion (1/°F) 6.5x10-6 6x10-6 6x10-6

Shear Modulus of Elasticity (lbf/in2) 11.2x106 0 0 * FE model was re-run using Echert=.01Econcrete=3e4

Different models were constructed to study the boundary effects and the effects of the side-rails. Assuming fixed boundaries over the deck and girders, the first bending mode was 18.72 Hz, which compared well to the actual test results. This value was then taken as the actual field condition. Detailed results are shown in Table 5-2.

31

Figure 5-1 shows the primary bending mode shapes of the different FE models: Figure 5-1(a) shows the bridge with free-free boundary conditions; Figure 5-1(b) shows fixed girder boundaries; Figure 5-1(c) shows fixed boundaries for both the deck and the girders; and Figure 5-1(d) shows the bridge without the side-rails and fixed boundaries. The vibration frequencies of each model are listed in Table 5-2 for two different chert elastic moduli.

Table 5-2. FE model results for full-scale bridge model

Boundary Conditions Mode No. 1 2 3 4 5

a) Free-free, with side-rail Mode Type 1st Diagonal

Bending Weak Axis Bending

2nd weak axis bending

1st strong axis Bending 1st Torsion

Echert = 3x105 10.06 Hz 16.44 Hz 23.79 Hz 30.56 Hz 36.72 Hz Echert = 8x104 6.17 Hz 9.91 Hz 15.03 Hz 22.68 Hz 18.95 Hz

b) Fixed-fixed, girders only

1st Bending Mode

1st Torsion Mode

1st Diagonal Bending Mode

Echert = 3x105 20.61 Hz 25.69 Hz 33.45 Hz Echert = 8x104 16.83 Hz 21.79 Hz 26.75 Hz c) Fixed-fixed, girders and bottom of deck

1st Bending Mode

1st Torsion Mode

1st Diagonal Bending Mode

Echert = 3x105 22.88 Hz 27.74 Hz 35.32 Hz Echert = 8x104 18.72 Hz 23.23 Hz 27.98 Hz d) Fixed-fixed, girders only, no side-rails

1st Bending Mode

1st Torsion Mode

1st Diagonal Bending Mode

Echert = 3x105 22.65 Hz 27.79 Hz 38.46 Hz Echert = 8x104 18.64 Hz 23.03 Hz 29.64 Hz

Boundary Effects Table 5-2 shows that if the bridge was totally free, it would first experience a diagonal bending because it is a relatively wide, skewed structure. However, when the boundaries were fixed, the first mode was symmetric bending along the span, followed by the first torsion mode. This is consistent with the experimental observation of the actual bridge behavior, thus confirming the validity of the FE model. The fixity of the bridge deck was also questioned. When only the girders are fixed, the first pure bending frequency was much lower than the actual frequency (compare items b and c in Table 5-2). When the boundaries of the deck were fixed, the frequencies (18.72 Hz and 23.23 Hz) were closer to the actual measurements (18 Hz and 24 Hz, Section 4). Hence, the actual bridge is completely fixed. FE simulation was also used to determine the contribution of the side-rail to the overall stiffness. Figure 5-1(d) shows the FE model without side-rails, and the vibration frequency presented in Table 5-2 indicates that the side-rails did not contribute significantly to the overall stiffness of the bridge.

32

Figure 5-1. Finite element models.

Summary The finite element analysis showed that the bridge behavior was not influenced by the addition of the side rail. The boundary condition for the bridge had complete fixity near the two abutments. When proper boundaries were given, the model behaved exactly like the actual bridge with the fundamental mode as the first bending mode. The vibration frequencies for the FE model also were close to that of the actual bridge. Hence, it is concluded that the FE model was accurate in portraying the actual behavior of the bridge with full composite action.

33

Section 6. Discussion Discussion on Bridge Monitoring Methodology A brief summary of the proposed methodology can be illustrated using Figure 6-1, which shows a car passing over a bridge (right hand side). The car exerts a load, P, on the bridge, causing it to deflect an amount, δ (exaggerated in the picture). Modeling the bridge as a loaded spring (left hand side), the stiffness, K, of the bridge is analogous to the spring constant, K. Assuming linear elastic conditions, the load P on the bridge is then equal to δ*K. If the allowable deflection of the bridge is kept constant, then as the bridge deteriorates, its stiffness will decrease. This decrease can be determined.

If vibrations under ambient conditions were measured, then the vibration frequency of the bridge could be determined as a function of its mass and stiffness: ( )MKF = . The stiffness, K, and mass, M, terms are the same as for the statically loaded spring. As the structure deteriorates, its stiffness will decrease, which means it will be more flexible. Hence, it will have a lower frequency. By measuring the vibration frequency, ∆F, periodically, then the change in stiffness, ∆K, can be determined.

mK

F∆

=∆ (6.1)

mFK 2∆=∆ (6.2)

Figure 6-1. Proposed SDOF spring model for load capacity determination.

34

Reviewing Figure 6-1, the change in (load) capacity, ∆P, can be determined if the deflection is maintained as a constant. By subtracting ∆P from the maximum load, P, the new limiting load can be calculated as follows:

PPP it ∆−=lim (6.3) Summary of Bridge Model and Actual Bridge Study The results of this research thus far show the potential of the proposed testing methodology. The fundamental investigation using the miniature model indicates that the calculated stiffness reductions from both static and dynamic tests seem to correspond with each other within a reasonable range, thus validating the testing methodology. This is further confirmed by the analytical studies using FE modeling. The uses of the miniature model are of two fold: 1) the proof-of-concept study of using dynamic techniques for damage level prediction and 2) the feasibility study of load capacity prediction using dynamic and static tests. Since it is not feasible to damage an actual bridge, the miniature bridge allowed a proof-of-concept study to correlate stiffness reduction due to damage with frequency shifts. Since the miniature bridge is not an exact scaled-down model of the bridge, the absolute values of frequency and stiffness of the two structures are not compatible. However, using relative values, the results from the test on the bridge model indicate that a 20% girder stiffness reduction can result in a 10 % frequency shift. Since the model was tested under similar boundary conditions and bending modes, the same order of magnitude of frequency shifts can be expected on an actua l bridge under the same damage scenario. Actual tests on the bridge showed that vibration frequency measurements were functions of mass and speed of the passing vehicle. It was shown in the ambient traffic test that a 12.7% frequency shift due to different weights was possible, hence a constraint on the vehicle type needs to be established. The same vehicle passing at different speeds, shows a maximum of 8.8 % shift, indicating a control of vehicle speed is also essential. Concerns for actual bridge testing include the excitable range of vibration, the number of excitable modes, the excitation method, the sensor selection, the number of sensors required, the sensor placement locations, the damping of the structure, and the accessibility of the bridge girders. From the testing of the actual bridge, it is clear that the current method of testing would suffice for most LT20 bridges. Although almost all bridges vibrate in multiple modes during ambient excitation, it is evident that this technique works best when the dominant mode is the first bending mode. It should be noted; however, that a consideration of the total modal energy contributing to the system could provide a more accurate assessment of the load capacity. However, at the present, only the dominant mode could be considered. To ensure the capture of the first bending mode, a full-scale modal test would be highly recommended at the beginning of monitoring. Many of the lessons learned in this investigation are unique to short span LT20 county bridges. Even though these bridges may not be the most complicated bridges, the application of dynamic

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testing on these bridges presents a unique problem involving both logistics in application and measurement approaches. Based on the available data, the use of the DLFA values for load capacity calculations was not confirmed. This reflects on one of the difficulties in using ambient vibration for bridge monitoring. Since traffic load was not simulated on the miniature bridge model, the laboratory tests do not provide additional evidence supporting the use of DLFA values. Further studies are much needed in this area, which can only be accomplished with better-controlled dynamic tests on actual bridges. To ensure only measurement of bending vibrations, the strategic placement of sensors is critical. The best result occurs when the vehicle is driving across the center of the bridge because no torsion modes are excited. However, that may not always happen. Hence, to capture the first bending mode, at least two sensors should be used on the bridge. One of the sensors should be attached at the point of maximum displacement for the first bending mode. The second sensor should be placed at a location away from the center. Two sensors are also needed to ensure the repeatability of captured signals and to determine the dynamic load factors. Proposed Dynamic Load Rating Algorithm Figure 6-2 shows the analysis algorithm that could be integrated into an automated signal acquisition, processing and interpretation system with long-term installed sensors. The baseline values for the existing structure should be determined first – this can be accomplished by conducting a full modal test on the bridge. The captured signal is first transformed into frequency domain and used to pick up the dominant mode. It should be cautioned that significant signal processing may be required to ensure the capture of the dominant mode. By comparing the existing dominant frequency with the undamaged frequency of interest, then the frequency shift due to likely bridge damage can be determined. Assuming the bridge did not lose significant weight (< 10%, Section 4), the drop in stiffness can then be determined. The original weight of the bridge can be determined from material supplier’s data or estimated from the original construction shop drawings. The change in stiffness would then be used to determine the remaining capacity of the bridge with a pre-established minimum deflection requirement. This remaining capacity can then be used to re-evaluate the existing load posting. Limitations of this proposed approach may include having a priori knowledge of the bridge’s original conditions and the change of conditions in the course of bridge repair, such as the addition of wearing sur faces, and the unreported changes of bridge conditions during contractors work.

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Potential Benefits This research can benefit ALDOT by providing a more accurate and efficient assessment tool for determining load capacity of highway bridges. This will be useful to ensure safe passage of the public over aging bridge structures. The more accurate load rating can improve the management of the state’s highway bridges. The results of vibration measurements on selected bridges will also directly benefit ALDOT maintenance engineers by validating their strain measurements during their bridge load tests. The use of ambient vibration minimizes interruption to on-going traffic and improves safety for bridge inspectors and the public. Limitations The proposed approach should be treated as a supplement and not a replacement to existing bridge inspections. As shown in the arguments provided in the previous sections, the proposed dynamic load rating technique gives engineers a rapid assessment of remaining capacity. However, this technique does not reveal local damage information, which may be critical to the stability of the whole bridge.

Figure 6-2. Flowchart of bridge dynamic load rating. (Miller, 2001)

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Another limitation of this technique is the assumption of a linear elastic relationship in the SDOF spring mass model. While the conservative AASHTO design deflection limits and the existing inspection procedures should suffice ensure safety, engineers should still rely on their education and field experience when determining the maximum deflection allowable on a bridge. Since the tests in this research were conducted on a single bridge with limited vehicle passages, this poses limitations to the current study. If possible, for ambient tests on bridges, all traffic information (vehicle type, speed, direction of travel, and lane position) should be recorded. To compute the DLFA, at least two similar vehicles should be measured at varied speeds (preferably one very slow and one at normal speed). Continuous monitoring may be necessary for a long period of time if the traffic on the bridge is sparse. An automated measurement system; such as a remote sensing system, could be very helpful in this case. A priori knowledge of the exact weight of the bridge may not be necessary. However, more study is needed to understand how the vehicle weight would impact the vibration behavior of short span (less than 20 ft) bridges. Currently, specific vehicle types may be selected as standards for bridge monitoring.

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Section 7. Conclusions The results of this preliminary study, which developed an ambient, vibration-based bridge rating method for small county bridges, has been presented. The results indicated that the method can be developed into a reliable technique to predict the remaining capacity of a bridge. Several lessons can be learned from this study. From the miniature bridge model study, the following conclusions were drawn.

1. The bridge model tests validated the compatibility of the stiffness determined from the measured dominant vibration frequency and the stiffness from static tests;

2. Both dynamic and static tests indicate the reduction of stiffness due to progressive

damage.

3. The FE results validated the experimental results.

4. The FE results indicated that the frequency shift, as a result of damage, was a function of the damage location.

From the actual study of the bridge, the following conclusions were drawn:

1. The dominant mode of vibration of the Shelby County bridge was the first bending mode during ambient traffic excitation.

2. The boundary of the bridge could be assumed to be fixed.

3. The DLFA computed from vibration data was consistent and may be used on short span

bridges. 4. The weights and traveling speeds of the passing vehicles are critical to the dynamic

behavior of the bridge.

5. From the FE study, the addition of overlaying chert on the bridge significantly changed the overall mass of the bridge, and had be considered during the analysis.

6. The side-rails of bridge did not contribute significantly to the stiffness of the structure;

hence, they were ignored in the study of the bridge model.

7. Careful placement of the sensors was critical.

8. ;The minimum number of sensors required on a bridge for the proposed testing method was two.

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9. From the results, an algorithm for field evaluation of the load capacity of a bridge was proposed in Section 6 of this report. This algorithm can be further enhanced and refined through for future studies.

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Section 8. Recommendations for Future Studies Vibration Testing Methodology This report indicates the feasibility of using the proposed technique in bridge monitoring; however, due to the scope limitation, the results are not readily extendable to all state-owned bridges. Future studies should include testing of different bridge types (i.e., timber bridges, prestressed concrete bridges) and multiple-span bridges. It may be necessary to consider using composite mode shapes of multiple modes for the more complicated structures, since mode identification would be more complicated for multi-span bridges. Probabilistic approaches are typically used when dealing with ambient traffic when multiple vehicles are crossing the bridge.– This may need to be studied in the future. Bridges with other ambient loads, such as wind and seismic loads, may have different modal behaviors, hence, cross- interference between lateral, transverse and longitudinal vibrations may need to be studied. Wireless Networking Vibrations caused by vehicles crossing the bridge are detected by sensors in the form of digital signals. These data are then transmitted to the data collection system by using DAQ equipment. To eliminate difficulties in data collection, the data can be transmitted by wireless technology to a database for analysis. As an example, Figure 8-1 shows a proposed wireless technology for the bridge vibration monitoring. This set up utilizes state-of-the-art cellular technology and Bluetooth LAN (Fisher 2001). Cellular technology can be used for bridges located in the cellular coverage area, and Bluetooth LAN for those located outside the coverage area. Feasibility of the actual application of each wireless technique still needs to be studied in the future (Raygan and Callahan, 2001). Another area of needed study is the logistics in applying this technique in monitoring actual bridges. The frequency of data collection is dependent upon the average daily traffic (ADT). If possible, inspections should be done every six months with sampling periods of two days at three times a day. The sampling duration may be 30 seconds of sampling time, but is dependent on the dominant vibration frequencies of the bridge. This is more of a bridge management issue and is outside of the scope of this study. Finally, to augment this technology into existing BMS, studies are needed to establish a network system that will provide collective data and analysis of results on the conditions of each bridge. The evaluation hierarchy and rating systems, for example, need to be established for a workable network system.

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Figure 8-1. A proposed wireless solution of the bridge sensing system. (Fisher, 2001)

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Appendix A. Acknowledgements Foremost, we would like to thank Mr. Fred Conway and Mr. George Connor of the Alabama Department of Transportation, for their generous support, without which we will not be able to solicit the support of this interesting research project. We would like to thank Mr. Tom Grimes, Mr. Kenneth R. Cole and Mr. Mark McRae of the County Engineer’s Office of the Shelby County Highway Department, for their generous support and assistance in facilitating this project. Dr. Srineevas Alampalli of the Transportation Research and Development Bureau of the New York DOT and Dr. Mustafiz Chowdhury of the Weapons and Materials Research Directorate of the U.S. Army Research Laboratory are thanked for their expert advises and technical contributions. We thank Ms. Sarah Miller (Summer NSF-REU student) for developing the testing algorithm. We would like to acknowledge Drs. Dale Callahan and Steven Jones for meeting with us relentlessly on a regular basis and for contributing to the wireless technology and network concepts for future studies. Glen Fisher, David Robertson and Marcos Lawyers are three high school students who participated, through the CAREER SUCCESS project of the Alabama Heritage Center, in the research during summers of 2001 and 2002. We appreciate the funding provided by the UTCA for this report and the matching funds and other support from the Department of Civil and Environmental Engineering at UAB. Last but not least, we are grateful to Dr. Dan Turner, Dr. Fouad H. Fouad and the other reviewers at UTCA for their feedback on this project, and Dr. Shirley Clark for literary contributions.

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Appendix B. Lists of Acronyms and Symbols List of Acronyms AASHTO = American Association of State Highway Transportation Officials ACI = American Concrete Institute NDE = Non-Destructive Evaluation MAC = Modal Assurance Criteria COMAC = Co-Ordinate Modal Assurance Criteria BMS = Bridge Management System FEM = Finite Element Method DLF = Dynamic Load Factor DLFA = Dynamic Load Factor for Acceleration DLFM = Dynamic Load Factor for Moment DAD = Dynamic Amplification factor for Deflection DAM = Dynamic Amplification factor for Moment SDOF = Single-Degree-Of-Freedom

List of Symbols DF = distribution factor among girders tf = flange thickness Bf = flange width D = depth tw = web thickness

=fasty&& acceleration amplitude for vehicle at high speed

=slowy&& acceleration amplitude for vehicle at low speed

=dynamicy&& acceleration amplitude for vehicle at high speed

=staticy&& acceleration amplitude for vehicle at low speed S = load length x = distance to a reference point on the bridge l = span of the bridge y = assumed deformation shape f = first mode vibration frequency f’ = vibration frequency due to added mass

=k~ keffective, effective stiffness

='~k k’effective, new effective stiffness ∆k = change in stiffness

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Appendix B (continued)

=m~ effective mass ∆m = vehicle mass E = elastic modulus I = moment of inertia Amax(t) = max channel amplitude for time domain Amax(f) = max channel amplitude for frequency domain α = speed parameter V = velocity of vehicle IF = impact factor f = original frequency f’ = new frequency ∆f = change in frequency kstatic = stiffness, static load test Φ(xn) = normalized shape function xn = normalized ordinate ρmass = mass density υ = Poisson’s Ratio δ = static displacement δff = static displacement, fixed-fixed conditions ∆max = maximum allowed deflection P = load capacity P’ = new load capacity Pposted = posted load capacity Pcase 1 = load capacity for undamaged case Pcase 2 = load capacity for damage case 2 Pcase 3 = load capacity for damage case 3