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Field Evaluation of Dynamic Load Factors for Historic Through-Truss Bridges
Abstract
The late 1800s was a time of great innovation in bridge engineering. The advent of steel and the demand for longer spans under higher loads spurred the development of many new bridge designs. Out of this innovative time period, a wide range of historic through-truss bridges were developed and constructed. These bridges, now well beyond their design life, are being evaluated for capacity; many being demolished, few being rehabilitated. The evaluation process requires the estimation of the complex dynamic behavior of historic through-truss bridges under traffic loading. Structural engineers often evaluate complex dynamic behavior with the use of a dynamic load factor (DLF), which enables the enveloping of dynamic response values by scaling the maximum static response. For this reason the current study set out to evaluate the magnitude, distribution, and influential variables of DLF for historic through-truss bridges. This was accomplished through a combination of field evaluation of existing specimens, and digital signal processing; to produce both the maximum static and dynamic response values for instrumented bridge members for each traffic event. Scatter plots, correlation coefficients, and histograms were then created to evaluate DLF magnitude, distribution, and correlations with test variables. Correlations and trends were investigated between DLF magnitude and: maximum static strain, vehicle speed, vehicle static weight, and bridge span. The most influential variable on the magnitude of DLF was determined to be member peak static strain. The present study concludes that historic through-truss bridges exhibit DLFs with magnitudes higher than contemporary slab
on girder bridge types.
Table of Contents
List of Figures……………………………………………………………………………………………………………… viii
List of Tables………………………………………………………………………………………………………………….. x
Acknowledgments…………………………………………………………………………………………………………. xi
Chapter 1 Introduction …………………………………………………………………………1
1.1 Background ……………………………………………………………………………………..1
1.2 Problem Statement ……………………………………………………………………………2
1.3 Focus of Research …………………………………………………………………………….2
1.4 Scope of Research …………………………………………………………………………….3
1.5 Objectives ……………………………………………………………………………………….4
Chapter 2 Literature Review ………………………………………………………………..5
2.1 Introduction ……………………………………………………………………………………..5
2.2 DLF Definition…………………………………………………………………………………5
2.3 Code Prescribed Dynamic Load Factors ………………………………………………7
2.3.1 Constant DLF ………………………………………………………………………..7
2.3.2 Length Varying DLF………………………………………………………………8
2.3.3 Frequency Varying DLF ……………………………………………………….10
2.4 Dynamic Field Testing of Bridges …………………………………………………….11
2.5 Other DLF Studies ………………………………………………………………………….11
2.5.1 Field Determined DLF ………………………………………………………….12
2.5.1.1 Field Testing Procedure ……………………………………………..12
2.5.1.2 Field Testing Results………………………………………………….13
2.5.1.2.1 Girder Bridge Studies …………………………..14
2.5.1.2.2 Box Girder Bridge Studies …………………….15
2.5.1.2.3 Truss Bridge Studies …………………………….16
2.5.1.2.4 Comprehensive Bridge Types ………………..16
2.5.2 Analytically Determined DLF ……………………………………………….17
2.5.2.1 Three Dimensional Analysis ……………………………………….17
2.5.2.2 Two Dimensional Analysis …………………………………………19
2.6 Low Pass Digital Filters …………………………………………………………………..20
2.7 Summary ……………………………………………………………………………………….21
Chapter 3 Study Design ………………………………………………………………………22
3.1 Introduction ……………………………………………………………………………………22
Chapter 4 Experimental Program ……………………………………………………….24
4.1 Introduction ……………………………………………………………………………………24
4.2 Traffic Testing Procedure ………………………………………………………………..24
4.2.1 Data of Interest …………………………………………………………………….24
4.2.2 Data Acquisition System……………………………………………………….25
4.2.2.1 LVDT Sensors ………………………………………………………….26
4.2.2.2 Rubber Coated Tape Switches …………………………………….29
4.2.2.3 Analog to Digital Conversion ……………………………………..30
4.2.3 Member Selection ………………………………………………………………..31
4.2.4 Controlled Test Vehicle Selection ………………………………………….32
4.3 Modal Testing Procedure …………………………………………………………………33
4.3.1 Data of Interest …………………………………………………………………….33
4.3.2 Data Acquisition System……………………………………………………….34
4.3.2.1 Analog Signal Creation ………………………………………………35
4.3.2.2 Mechanical Force Generation ……………………………………..36
4.3.2.3 Force Validation………………………………………………………..37
4.4 Bridge Selection ……………………………………………………………………………..38
4.4.1 Bridge 1 ………………………………………………………………………………39
4.4.2 Bridge 2 ………………………………………………………………………………41
4.4.3 Bridge 3 ………………………………………………………………………………43
4.5 Summary ……………………………………………………………………………………….45
Chapter 5 Analytical Program …………………………………………………………….46
5.1 Introduction ……………………………………………………………………………………46
5.2 Static Cutoff Frequency …………………………………………………………………..47
5.2.1 Theoretical Static Frequency …………………………………………………47
5.2.2 Static Influence Lines …………………………………………………………..48
5.2.3 Power Spectral Density …………………………………………………………48
5.3 Dynamic Cutoff Frequency ………………………………………………………………49
5.3.1 Frequency Response Function (FRF) ………………………………………..49
5.3.2 Theoretical Modal Frequencies …………………………………………………50
5.3.3 Power Spectral Density of Traffic Data ……………………………………..51
5.4 Digital Filtering ………………………………………………………………………………52
5.5 DLF Calculation……………………………………………………………………………..54
5.6 Summary ……………………………………………………………………………………….55
Chapter 6 Results and Comparative Study ………………………………………….56
6.1 Introduction ……………………………………………………………………………………56
6.2 DLF Magnitude ………………………………………………………………………………56
6.3 DLF and Maximum Static Strain ………………………………………………………63
6.4 DLF and Vehicle Speed …………………………………………………………………..68
6.5 DLF and Vehicle Static Weight ………………………………………………………..71
6.6 DLF and Bridge Span ……………………………………………………………………..73
6.7 Summary ……………………………………………………………………………………….76 Chapter 7 Conclusions ………………………………………………………………………..77
7.1 Introduction ……………………………………………………………………………………77
7.2 Summary ……………………………………………………………………………………….78
7.3 Recommendation for Future Research ……………………………………………….81
References …………………………………………………………………………………………..82
Appendix A: Selected Strain Time Histories ………………………………………………………..84
Appendix B: Selected Power Spectral Densities …………………………………………………..88
Appendix C: Matlab Code from Analytical Program …………………………………………..92
1. Introduction
1.1 Background
The late 1800s was a time of great innovation in bridge engineering. The advent of steel and the demand for longer spans under higher loads spurred the development of many new designs. Out of this process, through-truss bridges of many designs became common structural forms used in the Northeastern United States. These now historic bridges have unique and aesthetically pleasing geometric forms that are rarely exhibited in modern construction practices. Only a select few remind us of these once prominent structural forms, now in danger of being lost as many bridges have been replaced or swept away in floods in the past century.
Adding to this danger, recent bridge collapses like the I-35W disaster in Minnesota have focused national attention on the state of America’s deteriorating infrastructure. This renewed focus in conjunction with the age and deterioration of historic truss bridges, puts these structures in serious risk of being found structurally deficient, demolished, and replaced. This would result in a great loss of American structural and architectural history.
A primary factor in determining the fate of a historic bridge lies in the treatment and understanding of their complex dynamic behavior when exposed to contemporary traffic loading. The most commonly used technique in practice for dealing with complex dynamic loading is the application of a dynamic load factor (DLF). This technique allows bridge dynamics to be evaluated in a static analysis by scaling the magnitude of a static traffic load to envelope the relatively higher dynamic loads of moving traffic. The bridge components can then be designed or evaluated for this effective static load, removing the need for detailed dynamic analysis. Standard values for dynamic load factors exist in all major bridge construction codes, but have been developed primarily for use with modern bridge forms such as girder bridges. Historic truss bridges having a lower mass to stiffness ratio are likely to exhibit different dynamic behavior than modern girder bridges resulting in different dynamic load factors.
1.2 Problem Statement
Previous research on the dynamic behavior of historic bridges has not provided a widely accepted DLF. This leaves only approximations of the dynamic behavior resulting from the extension of research performed on modern bridge types. Due to the complex geometries and lower mass to stiffness ratios, it is likely that these truss bridges do not behave in the same manner as previously researched bridge types and, therefore, require different DLFs when evaluating service conditions. The use of modern codified DLFs could be unnecessarily condemning many historic bridges. This concern warrants research specifically dealing with the dynamics of historic truss bridges.
1.3 Focus of Research
The broad subject of dynamic bridge response will be narrowed to the determination of dynamic load factors used to scale response to service loads for the evaluation of historic truss bridges. The domain of historic truss bridge types encompasses a wide variety of different bridge geometries; Pratt and lenticular arch trusses will be the focus of this research. Pratt trusses were selected due to the relative abundance of existing examples open to traffic and their generic geometry that will provide a baseline for historic bridge behavior. Lenticular arch trusses were selected to help the preservation effort of their limited numbers and the relative lack of knowledge of their behavior. For lenticular arch trusses, the contribution of the longitudinal girder in carrying the applied loads to the supports will also be investigated in addition to the DLF. This secondary investigation is a result of the unknown design intent of the longitudinal girder, which complicates the calculation of accurate member forces.
1.4 Scope of Research
The research presented will determine, through field testing, specific dynamic load factors for lenticular and Pratt truss bridges. The results of the study will provide a more accurate DLF for the evaluation of service conditions of historic bridges. This analysis can then be used to aid in the structural certification of the remaining examples of these structural forms. Through better understanding of the dynamic behavior, retrofit and restoration efforts are expected to be more effective in maintaining the structural health for future generations.
Specifically, bridges will be selected for field-testing to meet the following criteria:
- Pratt or lenticular truss geometry
- Date of original construction: 1880 – 1900
- Through-truss design
- Open to highway traffic
- Ideally, unaltered original construction
Three bridges were selected for field-testing using one or more of the following three loading conditions: controlled truck traffic, normal traffic, and controlled dynamic shaker testing. Under controlled truck loading various vehicle velocities will be used to test the influence of velocity on DLF. Instrumentation will be placed on up to sixteen members of interest in order to record the bridge response under the previously described loading. These response quantities will then be used to calculate DLFs for each test case.
To evaluate the influence of many competing variables several test parameters will be controlled or documented for each test case in order to perform a comparative study of the resulting DLF. The test parameters considered to influence DLF and corresponding values to be controlled or documented for the present study are:
- Span length (natural frequencies): 100, 150, 200+ft
- Vehicle speed
- Truck testing: crawl, 1/3, 2/3, full speed limit
- Normal traffic testing: approximated using know distance and time
- Vehicle static weight
- Truck testing: constant, documented value
- Normal traffic testing: obtained through digital filtering of field data
1.5 Objectives
The primary objective of this research was to experimentally calculate Pratt and lenticular truss specific DLFs. The secondary objective of this research was the determination of relationships between parameters of interest and the DLF. The final and furthest reaching objective is to provide this information in an effort to reduce the cost of accurate analysis of historic truss bridges and therefore aid in preservation efforts.
