Bundesanstalt für Materialforschung und -prüfung

International Symposium (NDT-CE 2003)

Non-Destructive Testing in Civil Engineering 2003
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Bridge Diagnostics by Field Testing (Verification of Girder Distribution Factors and Dynamic Load Factors)

Junsik Eom and Andrzej S. Nowak
University of Michigan


A rational bridge management requires a good knowledge of the actual loads, load distribution, load effects and structural condition (load carrying capacity). An important part of the rating equation concerns the distribution of the live load to the main load carrying members of the bridge, and to the individual components of a multi-component member. Typically, in design and rating, load distribution to main supporting members is based on the code specified values (AASHTO). However, this distribution is affected by several variables, which greatly complicate the analysis. Except by field testing, it is virtually impossible to find exact values of girder distribution factors. Moreover, prior analytical studies showed that in most cases the current code provisions are too conservative. However, for short spans and girder spacing, they can be too permissive. Therefore, this study focused on these structures to verify the validity of the current code specified distribution factors and dynamic load factors, particularly for short span bridges. To accomplish this objective, field tests were carried out on several highway bridges in Michigan. Girder distribution factors (GDF) and dynamic load factor (DLF) were obtained from crawling and regular speed truck tests. Superposition of girder distribution factors from single truck loadings were calculated for each bridge. The results are taken as the maximum effect caused by the combination of different truck positions in each lane. The measured values are compared to AASHTO (2002) and AASHTO LRFD (1998) specified girder distribution factors for one lane and two lane girder bridges. All measured GDF's are well below AASHTO Code specified GDF's. The dynamic load is defined as the ratio of dynamic stress to static stress. Field measurements are performed to determine the actual truck load effects and to verify the available analytical models. The tests are carried out on several steel girder bridges. Measurements are taken using a system with strain transducers. For each truck passage, the dynamic response is monitored by recording strain data. The field measurements confirmed the results of analytical studies. The strain/stress due to dynamic load is nearly constant and is not dependant on static strain/stress. Therefore, the dynamic load factor is reduced for heavier trucks.

1. Introduction

Previous load test results performed by the University of Michigan research team showed that even bridges identified by analytical methods as deficient, can still carry normal traffic. Therefore, there is a need for more accurate prediction of the actual load and strength. The refined load distribution factors (GDF) and dynamic load factor (DLF) are the key elements in analyzing both the new and existing bridges. Extensive analytical studies performed in conjunction with the development of AASHTO LRFD Code indicated that GDF's specified by the AASHTO Standard Specifications (2002) can be inaccurate. In some cases the specified values are overly conservative, and in other cases they are too permissive. Knowledge of the accurate GDF's and DLF's is needed to determine the actual value of live load (truck load) effect for bridge girders. Overestimation of GDF's and DLF's can have serious economic consequences, as deficient bridges must be repaired or rehabilitated. Therefore, improving the accuracy of code specified GDF's and DLF's can lead to a more realistic calculation of the load carrying capacity and eventually permit more bridges to remain in service with or without minor repairs. Therefore, the objective of this study is validation of the AASHTO Code specified GDF's and DLF's for steel girder bridges with spans between 10 and 45 m. The validation was carried out by field tests.

2. Selected Bridges

This study is focused on steel girder bridges with simply supported spans from 10 to 45 m. These structures constitute 65% of bridges in Michigan. It was observed that many steel girder bridges are considered deficient and in need of repair or replacement due to insufficient live load carrying capacity. A considerable number of short span steel girder bridges may be saved by evaluation using a more accurate value of GDF's and DLF's. Analytical studies also point to a reduced conservatism in code-specified GDF's for shorter spans.

In this study, the selection of bridges was based of the following criteria; structural type and material (steel girder bridges); span length (short and medium spans, between 10 m and 45 m); number of lanes (two lane bridges); skewness (less than 15 degrees); traffic volume (an average daily traffic (ADT) of less than 12,000). Finally 17 bridges were selected. A typical cross-section is shown in Figure 1. The specific details about the selected bridges are shown in Table 1.

Fig 1: A Typical Cross-Section of Selected Bridges.

No. Span
No of Girder
Girder Spacing
Year Con. Skew ADT
Table 1: Selected Bridges.

3. Instrumentation and data acquisition

The strain transducers were attached to the lower and/or upper surfaces of the bottom flange of steel girders at midspan, depending on the accessibility. Strain transducers were connected to the SCXI data acquisition system from the National Instruments. The data acquisition mode is controlled from the external PC notebook computer, and acquired data are processed and directly saved in PC's hard drive.

The data from all instruments was collected after placing the trucks in desired positions or while trucks were passing on the bridge. For the normal speed tests, a sampling rate of 300 per second was used for calculation of the dynamic effects. This is equivalent to 11.4 samples per meter at a truck speed of 95 km/h. The real time responses of all transducers are displayed on the monitor during all stages of testing, assuring safety of the bridge load test.

4. Test loads

The measurements were taken under passages of one and two vehicles, each being a three-unit 11-axle truck with known weight and axle configuration. The actual axle weights of the test trucks were measured at the weigh stations prior to the test for all bridges. An example of 11-axle trucks is shown in Figure 2 with a typical axle configuration.

Fig 2: Typical Axle Configuration of 11-Axle Trucks used in Tests.

Strain data was used to calculate GDF's. Superposition of strain data for single trucks was compared to the results obtained for two trucks side-by-side, as the verification of the linear-elastic behavior of the bridge.

5. GDF's and DLF's Specified in the AASHTO Codes

Measured GDF's are compared with the values calculated according to the current design codes. Throughout the paper, GDF's are expressed in terms of axle load for the full truck rather than a line of wheel loads (half truck). For the bending moment in an interior girders, the AASHTO Standard (2002) specifies GDF's as follows. For steel girder and prestressed concrete girder bridges, with one lane, GDF is:


and for steel and prestressed concrete girder bridges, with multi lanes,


where S = girder spacing (m).

The AASHTO LRFD Code (1998) specifies GDF as a function of girder spacing, span length, stiffness parameters, and bridge skew. For bridges with skew less than 30 degrees, the GDF's are specified as follows. For the bending moment in interior girders with one lane loading, the GDF is:


and for multi lane loading:


Where S = girder spacing (mm); L = span length (mm); Kg = n (I+Aeg2); ts = thickness of concrete slab (mm); n = modular ratio for the girder and slab materials; I = moment of inertia of the girder (mm4); A = cross section area of the girder (mm2); and eg = distance between the centers of gravity of the girder and slab (mm).

Most bridge design codes specify the dynamic load as an additional static live load. In the AASHTO Standard (2002), dynamic load factors are specified as a function of span length only:


where DLF = dynamic load factor (maximum 30 percent); and L = span length (m). This empirical equation has been used since 1944. In the AASHTO LRFD (1998), the dynamic load factor is equal to 0.33 of the truck effect, with no dynamic load applied to the uniform loading.

6. Test Results

For each bridge, the collected strain data served as a basis for the development of the measured GDF and DLF values. The GDF values caused by two trucks side-by-side are summarized in the Table 2 and compared with code specified GDF's. The measured GDF's are the maximum values from different truck loading positions.

Fig 3: Ratio, Test / AASHTO Standard GDF (2002).

Figures 3 and 4 compare the GDF's obtained from the tests with those specified in the codes. In Figure 3, test values are compared with those in AASHTO Standard (2002), and in Figure 4 with AASHTO LRFD (1998). In both figures, the ratio of GDF's are plotted versus span length and girder spacings. A large degree of variation can be observed in the figures even for bridges with similar structural parameters. In figure 3, it can be seen that GDF's specified in the AASHTO Standard (2002) are conservative in all selected span and girder spacing range, and are extremely conservative for bridges with longer span length and large girder spacing. It was observed for bridge No.17, which has the longest span length and girder spacing, that the measured GDF is just more than 50 percent of the value specified in AASHTO Standard (2002). In contrast, GDF's specified in AASHTO LRFD (1998) do not differ much depending on span length and girder spacing. Still, the GDF's specified in AASHTO LRFD (1998) is conservative in most cases. For one bridge (No. 9), the measured GDF is larger than the GDF specified in AASHTO LRFD (1998). However, the difference is less than 2 percent. On average, the code specified GDF's are less than 80 percent of the measured values.

Fig 4: Ratio, Test / AASHTO LRFD GDF (1998).

Fig 5: Strain Vs. Dynamic Load Factor.

Two examples of relationship between DLF and static and dynamic strains is shown in Figure 5 for Bridges 10 and 11. The open circles correspond to static strain. and black solid squares correspond to dynamic strain. Dynamic strains remain nearly constant, while static strains increase as truck loading increases. This results in large dynamic load factors for low static strains. In all cases, DLF's corresponding to the maximum strain caused by two trucks side-by-side, are less than 0.10 at the most heavily loaded girders.

Girder spacing
AASHTO Standard
Table 2: Comparison of Measured GDF's with Code Specified GDF's.

7. Summary and Conclusion

Diagnostic tests were performed for 17 selected short and medium span steel girder bridges using 11-axle truck loads. GDF's are calculated from the strain measurements. In most cases, GDF's observed in the tests are consistently lower than specified in AASHTO Standard (2002) and AASHTO LRFD (1998). A large degree of variation is observed. The AASHTO LRFD (1998) specified GDF values are more consistent than those in AASHTO Standard (2002). For bridges with longer spans and larger girder spacing, the values in AASHTO Standard (2002) are excessively conservative. Dynamic load is lower than specified values by AASHTO Standard (2002) and AASHTO LRFD (1998). For two trucks side-by-side it is less than 0.10. Dynamic load decreases with increasing static load effect.

8. References

  1. AASHTO LRFD Bridge Design Specifications (1998). American Association of State Highway and Transportation Officials, Washington, D.C.
  2. AASHTO Guide Specification for Strength Evaluation of Existing Steel and Concrete Bridges. American Association of State Highway and Transportation Officials, Washington, D.C., 1989.
  3. AASHTO Standard Specifications for Highway Bridges (2002), American Association of State and Transportation Officials, Washington, DC.
  4. Eom, J. and Nowak, A.S., "Live Load Distribution for Steel Girder Bridges", ASCE Journal of Bridge Engineering, Vol. 6, No. 6, 2001, pp. 489-497.
  5. Ghosn, M., Moses, F., and Gobieski, J. (1986), "Evaluation of Steel Bridges Using In-Service Testing." Transportation Research Record No. 1072, pp. 71-78.
  6. Nowak, A.S. and Eom, J. "Verification of Girder Distribution Factors for Steel Girder Bridges." UMCEE 00-10, Department of Civil and Environmental Engineering, University of Michigan, Ann Arbor, MI.
  7. Nowak, A.S. and Sanli, A, and Eom, J. "Development of a Guide for Evaluation of Existing Bridges, Part II." UMCEE 98-13, Department of Civil and Environmental Engineering, University of Michigan, Ann Arbor, MI.
  8. Nowak, A.S. and Sanli, A, and Eom, J. "Development of a Guide for Evaluation of Existing Bridges, Phase II." UMCEE 99-13, Department of Civil and Environmental Engineering, University of Michigan, Ann Arbor, MI.
  9. Stallings, J.M., and Yoo, C.H. (1993). "Tests and Ratings of Short-Span Steel Bridges." Journal of Structural Engineering, ASCE, Vol. 119, No. 7, pp. 2150-2168, July.
  10. Zokaie, T., Osterkamp, T.A., and Imbsen, R.A. (1991), ;"Distribution of Wheel Loads on Highway Bridges," National Cooperative Highway Research Program Report 12-26, Transportation Research Board, Washington, D.C.
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