1. Assessment of dynamic loading of bridges
Aleš Žnidarič
Slovenian National Building and Civil Engineering Institute

2. Dynamic loading on bridges
ratio between maximum (dynamic) and static loadings - DAF
traditionally: max DAF of a single vehicle measured at different velocities and loadings
problem: combining the extremes of dead load and dynamic effects => very high DAF
continuation of work from SAMARIS:
theoretical studies (UCD)
experiments (ZAG)

3. Theoretical Studies

4. Definitions
Static Load effect – No interaction between vehicles and bridge is considered.
Total Load effect – Interaction between vehicles and bridge is considered.
DAF – Dynamic Amplification Factor (for a particular load scenario):
ADR – Assessment Dynamic Ratio (for a particular period):
There is considerable variation in dynamic amplification between runs of given vehicles at specified speeds and even greater variation when speed, vehicle etc. are changing. Theoretical studies are generally not good at predicting dynamic amplification. Models vary greatly in their complexity. As might be expected, the very simple models are generally the least accurate. Anything short of full 3-dimensional models give significantly different results to simple 2-dimensional models. Articulation is important – articulated tractor/semi-trailers behave quite differently to rigid 2- and 3-axle trucks. Suspension type is important. It is well known that air suspensions are considerably more "road friendly" than steel leaf spring suspensions and should be modelled differently. There are also modelling issues with suspensions and it has been shown that the Coulomb damping usually assumed is a simplification. Road profile is also very important. It has been shown that it is not just road roughness that affects the dynamic amplification in a bridge – the location of the particular bumps that make up the profile is very important and IRI is at best a very crude indication of the level of dynamics that can be expected. This is further complicated that trucks will not follow the exact same track each time they travel over a bridge and will therefore experience a slightly different profile which can have a significant effect. Finally, there is a dearth of knowledge on truck dynamic properties. Some spring stiffnesses, damping coefficients etc. are available for some trucks (and some good truck models exist for particular trucks) but there is little known about the model properties that should be used for the truck population at large.

5. Distribution of load effect
Combining probability of event with bridge response for the event allows for the full, exact distribution of load effect (static or total) to be obtained

6. Distribution of load effect
Examination of the upper tail of the distributions allow for characteristic values & ADR at any return period to be assessed

7. Influence of return period on ADR
Characteristic Value of static and Total Load effect obtained for various return periods
trend of ADR with return period to be assessed
variability of ADR reduces as return period increases

8. Multiple road profiles
repeated for 100 different road profiles (all of very good/good quality), i.e. IRI<6m/km
range of possible ADR reduces as return period increases
good representation of a site-specific 1000-year ADR is achieved by using only 1-month of data

9. Experimental work

10. BWIM shema Detekcija osi Meritve deformacij
Bridge weigh-in-motion measurements were done to collect sufficient information needed for experimental evaluation of the influence lines in both lanes and to statistically evaluate load distribution factors.
Meritve deformacij
Detekcija osi

11. Strain transducer

12. Bridge weigh-in-motion installation

13. Bridge weigh-in-motion installation

14. 186 m long bridge over 5 spans
Slovenia

15. 530m long orthotropic deck bridge
Poland

16. Presentation dd.mm.yyyy

17. Presentation dd.mm.yyyy

18. SiWIM – strain signals

19. DAF and SiWIM
updated SiWIM software calculates DAF by comparing measured with “static” signals
from 6 tested algorithms the one using FFT low-pass filter was applied:
spectrum calculated from hundreds of vehicles
only static component left to compare with dynamic signal
There is considerable variation in dynamic amplification between runs of given vehicles at specified speeds and even greater variation when speed, vehicle etc. are changing. Theoretical studies are generally not good at predicting dynamic amplification. Models vary greatly in their complexity. As might be expected, the very simple models are generally the least accurate. Anything short of full 3-dimensional models give significantly different results to simple 2-dimensional models. Articulation is important – articulated tractor/semi-trailers behave quite differently to rigid 2- and 3-axle trucks. Suspension type is important. It is well known that air suspensions are considerably more "road friendly" than steel leaf spring suspensions and should be modelled differently. There are also modelling issues with suspensions and it has been shown that the Coulomb damping usually assumed is a simplification. Road profile is also very important. It has been shown that it is not just road roughness that affects the dynamic amplification in a bridge – the location of the particular bumps that make up the profile is very important and IRI is at best a very crude indication of the level of dynamics that can be expected. This is further complicated that trucks will not follow the exact same track each time they travel over a bridge and will therefore experience a slightly different profile which can have a significant effect. Finally, there is a dearth of knowledge on truck dynamic properties. Some spring stiffnesses, damping coefficients etc. are available for some trucks (and some good truck models exist for particular trucks) but there is little known about the model properties that should be used for the truck population at large.

20. DAF measurements in ARCHES
ARCHES experiment:
25-m long simply supported span, susceptible to dynamics
2-month experiments completed (Sep. to Nov. 2006)
app vehicles
4 other evaluations
Experiment 2 in Slovenia:
to assess influence of pavement unevenness on bridge dynamics
to get realistic estimate of impact factors of extreme (multiple-presence) load cases to avoid combining the extremes of static loading and dynamic amplification which can yield to over-conservative estimates of traffic loading; this is particularly important when assessing existing bridges
to get statistically evaluated impact factors for entire 2-week population of vehicles before and after rehabilitation of the deck
bridge over Sava river with very bad pavement and high dynamics
bridge WIM electronics is being upgraded for measurements of dynamics
Due to the progress in the field of bridge weigh-in-motion measurements it will be for the first time ever possible to obtain and analyse impact factors of random vehicles including the multiple-truck events and thus to confirm theoretical conclusions that were obtained on the limited combinations of pre-defined vehicles.

21. Dynamic amplification

22. Dynamic amplification

23. Dynamic amplification

24. Dynamic amplification

25. Dynamic amplification

26. Dynamic amplification

27. Dynamic amplification
1 hour = 387 vehicles

28. Dynamic amplification
1 day = 4120 events

29. Calculation of DAF
CSHM2 workshop,

30. Calculation of DAF

31. DAF Vransko
The graph shows impact factors of vehicles passing the bridge. Preliminary analysis confirms that the theory of combining extremes of loading and of dynamic amplification is not realistic. As the loading is increasing, the impact factors are decreasing.

32. DAF Vransko – Extreme event

33. DAF Blagovica
We are mostly interested into such multiple-presence events. This is one of the extreme ones, recorded on the first day of measurements when a traffic camera was attached to the SiWIM system.

34. DAF – 12 m slab
The graph shows impact factors of vehicles passing the bridge. Preliminary analysis confirms that the theory of combining extremes of loading and of dynamic amplification is not realistic. As the loading is increasing, the impact factors are decreasing.

35. DAF – 8 m slab

36. DAF – 7.2 m slab (the Netherlands)

37. Conclusions
dynamic amplifications can be very high (>2), but these appear for single and/or lighter vehicles
DAF from design codes is too conservative for bridge assessments
ARCHES has shown that DAF/ADR is below 1.06
recommendations:
DAF = 1.1 or
measurements and/or modelling

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