Wednesday, March 21, 2012

From real traffic on a bridge to a square steel plate

Often, when people look at my experiments and my test setup, they are confused when I tell them that I am studying a bridge under traffic loads. How can a little steel plate of 300mm x 300mm or 200mm x 200mm help me to understand how a bridge behaves under traffic? Of course, there are several simplifications that we need to make to come to this point, and, likewise, we are indeed looking at a model of reality, what all the limitations a model has.

So, how do we go from a real bridge with trucks and cars and all that to a test slab with a steel plate?

1. From real traffic to load models

Real traffic consists of many different types of vehicles in different sizes, shapes and weights.We can measure the real traffic (you might have noticed that there are measurement points in the roads of the highways which study the traffic). To calculate a bridge with all these different vehicles would be a daunting task. Therefore, our typical engineering approach (which you also find reflected in the codes that tell you how to design a structure) is to use a load model. That load model is a simplified version of the real traffic. For different cases, there are different load models, and certainly your structure needs to fulfill all the structural requirements for all the different load cases it can be subjected to.

A typical load case works like this: it smooths out the cars and trucks over all of the lanes, in such a way that the load is smeared out over the entire surface (as if all the lanes would be packed and packed with cars, the case you have during a traffic jam). Next, you might consider that the rightmost lane has heavier traffic, and this makes you end up with a load which is again smoothed out, but only over the rightmost lane. This load together with the previous one (over all the lanes) will have a higher value than the value you have over all the lanes, because its whole purpose was to model the fact that the heavy trucks are on the right lane.

Then, we place some design trucks on the bridge that we are looking at. These design trucks are, in European practice, 4 squares that you draw on the deck of the bridge and in which you place a load. We consider the wheels to be 400mm x 400mm, at 1,2m distance along the span length and at 2m distance along the width. The first lane has the heaviest design truck, and the next lanes have increasingly less heavy design trucks. To study the worst case scenario, it is necessary to find the most unfavorable location of these design trucks all together on the bridge deck.

2. From load models to a loading plate

If you study the problem of the shear capacity of solid slab bridges, you will find that the contribution of the wheels of this design truck which I just explained is a major contribution to the occurring load. Because the wheels of the design truck are modeled as squares of 400mm x 400mm, it is also not really clear how to spread this load. If you look at the support, it is clear from engineering judgment that the effect of this concentrated load will have flared out a bit (you can compare this to throwing a rock in a pond - the water will ripple and the ripples will touch a larger length once they reach the borders of the pond, provided that it is a reasonably sized pond). The question for these wheel loads remains then how much they can be smeared out over the length of the support.

With all these issues at hand, we've determined that it is most interesting to look at the part of the load model that comes from the design truck. In some experiments done in Switzerland, 4 load plates are used to model the design truck just like we use it in the code. However, to study some basic phenomena, it is necessary to make another extra simplification.

And that last round of simplifications includes studying just one of the wheels of the design truck. Because the slabs I test in our laboratory are scale models, we also scaled the size of the wheel: we've used steel plates of 200mm x 200mm as well as steel plates of 300mm x 300mm.

And so, a little steel plate can hold in itself a whole simplification procedure of trucks and cars.


  1. Eva,
    Great explanation of how load models are used to perform both global and local analyses of bridges in practice - I am not particularly envious of the committee comprising CEN who has to integrate numerous load models from different EU states and recommend a single standardised approach (albeit complemented by National Annexes).

    To elaborate on the points of finding the most unfavourable location of these design trucks makes me really appreciate the technology we have available to designer's today i.e. Autoloaders and influence surfaces - for a highly skewed or curved bridges with high torsion finding the worst case hogging, sagging and shear at midspan, splices, piers and abutments is extremely difficuylt to do manually and would require much either much trial and error or conservatism without such tools. The complexity of applying the critical load also demonstrates that we're still a long way off predominantly using nonlinear analysis - the inability to superimpose loads means that as bridge designer's we'll still be using elastic analysis for the majority of tasks for a while yet.

    I'm interested in how the scale models were set up, particularly in the application of the wheel loads - I'll have a look through the Thesis you linked to, some pictures of the scale models you conducted would also be interesting to see!

    Best regards,

  2. Thanks for your input, Pete.
    I think the process of converging the national codes to the Eurocodes certainly in its whole has been a daunting task, that has been taking many years and many discussions.

    I agree with what you write about the most unfavorable position of the loads - and when I look at practical cases of straight solid slab bridges, I notice that almost every engineer takes a different approach to this (while that is supposedly an "easier" case than a curved or skewed bridge).

    I'll expand on my experimental setup in a post-to-come (might write it over the weekend). We used a half-scale model of a solid slab bridge, and to create continuity over the support, we used vertical prestressing bars which decreased the amount of rotation at the support and created a moment - I'll expand on that with pictures :)