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.