# What is the role of pillars in bridges?

As I can see in the picture, there are so many pillars which are holding the bridge. This picture gave a question to me that what are these pillars doing below the bridge?? An appripriate answer could be "these are providing support to bridge".

I tried to get the answer as follows:

In the first image there are two pillars holding a bridge of mass $M$, since gravitaional force is acting downwards thus pillars are bearing a force of $\frac{1}{2}Mg$.

In the second image there are four pillars bearing a force of $\frac{1}{4}Mg$. I'm assuming that mass of bridge is uniformly distributed and each pillar is bearing an equal amount of the load.

Now the question is that since the pillars are bearing the force, so if we make strong enough pillars to bear a large force then there will be no need of so many pillars.

But that is not the case, we see a large number of pillars holding a bridge. What is wrong with the work I did? Shouldn't the number of pillars depend upon the strength of the pillars we make rather than the length of the bridge ??

• Is the bridge a perfectly rigid body? Also, ever heard of momentum of a force? – valerio Nov 18 '16 at 19:00
• I think nothing in the universe is perfectly rigid. – Vidyanshu Mishra Nov 18 '16 at 19:01
• Correct. So, think about it. – valerio Nov 18 '16 at 19:02
• Also, redundancy is important when building any structure. – valerio Nov 18 '16 at 19:04
• It means being sure that if something is damaged in the structure the whole structure does not collapse. – valerio Nov 18 '16 at 19:07

There are three reasons:

1. Moment of the forces

In order for the structure to be stable, not only the vector sum of the forces must be zero

$$\sum \vec F =0 \tag{1}$$

the total moment of the forces must be $0$, i.e.

$$\sum \vec r \times \vec F =0 \tag{2}$$

Let's consider your bridge with two pillars: for the moment, we will assume that it is perfectly rigid. If the bridge only has to sustain its own weight, then your reasoning is basically correct. But if there is something on the bridge (like a vehicle), the force on the two pillars will be different, as explained for example in this video.

Now, you could say that the mass of the vehicles crossing the bridge is negligible w.r. to the mass of the bridge itself, or you could say that all we have to do is make the pillars stronger. This brings us to the next two problems.

1. Nothing is perfectly rigid

Your bridge is going to bend towards the center because of the moment exerted by its own weight and this is going to happen:

As you can see, the pillars are perfectly intact, but the bridge collapsed anyway.

1. Redundancy is good

If one of the two pillars collapse, your bridge collapses. Structures are always build using a certain degree of redundancy, i.e. they are build in such a way that if something fails, then the whole building is not compromised. In the case of bridges, this means that we have to build many pillars, to make sure that if one of them is compromised the structure remains intact.

• +1 nice answer, is it momentum or moment of force in the line just above the picture?? – Vidyanshu Mishra Nov 18 '16 at 20:04
• It is moment, thanks for pointing that out. The usual slip of the tongue...or should I say, of the fingers ;-) – valerio Nov 18 '16 at 20:06
• Regarding reduncandy, I'd be pretty sure a bridge like the Millau Viaduct would be catastrophically compromised if only one of the pillars failed. These pillars are probably so sturdy that this is extremely unlikely though. – leftaroundabout Jan 2 '17 at 21:47

The reason of having pillars in bridges is just pressure. You know that the pressure become less if the contact area is increased. And by increasing the number of pillars the surface area in contact is also increases and the pressure on the bridge become less.

The number of the pillars does not depend by the load that each one of them can carry.

Mainly the number of the pillars is selected in order to reduce the distance between them and so to minimize the moments and so the stresses produced and act on the beams that holds the bridge's deck, as very nicely @valerio92 answered.

We can see from the photo that you uploaded, that in many cases this is not enough. So there's a little trick: the pilars are extended above the bridges deck, so that we can hang the deck using cables. This way we provide extra supports to the deck . These are the well-known 'Suspensions bridges' .

Of course there are plenty of other dynamic loads such as earthquakes, winds , sea waves etc that may determine the number of pillars but in general this is not the case.

In addition to the other answers, I think it's important to understand that you can't just make an arbitrarily strong pillar. Or rather, you can't make the ground the pillar stands on arbitrarily strong. So, depending on the geology that the bridge is standing on, you may need more or less pillars.

Of course you can get around this by making the pillars very big to spread the load, or sinking them very deep into the ground, but it may well be cheaper and more practical to have lots of pillars. Remember that this is engineering: everything is about complicated tradeoffs involving money, appearance, function & safety.

Not only do the pillars need to bear the weight of the bridge but the bridge itself also needs to bear it's own weight (i.e. Not snap). For this reason, lots of pillars can be used to support the bridge in more places, stopping this from happening.

Further, the more pillars, the less weight each pillar holds itself. If every pillar supported the maximum weight it could support then if one was to fail, or something happened to jeopardise the integrity of the pillar, the bridge may fail. Having lots of pillars reduces this risk.

There's another reason for these pillars that is yet to be mentioned in these answers.

If you look at the picture you can see that the pillars don't hold the bridge up on their own. They extend well above the bridge deck and have many cables coming off of them for suspension.

These wires provide some force to hold the bridge up away from the pillars, supporting the span.

As you can see from the image, as the bridge deck gets further from the pillar, the angle of the suspension cable becomes more horizontal.

If you want the cable to actually provide suspension force, it must be angled towards the vertical as much as possible. With more pillars, the maximum horizontal angle in the cables will decrease, as they are all close to a pillar. This means that closet pillars don't only provide more support against moments from below, but also from above.

Although the logic of multiple pillars can apply to every bridge, in suspension bridges this effect is especially important so that the cables can get the required vertical component of the tension.