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Cable-Stayed bridge (Intermediate)
Suggested viewing: Cable-Stayed bridge (Beginner)
DESCRIPTION AND LOCATION
In this tutorial we’re going to look at a creation of the University’s very own Department of Civil and Structural Engineering. Our Cable-Stayed Bridge model.
You may have seen this structure in the structure’s lab or the Engineering workrooms.
The bridge deck is made of timber, and the frame from aluminium, so the solid parts of the structure are quite flexible. The cables are high strength steel, so you should be able to guess already some things about where the load’s going.
The great thing about this bridge is that you can play around with the connections and loads, and get quite different behaviour. I’d strongly advise going to see it for yourself, walking along the deck and seeing how it behaves.
APPLIED LOADS
As with any structure we need to consider the effect of self-weight, but with this bridge the lightweight materials used should minimise this.
The most significant loads are going to be people walking across it. It’s important to be aware that with this bridge there will be cases where adding weight in certain places is actually going to improve the structural stability. We call these ‘favourable loads’, meaning they’re good for the structure, but not necessarily for the designer!
There could also be dynamic effects caused by exuberant students or lecturers jumping up and down on the bridge. This will mean designing for larger, but very short term ‘shock’ loads.
CONCEPTUAL/QUALITATIVE BEHAVIOUR
Supports:
In fact for this bridge there are two support cases. The central bracket which the two longest cables attach to, can be replaced by two separate brackets. What this does is to turn the bridge deck from a continuous beam into two cantilevers.
Removing the central connection obviously makes the bridge less stable, so why do it? Couldn’t we just design the bridge to have a continuous deck and be done with it?
It would be great to be able to do this. Unfortunately, for life-sized, 1000m long bridges you can’t get trucks big enough to carry them ready made, so they have to be constructed in-situ.
Cantilevering a structure out from the bank of a river may seem an inefficient way to go about building, but there’s really no better method, so each half-span has to be self-supporting.
Now, when modelling supports to analyse, we have to do a bit of mental gymnastics. You might notice that although the supports at the abutments are supposedly rigid on the diagram, our Cable-Stayed Bridge is actually just placed on the floor. There’s technically no connection at all.
This is because we’re designing for failure. To make an efficient structure, the rule is to work out what will just about fail, and then pick something slightly stronger (with a factor of safety of course).
So we model them as encastres. Then we can analyse the rest of the bridge with the assumption that the supports won’t move or rotate. We don’t actually know if they will or not yet, but we can forget about that until we’ve found out the loads on them, and can design them properly.
Imposed Loads (Variable Actions):
We’ll take the ‘fully constructed’ case, and put a UDL on the bridge deck. This load is modelling a situation like a group of people standing still on the deck. We have a decision to make here: whether to put loading between the piers or across the whole deck.
This is where the issue of favourable loads becomes practical. The end result of our analysis is going to show uplift in the areas shown in green, and having these areas loaded will disguise the effect of it. As a candidate for a critical load case, the diagram on the left is far more promising.
Now, the load on the deck needs to get to the supports on either side. The easy explanation is that the cables will transfer the load in tension down to the supports in the abutments.
But we want to really understand this structure, and that sort of explanation isn’t very helpful.
The first thing to notice is that the cables are not only pulling the bridge deck up to counteract the load, they’re pulling it in towards the piers. If we look at one cable and resolve forces we can see this clearly.
The cable is diagonal, so creates a horizontal component of force which must be resisted by something. And that something must be the deck itself going into compression.
We can go further, and say that the further we go towards the piers, the greater the compression force in the deck will get. You’ll get the compression from the previous piece of deck, plus an added component of horizontal force from the next cable.
When people walk across the bridge they cause it to deflect slightly, and because the bridge will want to spring back into its original shape after this load has been removed there will be a time associated with this deflection. The time it takes for the bridge’s deflection to return to zero, an oscillation.
If you happen to be walking with a similar rhythm as the oscillations of the bridge, your weight can either cancel out the oscillations or reinforce them.
Think of this like transferring your weight on a swing. You have to lean back at the top of each swing or your weight won’t be transferred into momentum. On a bridge deck, your footfalls at the bottom of each deflection will increase its size.
Compression in the deck increases as we move towards the piers
You can test this by standing on the bridge yourself. The weight of a person will compress the deck, and actually make the connections between the boards stiffer.
Notice that the cables are also creating compression in the column, but this time with the vertical components of tension from the cables.
Dynamic Loads:
If you have dynamic loads like footfalls that hit a resonant frequency of a bridge the effects can compound and become quite spectacular!
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