Embedded Files
Cable-Stayed bridge (Advanced)
Suggested viewing: Cable-Stayed Bridge (Intermediate)
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 and carbon, 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.
Dead Loads (Permanent Actions):
Let’s look at some of the more unusual aspects of this bridge, and see if we can understand their purpose.
The ‘H’ sections used for the columns have been orientated so their minor axes will bend in the same plane as the cables, the arrangement shown on the left.
This will mean the column is weakest in the direction that the force is being transferred! Is this a design fault or a brilliant inspiration from the engineer?
Well, I wouldn’t necessarily call it brilliant, but it is the correct configuration.
To begin with, although the forces are going through the cables they aren’t transferring any lateral force to the column, just axial compression. So from the point of view of the cross-section the loading is symmetrical.
Now, the failure mode of this column is likely to be buckling rather than crushing. Let’s look at the factors affecting buckling.
The buckling load of a column is basically affected by three things. There’s the material stiffness, which is constant throughout the cross-section, the effective length of the column and the Moment of Inertia, ‘I’.
We’d normally have different ‘I’ values because the loads wouldn’t be symmetrical, but here they are. The stiffness is also the same, but the effective length isn’t.
Hang on, you say, how can an effective length change for the same column?
The answer lies in the restraints. Around the minor axis the cables actually pin the column at the top. Whichever way it wants to move one set of cables will be in tension, preventing it from moving laterally along the axis in question.
Around the major axis the top is completely unrestrained. This is compensated somewhat by the fact that the support at the base of the column is in the plane of the major axis, giving it more restraint.
here the detail of the connection at the base of the column will provide different support conditions depending on whether it is buckling about the red axis or the blue axis
In the minor axis plane the support only acts as a nominal pin, but even allowing for this the effective length of the pier around the major axis is significantly longer.
In fact, this is exactly why the major axis has been orientated the way it has: to compensate for that longer effective length.
I don’t want to get too technical by going into the concept of effective lengths, but changing the support conditions in this manner will decrease the buckling capacity of a column by a factor of 4 (the effective length will double and the buckling capacity decreases by the square of the effective length).
Imposed Loads (Variable Actions):
Let’s look at some of the second order effects of the deflections.
This might sound scarily complicated, but really it isn’t. When we analyse things quite often we assume they don’t move, although in reality they do, even if it’s only very slight.
When we consider second order effects it means allowing for some deflection, and seeing how that will affect our structure. By doing this we can refine our analysis.
A good example of this is the half-bridge shown above, acting like a seesaw, with the weight of the foundations preventing overturning.
If we consider an example where the left and right sides are in perfect balance, and introduce a slight movement, (exaggerated in the diagram) then the effect on the moment equilibrium will be to decrease the lever arm of the resisting force. The lever arm of the overbalancing force will remain the same, or even increase.
The effect of this that at a load that’s close to failure, the system is unstable. What this means is that when it starts to go, it will keep on going, because the second order effects increase any imbalances.
Note this is only true because overturning structures rotate around the left hand side of their base if they are overturning to the left and vice versa. If the point of rotation was in line with the centre of the base both lever arms would decrease proportionally.
Page updated
Report abuse