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St. Pancras Bench
DESCRIPTION AND LOCATION
An aesthetically pleasing bench with smooth curves that can be found on the upper floor in St. Pancras Station behind the escalators. Although it may seem simple and ordinary at first sight, the curious thing about this bench is that it has an interesting way of resisting moment. APPLIED LOADS
The first step to analyse any structure is to recognise the loads the structure will be exposed to.
People tend to forget about dead loads but they are very important; in this case the dead load is the weight of the bench itself.
The obvious applied loads in this case are the vertical loads from people sitting on the bench, bags or packages being placed on it.
Horizontal loads are often due to wind or water, but in non-marine and low-rise structures these are often too small to worry about. The bench also has slender elements and a ‘thin’ cross-section which helps in minimising wind loads.
However, one might consider a person trying to push the bench or even raise it, children jumping around… etc. These could lead to uplift or over-turning of the bench.
CONCEPTUAL/QUALITATIVE BEHAVIOUR
Supports:
The bench only has two supports, it is interesting to notice (well for engineers at least) that the legs of the bench are not single vertical supports; providing the bench with higher resistance to moment.
The distance between the two parts of the leg act to create a moment; one of the legs goes into compression and the other into tension to resist small moments, with the distance between the two determining the size of the moment which will be generated.
To bring it to grips think about holding a ladder on your shoulder and supporting it with a hand; the closer you bring your hand to your shoulder the less stability you have. Similarly, standing with your legs apart on a train or a bus to stop you from falling when it brakes.
Another interesting observation about the legs is that they aren’t a single connection, they aren’t just a column. Imagine sitting on a chair and swinging back and forth; that swing is a form of moment resistance. The spacing between the legs allows the chair not to fall over, so you can thank engineers for that.
Dead Loads (Permanent Actions):
The dead loads are the weights of the bench, the arm rests and the legs. The bench has a uniform cross-section and so it can be assumed to have a uniform loading across it. So, for simplicity, we can model it as a simply supported beam (ignoring the moment resistance of the supports) with a UDL across it. Now let’s think about the deflection, it’ll be something like this:
Now where do you think the maximum bending will occur? That’s right, the middle! So if we draw the BMD the maximum moment will occur in the middle, and we know pin supports can’t stop rotation so the moment at the ends will be zero. Now what happens between these points?
Obviously the moment rises from zero to its maximum, but is it a straight line or a curve?
Moment = Force * Distance
So in our case as we move along the beam both force and distance are increasing proportionally, giving us a quadratic function.
The line will therefore be a parabola:
Imposed Loads (Variable Actions):
Now How would that BMD change if we consider a variable load? What would happen if a person sat on the bench?
Let’s model a person as a point load and see how this affects the BMD.
One way to go about this is to work out the BMD for the point load and then add it to the BMD of the UDL. Again we know that moments at the supports are zero and maximum at the point load; but this time there's a difference as the force is constant (the single point load doesn’t change) but the distance from either support increases so we have a linear relationship (i.e. a straight line with a slope):
Now if we add it to the UDL BMD (the parabola) we get the following combined BMD diagram.
OTHER THINGS TO THINK ABOUT
One interesting thing to think about is what if we modelled the bench with supports that allow for moment resistance?
Let’s say both supports can resist moment how would the UDL case change?
In the case of the UDL since the BMD is symmetric so what happens on one end will be reflected in the other end.
In the right hand support the moment resistance will be clockwise and in the left hand support the moment resistance will be counter-clockwise. If you try applying those rotations on a ruler you’ll see it bends upwards, which in this case is perfect as it opposes the downward bending.
Because the BMD is symmetric (due to the load being a UDL) then the moment resistance will be equal on both sides, but opposite to cause the beam to bend upwards; the BMD for such moment is shown below.
And if we combine it with the BMD of a UDL then we end up with:
Which as we can see is very helpful as it decreases bending moment everywhere along the beam, although the total difference in the maximum moments will be the same, the result is that the fixed ended case just 'pushes up' the whole diagram.
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