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St Pancras Lighting (Intermediate)
Suggested viewing: Beginner Tutorials
DESCRIPTION AND LOCATION
If these lights don’t seem familiar, you need to get out more often! These weird looking lights can be found in St. Pancras Station, London; lighting the way to many a weary traveller. The unsymmetrical awkward design should draw the attention of any engineer out there; exhibiting a beautiful balance of forces and an inverted arch that gives out the secret explaining why it’s there. APPLIED LOADS
For lighting systems, the only two applied loads we usually need to worry about are the self-weight and wind. The self-weight for this lighting is just the weight of its parts; the real issue is with wind loading that might, and often does, cause swinging.CONCEPTUAL/QUALITATIVE BEHAVIOUR
Supports:
We can see that the lighting is supported at each end; at the far end there’s a column that just attaches the lighting to the ceiling. A column attached to anything really doesn’t allow much motion or rotation; we can model the far connection as a column with a fixed connection.
The near connection is circular and is difficult to tell whether it’s a pin or a fixed connection, but pin connections are cheaper than fixed ones; which makes it more likely to be a pin. Anyways, analysing this structure will be much more interesting if it was a pin connection!
Dead Loads (Permanent Actions):
For the purposes of this tutorial we’re going to model the horizontal section of this lighting as a beam, and analyse its bending behaviour. This doesn’t fully explain how the structure will behave, although in most loading situations there will be at least some bending. For the full story you can check out the advanced version of this tutorial.
As we mentioned earlier the self-weight comprises the dead load. The cross section of the lighting is more or less constant but the arch clearly grows towards the middle. Because the overall cross-section grows towards the middle we cannot model the load as a UDL, instead we model it as a non-uniformly distributed load or simply a distributed load. Don’t confuse this with a BMD, this is a diagram showing the load distribution.
One of the many ways to get to grips with the analysis of a structure is by imagining the deflected shape.
The pin connection allows rotation so the beam will rotate and as we get further away from the pin the bending (sagging) will increase, reaching a maximum around the middle of the beam. The bending will then decrease approaching the corner; corners are very rigid so in order for the bending beam to connect with the corner it’s going to have to bend upwards (hogging) slightly.
The weight of the beam will cause the whole corner to rotate clockwise, bending the column it is attached to clockwise as well (bends to the right). In order for the column to connect with the fixed connection (ceiling), again it will have to bend in the opposite direction (to the left).
Now that we have the deflected shape, the next task is constructing the BMD. We know the moment is zero at the pin connection, and that it increases as bending increase; the line is a curve because the load is a distributed one.
Take notice that the function of the curve isn’t a quadratic function, because the value of the distributed load increases non-uniformly towards the middle of the beam, assuming the loading is quadratic then that would make the BMD a cubic function.
As we discussed earlier, near the corner the rotation direction switches which means that the BMD needs to switch sides as well.
The next steps are as simple as following the deformation diagram and drawing the BMD.
The BMD for the column will have a constant slope as there are no extra moments.
Finally, we just combine the BMDs to arrive at the full one.
We should always go back and check if the BMD agrees with the deflection of the structure.
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