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Bus Stop Bench (Beginner)
DESCRIPTION AND LOCATION
This is a really well designed and detailed stainless steel bench, located outside the fire station on Eyre Street in the centre of Sheffield (i.e. around the back of the new Market at the bottom of the Moor, and not far from Decathlon), the postcode for which is S1 3FG.
APPLIED LOADS
The first thing to do with any structure is to think about the loads which are likely to be applied to it. These are usually fairly obvious, but not always. Indeed, structures are sometimes subject to abnormal loads, which the designer needs to try and anticipate, and design for as appropriate.
In this case, obvious loads include the self-weight of the bench itself, and the weight of people sitting (or even standing) on the bench, as well as any bags and packages they may have. There will be some wind load on the bench (although the holes in the seat will reduced vertical wind loads), although this is likely to be nominal, and can therefore be ignored.
Not so obvious loads might include somebody trying to kick the bench over (in other words, a horizontal load applied to the seat or at the top of the post, which is likely to be far more onerous than any wind horizontal loading). Note that this would be an accidental load case, so EC1 allows us to apply a reduced load factor of 1.05 to it, as opposed to the standard load factor of 1.5 for an imposed load.
CONCEPTUAL/QUALITATIVE BEHAVIOUR
Supports:
Here, there is only one support (i.e. at the base of the vertical post) so all loads applied to the bench (including its self-weight) must be transferred through the horizontal seat, to the vertical post, and down to this support.
Dead Loads (Permanent Actions):
First of all, let’s think about the dead loads acting on the bench. There is the self-weight of the horizontal seat itself, plus the self-weight of the vertical post. Since the seat is of constant cross-section, it will have a constant self-weight along its full length.
Given that the horizontal seat is only supported at its centre (by the vertical post) it could potentially either rotate about the central post or cantilever about either side of the central post. The former would work if no external loads were applied to the bench (i.e. if it were only ever subject to its own self-weight) since the dead loads on either side of the vertical post are equal and opposite, and we would effectively have a see-saw:
Irrespective of whether the horizontal seat rotates about the central post or cantilever about either side of the central post, it can be seen that the bending moment increases from zero at each end of the seat to a maximum value at the central support, as shown below.
Note the bending moment (let’s call this ‘M’) at any position along the seat is equal to the dead load UDL (let’s call this ‘w’ kN/m) multiplied by the distance from the end of the seat to the position in question (let’s call this ‘x’) squared, all divided by 2. In other words, M = wx2/2. Note that this squared relationship between the applied load and the span is the reason for bending moment diagrams due to UDL loads being a curved shape.
If it helps, you can think of the seat as two separate cantilevers, with each seat subject to a constant uniformly distributed load (UDL), as illustrated.
Similarly, it can be seen that the shear force increases from zero at each end of the seat to a maximum value at the central support.
Note the shear force (let’s call this ‘S’) at any position along the seat is equal to the dead load UDL (‘w’ kN/m) multiplied by the distance from the end of the seat to the position in question (‘x’). In other words, S = wx. Note that this is a linear relationship, and explains why shear force diagrams due to UDL loads are an inclined straight line in shape.
Finally, let us consider the deflected form diagram. At the central post, the deflection will be zero, whilst maximum deflection will intuitively occur at either end of the seat. It can be shown that the maximum deflection in a cantilever subject to a UDL of ‘w’ kN/m equals wL4/8EI (where E = Young’s Modulus of the material and I = Second Moment of Area of the section). Note that this ‘to the power of 4’ relationship between the applied load and the span is the reason for deflected form diagrams due to a UDL load applied to the full length of a cantilever being a curved shape, as shown below.
OTHER THINGS TO THINK ABOUT
Why are there holes in the seat?
Good question! Potentially for drainage and/or to stop people getting sweaty bums!?
Why is there only one post?
Again, good question! Possibly to reduce the number of foundations / excavations, which can be time consuming to form and therefore expensive.
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