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Tesco Canopy (Intermediate)
Suggested viewing: Tesco Canopy (Beginner)
DESCRIPTION AND LOCATION
This canopy, made with circular hollow steel sections can be found in the Abbeydale Road Tesco car park, just outside the main entrance (postcode S7 2QB).
It’s a very interesting design because on first glance there seems to be a very large overhang. How can such a slender structure be supporting the canopy?
APPLIED LOADS
In most cases the loads on an everyday structure are easy to think of. You have the self-weight of the frame. There may be some uplift caused by pockets of wind collecting under the canopy. There will also be horizontal wind loads on the structure, and occasionally it might have to deal with snow on the roof, or other temporary loads of that nature.
However, the most significant design load case will almost certainly be a car or other vehicle crashing into one of the columns. Imagine the column buckling and the whole structure crumpling on top of a car!
As designers it is important to recognise all potential failure modes/scenarios and consider them in the design process.
The engineer could have thought about this in a variety of different ways. They could have installed protection around the column, as shown, designed for the force to be absorbed by the column by the equation:
(where δc is the car’s deflection and δb the barrier’s)
Or, the engineer could have positioned the structure to minimise the risk of such an accident, which given the position of the canopy was probably the preferred approach.
CONCEPTUAL/QUALITATIVE BEHAVIOUR
Supports:
The first and most obvious thing to start with is the base supports. Hopefully we can all see that they must be rigid connections, otherwise the canopy would just keel over.
Less obvious are the supports at the horizontal and diagonal struts. Are they pins, or rigid connections?
There are two ways of looking at this.
The first is to say: how could the support act? If we removed the diagonal strut, would the frame immediately collapse? Well, there’s a haunch there, and some thick steel sections, so I think that connection probably could support the weight, at least temporarily.
But we can also say: how does this support actually act? In some ways this is more useful, as the path a force takes is dependent on the stiffness of the members it is travelling through, the stiffer the path, the more force.
In this case, the struts can carry the external force axially (with tension and compression) so there’s no need to have rigid connections. The fact that the two members connect to the column at different positions effectively creates a couple, which is a (very efficient) way of resisting bending moments. They will probably act as pins.
Why are members carrying axial forces relatively stiffer than members acting in bending?
This is intuitively true. Your arm has a stiffer response when you hold something by your side than when you hold it away from your body. The reason behind it can be appreciated by looking at the stress profiles of members when they are deformed elastically.
When you load something in bending the maximum stress is only reached at the extreme fibres. In contrast, loading a member axially will result in constant stress throughout the cross-section.
There are different ways to make sense of this; assuming the member is put under the same load once as an axial load and the other as bending. Hence, the areas of the diagrams above are equal making the magnitude of the axial stress less than the magnitude of bending stress at the extremes.
Imposed Loads (Variable Actions)
Now, what if there was a case of uplift from the canopy, how would it be resisted?
This example demonstrates why two rigid struts are required for the canopy to do what it’s supposed to.
Beforehand we had a case where the diagonal strut was acting in tension, which normally could be carried by a cable. We could save material and make it easier to install.
Now however, we have uplift, which reverses the path the loads need to be carried. The situation is almost identical as that seen with the dead loads, except that the diagonal strut will go into compression, and the horizontal strut will go into tension. A cable on the diagonal would be no use: it has no compressive resistance, and would simply fail.
We also need to consider the possibility of snow loads.
During the winter there could be a significant weight of snow on the roof, so the arch section on top must be structurally strong and stiff, not just provide cover from the elements.
Why has an arch been used, instead of a flat roof?
You’ve probably heard that an arch is an inherently strong structure, but let’s compare it to how a beam behaves to understand why this is.
There’s a simply supported beam, and a 3-pin arch.
We’ll load both structures with a mid-span load, for simplicity, and see what happens when we make a cut and find moments.
In the beam, moments will increase linearly as we move towards the centre, but in the arch the moments will be smaller, and can even be zero if the applied loads match the shape of the arch. It’s because of those horizontal reactions.
One way to think about this is that because at each support one reaction is going clockwise and the other anticlockwise, they are ‘cancelling out’ rather than adding up. In this way you will always get smaller moments in an arch than a beam with equivalent loads.
OTHER THINGS TO THINK ABOUT
A 3-pin arch has been used for the roof instead of a 2-pin arch. Think about what the connections are doing and how each arch type would be constructed. Why do you think a 3-pin arch was used for this canopy?
The arches will generate horizontal reactions as well as vertical reactions, which engineers call ‘thrust’. How is this force going to get down to the ground?
Well, this horizontal thrust will go have two components of force relative to the struts. One is going to go outward and will be resisted by tension in both the struts. The other will apply a force to the struts perpendicular to the plane they are positioned in, and will cause bending.
This partially explains why the cross-sections of the struts are circular: as well as axial forces they will need to resist this bending moment created by the lateral thrust from the arches.
The arms of the canopy don't appear to have much stiffness in the horizontal direction to resist the thrust from the ends of the arches. Hence, it may be that the fabric roof covering is effectively acting as a tie member between the tips of the two arms of the canopy, such that the thrust forces at 90 degrees to the arms cancel out.
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