Embedded Files
Ship's Mast
Suggested viewing: Intermediate Tutorials
DESCRIPTION AND LOCATION
This is the mast of a yacht that was photographed in a port in Ischia, an island off the coast of Italy.
It may not be immediately obvious that boats or other moving things should be studied by Structural Engineers, but if you wanted to refute that statement then you’ll find few better examples than this: you can clearly see every member and work out what its role in the structure is, it looks very slender and elegant.
APPLIED LOADS
Let’s think about the forces that could act on the structure. Its self-weight is fairly obvious, and this mast is probably made of steel, so the self-weight will be a consideration, but probably not that significant
The dominant factor applying load is always likely to be wind loading in this case though. Otherwise the mast is pretty pointless. When the sails are up the wind could be blowing in any direction, so for this mast to satisfy the design requirements it must be strong and enough to resist the wind loads in any direction.
CONCEPTUAL/QUALITATIVE BEHAVIOUR
Supports:
At a first inspection it looks like there is only one support, the connection at the base of the mast. Look a bit closer and you can see that there are 3 cables connected to the ship. There’s two coming down from the bottom ‘yardarms’ (the horizontal members on a ship’s mast) and one substantial cable coming all the way down from the top.
These have an important role to play, as we’ll see.
Dead Loads (Permanent Actions)
The dead load here is the weight of the structure itself, and the weight of the sails. Now you can see why the cables are there. The weight of the yardarms makes them bend and deform downwards, but the deformation is limited here because they are supported at their ends by the cables, and the structure behaves as a truss. Note that the mast on its own wouldn’t need this support as it would act purely in compression.
Trusses are structural systems that are only meant to experience axial forces; tension and compression. Tension and compression aren’t fundamentally different animals to bending stresses. In fact, when a structure is put into bending, it’s actually just tension and compression forces combined, acting eccentrically to give a couple or bending moment.
What a truss does is to separate these internal forces into distinct members, some in tension, some in compression, which is structurally efficient and saves material. The mast is an even more extreme example of this. The cables have no resistance to being squashed as they’re so flexible, so they can only take one axial force: pure tension.
Looking at an example of two apparently different systems can illustrate this:
We can see that the bending of the beam above can be modelled by local compression and tension forces, which looks remarkably similar to a truss system. Our mast is working the same way. Instead of a bulky structure that ‘bends’ to resist loads we can use a web like structure where the individual elements shrink (i.e. in compression) or stretch (i.e. in tension).
Imposed Loads (Variable Actions)
When the sails are up, wind loads will apply lateral force to the yardarms. As long as these loads are in the same plane as either of the two trusses there isn’t going to be any serious bending stress in the yardarms, because the cables can carry the wind load just as they carry the weight of the structure.
In reality though, this is pretty unlikely. The winds are going to generate the biggest forces when they hit the sails head on, rather than with a glancing blow, as it were. There’s just more surface area in this direction to capture more wind. And more wind equals more force.
Making the situation even worse, there are no cables to support the yards in this direction. They are going to have to act as cantilevers and resist the load in bending.
Let’s think about how these forces will get to the ground. The yards will transfer a horizontal force to the mast in the same direction as the wind, which will try to bend the column. This is a lot of bending stress and if the mast was a giant cantilever the bottom would snap off pretty spectacularly in high winds.
This is where those cable supports come in. They are basically fixing the top of the mast in place by going into tension, so the mast is supported at both ends, and the bending moments are reduced.
Notice how at least three cables are required. It’s like pegging your tent into the ground with guy ropes. If you peg three in then at least one must always be in tension, provided they’re not all on the same side. One or two ropes are not enough.
OTHER THINGS TO THINK ABOUT
The yards will also transfer a twisting force to the mast, making it tend to rotate around its base. We call this force ‘torsion’. It acts like bending, but bending around the cross section, rather than along it.
It’s effectively what happens when you apply a load to a member which is eccentric about the support in two directions. Hence, a load applied to a yardarm is both horizontally eccentric about the centre line of the mast and vertically eccentric about the base of the mast.
How does a member resist torsion?
scale rule on left and standard ruler on right
Let’s think about two rulers with a similar amount of material in the cross section, a scale rule and a normal bog standard ruler. Try and twist both of them (apply torsion) and you’ll find the architect’s ruler puts up much more of a fight. The reason behind this is that although they are both similar sizes, the scale rule distributes material more evenly around its midpoint (centre of mass), giving it better torsional resistance.
The torsion is being resisted by shear forces forming a closed loop within the cross-section. Because the architect’s ruler has this distribution of mass it allows a larger loop to form and more of the material is being used to resist the torsion.
If you took it even further, a perfectly cylindrical hollow section would be even more difficult to twist, because the distribution of material is perfectly even, and can all be utilised to resist torsion in a closed shear ‘loop’. This is mathematically the most efficient way to distribute material around the centroid to maximise the torsional resistance (obviously you can only compare cross sections of the same area).
The horizontal yards also play a role in stopping the mast from buckling. A long, thin member like this mast has a tendency to bend out of plane when it is put into compression. When it is restrained at intervals as in this structure the length over which it can buckle is reduced, with the effect of greatly reducing this tendency to buckle.
Page updated
Report abuse