Mast Deflection with diamonds

Hello,
The stress and deflection of an unstayed uniform-section mast (like a Laser) can be found by using simple engineers bending theory for a cantilevered beam. How do you calculate the stress and deflection of the same mast, but with diamond wires attached (not shrouds) at 70% height? Can anyone explain this to me or recommend a text book that will?

many thanks.

 

If you have a CAD drawing and have defined the loads (hard part) then I could calc the stress strain for you. Note mast design is not simple theory, defining the loads can be the bit where you get it wrong, usually better to see what the other guy did and whether it broke.

 

The same basic arithmetic can tell you the change in stiffness from adding jumpers.

Simply measure the length of the legs and the span of the spreaders. Use the wire size to get elasticity, and you can predict what the change in stiffness will be compared to the tension in the diamond wires. Simple math, nothing fancy.

 

Thanks for the offer Mike. At the moment my design is still in its early stages, so I have no specific data.
RHough - Are you saying that the force applied to the mast with diamond stiffening is equal to the mast force without the stiffening minus the tension in the wire (applied as a point load at the point of attachment and resolved through the diamond angle). Then just calculate as normal?

 

Hi Toby

I am sure that some could work out exact solutions, but here is a more empirical approach which means that you have almost enough information to work it out for yourself.

But it does depend on the diamonds being in the same plane.

If the diamonds are lateral only the fore and aft deflection will be unaffected and can be calculated as you say.

For deflections in the plane of the diamonds (thwartships?)
Work out the deflection below the diamonds and above the diamonds by the method you gave - it will be unchanged

For bend in the area of the Diamonds - two scenarios
1/ If the diamonds are tight and the struts are "long" (maybe 6 times the mast width - similar to NS14 or Taser) and are set tight on the beach (not normal in these classes) there will be little deflection in the area covered by the diamonds - maybe 20mm for a 4m length of diamond from my experience - not much.

2/ If diamonds are looser the mast will deflect readily to the point where the diamond on the outside of the curve becomes tight. It will bend classically until that point - so you can use your calculation backwards (ie you know the deflection from the geometry already) to work out the loading that gives you that deflection if you wish. As the load increases at that point the diamonds will prevent much more than 20mm deflection over a 4m span beyond the deflection when the outside diamond initially becomes tight.

The point is, that if you use the information you already have and think about how the mast will bend before and after the diamond starts restraining the mast you will have a very close solution.

Hope this helps
Michael Storer
my boat pages

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Some comments that may or may not be useful

For an unstayed the highest bending moment is at deck level. or the point above which the mast is unrestrained.

Diamonds will not change this - so will not alter the strength of the section in that area.

However diamonds only on the sides of the mast will not provide any extra fore and aft support.

Unlike spreaders which can provide restraining forces because of static rig tension as well as sailing loads, generally diamonds are used simply to restrict bending by triangulating the mast and preventing it from bending. However as the stresses resolve back into the mast at the top and bottom points of the diamonds the mast needs to be the same stiffness/strength at those points compared to a mast without spreaders.

So if the mast needs to be the same stiffness/strength as a mast without diamonds . . .
1/ at the deck
2/ at the bottom termination of the diamonds
3/ at the top termination of the diamonds
. . . it is a bit hard to see how you can make much of a difference in cross section or gain another advantage.

 

Thanks for that, I need to digest what you say but my first thought is - if you are in Oz, shouldn't you be asleep now?!

 

Toby,

I am a deeply flawed human being!!!

Have been busy doing some work on my website.

By the way, somehow I missed RHough's post. It covers the bit I "dealt" with empirically. RHough is a retired rigger and is careful with his facts - well worth keeping an eye on what he says.

Best Regards
Michael
my boat pages

 

Thank you, I try to be as accurate as I can. However never do anything without checking the theory yourself... I've been known to drink while posting.

If you are familiar with spar structures, the area spanned by the diamond stays will act like a heavier section over that length. The diamonds can make the mast react like an extrusion with non-uniform cross section area.