Mast bend test calculations

Hoping someone here can help or point me in the right direction. We have a large-ish rotating wing mast that we don’t have any original design details on and wanted to do a gut-check on strength. Had an engineer helping us who guided me thru conducting bend tests on the spar to calculate the mast EI moments, but he’s since become so busy that he doesn’t respond. I have all the inputs (measurements, weights, deflection amounts, etc) and the engineer sent a set of outputs (see attached) but no further detail and no understanding of the calculations that went into it. Also have no way to update the numbers with more accurate data - some of the inputs like boat weight and even some of the dimensions were estimates that we now have accurate numbers for.

Anyone have any experience here or suggestions? Any help very much appreciated.

 

I have no experience, nor any exposure to the real numbers for a sailing craft, but those loads seem extraordinary. I mean, does the halyard winch really pull over 6,000 kg? Even halving that from the sheeve load at the masthead seems amazing.

Is that 9,000 kg for the shrouds the total between all the shrouds? Maybe that's divided among six stays, 1,500+ kg. That seems more reasonable, I guess.

What is, "Side Stay Compression"? It that what the shrouds put on the mast? So it is the total of all the shrouds.

This is a fascinating exercize. Someone who knows something will be along to help. This site is a fantastic resource and the engineers on here are generous with their endless knowledge.

 

Apologies, should have been a bit more clear: the primary thing I am looking for is a resource for how to calculate the mast EI from the bend test data. Whether that is someone I can hire, someone here with experience willing to share, or a reference source to read/learn from - happy for anything.

That attachment above has three sets of components: dimensions & weight of the boat/rig, calculated loads, and a single line for "mast tube max compression", which was the engineers calculated strength of the mast based on the results of the bend tests I conducted. There is an awful lot that would have gone into that calculation, and that's what I'm looking to understand. It's a wing mast, so we've got very different longitudinal and transverse moments, and how do those translate into a "max mast compression" strength number? I have the details of the bend tests as well as a rig sketch and all other info, which I'm happy to post when I get home, but unless someone is familiar with bend tests it seems the info would just be a novelty.

 

Ballpark all the calculated loads checkout. I was also surprised at first at the main halyard compression but I believe it should be 2X the halyard tension, which should be around 5,000lbs. The halyard winch is an Anderson 52 that's pretty well maxed out with the main up full. Main is 1,000SF, weighs 250lbs with battens.

That's the max load on a single cap shroud at max righting moment. Also seems accurate, at least with the inputs given.

That's the compression imparted into the mast from the cap shroud tension at max righting moment.

 

That's straight forward enough, given the material used and the sectional shape.
Since that is the EI.

 

Hi OcmRzr,

Seems like there are different subjects here :

Formulas that are used to exploit the measurement depends on the test configuration. Can you describe the protocole you use ?

these calculations do not answer the question of the EI's. It's a mast compression calculation based on a rigging configuration. A safety factor is presented, which may indicate some knowledge a the geometrical moment of a section. [/QUOTE]

Seems like you wish to use the results of the test to your own purpose. Looks like this wing sail will be rigged with 2 shrouds, one fore stay. I can prepare a small spreadsheet to reproduce the calculations of your engineer, if that is what you want. Since calculations are statics and linear, the FoS will be updated as well.

 

Apologies @Alan Cattelliot, I missed your response. It's the strength of the mast I'm trying to determine. I conducted bend tests according to the attached layout, the results of which are also attached, and the engineer apparently calculated a "Mast Tube Max Compression" number of 242,452kg. I have no idea what he did to get there. That's what I'd like to understand. Attaching a rig sketch and the cross section of the mast as well for reference.

 

@Ad Hoc mast section sketch attached.

 

That looks like a C spar in composites. Very typical of wing sail mast. Do you have dimensions, length of mast, layup schedule, type of material, method of manufacture, sail layout, righting moment? These are the details needed to calculate.

 

You need to get to the point where there are no assumptions, hopes or appearances. Thicknesses and type of material need to be determined. From there, the EI can be calculated. Also, is the section constant or does it have taper and reinforcements? Was this a prototype mast?

 

It is just that...a sketch.
There is no data.

 

@rxcomposite @gonzo @Ad Hoc

While I appreciate the responses, I am not looking to calculate EI, I am looking to back into it. That’s the whole point of a bend test - you don’t need to know modulus or 2nd moment of area of materials/components or construction details or anything else. Deflection under load will give you EI, assuming you have the math. That’s what I do not currently have and am seeking - someone who has experience with bend tests and/or deflection calcs.

I see no point in trying to forward calculate EI - in our case it would involve too many assumptions and uncertainties, whereas the bend tests give a certain answer.

 

Yup. The EI would be very elusive. This is a non constant cross section and the thickness vary along the length.
Since this is a stayed mast, lay it flat, supported at both ends, mark divisions along the length, and gradually place uniformly varying load (sandbags) at intervals along the length. Measure deflection at the centroid, or if you want, each interval.
You may want to know the max righting moment beforehand so that you will know the limit, otherwise, just keep loading until you are satisfied it will not break or deflect too much.
In composites, strength is not a problem. Deflection is.

 

This is a non stayed mast, partially supported above base, non uniform section but you should get the idea.

 

If that is all you seek, it is straight forward.
Assuming one end built in, the other end free to deflect,

Deflection = w.L^3/3EI