Euler Factors for Mast Design

[Wynand N]

Pauls, do yourself a favour and get the following book; Sailing Rigs and Spars by Matthew Sheahan.

On pages 16 & 17 (and other) is about everything you need to know to calculate the scantlings using Euler's formula with different load conditions, panels, inertia etc.

Just one little error on page 18 with wrong value used in a formula. The book also let you calculate stays and shrouds with lots of data and graphs all over.

I can scan these pages and post them by might have some flack with copyright issues, unless everyone will forgive me for that and I might just attach them for you

[MikeJohns]

You can scan a few pages for educational purposes. No problem, educate us

[Wynand N]

Rather let the scans educate all of us, Im just a humble boilermaker
Pauls, you should find what you need from some of these few pages, if not, I'll make another few scans for educational purposes

Pardon the notes on one of the pages made by me...

[idkfa]

If a composite mast is made pre-bent, say about 3-4 diameters worth. Does it still obey Euler or approx how much deivation (diameters) before it no longer does?

Columns can take lots of load, so long as they remain in column, so how is pre-bend treated.

[idkfa]

If we simplify the mast to be straight sections; deck - spreaders and spreaders - shrouds. (see diag) Then my question is at what angle does the column fail like a column (Euler) and not a joint?

[latestarter]

The following is based on my knowledge of structures, I have never calculated a mast.


Euler still applies, you just modify for the extra effects.

When a compressive force is applied to a column that is not straight it gives rise to a bending moment calculated by the compressive force times the eccentricity, which is the offset relative to the straight line joining the top and bottom of the column. (in your term pre-bend)


The column is calculated by combining all the applied forces.

Adding up all the compressive forces and dividing by the cross sectional area and the permissible compressive stress. Say A

If the column is not symmetrical the total bending moments in the xx and yy axes are divided by their respective section moduli and by their permissible bending stresses giving results, say B and C.

Provided A + B + C is less than 1 it is considered to have passed.

As the slenderness ratio of the column increases, the allowable compressive and bending stresses decrease.

[latestarter]

My previous post was based on designing buildings where deflections are kept small.

In the case of masts where the shape of the mast can be temporarily altered to adjust the shape of the sails I think the same principles would apply, but as the mast curves the eccentricity will alter making the analysis more difficult.

[idkfa]

thanks latestarter, I'll make an attempt and post a bit later, found the following using your input.

http://www.efunda.com/formulae/solid.../eccentric.cfm

must confess I started the mould today! all a bit backwards but I have checked my design against similar ones, it just that I have a huge bend too (half length shown), so let's hope......

[Pauls]

I found some practical information on Euler factors for mast design. The subject is addressed by Pierre Gutelle. Translations of his work are available on this forum (the originals are in French). Gutelle has two charts, one for compression on adjacent panels and the other for length. The results from the two charts are combined and give a Euler factor for that particular combination. A useful piece of information I haven't found elsewhere.

Regards, Paul