Chainplate Calculations

[P69]

I created a spreadsheet to calculate the location of the center of the hole in a chainplate, where the shroud tang attaches to the chainplate. The width of the chainplate can be modified to match the raw material that is available.

Skene's book has a diagram and data table that gives dimensions of a chainplate and the location of the hole relative to the radius at the upper end of the chainplate.  The purpose of the offset is to leave more metal between the clevis pin/hole and the upper end of the chainplate.  This gives more strength to resist the upward pull of shroud/stay.  The dimensions in the table are calculated to give a yield strength that is approximately equal to the breaking strengh of the wire.  For example, a 1/4" wire dia has a break strength of 8200 lbs; therefore, according to Skene's table the chainplate must be 1/4" thick, with a 1/2" hole and a 1/8" offset.  The width needs to be  1.375"  wide.  If that width is not available, you can enter the available width in the row labeled "Available Width" and see how that will affect the chainplate strength. If you leave "Available Width" blank, the spreadsheet will use Skene's value for width (2r).

The thickness can also be modified to see how strength will be affected by thickness and width to match that available material.

Skene's table shows basic dimensions such as thickeness, width, hole diameter for a chain plate, given the wire size.  It also shows an "offset", which is used to offset the center of the hole downward (away from the upper end of the chainplate) by a distance that varies with the wire size.

This spreadsheet uses these variables and calculates a value that is the distance from the upper edge of the chainplate to the center of the hole ("Vertical Distance to Center"). This value is just the sum of the offset and radius.  When  you drill the hole, just measure down this distance along the centerline to mark the center of the hole.

The labeled "Calc Yld Strength (chainplate)" calculates the yield strength of the chaniplate with the given dimensions. I added this as a comparison against Skene's table. His goal was to have chainplate specs that resulted in a chainplate that has a yield strength of greater or equal to the break strength of the wire.

The only value that one might want to change is the yield stregth in the upper-right. I chose 41,200 psi for the yeild strength of 316 stainless steel. I had difficulty finding the exact value for yeild strength; it varied among the different steel suppliers.

If a different metal is use or if a differnet yield strength is desired, one can change that value and see how that will affect the breaking strength of the chainplate.

Also, if increasing the chainplate thickness is considered, one can modify the spreadsheet with the new thickness and see how that will affect the strength of the chainplate.

What I don't know how to calculate is the number, diameter of the bolts, and bolt spacing that fasten the chainplate to the bulkheads.  It would be nice to integrate that into this spreadsheet so it can output the width, thickness, length, bolt spacing and diameter.


Source:
"Skene's Elements of Yacht Design", 8th Edition. Editor: Francis S. Kinney, Putnam and Sons.
Data table and diagram are on page 188

[Dale Tanski]

I'm not sure why you would spend the time to determine what you already have, unless you have a lust for engineering and its intricate possibilities. As with all technical endeavors, you will often find that the more versed at such calculations you become, the less you will actually be sure of, as the possibilities of the unknown escalate quickly.
Such is the case regarding your concern of the attachment bolts. Continuing down that road, questions regarding the transfer of the loads to the hull such as the sheer strength of the bolts, the relationship regarding their single sheer orientation, the tear out strength and condition of the bulkhead material, the angle of attachment and how it effects the loading, the tensile stress induced in the fasteners by tightening and how that effects the overall strength of the connection. 
How far down the rabbit hole does one go?  Is the wire size correct? Did somebody along the way modify that diameter? Are the attachments to the spar sized properly and installed and maintained properly?  The end swedges?  The rigging pins? 
One thing that I have learned along the way, if it has lasted 40 years under all sorts of inappropriate occurrences, it was correctly designed to begin with.  Life is too short...
Dale

[P69]

Rabbit holes are fascinating places; one can find interesting paths to discover.  You are correct, the more one learns, the more one realizes there is much more to discover.  It was curiosity that led me to develop that spreadsheet, the same curiosity that caused me to lose countless hours learning about and calculating the lead of our rigs (CE vs CLR lead)

https://pearson365.com/forum/index.php?topic=1688.0,   The P367 has a lead of approximately 15.8%

Unfortunately ascertaining the data needed for inputting into the lead formula depends heavily on scaled drawings, although I wonder if a combination of geometry and trig might eliminate some of that scaled drawing work. That would be fun to dust off the old trig book and refresh my memory.  That could be an interesting spreadsheet, Thanks Dale.

Another reason for learning  this is to cross-check what exists. My chainplates might or might not be original, although when comparing the craftsmanship and appearance of shroud chainplates with the stem fitting, they are very similar, leading me to believe that they are original.  It's good that I will replace them.

I would like to find formulae that calculate the bolt number and spacing so I can design the series drogue chainplates at the transom, as well as replacement chainplates.  Although trust must be placed in the designer's plans and the workmanship of the build, it can be reassuring to know, by calculated results) that something was in fact built correctly.

You raise a good point about the the tear-out strength of the bulkheads through which the chainplates are bolted.  Looking at them, it is a little unnerving to realize that all which holds that chainplates in place is the bond (chemical and mechanical)  of the layers of cloth/mat and polyester resin used to tab those bulkheads to the hull. That's it!. No matter how strong your chain plates are or how good your swages/staylocks are, the weak link might actually be the bulkhead/hull interface; however, I don't know of any dismasting caused by failure of that connection.

Calculating strength of fiberglass is difficult because of the large variation in layup quality.

Dale, for many of the questions you brought up (wire size, spar attachments, rigging pins), there is a set of formulae that I incorporated into a spreadsheet that actually calculated the stress imposed on the rigging, based on spar length, number and length of spreaders.  I don't know where that spreadsheet it; it was lost years ago deep in the folder tree of an external storage drive.  The sheer strength of the bolts is very simple for a single bolt (((thickness * (width - dia of hole)) * yield strength)*0.60) [this is a widely accepted approximation off sheer strength], but knowing how the stress is distributed among multiple bolts and to what degree does  compression of the substrate (how much to tighten the bolts) affect that distribution would be very interesting.

For most folks, knowing this doesn't matter, except for those who want to know or those who want to modify their boat. For example, how far forward could one move the head stay onto a bow sprit before lee helm is introduced?  Generally, when the wind picks up, weather helm increase. If balanced well, full sail could be carried in heavier wind with less weather helm. Of course excess healing would be deleterious to speed if full sail were carried too far (well-cut sails also needed).  If one wanted to replace SS chainplates with silicon bronze or titanium, what dimensions would be needed so they would be strong enough without wasting excess material?

The same questions for chainplate dimensions/bolt sequence might be applied, perhaps with variables for the fiberglass toe rail substrate,  to determine whether or mooring cleats are adequately installed or to what to use when installing additional cleats. That leads into the whole other question of cleats' backing plates, which are needed to distribute stress.  What would be be more effective at distributing load:  a backing plate, or the same thickness of 1708 and epoxy laid up under the toe rail, perhaps also laid up in the entire concave profile of the underside of the toe rail and extending a foot fore and aft. Is the effectiveness of a backing late  simply a matter of surface area or is there an advantage to using a different medium (SS or AL) to form two layers (cleat base and backing plate) that sandwich/compress the toe rail?

I think I'll try to find that rigging strength spreadsheet and run the numbers to see if they correspond to the break strength of 1/4" lowers and 9/32" uppers.

Well, looks like I fell into another rabbit hole tonight.   Thanks for bringing up those additional factors to consider.

[Dale Tanski]

There is an old saying...
Shoot the engineer and start production.
Dale