"... 90% of the load is carried by the first three threads, and 99+% by the first seven."
I believe that is a generalized statement that was never meant to apply either rigorously or even as a good approximation to all specific threads. It was intended to illustrate the fact that fasteners do stretch and in stretching, a threaded fastener will have a quickly diminishing amount of the load carried by each additional thread that is in engagement. So I doubt that a fine thread will actually have that 90% of the load carried by the first three threads as a coarse thread would. First, the coarse thread will have more stretch because the core area, withing the minor diameter, will be smaller than the core area in a fine thread with the same OD. That alone would provide a lessor amount of decrease in the percentage of the loading on the threads of a fine threaded fastener. A more fair statement may be to express this in terms of actual linear measure (inches or mm) instead of a thread count.
This increase in the core area in fine threaded fasteners and corresponding decrease in the amount of stretch per inch or mm of the length of the fastener may even surpass the simple change over to linear measure and fine threaded fasteners may even distribute that first 90% of the load to an even longer section of the internal threads. That would provide an even greater increase in the strength than just the increase in core area would account for.
Others have questioned the assumption that the shearing action will occur at the base of the threads. They say that it may, instead occur at another point, perhaps at or near the pitch diameter. I can point out that many, indeed most threads that I have seen that stripped have failed at or near the major diameter of the internal threads when the failure was in a tapped hole in a large metal part and at the minor diameter of the external threads (the bolt threads) when it has happened on a bolt and nut combination. I have never seen threads fail at the pitch diameter: indeed, for that to happen, both the internal and the external thread would have to fail at the same time and at the same level of stress. To my mind, the logical conclusion from this is to conclude that the failure will almost always be in the weaker thread. That weakness maybe due to the material itself. Even a grade 3 bolt in a threaded hole in cast iron will be significantly stronger than the cast iron and so the internal thread will probably fail first. And when a bolt and nut are compared, the base of the threads on the bolt will be at/near the minor diameter of the thread so they will have less area then the threads in the nut where the base of the thread form is at/near the major diameter and therefore have more area. So the threads on the bolt will often fail before those on the nut. This, of course, assumes that the bolt and nut are the same grade. A grade 8 bolt with a grade 3 nut does not count.
Thus, overall I must say that fine threads are probably stronger than coarse threads for the same OD and linear length of thread engagement. This may also be true for a given thread count for the engagement, but there may be exceptions there and each case should be considered on it's own merits.
By the way, that failure of the threads does not progress a full three threads at a time. It would actually progress one at a time or more realistically, around each thread in turn. Of course, this can occur either slow or fast and could take a long time or seem to be almost instantaneous.
On top of all of this, I can also say that in my own, personal observations, more screws fail by just breaking at the minor diameter, somewhere near the first engaged thread. Both the internal threads and the external threads are usually stronger than the core of the screw below the minor diameter.
One thing to note is that you will need to balance shear and tension. As others have mentioned, a smaller (finer) threadform will remove less material from the fastener than a coarse one. This gives you more tensile carrying capacity in the fastener. The threads themselves, however, are loaded in shear. The calculation for that is based upon the area of the roots of the threads, on both the male and female side. If the materials are dissimilar, you need to use the weaker one. Most often the female is chosen to be softer than the male, for reasons I can't quite dredge up without my copy of the Machinery Handbook out.
Having more of these teeth doesn't always translate to having enough strength because of elastic deformation! If I remember correctly, 90% of the load is carried by the first three threads, and 99+% by the first seven. If you exceed the shear strength of the teeth, the failure will cascade down the fastener, three threads at a time, and you will strip it out.
When did this become an engineering forum, anyway?
