EdgeDistance,
The fastener load value of 187 lbf comes from the matrix solution to a set of simultaneous equations representing the fastener and plate element set up.
I am assuming you are referring to Swift's paper "Repairs to Damage Tolerant Aircraft" where he gets an example load of 187.2 lbf.
In an idealized strip, as you pointed out, some of the displacements have to be equal. For example if you look at Figure 3 of that paper, the displacement of skin element 4 must be equal to the displacement of fastener 4. We also know that the loads in the final element of a skin or doubler must be equal to the end fastener load (for the simple idealized Swift example). We also can say that a bypass load in an interior element must be the same as the load in a preceding element of the same part, less the intervening fastener load.
These things help us set up a system of constraining equations. The displacement compatibility is based on the compliance or stiffness of each element. Swift came up with his own equation for fastener stiffness. The resulting system of linear algebraic equations for a three row single shear joint looks like this (keep in mind this is a simple joint case):
You would have to expand this for additional parts and fasteners, but you get the idea.
Subscripts - "S" is for skin layer element, "F" is for fastener, and "R" is for repair layer element. These equations just come from the displacement equations. Try it yourself by calling the displacements delta = P*c where c = L/(A*E) for a plate. For a spring (fastener element), c comes from the swift equation. Then isolate P in each of your displacement compatibility equations and you should end up with a system like above.
To solve for Pf1, Pf2, and Pf3, you need to solve the system which is easiest with linear algebra. You will need to take some determinants.
Keep em' Flying
//Fight Corrosion!
