No coffee yet, but I'll give this a go. I'm no instrumentation engineer but, I've been around it a bit, albeit many many years ago. My wife should actually be doing this, as she is actually a test engineer and uses these devices regularly. Those of you that know better, please be gentle.
The strain gage is a thin piece of plastic. There is a super thin electrical circuit laminated in the gage that is energized with very small amount of voltage and measured on the output side of the circuit. When they stretch/compress, they change the resisitance of the circuit and the output voltage changes in a predictable and highly repeatable level. Strain gages are calibrated individually, I assume by stretching them a predetermined amount and measuring the change in output voltage. It is this technology that many electronic scales and other electronic force measurement devices use.
Metals stretch and compress then return to shape. This is known as elastic deformation. If metal deforms too much it does not return to the original shape and it's called "plastic deformation" or "yielded", past the yeild point, etc.. What we're interested in on our guns is elastic deformation. Each time you fire your gun, the barrel expands, the frame opens up a bit, etc.. We want to measure how much the barrel expands around the cartridge and then convert that to pressure of the cartridge. Kind of a ass backward way for a typical engineering project. Normally, an engineer knows the metal composition and strenth and fatigue characteristics and then wants to gather strain data and convert it to stress data. Stress is a measurement of applied force over an area of the metal. For example, a 1 square inch bar of metal stretched with 35,000 pounds would have 35,000 psi stress. An engineer may know that his steel being tested can sustain essentially unlimited cycles of stress up to say 35,000 psi without fatigue cracking. If his part will see a high number of cycles, he will want to stay below a certain stress level known to take unlimited cycles without cracking, just like we do with barrels.
With Bill's setup, the barrel wall is measured accurately in the location he wants to measure pressure. The inside diameter of the chamber is measured at that location, as well as the outside diameter. The wall thickness and diameters are input to a program and when the gun is fired, the device measures the stretch of the area and then converts it back to the force required to stretch it that much.
The strain gage only works accurately because metals behave very predicably. They stretch a known amount under a given load. Steels of a variety of alloys behave very similarly to each other. That is why we can stick a straingage on a gun of somewhat known steel alloy and have it be accurate.
So, a recap.
Strain gages measure stretch. They are calibrated individually by the maker by stretching them and measuring voltage change. We glue them on the chamber. they measure the stretch, then the device Bill has calculates the internal pressure required to stretch the chamber that much.
I either forgot a lot of stuff or gave too much info for some.