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I'm working with a design team to take quick and accurate measurements of the middle upper arm circumference in third world countries to assess malnutrition in children. One of the issues in taking measurements is people pulling variably on the tape measure around the arm. My team and I were trying to figure out if we made a device that applied the same amount of tension to a band around the arm, would it cause a different compressive force for different sized arms (out intuition is yes because the force would be spread out over a larger area). The real question is if the difference in compressive force is significant in affecting measurements.

So we tried to calculate the compressive force of a band around a cylinder with one end of the band fixed and the other end pulling with a tangential force to the cylinder and weren't able to find any equations defining this. The closest we got was circumferential hoop stress.

Anyone have any clue how we might calculate this?