problem: A load cell based on a “proving ring” is shown below. The circular portion of the load cell has an inner radius of 1.25 in and outer radius of 1.50 in. The ring has a depth (i.e., thickness) of 0.50 in, and is made of 2024-T4 aluminum (E = 10.6 Msi, ν = 0.32).  Four identical uniaxial strain gages (gages G1 - G4) are bonded to the ring at the locations defined in Figure below, and wired together in a Wheatstone bridge as shown in Figure below. The cell is designed to measure tensile loads ranging from 0 to 200 lbf.

Predict the output of this load cell based on “Curved Beam Theory” (reviewed on the following page), assuming a gage factor of 2.00.  

Figure: Strain-Gaged Proving Ring (Gage Numbers Circled)

Figure: Wheatstone Bridge