Correction of an error in equations for extended ring transducers

A set of analytical equations were derived for the bending moment in an extended ring transducer in a previous article published in the Transactions of the ASAE in 1975. These equations are sometimes used as an approximation for bending moment in an extended octagonal ring transducer. The final equation for bending moment in the left-hand ring contains several typographical errors including an incorrect sign which is not readily obvious, and will result in incorrect bending moment calculations under certain loading conditions. The present article identifies the error, and provides the corrected final equations for bending moment in the ring sections. A qualitative check on the equations is made by comparing the sign of the bending moment predicted by the equations determined from elementary mechanics.