Torsion of beams whose sections are bounded by certain quartic curves

Abstract

C auchy integral methods are applied to the torsion of a solid isotropic cylinder whose section is bounded by a quartic curve which is the inverse of an ellipse with respect to any point on its major or minor axis. The complex torsion function, the torsional rigidity and the shearing stresses are explicitly determined in the general case, and particular values are found to agree with those already known for Booth's lemniscate and the elliptic limacon. The distribution of shearing stress on the boundary is computed in two particular examples.