Computer tables of torsional rigidity for convex cross-sections
Faculty of Computing, Health and Science
School of Engineering
The last decade has seen the implementation, in mathematical software, of „tables‟ for engi-neers, e.g. Mathcad‟s „Roark‟s Tables of Stress and Strain‟ (released 1994) and Mathematica‟s „Structural Mechanics Pack‟ (released 1997). Along with the commercial products, there is modest „open-source‟ effort: see http://www.maths.uwa.edu.au/~keady/torsionCAS.html Let D denote the cross-section of a beam. The obvious way to find numerically the elastic torsion function for a shape D (and thence the torsional rigidity of D) is via one of the several boundary integral methods and this has been done for at least three decades. We compare old and recent implementations. The Computer Algebra capabilities of Mathcad or Mathematica enable verifications of the exact formulae, coding up or derivation of mathematically proven bounds, and more. In this paper we illustrate the cross-checking of numerics and bounds, using isosceles triangles – and entries in Roark‟s Tables - as the main example.