Torsion of beams of ⊥- and ∟- cross-sections

Abstract

The problem of the torsion of beams of ⊥- and L-cross-sections has received attention from very few authors despite its important technical applications. The first mathematical solution in this connection was obtained by F. Kötter in 1908 for an L-section both of whose arms are infinite. He attacked the problem by the use of the known solution of the rectangle and by application of the scheme of conformal transformation. Kötter's method, however, does not lend itself readily to the solution of the problem involving more than one re-entrant angle. The first solution for the torsion of a beam whose cross-section is a rectilinear polygon of n sides was published in 1921 by E. Trefftz who also applied his method to an infinite L-section. Recently I. S. Sokolnikoff has suggested a more general method depending upon the fundamental theorem of potential theory that a harmonic function is uniquely determined by the values assigned along the boundary of the region within which the harmonic function is sought, the boundary condition and the region being subject to certain well-known assumptions of continuity, connectivity, etc. As an illustration of his method he has given an approximate solution for a ⊥-section whose flange and web are both infinite.

Review of Integral Experiments for Minor Actinide Management

“…Spectral indices such as fission in 237 Np (F7) over fission in 239 Pu (F9) and capture in 237 Np (C7) over fission in 239 measured in two core configurations labelled "reference" and "moderated" [49]. In the reference configuration, the test zone of PROTEUS was loaded with a regular hexagonal lattice of PuO2/UO2 fuel rods containing 15% plutonium [50]. The median energy was about 185 keV.…”

The Torsion of Elastic Cylinders with Regular Curvilinear Cross Sections

“…Bibliographies dealing with the subject are to be found in [1]*, [2], and [3]; the last reference brings together a considerable amount of the existing knowledge pertinent to this area of elasticity theory.Complex variable methods have been applied to obtain solutions for the problem by several authors. Using the Schwarz-Christoffel transformation Seth [4,5] has investigated the torsion problem for various regular rectilinear polygons as well as the torsion of beams of -Land L -cross sections. The case of a cylinder whose cross section is bounded by two circular arcs has been considered by I. S. and E. S. Sokolnikoff [6].…”