The Torsion Problem of Curved Beams

Abstract

Given a beam in elastic equilibrium whose mean fibre is a continuous curve and which is acted upon by couples of arbitrarily directed axes, the problem which we set is to determine: I. The system of forces acting on any section normal to the mean fibre. II. The stresses existing in this section and the limiting of those stresses. Determination of the forces acting on a section.-We first consider a section ABC of a plane curved beam represented in Fig. 1, by its mean fibre, with a torsional moment applied at A in a plane normal to the mean fibre. The moment applied at A is represented by the vector AA' following the ordinary conventions of mechanics. To determine the forces acting on a Section B normal to the mean fibre at B, we prolong AA' until it intersects the trace BD of the section. At D we carry DD' = AA' which we decompose, in conformity with the de St. Venant principle of elastic equivalence of statically equivalent systems, into its components DD' and DD"', tangential and normal, respectively, to the trace BD. Then the vectors

A Look at an Old but Still Current Problem

“…From 1925 on, however, a change occurred and a new concept for the chem ical regulation of respiration had to be considered. J. F. and C. Heymans (35,36) showed, indeed, that chemoreceptors peripherally located in the aortic arch area act reflexly on the respiratory centre. Perfusing the isolated head of a recipient dog by means of a donor dog, the perfused head being connected with the body of the recipient by means of the vagus nerves only, these investigators observed that asphyxia or anoxia of the body of the re cipient induced a reflex stimulation of the respiratory centre of the perfused head.…”

Untitled

“…From 1925 on, however, a change occurred and a new concept for the chem ical regulation of respiration had to be considered. J. F. and C. Heymans (35,36) showed, indeed, that chemoreceptors peripherally located in the aortic arch area act reflexly on the respiratory centre. Perfusing the isolated head of a recipient dog by means of a donor dog, the perfused head being connected with the body of the recipient by means of the vagus nerves only, HEYMANS these investigators observed that asphyxia or anoxia of the body of the re cipient induced a reflex stimulation of the respiratory centre of the perfused head.…”