The author mentioned in his Main Lecture(1) the success achieved in the analysis of three-dimensional media, for small and large displacements, as well as anisotropic and non-elastic behaviour, by the introduction of tetrahedron elements of constant strain and stress(2), see also technical note 1 of this series(3). A cardinal point of the theory is the specification of natural strains, stresses and stiffness. At the same time attention was drawn to certain difficulties arising in the interpretation of the stresses at the nodal or other points, which are more severe than for constant strain triangles, the corresponding elements in the two-dimensional case. It was suggested in the lecture that a considerable improvement might be achieved by the specification of a linearly varying strain or stress state within the tetrahedron. The solution of this problem, limited to small displacements, is summarised in this fifth technical note and its application is to be demonstrated on an example in the printed lecture.

Of the Several Methods available for the measurement of boundary shear, the simplest is perhaps the Preston tube. It is a total head tube resting on the boundary for which the difference between the dynamic pressure on the tube and the static pressure on the boundary is correlated with the boundary shear. It was evolved by Preston in 1954 mainly from similarity considerations and the existence of the wall law. In 1955, Hsu obtained Preston's original calibration curve theoretically for the one-seventh power law. In this note, a theoretical calibration curve is developed for the logarithmic law which describes the velocity distribution for larger Reynolds Numbers.

“The Rank Technique” is a method for automatic selection of redundancies in the Matrix Force Method. The method was developed for the complete linear analysis of general plane frames, but is equally applicable to other forms of two- and three-dimensional configurations whose state can be expressed as a system of linear equations. An attractive feature of the method is that the structure is systematically and automatically investigated to determine its basic characteristics. The first point considered is whether the structure is stable or unstable for the prescribed load conditions; if stable, whether determinate or redundant and if redundant, the degree of redundancy. A consistent set of redundants is automatically isolated. For general structures the technique automatically generates the basic and redundant load systems in an indirect manner which can be made readily available, if required. The initial development of “The Rank Technique” was carried out in collaboration with Robert R. Regl and is given in reference 1.

The Familiar process of dimensional analysis for aerodynamics equates a force to a function of several variables liable to affect it, in terms of the dimensions M, L, T, and yields the numbers known as the Reynolds number and the Mach number of the flow. These numbers are generally regarded as useful and sufficient means of denoting the regimes of flow in conventional circumstances, where the force developed on a body results solely from the relative motion between the body and a mass of fluid.