Journal of Engineering Mechanics

The two widely used methods of finite‐difference viscous‐flow calculation, the vorticity transport and primitive variable approaches, are applied to the analysis of flow through a plane short‐radius bend flanked by sections of straight conduit. Additionally, the vorticity transport method is employed in a direct (using combined rectangular and polar coordinates) and an indirect calculation (using a nonorthogonal coordinate transform). The solution for all three methods are found to be in essential agreement at a Reynolds number of 72. Because of the sharp curvature, the primitive variable method required pressure adjustment using a Poisson equation; velocities were adjusted by the divergence equation and advanced in time by the momentum equations. For the short‐radius bend, the matching procedures involved in the primitive variable approach were found to be crucial in developing smooth field transitions from one coordinate system to another. The adjustment of the coefficients in the transform vorticity transport method for the same regions (but not along the junction lines) were easily made and the comparisons with results from the other methods were excellent.

The problem studied in this work is that of a uniform, uniaxial tensile load applied to an infinite body with a smooth, circular rigid inclusion. The body surrounding the rigid shaft is a linear elasto‐plastic, work‐hardening material. The aluminum alloy, 2024 T4, is used to characterize the material parameters of the infinite body. The problem of analysis of displacements, stresses, and strains in elements made of this body subject to arbitrarily large deformations under the conditions of plane strain is formulated in terms of the finite element method. The constant strain triangular element is used. The method of solution to this problem may be applied to any other cylindrical shape of the rigid inclusion in the infinite body.

The theory of stochastic processes is applied to the problem of stress transmission through granular media. Earlier work on this topic is critically reviewed and a general theory is proposed which may prove capable of providing useful information about stress distributions in particulate media, though it is incomplete in its present state. The theory, at least in its current form, is linear, and it generalizes earlier theories of this kind. Like them, this theory can, at least qualitatively, give better agreement with the measured distribution of vertical stress than linear elastic theory, though the Boussinesq and Flamant results can also be incorporated into the proposed scheme. The condition that no tensile stresses exist can also be imposed in a natural manner.

The dynamic behavior of rigid‐block structures resting on a rigid foundation subjected to horizontal harmonic excitation is examined. For slender structures, the nonlinear equation of motion is approximated by a piecewise linear equation. Using this approximation for an initially quiescent structure, safe or no‐toppling and unsafe regions are identified in an excitation amplitude versus excitation frequency plane. Furthermore, several possible modes of steady‐state response are detected, and analytical procedures are developed for determining the amplitudes of the predominant modes and for performing stability analyses. It is shown that the produced stability diagrams can be beneficial to assessing the toppling potential of a rigid‐block structure under a given amplitude‐frequency combination of harmonic excitation; in this manner the integration of the equation of motion is circumvented.

The Sydney Tower, the tallest building in Australia, is 820ft (250m) high and with the base of the structure anchored on the roof of a 15 storey building, it stands 1000ft (305m) above street level. The tower is one of the first buildings with the installation of a large scale tuned mass damper (TMD). The doughnut-shaped water tank near the top of the turret, which normally serves as the tower's water and fire protection supply, was incorporated into the design of the TMD to reduce wind-induced motions. Energy associated with relative movements between the tower and the water tank is dissipated by 8 shock-absorbers installed tangentially to the tank and anchored to the floor of the turret. A secondary TMD of similar design was later installed on the intermediate anchorage ring to further increase the damping level, particularly in the second mode. Full scale measurements were taken to determine the natural frequencies of vibration and damping. Dampings of the tower were determined for different damper configurations. The natural frequencies of vibration were found to be 0.10 Hz and 0.50 Hz for the first mode and second mode respectively. Significant increases in damping levels, particularly in second mode, are produced by the water tank tuned mass damper and the secondary damper.

This paper is concerned with the optimal shape of cables subject to external loads only. Design-dependent loads (e.g. selfweight) are assumed to be negligibly small. Consequently, the cable axis is given by the funicular for the prescribed loads. However, the equilibrium condition still admits an infinite number of solutions, each of which is associated with a different value of horizontal support reaction. Using calculus of variations, a necessary optimality condition for minimum volume (or weight) is derived which eliminates all other possible solutions except for the optimal case. On the basis of this optimality condition, a general procedure is developed to construct the optimal shape of the cables and it is applied to some examples for illustrative purposes.