抄録
Circular plates are often used to connect a number of chords for steel space trusses. Although they are subjected to compressions and/or tensions on the circumferences, neither their stress distributions nor maximum stresses are available on any handbooks or mannuals. To provide useful data for design, this paper discusses the stresses for circular plates by Fourier series expansion technique. By expanding a external load distribution to a Fourier series and using Airy's stress function in the polar coordinates the stresses are obtained. For two tensile and two compressive loads alternately working on the plate as depicted in Fig. 1, there is a pure shear with τ_<γθ>=1.27 P/a at the center of the plate, providing P is the magnitude of the load at one place. For external load distributions shown in Figs. 3, 5 and 7, the maximum shear stesses are 1.0 P/a, 1.1 P/a and 1. 2 P/a, respectively. By their magnitudes the thicknesses of the plates are determined in structural design. Those plates simply submitted to tensions or compressions represented in Figs. 9, 11 and 13 have only small shear stresses, which are not important in the sense of design. The normal stresses, ar and ag, at the centers are obtained by dividing the total magnitudes of the external loads, ΣP, by the whole lenghts of the circumferences. From the photoelastic experiments the stresses for polygon plate are found close to those for the circular plate with the average radius of the inscribed and circumscribed circles.
