Engineering Transactions, 4, 4, pp. 443-456, 1956

W Sprawie Doboru Optymalnego Kształtu Prętów Osiowo Ściskanych

M. Życzkowski
Instytut Podstawowych Problemów Techniki PAN
Poland

The problem of the most suitable form for axially compressed bars subjected to Hooke's law (i.e. undergoing elastic deformation) has been tackled by many investigators. The. results obtained have not found direct application in engineering practice because the cross-sectional area of the free end for a bar built-in at one end, or the cross-sectional area of each of the ends of a bar resting on two hinged supports should tend to zero. This would cause an indefinite increase of stress and a deviation from Hooke's law. In solving the problem of the most suitable form for a compressed bar it should therefore be assumed that the buckling will be elastic-plastic.
This problem is solved in the present paper from the point of view of practical requirements, limiting oneself to the choice of the best taper for a uniformly tapered bar (pyramid or cone), the variational problem being thus replaced by the problem of the extremum of a function of one variable. The results of the author's paper [10] giving the values of critical forces for elastic-plastic buckling of such bars, calculated by means of Ylinen's theory, are used. The results of the paper are represented in Diagr. 2 and Table 4 enabling the determination of the best taper and dimensions of the bar and showing that the possibilities of material economy and weight reduction depend on the «plastic characteristic» of the bar determined by Eq. (3.3). Using Diagr. 2 and Table 4 a numerical example is solved.

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