An Elastoplastic Analysis of Uniform Bars with Initial Deflection under Opposite Tension Loads at Ends (Report 1)

Plastic Region Being Not on Compression Side

Abstract

In this paper the elastoplastic analysis of uniform bars with initial deflection under opposite tension loads at the center of both ends is presented.
It was found that the problem is too complicated to examine fundamental aspects of behavior of such bars, because of the transcendental implicit result from the strict solution, the derivation of which is described in Appendix.
Whereas the column problems under axial compressive load have been investigated by many researchers, in those cases an approximate method where the equilibrium is considered only at the midpoint of the bar, contributed considerably to clarify the features of the problem with sufficient accuracy.
We applied the same approximate approach to get the solution showing clearly the behavior of uniform bars initially curved and subjected to opposite tension loads at both ends.
It is remarkable that in cases where the initial deflection and the slenderness ratio are restricted in some limit, only one side of bars becomes plastic before the entire cross-section reaches the ultimate state of uniform tensile stress along the total length of the bars, although the change of stress distribution is rather complicated These cases are treated in this report.
The remaining cases where both sides of bars become plastic and consequently the unloading in the plastic region must be considered, will be reported in the forthcoming papers.