STABILITY OF RODS WITH INITIAL IMPERFECTIONS IN THE FORM OF ECCENTRICITY OF LOAD APPLICATION UNDER LINEAR AND NON-LINEAR CREEP CONDITIONS

Abstract

Stability of a compressed rod having initial imperfections in the form of eccentricity of applied load under conditions of linear and nonlinear creep is considered. It is noted that all real elements have some initial imperfections in the form of technological deflections, eccentricities of applied loads, etc., so they begin to bulge from the very beginning of loading. Another important factor in stability theory is the consideration of material creep. In this regard, the loading process is divided into two phases: the instantaneous loading process and the creep phase under constant external load. Moreover, creep can be time-limited or unrestricted. In the paper formulas for determination of critical forces of stability loss of the rod having initial imperfections, under short-term and long-term action of load are obtained. The equation allowing to determine time of the first crack appearance is derived. Derived are equations the roots of which are loads at action of which the first cracks appear at initial moment of time and at arbitrarily long period of load action. Analysis of acting force determining the character of rod deformation is executed. From the constructed stability equation it is possible to determine the critical force corresponding to the critical length of the section with cracks. For similar problems in nonlinear formulation formulas for determining critical force and critical displacement corresponding to maximum load are obtained. For the case of long duration load the equation which establishes relationship between load and displacement is obtained. Equation for determination of critical force under prolonged action of load has been derived. It has been established that critical displacement is the same under short- and continuous action of load. It is shown that at any intermediate moment critical displacement can be achieved under load lying in certain interval. Keywords: stability, rod, initial imperfection, eccentricity, linear creep, non-linear creep, critical force, crack, critical displacement.