On an Elastic-Plastic Beam with the Rotation Constraint at the Support

The behaviour of the geometrically linear elastic-plastic beam with the rotation constraint at the support is analysed. The problem considered belongs to the mechanics of systems at unilateral constraints. It appears that there exists an optimum value of the support limit rotation which is associated with the maximum elastic strength of the beam. The elastic strength increase requires slackening or prestressing of the structure, what depends on load position on the beam. The analysis of this problem shows the close qualitative relationship between slackening and prestressing of the structure. In the elastic-plastic range the loading and unloading cycle up to the ultima:te load is considered. It appears that after unloading of the beam when the limit rotations are less than the optimal ones there are no residual deflections and stresses. For a larger value of limit rotations the residual deflections ana stresses occur but the stress state after unloading corresponds to that of the reference beam with the optimal rotation constraint. It seems that the observations described in the paper - may be utilized in optimization, identification, shakedown and fatigue strength problems.