FEATURES OF BENDING OF CURVILINEAR ABSOLUTELY ELASTIC BARS

Abstract

In construction mechanics, the linear theory of bending is used to calculate deflections of beams. It gives an approximate result, but it is quite acceptable for practice, since the deflections of the beams are small compared to their length. In the case of significant deflections of the rods, when the curvature of the elastic axis is significant, a nonlinear theory is used. It is based on the position of resistance of materials, according to which the curvature of the elastic axis is directly proportional to the applied moment and inversely proportional to the stiffness of the rod. Such types of elastic bending are present in agricultural tillage equipment. Thanks to the elasticity of the rods, which can be working bodies or connect the working bodies to the frame of the machine, pulsating loads are extinguished. Bars in the free state can have an initial curvature of the elastic axis, which can be constant or variable. One end of the rod is rigidly attached to the machine frame, and the other is under the influence of the applied force. If the curvature is constant, that is, the elastic axis of the rod is an arc of a circle, then the deformation will be the same regardless of which end of the rod is attached to the frame. For rods with a variable curvature of the elastic axis, this is important. The following cases are considered in the article, corresponding calculations were made on the basis of which the shape of the elastic axis of the rod after its bending was found. Curvilinear rods of variable curvature have a different value at the ends. In this regard, the shape of the elastic axis under the action of the tracking force of the pinched rod will depend on which end it is pinched. The moment under which the elastic axis of the rod is deformed depends on the shoulder, that is, on the length of the arc of the elastic axis.The length of the arc of the curve can increase only in one direction from the reference point. If the rod is clamped at the opposite end, then the direction in which the shoulder grows, i.e. the length of the arc, must be changed. For this purpose, a method of solving this problem is proposed, which allows you to take any section of a curved rod and examine it for bending by the following force when one or the opposite end is pinched.