Calculation Method of Straight Unsupported (Freely Deformable) Bars Subjected to in Plane Bending Stress

Abstract

This paper describes a method of determining the cross section arrows and rotations of a straight unsupported bar subjected to bending stress. The straight bar is in a state of static balance while subjected to external loads and not resting on any external point. The calculation relations obtained enable the specialists to determine both the rotation and the displacement of all the cross sections of a straight unsupported bar, which occur further from the external in-plane bending loading. Please note that these displacements are calculated against the initial position of the straight bar. When the exterior bending stress starts to be higher than zero, the unsupported bar is in a continuous static balance and it bends continuously until the exterior load reaches its highest value. According to the method described hereunder, the arrow and rotation are calculated for this last bar position. The same method is also employed to determine the positions of the cross sections that do not undergo any displacement from their initial position. Along the whole straight bar, these sections are at least two.