Bending of Curved Tubes

Abstract

Publisher Summary This chapter analyzes bending of curved tubes. In 1910, A. Bantlin found, experimentally, that a curved tube is much more flexible in bending than a straight tube of the same cross section. The following year Von Karman gave a theoretical explanation of this phenomenon. Briefly, for a curved tube, there is a tendency for the cross section to flatten because of the continual change of direction of the stresses, which are parallel to the center line of the tube and which balance the applied moment. When flattening takes place, the strain in the outermost fibers of the tube, for a given change of curvature of the center line of the tube, is less than it would be if there were no flattening of the cross sections. Consequently, a smaller bending moment is required to produce a given change of curvature. This chapter presents equations for bending of a tube with uniform circular cross section. Trigonometric series solution for the tube with uniform circular cross section is presented. The equations for bending of a tube with uniform elliptical cross section are also discussed.