Critical Plastic Bucking Parameter for Tubing in Bending Under Axial Tension

Abstract

INTRODUCTION Buckling of tubing with moderate diameter to thickness ratios subjected to pure bending, does not take place in the elastic range but occurs by local rippling on the compressive side of the tubing after yielding has taken place. A recent paper by Wilhoit, Merwin, and Jirsa (1) presents a theoretical method of predicting the curvature and wave length at buckling in the plastic range for pure bending and compares theoretical results with previously measured experimental results for full sized pipe. This paper builds upon a solution by Gerard (2) for plastic yielding of thin-walled cylinders in compression using the Ramberg-Osgood (3) representation of the stress -strain curve in pure tension. Wilhoit and Merwin (4) extended a procedure developed by Ades (5) to predict the moment- curvature relationship in both the elastic and plastic ranges for tubes subjected to bending plus axial tension. The present paper extends the theoretical results of reference (1) to the case of bending with axial tension by using the technique developed in reference (4). Since reference (1) bases buckling on a critical strain on the compressive side of the tubing, it was only necessary to use the method of reference (4) for each case investigated to find the curvature corresponding to the critical strain. Thin walled welded steel tubing 2½ inches in diameter with diameter to thickness ratios from 35 to 83 were tested in a loading frame built to allow a bending load to be superimposed on an axial tensile load. Theoretical and experimental results are compared. TEST SPECIMENS All test specimens were obtained from round welded mechanical tubing MT-1010/202½ inches in diameter with nominal thickness 0.065 and 0.049 inches. Test specimens approximately 20 5/8 inches long were cut to fit into the loading frame. From the 0.048 inch tubing (the actual thickness of the 0.049 inch nominal thickness tubing was 0.048 inches while the actual thickness of the 0.065 nominal thickness tubing was 0.069 inches), specimens with average thickness of 0.036 inches and 0.029 inches were machined. In order to make these thicknesses of 0.036 inches and 0.029 inches more nearly uniform eight inch lengths of the .048 inch tubing were inserted into special mandrels and then machined to size. These turned down lengths were then welded to.048 inch tubing end pieces to form the test specimen. Thicknesses were still found to vary considerably for these turned down specimens and average thicknesses after testing were ultimately used. It should be noted that tubing of 0.069 inch thickness was used for three tests while tubing originally of thickness 0.048 inch was used for the other nine tests.