External Pressure Loading of Spiral Paper Tubes: Theory and Experiment

Abstract

A closed-form elasticity solution is developed to predict stresses and strains in spiral paper tubes loaded axisymmetrically. No assumptions are made on stress distributions through the tube wall. Thus, the solution is valid for thick-walled tubes. The validity of this solution is established by comparison with experimental results. Measured strains in tubes subjected to external pressure showed remarkable agreement with the elasticity solution. After experimental verification, the elasticity solution is used to examine stress distributions in paper tubes loaded in external pressure. In both paper and isotropic tubes, the hoop stress dominates the other three stresses. However, the hoop stress distribution in paper tubes was radically different from the isotropic case. In paper tubes: (1) hoop stress was concentrated at the outer wall, especially for thicker tubes and (2) maximum hoop stress remained constant as tube thickness was increased. These differences can be attributed to the extremely small modulus in the radial direction of a paper tube. The hoop stress distributions indicate that isotropic, thick-walled cylinder theory is inapplicable for modeling paper tubes.