HOOP STRESSES AND ORTHOTROPIC BEHAVIOR-THEORY FOR UNIAXIALLY COMPRESSED CYLINDERS

The classical theory for axially compressed cylinders was in structura l error mainly in evaluating the hoop stress and in computing the flex ural rigidities for different shell directions. The aim for this inves tigations is to correct the structural errors in the classical theory, apply these structural fundamentals to the equilibrium equation for a xially compressed cylindrical shell and explain its mathematical deriv ation. The present investigation proves that the hoop stresses exist o nly in the prebuckling state and has no existence after forming the in itial circumferential buckling even at the final longitudinal buckling . This paper also proves that shells are orthotropic structures its fl exural rigidities are related to the flexural rigidities of the buckli ng mechanism at failure. Consequently the equilibrium equation in the orthotropic form applied successfully to the axially compressed cylind er and solved in terms of shell coefficient H, this shell coefficient is related to the shell effective width. By comparing the theoretical results to previously published experiments it was found that the shel l coefficient is constant for shells in elastic region, its value affe cted by method of manufacture and method of load application. While fo r thicker shells in plasto-elastic region it was found that the shell coefficient H varies linearly with the radius to thickness ratio, the slope of this linear relation is related to the method of manufacture and the constant term is related to the method of load application. Fo r ''near-perfect'' thin cylinder it was found that the higher stresses are obtained due to reduction of the circumferential wave number or i ncrease in the axial half wave number. At the end numerical examples f or the application of this method are given.