Torispherical Shells under Internal Pressure—Failure due to Asymmetric Plastic Buckling or Axisymmetric Yielding

Abstract

In the diameter-to-thickness range 250 < D/t < 1000, internally pressurized torispherical shells can fail either by plastic buckling or by axisymmetric yielding. However, the present Code rules cater only for the axisymmetric yielding mode and they also restrict the D/t ratios to being less than 500. The rules are based on limit analysis results and these can be conservative for this problem. With regard to internal pressure buckling, there are as yet no design rules in either the American or the British pressure vessel Codes to prevent its occurrence. To provide guidance for a more accurate formulation of design rules for both of these failure modes over the range 300 < D/t < 1500, the authors have made a series of calculations to determine the values of Pcr (the internal buckling pressure) and pc (the axisymmetric yielding pressure) for perfect torispherical shells. The availability of these results, obtained with a finite-deflection shell theory, enables curves to be drawn showing when buckling is the controlling failure mode and when axisymmetric yield controls. A comparison is also made, for D/t < 600, between the controlling failure pressures mentioned above and the Drucker-Shield limit pressures. The ratio between the former and the latter varied between 1.2 and 1.8, depending on the geometry of the shell and the magnitude of the yield point, σyp. Considerable economies in the designs of many torispherical shells could, therefore, be achieved if the relevant sections of the Codes were to be modified to take advantage of the foregoing results. The controlling failure pressure curves also indicate how Code rules to prevent plastic buckling for D/t > 500 might be formulated. For the benefit of designers, the numerical values of pcr and pc were transformed, using curve-fitting techniques, into simple approximate equations. Although these equations are for perfect torispherical shells, they should be very beneficial when analysing the related problems of fabricated torispheres in practice.