A review of simple formulae for elastic hoop stresses in cylindrical and spherical pressure vessels: What can be used when

Abstract Classical simple formulae for elastic hoop stresses in cylindrical and spherical pressure vessels continue to be used in structural analysis today because they facilitate design procedures. Traditionally such formulae are only applied to thin-walled pressure vessels under internal pressure. There do exist, however, some variations of these formulae that remain simple yet permit wider use. Here, by reviewing various underlying rationales for simple hoop stress formulae, we make a determination of when and how well different formulae apply. For the formulae that do apply to thicker vessels than usually recognized, we give companion results for external pressure.

[1]  G. Lamé,et al.  Leçons Sur la Théorie Mathématique de L'élasticité des Corps Solides , 2009 .

[2]  R. V. b. Southwell,et al.  An introduction to the theory of elasticity for engineers and physicists , 1936 .

[3]  S. Timoshenko,et al.  THEORY OF PLATES AND SHELLS , 1959 .

[4]  P. E. Leonard Spiegel,et al.  Applied Statics and Strength of Materials , 1991 .

[5]  Irving H. Shames,et al.  Introduction to Solid Mechanics , 1975 .

[6]  William Bickford,et al.  Advanced mechanics of materials , 1998 .

[7]  Eugene F. Megyesy.  Pressure Vessel Handbook , 1975 .

[8]  A. Ugural,et al.  Advanced strength and applied elasticity , 1981 .

[9]  Henry H. Bednar.  Pressure Vessel Design Handbook , 1981 .

[10]  J. Keith Nisbett,et al.  Shigley's Mechanical Engineering Design , 1983 .

[11]  I. S. Sokolnikoff.  Mathematical theory of elasticity , 1946 .

[12]  H. Lamb.  Statics: including Hydrostatics and the Elements of the Theory of Elasticity. , 2010, Nature.

[13]  R. Budynas,et al.  Advanced Strength and Applied Stress Analysis , 1977 .

[14]  Joseph Edward Shigley,et al.  Mechanical engineering design , 1972 .

[15]  E. A. Avellone,et al.  Marks' Standard Handbook for Mechanical Engineers , 1916 .

[16]  Robert L. Norton,et al.  Machine Design: An Integrated Approach , 1996 .

[17]  Strength of materials : a unified theory , 2004 .

[18]  Steven R. Schmid,et al.  Fundamentals of Machine Elements , 1999 .

[19]  H. Saunders,et al.  Mechanics of Materials (2nd Ed.) , 1986 .