Engineering Transactions, 13, 2, pp. 281-296, 1965

### Stan Graniczny Rury Grubościennej przy Jednoczesnym Skręcaniu, Rozciąganiu i Różnicy Ciśnień

J. Skrzypek
Katedra Fizyki I Katedra Mechaniki Technicznej Politechniki Krakowskiej
Poland

M. Życzkowski
Katedra Fizyki I Katedra Mechaniki Technicznej Politechniki Krakowskiej
Poland

This is a detailed analysis of the limit state of a thick-walled tube in a triply combined case loading, namely with a torque, a pressure difference and a longitudinal force.
General equations describing the limit state of a thick-walled tube are established in [10] for a more complex case of combined tension or compression, torsion, radial inner and outer pressure, and circumferential axial and shear loadings.
However, a discussion of particular cases and examples of numerical computation have not been given in either the paper mentioned above or in [11], in which the above problem is generalized by adding thermal loads and mass forces. In the present publication, the formulae obtained are adapted (shear loadings being disregarded) for numerical computation by reducing all the integrals involved to normal elliptic integrals. All the quantities involved are expressed in dimensionless form.
On the basis of the expressions obtained for the pressure difference, longitudinal force and torque examples of numerical computation are given. The limit curves are presented in the particular cases of
a) combined longitudinal force and pressure difference,
b) plane state of strain,
c) combined torque and pressure difference with no axial force.
All the computations have been performed using tables of elliptic integrals of V.M. BELAKOV, R.I. KRAVCOWA and M. G. RAPPOPORT [1]. The diagrams have been performed assuming for the ratio of diameters, ß = 1/2.

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#### References

[in Russian]

P. F. BYRD, M.D. FRIEDMAN, Handbook of elliptic integrals for engineers and physicists, Springer-Verlag, Berlin-Göttingen-Heidelberg 1954.

[in Russian]

[in Russian]

J. E. PANARELLI i P. G. HODGE, Interaction of pressure, end load, and twisting moment for a rigid-plastic circular tube, Transaction of the ASME-Series E, J. Appl. Mech., 3, 30 (1963), 396-400,

[in Russian]

M. WNUK, Stan graniczny pręta jednocześnie skręcanego i rozciąganego przy dowolnym kształcie przekroju, Rozpr. Inzyn., 3, 10 (1962), 565-581.

M. WNUK, Przykłady obliczania krzywych nośności granicznej, Rozpr. Inzyn., 4, 11 (1963), 611-634.

M. ŻYCZKOWSKI, Przypadek jednoczesnego rozciągania i skręcania pręta o przekroju kołowym

W zakresie sprężysto-plastycznym, Rozpr. Inzyn., 2, 3 (1955), 285-322.

M. ŻYCZKOWSKI, The limit load of a thick-walled tube in a general circularly symmetrical case, Arch. Mech. Stos., 2, 8 (1956), 155-178.

M. ŻYCZKOWSKI, Certain general formulae for plane circularly symmetric plastic states, Arch. Mech. Stos., 4, 10 (1958), 463-478.