Engineering Transactions, 14, 4, pp. 629-652, 1966

### Stan Graniczny Wirującej Rury Grubościennej w Niektórych Złożonych Przypadkach Obciążenia

J. Skrzypek
Politechnika Krakowska
Poland

A number of new solutions are given for combined loads of thick-walled tube with special consideration of the mass forces resulting from steady or non-steady rotation. In the quadruple case of combined normal pressure, longitudinal force, torque and radial mass force the equations of the limit surface (3.6) (3.8) (3.10) and (3.11) are derived. The solution is ex- pressed in terms of elliptic integrals reduced to the normal form. In particular, the combination of a torque and a mass force may be of practical importance, because if the tube rotates it is acted on as a rule by a torque. Solution is obtained with the assumption of 1) plane strain, (4.7) and (4.8), 2) no axial force, (4.18).

In both cases simple approximation formulae of the Hermitian type (4.15), (4.25) are also given thus enabling the computation of a limit curve with sufficient accuracy.
The mass forces produced during non-steady rotation are taken into consideration together with the tangential (circumferential) and normal (radial) pressures. Plane strain is assumed. The final equation (5.15) is given, as before, in a form suitable for numerical computation, expressing all the quantities in a dimensionless form. The validity range of the solutions obtained is also discussed assuming that the limit load is reached in the entire volume of the material (volume destruction). For the curvilinear part of the limit curve obtained in this manner (Fig. 6) a convenient approximation relation is given, (5.32).
On the basis of the approximate solution (6.1) the optimum starting process of the cylinder is discussed assuming that the limit load is reached. For all the problems discussed examples of numerical computation are given as well as examples of drawing of the limit curves.

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