Engineering Transactions, 16, 2, pp. 209-231, 1968

Stateczność pierścienia usztywniającego sprężysto-plastyczny walec zginany

J. Murzewski
Politechnika Krakowska

The problem of general instability of a ribbed cylindrical shell has not yet been solved in a satisfactory manner, although many works have been done in this domain, [1, 2, 4, 5, 8, 10,
20 and 21].
The present author's considerations are based on the assumption, that the way in which the: collapse of a ribbed shell is produced, is different than described for isotropic shells in Refs. [13] and [19], and proceeds by stress concentration and plastic strain of the shell at the place of its. connection with a transversal rib. As a complement to the experimental investigations and the simplified analysis of the limit load, published in separate papers, [16, 17], the present work contains a theoretical study of the problem considered. It is concerned with the bending of an: infinitely long tube stiffened by a single concentrated ring, assuming that the structure is isotropic [Eqs. (1.12), (1.13), (1.14) and (1.20)] or orthotropic [Eqs. (3.9), (3.10) and (3.11)].
The solution is based on the differential equations of W. Flügge (1.1) or (3.4) for cylindrical shells. The elastic action of the shell on the ring (1.22) is determined as well as the "second order" action of the vertical components of the membrane forces (1.23) in the case of formation of a plastic hinge along the ring. For such type loads (Fig. 4) the stability of the elastic stiffening ring is analysed. In the case of a regular shell (with no plastic hinge) the critical value of the longitudinal force in the ring is obtained. In the case of formation of a plastic hinge the ring is subject to compressi and bending, (2.15), (2.27). On the basis of these results the behaviour of a bent tube is described in the general case (Fig. 8).
The load limit is marked, as a rule, by the formation of a plastic hinge and the buckling of the shell which produces the collapse of the tube. Only in the case of very strong transversal ribs a thin-walled ribbed shell can become plastic partially or almost completely.

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H. BECKER, Handbook of Structural Stability. Part VI. Strength of Stiffened Curved Plates and Shells, NACA TN 3786. Washington 1958.

H. BECKER, G. GERARD, Elastic stability of orthotropic shells, J. Aerospace Sci., 4, 29 (1962), 105-114.

[in Russian]

L. H. DONNELL, A new theory for the buckling of thin cylinders under axial compression and bending, Trans, ASME, 11, 56 (1934), 795-806.

D. D. DSCHOU, Die Druckfestigkeit versteifter zylindrischer Schalen, Luftfahrtforschung, 3, 11 (1935), 223-234,

W. FLÜGGE, Die Stabilität der Kreiszylinderschalen, Ing.-Archiv., 5, 3 (1932), 463-506.

W. FLÜGGE, Stresses in Shells, Berlin-Göttingen-Heidelberg, 1966.

G. GERARD, Minimum Weight Analysis of Compression Structures, New York 1956.

G. GERARD, Plastic stability theory of geometrically orthotropic plates and cylindrical shells, J. Aerospace Sci., 8, 29 (1962), 956-962.

N.J. HOFF, General instability of monocoque cylinders, J. Aerospace Sci., 4, 10 (1943), 105-114.

[in Russian]

E. KAMKE, Differentialgleichungen. Lösungsmethoden und Lösungen, 5 wyd., Lipsk 1956.

L. H. KARMÁN, H. S. TSIEN, The buckling of thin cylindrical shells under axial compression, J. Aeron. Sci., 8, 8 (1941), 303-312.

H. LUNDGREN, Powłoki walcowe [tłum.], Arkady 1963.

J. MURZEWSKI, Stateczność ogólna żebrowanych powłok walcowych przy zginaniu, II Konferencja Naukowo-Techniczna, Konstrukcje Metalowe w Budownictwie i Mostownictwie.

J. MURZEWSKI, Badania doświadczalne żebrowanych powłok cylindrycznych na tle klasyfikacji możliwych form niestateczności, Czasopismo Techniczne, 1, 70 (1965), 1-7.

J. MURZEWSKI, Tests on models of cylindrical shells, Arch, Inzyn. Ladow., 3, 13 (1967), 375-397.

W. OLSZAK, P. PERZYNA, A. SAWCZUK i in., Teoria plastyczności, PWN, Warszawa 1965.

P. SEIDE i V.J. WEINGARTEN, On the buckling of circular cylindrical shells under pure bending, J. Appl. Mech., 1, 28 (1961), 112-116.

T. R. SHANLEY, Weight - Strength Analysis of Aircraft Structures, New York-Toronto-London 1952.

J. L. TAYLOR, The Stability of a Monocoque in Compression, R.M. No 1679, British A.R.C, 1935.