**8**, 3, pp. 423-461, 1960

### Ogólna Teoria Stateczności Prętów Cienkościennych z Uwzględnieniem Odkształcalności Przekroju Poprzecznego. Cześć I. Pręty O Prostym Przekroju Poprzecznym

The reactions Prr Mys between the walls cons tituting the reactions of a plate compressed in one direction with longitudinal edges undergoing edge displacements 4, 0 (Fig. 11,12), can always be expressed in terms of 5, N, P and the rotation angles Y of the edges. The relevant formulae (3.8), (3.9), (3.10) are obtained by solving the Eq. (2.9). As a result there remain always in all the equations of the type (2.7) and (2.10) the three unknown displacement components of the bar 5, n, q and the rotation angles yn, determining the de- formation of the cross-section. Setting the determinant of the system of homogeneous equations thus obtained equal to zero, we obtain the buckling condition in the form of a transcendental equation, in which the unknown is the dimensionless coefficient k = G|E (where o is the critical stress).

In Sec. 4 detailed analysis of stability is given for the most important types of cross-section. In Sec. 5 plate buckling of the walls is considered as a particular case, which may be obtained by assuming § = n = Q = 0 in the general equations obtained. In Sec. 6 numerical results are given and a discussion for flexural buckling of a channel section. These results are compared with those of the Ref. [4] where indeformable flanges were assumed.

The conclusions may be formulated thus: 1. The influence of the deformability of the cross-section on the critical force in rolled profile bars is insignificant and amounts to a fraction of one percent. 2. In bars with very flexible web and broad flanges this influence may be greater, but in practice it exceeds a few per cent only in rare cases. 3. The influence of the deformability of the cross-section increases rapidly with decreasing the length of the bar. In very short bars it may reach theoretically a few tens per cent. In these cases the critical force does not differ practically from the critical force for plate buckling of the walls computed for n = 1 (Fig. 28, Table 11); 4. It may practically be always assumed that the flanges are indeformable. The errors are significant only in the case of very thin flanges. 5. The influence of bar deformations on local buckling is insignificant and may be disregarded.

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#### References

[in Russian]

A. CHUDZIKIEWICZ, Wpływ odkształcalności przekroju poprzecznego pręta cienkościennego na siłę krytyczną Eulera, Rozpr. inyn., 1, 8 (1960).

A. CHUDZIKIEWICZ, Wpływ odkształcalności przekroju poprzecznego na siłę krytyczną wyboczenia skrętnego pręta dwuteowego, Rozpr. inzyn., 1, 8 (1960).

A. CHUDZIKIEWICZ, Giętne i gietno-skrętne wyboczenie pręta ceowego o odkształcalnym przekroju poprzecznym, Rozpr. inzyn., 2, 8 (1960).

F. BLEICH, Buckling Strength of Metal Structures, New York 1952.

E. STOWELL, C. LIBOVE, E. LUNDQUIST, G. HEIMERL, Buckling Stresses for Flat Plates and Sections, Proceedings ASCE, 77, 1951.

R. DABROWSKI, Praktycznie ważne przypadki wyboczenia skrętnego prętów cienkościennych, Arch. Inzyn. ladow. 1, 1956.