Thin-walled elastic beams

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Thin-walled elastic beams

Author: Vasiliĭ Zakharovich Vlasov | Size: 16.9 MB | Format: PDF | Publisher: National Technical Information Service | Year: 1963 | pages: 493

The main results of Vlasov' s investigations are contained in his books "Tonkostennye uprugie sterzhni" (Thin-walled Elastic Beams) (First· Edition, 1940). "Stroitel' naya mekhanika tonkostennykh prostranstvennykh sistem'' (The Structural Mechanics of Thin-walled Spatial Systems) (1949) and "Obshchaya teoriya obolochek i ee prilozheniya v tekhnike" (The General Theory of Shells and its Application in Engineering) (1949), . The first of these books was awarded a Stalin Prize, First Class, in 1941 and the two others a Stalin Prize, Second Class, in 1950, The earlier monographs "Novyi metod rascheta tonkostennykh rizmaticheskikh skladchatykh pokrytii i obolochek" (A New Method of Designing Thin-walled Prismatical Hipped Roofs and Shells) (1933) and "Stroitel'naya mekhanika obolochek" (The Structural Mechanics of Shells) (1936) were essentially absorbed in the last two books,
The most important results were obtained by V. Z. Vlasov in the theory of cylindrical shells of intermediate length whose contour is either curved or of the form of a broken line (hipped systems). Vlasov introduces an exceptionally simple design model in which the shell is replaced by a spatial system of an infinite number of curved arcs, connected by ties which transmit the forces but not bending or torsional moments. In other words, the shell is inomentless [in a "membrane state"] in the longitudinal direction and may deflect transversely. This is the key to the behavior of a cylindrical shell of intermediate length, as Vasilii Zakharovich so elegantly demonstrated. Subsequent checking of his hypotheses has verified their complete validity. V. Z. Vlasov reduces the design of a cylindrical shell to that of a aiscrete-continuous system, and the partial differential equations of the shell to a system of ordinary equations. Vlasov' s variational method for the reduction of partial to ordinary differential equations is important in itself. Vlasov assigns the shell a finite number of degrees of freedom in transverse displacement and an infinite number in longitudinal displacement.
The calculation of the transverse displacements is then elementary and for the longitudinal displacements we obtain differential equations of a type familiar from the theory of structures.
Such methods were worked out by Vasilii Zakharovich Vlasov for the design of shells and hipped systems of open and closed section, and the design for stiffness of cylindrical shells with one or several ribs.
The theory of thin-walled beams may be obtained from the abovementioned theory. The basic features of the design of thin-walled structures were known before V. Z. Vlasov. It had been established that the Euler-Bernoulli technical theory of the bending of beams was not applicable to thin-walled beams because of the distortion (warping) of the section which has to do with the way of applying the statically equivalent loads to the end faces etc. The statement of the problem and its solution are very
fully described in Vlasov' s treatise on thin-walled beams. Design models for beams are lucidly described. In the expression for the normal stress there appears, besides the three usual terms, a term determined by the law of sectorial areas.
The theory permitted a complete solution of the problem of flexuraltorsional instability and of the vibrations of thin-walled elastic beams, and also the development of methods for the design of beams with elastic and rigid connections and of beams under transverse loads.

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Thin-walled elastic beams

Author(s)/Editor(s): Vasiliĭ Zakharovich Vlasov | | Size: 17.66 MB | Format: PDF | Quality: Unspecified | Year: 1961 | pages: 507

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