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Determination of the Buckling Load of Struts with Successive Approximations

Published online by Cambridge University Press:  28 July 2016

J. Ratzersdorfer
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Extract

In cases of tapered struts with hinged or built-in ends where the exact determination of the buckling load is complicated it may be useful to apply a method of successive approximations.

Let us first consider a bar of the length l with hinged ends under the action of the compressive force P. The differential equation of the bending line becomes

where v is the deflection at the section u, v with the moment of inertia I (u) and E is Young's modulus. At the ends of the bar the deflection v is equal to zero (Fig. I).

Type
Research Article
Information
The Aeronautical Journal , Volume 47 , Issue 387 , March 1943 , pp. 103 - 105
Copyright
Copyright © Royal Aeronautical Society 1943

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References

Note on page 103 * See also writer's book: Die Knickfestigkeit von Staben und Stabwerken (Buckling of Bars and Bar Systems), p. 117, Vienna, 193 , and his paper in R. Katzmayr's Beiträge zur Flugtechnik, p. 36, Vienna, 1937.

Note on page 105 * The accurate value has been calculated by A. N. Dinnik. Design of Columns of Varying Cross Sections. Transact. of the American Society of Mech. Engineers, 1928. Westnik Ingenerow, 1929