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Published online by Cambridge University Press: 28 July 2016
I. In recent years a systematic research has been made into the methods available for determining the stresses in three dimensional braced frameworks, and in particular into frameworks of the type represented by the hull of a rigid airship. Much of the research has been of a generalised character, intended to act as a useful guide to the designer rather than to deal with any particular problem of loading with which he may be confronted; attention has therefore been largely (though not entirely) concentrated on the stresses in a fully braced parallel tubular structure such as is shown in Fig. I, in which the wire bracing or “ tension ” members are initially strained so as to be capable of carrying compression,— the slackening off of wires, which will of course take place before failure, being considered subsequently by the “ device of the separate panel.”
1 R.Ae.S. Journal, May, 1926, “ Experimental Stress Analysis of Frameworks with Special Reference to Problems of Airship Design,” by A. J. S. Pippard. See also R. & M. 948, 971 and 977.
2 R.Ae.S. Journal, November, 1926, “ Stresses in Rigid Airships,” by R. V. Southwell.
3 R. & M. 737, 790, 791 and 819, “ On the Determination of the Stresses in Braced Frameworks,” by R. V. Southwell.
4 R. & M. 800.
5 R.Ae.S. Journal, December, 1931, “ A Contribution to the Analysis of Primary Stresses in the Hull of a Rigid Airship,” by L. Chitty and R. V. Southwell.
6 Proc. Roy. Soc. A, Vol. 139, 1933, “ On the Calculation of Stresses in Braced Frameworks,” by R. V. Southwell, F.R.S.
7 “ Application of a Method for Determining the Stresses in Braced Frameworks,” by L. Chitty.
8 See footnote (1).
9 See footnote (3).
10 Somewhat similar assumptions are made by Dr. H. Ebner in a valuable paper relating to frameworks of rectangular cross-section: 235. Bericht der D.V.L., “ Die Berechnung regelmässiger, vielfach statisch unbestimmter Raumfachwerke mit Hilfe von Differenzengleichungen,” by H. Ebner.
Note on Page 274 * As a first estimate Ω= (Young's Mod. x cross-sectional area)/ (length)3; in practice allowance may have to be made for end fittings, etc.
11 cf. C. Smith, Treatise on Algebra, Fifth Ed., end of §259.
12 See Appendix.
13 §§17–20 are inserted for the complete understanding of the equations; the general forms covering all special cases unless α=f=l will be found in §21.
Note on Page 281 * There would be no advantage here in substituting (jα-ζ) for jα, if ζ≠0, as the types associated with the two values for є, though existing, would not be distinct (§3).
14 Proc. Roy. Soc. A, Vol. 139, p. 475ff., §26, and in Mr. J. B. Owen's work (T.3407b).
15 The values for U'λ, V'λ, W'λ are, of course, arbitrary to the extent that they may be increased or decreased by any multiple of the first solution.
Note on Page 285 * The last term rTOJ is only required if the radial members are omitted in the intermediate bulkheads and then only provided n≠l.
Note on Page 286 * This last term is only required when the radial members are omitted in the intermediate bulkheads, and then only provided n≠l.
17 See R. and M. 1528, Appendix I.