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Calculation of Stresses in Aeroplane Wing Spars*

Published online by Cambridge University Press:  18 August 2016

Arthur Berry
Arthur Berry*
Affiliation:
King's College, Cambridge
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Extract

The following method of calculating the stresses in the spars of an aeroplane wing is essentially a simplification in form of the method given in the paper “Some Contributions to the Theory of Engineering Structures, with special reference to the Problem of the Aeroplane,” by Messrs. H. Booth and H. Bolas, issued by the Air Department of the Admiralty in April, 1915.

Type
Research Article
Information
The Transactions of the Royal Aeronautical Society , Volume 1: The Calculation of Stresses in Aeroplane Wing Spars , November 1919 , pp. 3 - 33
Copyright
Copyright © Royal Aeronautical Society 1919 

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Footnotes

*

The greater part of this paper, §§ I—8 and the Tables, was first issued as Confidential Information Memorandum No. 9 by the Air Department of the Admiralty, November, 1916, and reissued by the Air Board, July, 1917. Articles 9, 10 were issued as Confidential Information Memorandum No. 32 by the Air Board, July, 1917. I have omitted part of the original introduction, added a footnote on p. 6, and added two notes at the end; these additions have been enclosed in square brackets. Otherwise only trivial verbal changes has been made.

References

Note on Page 4 * For proofs see Mathematical Appendix.

Note on Page 6 * This is an overstatement; e.g., if a member AB is next to a very short member BC. the case approximates to that of a beam encastred at B, in which case Euler's load may be exceeded. Such cases, however, seem seldom to occur in practice; the question has been fully treated by W. L. Cowley and H. Levy, in papers issued by the Advisory Committee on Aeronautics during the war, and recently in Proc. Roy. Soc., June, 1918. The case when α is near 90° is also treated briefly in note II- (p. 32).]

Note on Page 6 † Five-Figure Tables of Mathematical Functions, by John Borthwick Dale: Arnold, 1903. Five-Figure Logarithmic and other Tables, by Frank Castle : Macmillan & Co., 1909. Fuller tables of the hyperbolic functions, including tanh α and coth α, are given in Smithsonian Mathematical Tables : Hyperbolic Functions : prepared by G. F. Becker and C. E. van Orstrand : Smithsonian Institution, Washington, 1909, but as this book may not be available, a table of tanh θ from θ = o to θ = 2 is given in Table III. (pp. 30, 31).

Note on Page 7 † It is here assumed that the tvro overhangs are not equal. If they are equal is the same as and these formulæ can be slightly simplified. There is a further simplification if as usual w 0 = w 1 = w 2 …, and …

Note on Page 8 * See Mathematical Appendix, Formula (28). In this and the following formulæ it may be more convenient to replace α/α by I/μ.

Note on Page 8 † It is usually negative, and in the strict mathematical sense a minimum.

Note on Page 8 ‡ Sec Mathematical Appendix, Formula (35).

Note on Page 8 § Sec Mathematical Appendix, Formula (31).

Note on Page 8 ∥ It may be worth while remarking for the benefit of any reader nol familiar with hyperbolic functions that tanh θ, coth θ, sech θ, cosech θ, can be obtained from sinh θ, cosh θ, by the same formulæ as for the corresponding trigonometrical formulæ, viz. :—

tanh θ = sinh θ/cosh θ, coth θ = cosh θ/sinh θ, sech θ = I/cosh θ, cosech θ = I/sinh θ. It may be noted also that when θ is small, tanh θ is nearly equal to θ, and that tanh (—θ) = — tanh θ, cosh ( — θ) = cosh θ.

Note on Page 9 * See Mathematical Appendix, Formula (29).

Note on Page 10 † See Mathematical Appendix, Formula (32).

Note on Page 21 * [Originally issued by the Air Board Technical Department as Confidential Information Memorandum No. 32, July, 1917.]

Note on Page 22 * I am indebted to Miss H. P. Hudson, O.B.E., for most of the arithmetical work in this article.

Note on Page 32 * A closer approach to reality, with a corresponding increase in complication, would result from allowing for the extensibility of the struts, deformation of fittings, etc.