1. It seems strange to one accustomed to the aeronautical literature to see the theory of flexural-torsional instability ascribed to Timoshenko and no reference made to the work of Wagner and Kappus in Germany, or An American Method of Developing Analytical Curves- H . L. Cox in this country. There is one point of extension of the theory of the bending- A Report of Investigations on the torsion effects, which is given in an article by Hoff in the Journal of Royal Aero. Society, Buckling of Light Alloy Struts Feb. 1943 (Appendix) and which concerns the phenomena occurring in 'thick' sections, that might well narrow the gap noted by the subject matter being set down in typewritten The Analytical Development of Curves and authors between theory and experiment in Streamline Shapes. By Harry H . Haase. (Deemar form, and it contains a fair amount of alge this field. Co, Amityville, Long Island, New York. $4.50). braical formulae. The typewritten characters 2. The absence of any references to tangent or are bold and in this form greatly assist in the reduced modulus in dealing with the prob From the foreword it is learned that Mr H . H. clarity of reading. lems of instability again seems strange to the Haase has been employed by the Republic Avia Th e contents are split up into five chapters. aeronautical engineer. When a strut is com tion Corporation of America for some years on These deal with: Ch. 1, Th e Circle and Ellipse pressed to a stress beyond the limit of propor the development of analytical curves as applied giving the usual equations such as are common tionality for the material, the appropriate to aircraft shapes. Both in this country and in text-books dealing with co-ordinate geometry. modulus, for use in a 'small deformation' test America the old method of fairing lines 'by eye', Ch. 2 deals with power curves giving equations for stability, is, at least in regions of increas i.e. graphically, has been largely superseded by of the circle and ellipse expressed in terms of a ing compressive stress, the tangent modulus treating an envelope shape analytically—find constant x taken to the nth power. It also deals and not the full E. The application of this re ing equations for the controlling profile lines with the combination of circle and ellipse, and sult leads to a 'strut formula' which would and calculating ordinates to enable the envelope two ellipses, single and multi-term power curve seem to be more logical than that of Perry in shape to be set down with a great degree of ac equations. In Ch. 3—Curvature and Points of that it leads to a deviation from Euler even in curacy and fairness. Inflection—the author explains how to deter the case of zero eccentricity and so forms a This book is intended to serve as a text-book mine if reverse curvature exists in a curve of a true basis for the assessment of eccentricity giving the particular method employed by the specified equation and how to remedy it if effects. Republic Aviation Corporation to evolve alge found. He also deals with changes of slope and These considerations apply also to cases braic equations for various curves, enabling the changes of curvature. Ch. 4 deals with further of local instability. Local instability stresses ordinates of a curve to be expressed as a func applications of power curves. It is, of course, of 30 tons/in2 in D.T.D. 364 such as are tion of the abscissae by means of a polynomial impossible to deal with all the varied combina given in FIG. 79 of this report are most un with fractional exponents. tions that may arise but further examples are real, when one considers that the 0·1 per Mr Haase, in his book, deals essentially with given of combining parts of circles to an ellipse, cent Proof Stress has a value of 27· 5 tons/ what he terms 'power curves' so called because and transition curves for convergent, parallel in2. the powers, or exponents of the dependent vari and divergent lines. The last chapter explains Consideration of these effects would, in ables of the equations, are the main factors that the method adopted to determine areas and the reviewer's opinion, have greatly im govern the shape of the curves. Quite a number volumes for curves developed by the Republic proved the value of the analysis of this report. of American aircraft firms using the analytical method. 3. The results of the material tests reported here method of determining envelope shapes confine H. G. B. are of great interest. The equality of Young's themselves to second-degree curves (conics), and Modulus in tension and compression is in the aircraft industry in this country also, se The Strength of Light Alloy Struts. By J . F . Baker established for these materials and a contri cond degree curves find favour in preference to and J. W. Roderick. (The Aluminium Develop bution is made to the statistics on the rela power curves. There is, of course, no hard-and- ment Association, 33 Grosvenor Street, W.1, tive magnitudes of the 0·1 per cent Proof fast rule—both forms of curves may be used, 21s.) Stress in tension and compression. An accu some forms being more easy to calculate than rate determination of the value of Poisson's others, and each must decide for himself which This report gives an account of work on the Ratio by the measurement of lateral con type of curves it is preferred to use. In the buckling of struts carried out at Cambridge struction in a tension test shows that the writer's opinion, however, there is this funda University and sponsored by the Aluminium value of 0·3 , normally assumed in the air mental difference—power curves cannot be Development Association. It begins with a sum drawn graphically until the necessary equations craft world for aluminium alloys, is, for the mary of the known theory of flexural, tor materials considered rather low, and should have been determined and a sufficient number sional and local forms of instability and then be replaced by ⅓. of values worked out to enable the curve to be proceeds to an account of fundamental tensile plotted. With second-degree curves they can In view of the remarks in (2) above it and compressive tests made upon cylindrical readily be drawn graphically quite independ seems a pity that no plots of tangent modulus bars cut from material to the specifications ently of the analytical assessment and to be able are given for the materials tested. D.T.D. 364, 423A and 297, which were used in to do this is a tremendous advantage. Any or 4. The test results and comparison with theory the manufacture of the main test specimens. dinary draughtsman can graphically put down a made in this report show that, whereas There follows a detailed account of the experi conic to a set of particular requirements to his flexural instability implies failure, local and mental techniques used in the main series of own immediate satisfaction and to any scale. If particularly torsional instability do not im strut tests, the results of which are given finally the line is not entirely acceptable it can be re mediately produce collapse. This is in ac in the form of a most interesting series of graphs drawn in the matter of minutes. Having estab cordance with experience in aircraft struc in which failing stress is plotted against slender- lished a satisfactory line it can be repeated tural testing, and points to the need for a ness ratio for each of the sections tested and graphically at will without a table of ordinates, post-buckled theory for torsion leading to a compared with the relevant theoretical curves. but if it is desired it can also be treated analytic secondary collapse due to local or material Th e authors conclude that for the sections ally and values for the specific curve can be cal failure. tested, which include angles, channels, tees and culated. I-sections, there is no single formula of the In conclusion the reviewer feels that the thanks of the aircraft engineers should be ex This cannot be done with 'power curves' al Perry type which will adequately account for tended to the authors of a really first-class ex though Mr Haase shows in his book that with the observed failing loads. In attempting t o relate perimental investigation into struts of light experience it is possible to assess the type of theory and experiment they find most success in alloy, and hopes that someone in the aircraft curve that will result from an equation whose dealing with flexural and local types of failure. For the flexural-cum-torsional types they find world may find time to analyse these results by exponent is fixed. T o work the other way round that the theoretical values fall below the experi- the methods now used in aircraft design offices. and find the equation or equations that will fit a mental for the smaller values of slenderness W. S. HEMP particular line already drawn can be very ratio. tedious. In dealing with the analytical development of This investigation was carried out to provide BOOKS RECEIVED shapes there is no one specific line of approach design information for the use of civil engineers. All books received from Publishers arc listed under this heading. and it is largely a matter of personal opinion and However, since the materials used were light Extended reviews of a selection arc published later. Inclusion in preference as to which method is adopted. For alloy the results arc of interest to the aero this list, therefore, neither implies nor precludes, in any particular instance, further notice. those who may be interested in power curves nautical engineer as well. The problems in this book gives a practical and concise presenta volved have been studied for many years by Research In Industry. Paper bound, 84 pages. [H.M. tion of its applications to aircraft primarily. It aircraft designers, and so perhaps it will not be Stationery Office. 1s. 6d] is a book for the mathematician rather than the out of place here to comment on some of the German Gas Turbine Developments during the Period draughtsman. results obtained, and to compare the theory 1939-1945. Paper bound, 46 pages, illustrated. The set-out of the book is very legible, the with that normally used in the aircraft world: [H.M. Stationery Office 1s.] March 1949 85
Aircraft Engineering and Aerospace Technology – Emerald Publishing
Published: Mar 1, 1949
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