Aircraft Engineering and Aerospace Technology
, Volume 20 (10): 1 – Oct 1, 1948

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- Publisher
- Emerald Publishing
- Copyright
- Copyright © Emerald Group Publishing Limited
- ISSN
- 0002-2667
- DOI
- 10.1108/eb031678
- Publisher site
- See Article on Publisher Site

theory to work satisfactorily. This merges with the larger question of the significance of duc tility in structural design. It has doubtless saved many stressmen's skins, but to date it has never entered quantitatively into design. then chooses the sizes of the members of his Theory of Limit Design. By John A. van den Broek Professor van den Brock draws attention to structure so that they will just carry the required [John Wiley: Chapman & Hall. 30s.] the need for ductility in the attachment of the loads. The result is a structure which is capable members of a structure designed by the methods Reviewed by W . S. Hemp of carrying the loads demanded of it and which of Limit Design. It is doubtful whether this duc will indeed carry those loads in the manner as tility is present in aircraft riveted joints and it is sumed, just prior to failure. At the ultimate load, HE 'Theory of Limit Design' is a theory undoubtedly absent in spot-welded or reduxed the distribution of load among the members will whose philosophy and methods will be joints. The rule that a line of rivets ultimately be determined by their relative strength, rather familiar to most aeronautical engineers. transmits load uniformly is certainly untrue for than by their stiffness. The term 'Limit Design' may not be familiar and a redux joint. so it is probably necessary, before making com Commentary (e) The theory, that the ultimate strength of a ments upon the theory, to give a short résumé. structure must of necessity be estimated by such (a) Aircraft designers are required to show that methods as Limit Design, is by no means univers their structures will meet two stressing condi ally valid in aircraft design. An aircraft struc Résumé of the Theory tions. They have to demonstrate that no serious ture may well fail by flexural instability of its permanent deformation will result from the ap The 'Theory of Limit Design' is a theory of the stringers or general instability of all its reinforc plication of a Proof Load, as well as to show design of structures under their ultimate loads. ing members at stresses below the elastic limit. that failure will not occur at any load less than Like the Theory of Elasticity, it bases itself upon In this case stress calculations based upon the a certain Ultimate Load. To ensure satisfaction considerations of equilibrium and continuity of Theory of Elasticity would seem appropriate. of the Proof Requirement the appropriate theo displacement, but replaces the simple Hooke's (f) The application of Limit Design to frame retical method would seem to be the Theory of Law by a generalization, which allows for un works requires a knowledge of the post-buckled limited ductility at a 'yield stress'. The stress- Elasticity, combined with certain allowable behaviour of struts. This problem presents no strain diagram is thus assumed to consist of two stresses which will be the yield or proof stresses difficulty for slender struts, but, as experimental for the materials concerned. It is in calculations straight lines—one with a slope equal to Young's results given by van den Broek show, there is an for the Ultimate Requirement that the methods Modulus passing through the origin, while the appreciable drop in load after buckling for struts of Limit Design are appropriate if at all. How other is a line of constant stress equal to the yield of medium length. This is a class of problem ever, if, as it must be confessed is often the case, stress. which previous design methods would not have the assumption is made that compliance with the Application of the basic assumptions is brought to the forefront. As van den Broek con Ultimate Condition implies satisfaction of the usually made only to conditions of ultimate load. tinually emphasizes, it is entirely a matter of Proof Condition, then Professor van den Brock's Thus, in the case of a bar in tension, eccentrici 'sense of value'. opinion, that the Theory of Elasticity has held ties, minor defects and initial stresses are ig its dominant position in engineering practice too nored, and when ultimate conditions are reached, Conclusions long, would seem to be worthy of serious con a uniform distribution of stress across the section sideration. The following conclusions would seem to be is assumed, equal, of course, to the yield stress. admissable as to the significance of Limit Design Similar conditions of uniformity are assumed in Although as yet not formally compelled by for the aircraft engineer: way of a bolt hole. Where the Theory of Elasti Requirements, aircraft engineers are giving seri (a) The Theory of Limit Design is valid for or city gives magnification factors, the Theory of ous consideration to failure by repeated loads. Limit Design supposes that ductility has re thodox structures made from mild steel. Regions of plastic flow undoubtedly play a moved the lack of uniformity, before the ulti crucial part in this type of failure, but they may (b) Although the aircraft designer often makes mate load is reached. In the same way a line of well be quite small in extent, so that the govern use of these methods, they are by no means rivets is assumed to share the transmitted load ing stress distribution will be more accurately universally valid and may often, when ap equally, whereas Elasticity Theory concentrates calculated by Elasticity methods rather than by plied to joints, be positively dangerous. the load at the ends. Limit Design. (c) It may perhaps be proper for a civil engineer to forget much of his Theory of Elasticity, In the case of a beam, the usual assumption of (b) The method of design which proceeds from but the aircraft engineer must continue his linear variation of direct strain leads ultimately a chosen load distribution to a structure capable studies, since many of his problems fall into to a condition in which the section divides into of carrying these loads, will be recognized by all that field. The consideration of plastic stress two regions of constant stress, one tensile and aircraft stressmen as perhaps the most import one compressive and both equal to the yield ant part of their stock in trade. The theorem, that distributions must continue to occupy the at stress. When this condition is effectively reached a structure is strong enough if there exists a tention of the aircraft engineer, but they can not, as Professor van den Broek advocates, at a section, further increase in curvature will statically correct diffusion of load which does replace his other techniques. take place at constant bending moment. This re not fracture any component or joint, is the sult may be applied to redundant systems—for foundation upon which all difficult stressing is example, doubly clamped or continuous beams. based. This is 'pure Limit Design'. The aircraft In the former case, when the loading is uniform engineer may well join the civil engineers, who BOOKS RECEIVED the conclusion is reached that ultimately the after having a lecture by van den Broek, realized bending moment at the centre will equal the that 'they had known it all the time'. All books received from Publishers are listed under this heading. Extended reviews of a selection are published later. Inclusion in clamping moments, both being equal to the limit (c) In all fairness it should be stated that the tech this list, therefore, neither implies nor precludes, in any particular instance, further notice. ing moment for the section. This is again in con nical foundations used in the Theory of Limit tradiction to Elasticity Theory. Bulletinul Institutului National de Cercetari Tehnologica. Design have, of course, appeared before in other Vol. I, Nos. 1-4, 1946. Paper bound, 139 pages, Similar arguments may be applied to frame places under the titles 'Plasticity', 'Stressing Be illustrated. [Institut de Recherches Technologiques works, but here, in addition to load limitation yond the Elastic Limit', etc. The significance of de Roumanie, Str. Matei Millo, 7, Bucharest. Free.] due to yielding, one has to consider cases of van den Broek's work may be described as the Bulletinul Politehnicii Gh. Asachi din Iasi. Tome 2, buckling as struts. However, experiment shows systematic development of an 'Ultimate Strength Fase 2, July-December 1947. Paper bound, 356 that the load-compression relation for slender of Materials'. The development of solutions to pages, illustrated. [L'Ecole Polytechnique, Jassy, struts is of the same form as the stress-strain re problems involving more than one component of Roumania. Free.] lation assumed in Limit Design Theory. The stress would, however, fill what is quite a serious Standard Valves. [Standard Telephones and Cables Ltd., Connaught House, Aldwych, W.C.2. 15s. 6d. basic theory is therefore still applicable and one gap in this theory. post free.] concludes that, in the case of a redundant frame (d) The Theory of Limit Design stands or falls The Workshop Yearbook and Production Engineering work under increasing load, successive members by its assumption of ductility. This is clearly Manual. II. H. C. Toun. 549 pages illustrated. yield or buckle until the whole structure becomes justified for structures made of mild steel. The [Paul Elek. 35s.] determinate and docs not fail until a further important question for aircraft design is, of Bulletin de l'Institut National de Rêcherches Tech member reaches its ultimate load. In this case, as course, whether it is justified for aluminium and nologiques de Roumanie. Vol. II, 1947, Nos. 1-4. previously, continuity of displacement is ensured magnesium alloys. Professor van den Broek Paper bound. 244 pages illustrated. [The Institute, by the ductility of the material. gives experimental evidence, consisting of tests Str. Matei Millo, 7, Bucharest. No price stated.] These considerations lead to what is the cen on beams, to show that his theories are justified Supercharging the Internal Combustion Engine. E. T. Vincent. 314 pages illustrated. [McGraw-Hill. 30s.] tral doctrine of the theory. This states that in the for these materials. Aeronautical Conference, London, September 1947. design of a redundant structure the magnitudes There is much discussion these days of the J. L. Pritchard and J. Bradbrooke. 704 pages illus of the redundant loads may be chosen by the possibility of producing alloys with larger values trated. [Royal Aeronautical Society, 4 Hamilton designer. His choice will be guided only by such of Young's Modulus. If this is to be achieved it Place, W.1. Members 52s. 6d. Non-Members considerations as weight saving or economy. will probably be at the expense of ductility. An 725. 63.] There is no need to perform the, often elaborate, important question for the future of Limit De The Sealing Mechanism of Flexible Packings. C. M. calculations demanded by the Theory of Elasti sign is the determination of the amount of duc White and D. F. Denny. Paper bound, 112 pages city. Knowing his load distribution the designer illustrated. [H.M. Stationery Office. 10s. 6d.] tility (elongation) which is necessary for the October 1948 303

Aircraft Engineering and Aerospace Technology – Emerald Publishing

**Published: ** Oct 1, 1948

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