著者

内藤 子生 高田 守正

出版者

一般社団法人 日本航空宇宙学会

雑誌

日本航空學會誌 (ISSN:18835422)

巻号頁・発行日

vol.5, no.44, pp.1205-1224, 1938-12-05 (Released:2009-07-09)

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The stress analysis of the wing is now in general calculated by the idea of so called "elastic axis". But the idea is based on the assumption that the metal covered wing is so rigid to torsion that any torque offers to the wing no torsional deflection, and that the torque offers no stress to flangess. Therefore it may be easily supposed that the former idea may fail in the case of large torque. The present paper discribes a rational and rigorous method of stress analysis for wings which was developed and successfully applied by the authors in desigh of an aeroplane. The principle of the present method is based on the well known fact that the total deflection of a beam is the sum of the bending deflection and the shear deflection, considering the whole structure as statically indeterminate. Applying the principle of minimum strain energy, the authors calculated both the energy of bending and the energy of shear as shown in the eqn. (13) of illustrative problem. So the paper notes to the idea of "Shear Lag", and treats it analytically. Fig.3 is the illustrative problem. Flanges are considered to take fiber stress only. Webs, skins and ribs are considered to take shear stress only, recieving no fiber stress in X direction. Shear stresses in webs and skins between ribs are considered constant, changing only at ribs. Balance of the forces are expressed in six components, eqns (1)→(6). The idea of Fig.4 leads to eqs (7)→(10). They may be reduced to the relation (11). Statics gives no farther relation, q is indeterminate and must be solved by the principle of mininum strain energy. Total strain energy may be expresseed by (13), equation for q by (14), required solution for q by (15), and the other unknown by (11) & (15). Thus the inter-action of ribs and skins to both spars are easily calculated, which should be compared with the theory of Paul Kuhn, treating the rib action in the wing of wooden spar (N.A.C.A. Tech. Rep. No 508, 1935). Chapter 5 and 6 are the formula which were practically applied by the authors in the design of a seaplane. In the appendix (the last chapter), phisical meaning of expression (15) are developed. When L=∞ or G=∞, exp. (15) is reduced to the idea of "elastic axis, " in which the first term is for bending and the recond term is for torsion. When tv=tL=0, exp. (5) is reduced to the formnla for fabric covered wing. Thus it is concluded that the idea of "elastic axis" can be correctly applied only for the region far away from wing root and not for the region near the wing root, where the present method is varlid and beneficient.