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Aviation History
1936
1936 - 1595.PDF
SUPPLEMENT TO FLIGHT 40 THE AIRCRAFT ENGINEER JUNE 18, 193. CONCENTRATED LOADS on WINGS The Growing Tendency towards Utilising Wing Space Results in a Number of Concentrated Loads being Put on the Wing Structure : The following Note Deals with the Effects of such Loads on a Two-spar Wing Structure By J. B. B. OWEN, B.Sc, One-time Meyricke Scholar (Oxon) and Drap?rs Scholar (Wales) IN his article on " The Stressing of Monoplane Wings," which appeared in the March 26th and April 30th issues of The Aircraft Engineer, Mr. H. N. Home has shown how great simplification may be effected in the application of thejnethods of R. & M. 1617 (Ref. 1). His article and the R. & M. quoted are primarily concerned with distributed loads. The practice of mounting engines, etc., on wings introduces, in addition, concentrated loads. The following paragraphs give a brief discussion of the effect of such loads. Attention will be confined to a two-spar wing. The first process in the methods of stress determination referred to above is to divide any system of normal loading on a wing structure into (1) a system of loads which alone cause nothing but flexure, and (2) a system of torques (Ref. 3). Loads of the first system require that the deflections of the spars are equal at all points. This condition may be reduced to the satisfaction of the equation :— /dR\ .*.- R.) - l£) m j u> dx 4- d*R Jx- w, dx dx (1) (Ref. 2) for all values of a from o to /. In this equation wx is the load per unit run on the wing at the general section distance x from the wing tip, wa is the load per unit run at the section where x = a. Other quantities have significance similar to that of Mr. Home's article ; in particular rawa is the front spar load per unit run, (1 — r„)wa the rear spar loading intensity at the section x = a. At a section where a concentrated load is applied, say at x = c, the load per unit run becomes very large, i.e., Concentrated Load W Small elementary length hx In the limit when the load is absolutely concentrated hx vanishes. Then ivc must approach infinity. But the product wc hx is finite and equal to W. Consider the integrals of equation (1) as the limiting value when dx approaches zero of the sum of all such quantities as wx dx from o to a. Whether or not concentrated loads are out board (or inboard) of the section x = a, it then follows that the integrals of equation (1) are real and finite. In fact, this equation may be written for distributed and concentrated load systems as :— K'oK R. \dx ) a Outboard Shear at x = a (d2R\ Bending Moment at x = a .. (2) At a section of concentrated load as at x = c, since w„ approaches infinity, the load per unit run on the front (1) " Stiffness Determination in Certain Cantilever Wings " by H. R. Cox, J. Hanson and W. T. Sandford, May, 1934. (2) Cf. R. and M. 1617 equation (Sa). (3) Ibid., paragraph 2. spar, viz., w, rr must tend to infinity unless rc vanishes. In this case the rear spar load intensity wc(\ — rc) must approach infinity. A difficulty thus arises in utilising rfR d-R equation (2) at such points. Provided — and are dx dr2 finite, which is usually the case, the right-hand side of equation (2) is finite. It follows that wc(rc — Rc) is also finite. But w, tends to infinity, so rc — R(. approaches zero, i.e., rc tends to the value Rc. It follows that the load (not the load per unit length) on the front spar at this point, wc rehx = re W must tend to the value Rc W. The load on the rear spar is then (1 — Rf)W. When the spars are parallel Rr = ( -—— \c Then the concentrated load is shared between the spars in the ratio of their moments of inertia at the section considered. The results of the above paragraph and equation (2) therefore determine the partition of a given load system between the two spars so that they deflect equally at all sections. The difference between the resultant action at each section of this specially partitioned loading and the given loading gives the torque distribution on the wing. This method of calculating the distribution of torque obviates the conventional reference to " a flexural line " which, in certain cases, may lead to difficulty, e.g. if the distributed load wv is vanishingly small at the section x = v, but the right-hand side of equation (2) is finite : then w v(rv — RJ is finite. Since R„ is finite, and wv vanishes, then rr approaches infinity. The torque distribution at the section considered is then that due to vanishingly small distributed load wv at an arm equal to the " distance r, " to the " flexural line " which is now at infinity. The actual torque distribution at this section, however, is finite. To calculate its magnitude resort must be made to some other device. The method of paragraph 6 is clearly an easy way out of the difficulty. The following examples will illustrate the application of the method outlined above. The semi-span of the wing 80 120 160 200 240 0ISTANCE. FROM WING TIP (INS)
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