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Aviation History
1932
1932 - 0863.PDF
AUGUST 26, 1932 61 THE AIRCRAFT ENGINEER SUPPLEMENT TO FLIGHT of course, so lasting as tool steel, and dies made of it should be carefully watched and replaced at the firsl sign of wear. General Remarks. Tolerances. Adequate allowance should always be made for variations in both width and thickness of strip. Lubrication. For rolling steel or drawing it through rolls, a light oil should be used. For drawing through dies a moderately heavy oil is better. Aluminium and Duralumin may be worked dry in rolls both on the mill and the drawbench, but paraffin will be found to improve the working of Duralumin. For drawing through dies, paraffin should be used for both metals. Bend Radii. In Table II will be found a list of maximum and minimum bend radii for various materials. The minimum values are governed by the tendency to crack in working, and the maximum by crumpling failure under load in service. For non-structural work, the latter, naturally, do not apply, i TABLE II Minimum and Maximum Bend Radii for Various Materials Given in terms of the Thickness R = Inside Radius of Bend. / = Thickness of Metal. Material H.T. Alloy Steel Mild Steel, thinner than 14 G.... Mild Steel, 14 G and Thicker ... H.T. Stainless Steel L.T. Stainless Steel Duralumin Thinner than 14 G.... Duralumin 14 G and Thicker ... Aluminium R/« Minimum 2 1 n 2 U 2 2 1 Maximum 30 30 35 20 30 20 30 APPLICATIONS OF THE POLAR DIAGRAM By E. H. ATKIN,* B.Sc.(Lond.) BY far the most important practical addition to the methods of stressing aircraft structures introduced within the last four or five years is the method of the polar diagram.(1) By its aid the strength of beams under compressive end load, which have concentrated loads, changes of distributed load in the bay, and changes of moment of inertia in the bay, can be determined with a speed and facility undreamed of under the old analytical method. Where the booms of aeroplane spars are graded according to the bending moments imposed upon them, alternative arrangements of strengthening pieces can be investigated in a fraction of the time previously required. Indeed the labour of the old analytical method was so great that the time required for such an investigation was prohibitive. But in spite of the obvious superiority of the polar diagram, its power and possibilities do not appear to be as widely appreciated as they should be. Many people seem to think there is something mysterious, something occult, about what rests, as a matter of fact, upon a very simple recognisance. This simplicity of principle is, of course, common to many other elegant methods of geometry and analysis. The polar diagram is based on the fact that the solution of the general differential equation of a beam under lateral load and compressive end load can be looked upon as the polar equation to a circle passing through the pole. As this equation will be useful for a certain purpose later on it will be well to give it here, together with its solution. The equation is d2M ^+^M = W' & and the solution M = A sin ax — B cos ax or alternatively w M a- C (cos ax - £) (2) Where A and B, or C and s are constants of integration. It will also be useful to note that the true shear S is given by S = — = — a C sin (ax — e) (3) dx The notation and sign conventions used here will be those generally accepted. (2) For any symbols and conventions special to the polar diagram reference should be made to the original report. It is also assumed in the following sections that the reader has acquainted himself with the main geo metrical constructions of the polar diagram. (1) Change of Moment in a Bay While designing spars for a biplane one is sometimes faced with the problem of allowing for a change of moment away from a point of support. This can arise by reason of the local stiffening of one flange of a spar. In some cases the effect is considerable, and, as the stresses due to bending are usually increased thereby, its neglect will lead to optimistic reserve factors. Take, for example, the case in which the insertion of a liner in the compression boom of a spar doubles its effective gauge. If the centres of area of the booms are 6 in. apart, the introduction of the liner will move the neutral axis of the spar an inch towards the compression boom—a considerable offset for an average spar with end load. The polar diagram enables us to allow for this in the simplest possible manner. OF CHANGE OF MOMENT Mr. Atkin is on the Technical Staff of A. V. Koe & Co., Ltd. Referring to Fig. 1 we have the case of a beam with a change of moment in the bay. In general this is accompanied by a change in the moment of inertia of the section, but, to avoid confusing the two constructions, the diagram assumes that the moment of inertia is constant throughout the span. Once the construction of Fig. 1 is mastered no difficulty 802e
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