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Aviation History
1932
1932 - 0501.PDF
May 27, 1932 Supplement to FLIGHT Edited by C. M. POULSEN May 27, 1932 CONTENTS Page The Stress and Deflection of Uniformly and Axially Loaded Kings. By H. L. Milner, Wh.Sc., A.M.Inst.C.E., A.F.R.Ae.S 33 Engine Mounting Stresses. By R. Bodger 37 Technical Literature— Summaries of Aeronautical Kesearch Committee Reports .. .. 39 THE STRESS AND DEFLECTION OF UNIFORMLY AND AXIALLY LOADED RINGS. *By H. L. MILNER, Wh.Sc., A.M.Inst.C.E., A.F.R.Ae.S. BY making a simple though not unreasonable assump tion, the following article develops a theory of the stresses occurring in a ring of material when loaded in a special manner. On this basis it becomes possible to estimate the maximum stress and deflection in a ring of any cross section. The results so obtained can, by taking a particular case, be compared with those given by the usual flat plate theory, and it will be seen that the agreement is fairly close for a ring in which the thickness is small compared with the radial width of the section. As the ratio of thickness to width increases the disparity be tween the two theories diminishes. This is to be expected, because the basic assumption of the present article is that under strain each radial section of the ring rotates through a small angle, and this condition is more likely to be realised in a section having a large thickness to width ratio than in a thin ring. Consider a circular ring of uniform section carried by a circular support of radius R, and uniformly loaded on a circle of radius R2 as in Fig. 1. We assume that under this system of loading every radial section rotates through a small angle ty about some point 0 in the section. With this assumption we shall see that, in general, the point O will not coincide with the centroid of the section as might at first be expected. However, for the purpose of this investigation the exact location of 0 is unnecessary. All we need to know is the position of 00, where 0, is the projection of 0 on to the axis HK of the ring. In Fig. 2 the full lines represent the section before * Mr. Milner has for many years been a member of the Technical Staff Of the Gloster Aircraft Co., Ltd., and has specialised, particularly the last few years, on the development of the Gloster-Hele-Shaw Beacham Variable Pitch Propeller. ' F |jk t/**~ —t 16.1. i 1 H °' W R| K IM b the load is applied and the broken lines indicate the strained section. Circular filaments of the ring lying in the plane 0,0 will not change in length when the ring is strained, but all filaments above the plane will be subject to a tensile strain and below the plane the stress will be compressive. Take any point P in the section at a radius r from the axis. Let O.P make an angle 0 with 0,0. If under strain the section rotates through an angle 80, P will move to P, where POP = S*>. Let 0,0 = R. Let OP = x and the perpendicular from P on to 0,0 = y. Before strain the length of the filament passing through P was 2 n (R + x cos $) and after strain the length is 2 TT (R + x (cos 6 - 8f)). Hence the strain of the filament P is 27t(R + x COB (6 - 8$)) - 2TC(R + * coffi) 2TC(R + x cos 6) x (cos (8 — S4>) — cos 6) x sin 6-8(j> yhif (1) Since &<p is a small angle and = R + x cos 6, Let p be the circumferential stress in the filament passing through P, then p — Ee Ey84> = Etan p- (2) E being Young's modulus for the material of the ring and (8 the angle P0,0. 468
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