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Aviation History
1935
1935 - 1304.PDF
SUPPLEMENT TO FLIGHT 588ft 36 THE AIRCRAFT ENGINEER MAY 30, 153 Equation ((13);. Since the value of E ha? been assumed constant throughout the beam it can be eliminated from the equation. Considering again bay CB, Table (4). column (3) gives the values of a, and column (2) gives the corresponding values of I. Dividing column (3) by column (2) we obtain the values of — which when integrated (column (5)) give J -^-dx and the value of this ordinate at x = / is the first term on the left-hand side of equation [13] with the con stant E value eliminated. Column (6) of Table (4) gives the integration of column (5) and the value of the ordinate at x == / gives I I — (dx)2 which, when divided by 1 J v.' p I corresponds to the second term on the left-hand side of the Three Moment Equation (13). BAY BA. a, = I,Il6,000 FIG.8 C&Xx 7 FIG.7 CB y5x Y ®- (D»x f\ ®- P*N . ^^: \ f k c4. \ \ \f\ > 160 120 80 4-0 vx \ ' ^\ \ f S>1 »> \ i \ \ \ \ •5 0 •5 to 1-3 The remaining terms in square brackets on the left-hand side of equation (13) are obtained in a similar way, as is shown in Table (4). The procedure indicated by the right-hand side of equa tion (13) for the bay BA is then performed, though it has not been thought necessary to include the corresponding table, the nature of the necessary calculations being suffi ciently illustrated by the " left-hand side " Table (4) All the terms required to determine MB, and hence, the bending moment anywhere along CA, are now available. Collecting them, we have :— BAY CB. at = — 118,700 jg, = 58.36 y, = — . 5512 I = 200 347,600 —-dx = 464.0 -j-dx = 1.974 Mr = 45,000 (dx)-= -9,534,000 (dx)2 = 33,400 tj(dx)2 = 360.1 IO9.O y, = — .6709 / = 300 'dx = 5,737,000 jdx = 1,317 I dx = 4.303 -^(dx)2 — 367,400,000 ^(dx)2 == 151,000 (dx)2 = 1,352 «/ 0«/ 0 MA = 150,000 Substitution in (13) leads to :—• [— 347,600 -f 47,670] ME -f .5512 X 45,000 -f 118,700 58-36 -f 45,000 [1.974 ~~ 1 800] = [— 1,224,000] 150,000 + .6709MB — 1,116,000 [464 - 167] L - 503-3J 109.0 -f MB [ - 4.507] That is 12.70 MB = 2,800,000 or MB = 220,500 Finally (as will be clear to those who have studied §3, from equations (7) and (8)) the bending moment at any point x in CB will be given by MB _M..yi-«, pi •+ M, . yx o-x -r Pi and at any point x in BA by , MA - M. . y, - a, p x + M, . ya .. (15a) (156) TECHNICAL LITERATURE SUMMARIES OF AERONAUTICAL RESEARCH COMMITTEE REPORTS R EPORTS published by His Majesty's Stationery Office, London, which may be purchased directly from H.M. Stationery Office at the following addresses: Adastral House, Kingsway, W.C.2; 120, George Street, Edinburgh; York Street, Manchester 1, St. Andrew's Crescent, Cardiff; 15, Donegall Square West, Belfast, or through any ordinary bookseller. ON STRESS AND STIFFNESS DETERMINATION IN CERTAIN CANTILEVER WINGS IN WHICH THE RESISTANCE TO TWISTING IS APPRECIAWY DEPENDENT ON TORSIONAL SHEAR STRESSES. By H. Roxbee Cox, Ph.D., D.I.C., B.Sc, J. Hanson, B.Sc, D.I.C., and W. T. Sandford. R. & M. No. 1617. (17 pages and 8 diagrams.) May, 1934. Price is. net. Methods of designing modern cantilever wings are such that the existing con ventional methods of stress determination are frequently inapplicable. Considera tions of general design economy, as well as the prevention of flutter, loss of lateral control, and wing structural instability have led to wing constructions in which twisting moments are resisted by torsional shear stresses as well as by spar bending stresses. So, spars are found that are individually capable of efficiently resisting torsion as well as bending : in addition, or alternatively, we find the wing covering capable of resisting shearing actions, though generally incapable of appreciably contributing to the bending stiffness of the wing. This deliberate resistance to twisting by shear stresses in the structural material creates problems in stress ami stiffness determination to the solutions of which this paper is a contribution. The report leads to solutions of the strength and stiffness problem which are applicable to a number of actual wings, and for those wings the partition of the applied torque between the "differential bending" and " tube" elements of the structure is discussed. ARITHMETICAL SOLUTION OF EQUATIONS OF THE TYPE J,* \ji = CONST. By A. Thorn, D.Sc, Ph.D. R. & M., No. 1604. (11 pages and n diagrams.) March 4, 1933. Price 9d. net. It has already been shown* that in using the " interpolation " method of solution of the equation v2\jj — f(x, i'),the value at the centre of a square of side 2" can he calculated from a simple formula to a considerable accuracy. Other calculations enable an estimation of the value of ^ to be made at the centre of four squares. A similar type of analysis is here developed for the solution of the equation ot fourth order. * "An Investigation of Fluid Flow in Two Dimensions," A. Thom. R. *•' "• Ko. 1194. "The Flow Past Cylinders at Low Speeds," A. Thom, Proc. Roy. Soc.. Vol. lilj 1033.
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