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Aviation History
1934
1934 - 1408.PDF
SUPPLEMENT TOFLIGHT MARCH 29, 1934 THE AIRCRAFT ENGINEER In addition to the foregoing case, the table below shows, with references, the problems relating to critical instability that are known to me to have been solved. Reference (1) Plane panels shear KE(«/b)2 17 (2) Plane panels compression ... KE(t/b)2 8 (3) Curved panels shear KE(/r 19 (4) Tubes, torsion KEfi/r)1-35 (Empiric) 20 (5) Tubes, compression KE</V 21 (6) Segment of tube compression KEtf/r ... R. &M.1565 (7) Corrugated panels shear ... KE(</6)2 22 (8) Corrugated panels compression KE(«/fe)2 3 Appendix II Effect of Holes on Strength of Panel Bracing The necessity for the investigation of the case of lightened and reinforced plates subjected to shear forces is, at present, of more urgency than the case of similar plates subjected to end load. Unlike the former case, an approximate estimate of the strength of the latter can be made. The purpose of this investigation is to find by how much strength and stiffness of panels in shear are reduced by cutting hcles in them, and to find what forms of stiffening will restore the maximum elastic strength and stiffness for a minimum expenditure of weight. The first part of the investigation was confined to square panels with circular holes cut in them, and the method of test is as shown in Fig. 1. A square panel is secured to rigid bars freely pivoted at their ends. The pin centres are 22 in. apart, and the material is Alclad 0-022-in. thick. Panels tested to date are as follows :— (1) Plane sheet. (2) Sheet with 6-in. dia. hole (unbeaded edge). (^) ,, ,, "-in. ,, ,, ,, ,, (3) „ ,, 9-in. ,, ,, (weight of beading equal to weight of metal removed for hole). (4) ,, ,, ,, ,, ,, vertical stiffeners. (5) ,, ,, ,, ,, ,, vertical and horizontal stiff- eners. (6) ,, „ ,, „ ,, two laminated rings each side. (7) ,, ,, ,, „ ,, four laminated rings each side. All the panels except No. 7 are shown in Fig. 2. The results shown plotted against shear load in the graph, Fig. 3, are deflections measured at and parallel to the direction of loading. The investigation has not proceeded far enough to allow of the drawing of final conclusions. Two matters, however, arc worthy of comment. ! /\t / o OM> o-ao Q-»O 9 ———~ QCPLieTlON - IN* Mt*. -—• Fig. 3 : Graphs showing relation between load and relative displacement of scales shown in Fig. 1, App. II. No. 1, complete panel. No. 2, panel 6 in. hole. No. 2a, panel 9 in. hole. No. 3, as 2a, edge stiffened. No. 4, as 2a, vertical stiffeners. No. 5, as 2a, vertical and horizontal stiffeners. No. 6, as 2a, laminated rings. The sudden fall in stiffness indicated at points x, x, etc., on the curves cannot be associated with any observable pheno- menon on the panel while being loaded, e.g., appearance of tension waves or their permanence. From the aspect of restoring the greatest percentage of the original ultimate strength, the most effective type of stiffening weight for weight is laminated plates. As might be expected, the use of sectioned stiffeners (panel five, Fig. 2) results in greater stiffness over the first range of load, and this type of stiffening also gave the greatest elastic strength. The amount of elastic strength for these panels is not apparent from the curves shown in Fig. 3. This is an extremely important design consideration, the determination of the true elastic strength necessitating the use of elaborate strain measuring apparatus. Other forms of stiffening are being tested, and subsequently the investigation is to be extended to holes of various dia- meters and forms, and then to the case of lightened plates under combined end thrust and shear force. Appendix III Theory of Webs of Girders The following notes and formulae should be read in con- junction with the relevant part of the paper :— / = Tension in the web in stress units. H, = Load in tension boom in force units. Hr = Load in compression boom in force units. a = Angle of waves to horizontal. V = Load in vertical members in force units. Other symbols shown in Fig. 1. /= 2P/M sin 2a = 2Y/ht (for a = 45°) (1) H(, r = ± Px/k - (P/2) cot a = Vxjh - (£)P (for a=45°) (2) V = -F(d/h) tan a = -V(djh) (for a = 45°) (3) It is stated (Ref. 10, page 1) that when the load acts in one direction only or to a much greater amount in one than in the opposite direction, it pays to put the stiffeners at about 30° to the vertical; it is proved that the weight of the sheet web is lowered 15 per cent, and the stiffness is raised 55 per cent, by such means. The formulae for these cases follow, although it frequently happens that the external forces act for different cases in opposite directions, the total force in one direction not being greatly different from the total force in the opposite direction, thus the angle /S (Fig. 2) for general use should be taken as 90°. The following formulae apply, however, for any angle £, and cover the case of the stiffeners or struts (the words are used interchangeably though stiffener is probably the more appropriate) secured to the web. /= (2H/ht) l/sin2a(l -tan a cot j8) (4) HTC= ± Mfh - S/2 (cot a + cot p) (5) V1= - [(Si+ SR)/2] (djh) (tan a/sin /S) 1/(1 - tan a cot /3) ± Pw/sin ,8 (6) V2= -l(St+ SE)/2](d/7i) (tan a/sin 0) 1/(1 - tan a cot £) (7) S = Total shear force at section considered. M = Moment at section considered. SL = Shear to left of the strut under consideration. SR = Shear to right of the strut under consideration. Pw= External load at the strut under consideration. Other symbols have the meaning previously allocated or as shown in Fig. 2. Providing the spacing of the struts is not outside the limits one-half to one-sixth of the beam depth, the angle a is approximately equal to /3/2. Since the angle £ will, in general, be 90°, the formulae reduce to :— /= 2S/ht (8) HTC= ±M/A-S/2 (9) VB= -[(St+ S«)/2] (d/h) ± Pw/2 (10) PH = the external force applied at the strut V,,.
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