FlightGlobal.com
Home
Premium
Archive
Video
Images
Forum
Atlas
Blogs
Jobs
Shop
RSS
Email Newsletters
You are in:
Home
Aviation History
1932
1932 - 0575.PDF
JUNE 17, 1932 46 THE AIRCRAFT ENGINEER SuPPI-EMBNT TO FLIGHT TORSION CALCULATIONS FOR A REAR FUSELAGE WITH TWO OR MORE " UNKNOWNS." By H. DAVIES, B.A., A.F.R.Ae.S. Certain difficulties are encountered when an attempt is made to solve a rear fuselage for torsion, with two or more " unknown " forces at the stern end. In the following article Mr. Davies, who is on the Technical Staff of Hundley Page, Ltd., outlines a simple method of overcoming the difficulties. TORSION calculations for a rear fuselage structure, with two or more " unknown " reactions, are found to give rise to certain difficulties, which will be explained in detail below. The present article aims at presenting a simple method of overcoming these difficulties. As an illustration of the proposed method of treat ment, consider the fuselage shown below (Fig. 1). The fin and rudder are assumed to carry a factored side load of 2,400 lb. The diagrams show the dimensions of the rear fuselage structure, the size of the members, the relative position of the side load, and details of the two " unknowns." (It should be emphasised that the diagrams are imaginary, and refer to no particular aircraft.) N B. TOP LONGERONS 25 X 20G STEEL TUBES BTM •• 2 i" x 20 G TOP PLAN WIRES 5A<>~ B.S.F REMAINING '/A,' F1G.I. " Unknown " reactions have been assumed to act in the diagonal struts CB, cB, and in bulkhead CcdD. A total transverse force x is assumed to act in CBc, and a total transverse force y in bulkhead CcdD. The conventional method of treating the structure is to determine the load P in any member of the fuselage in terms of the two unknown reactions, as follows: — P = ax + Py + y where a. P and y are constants. Then with the usual notation: Resilience. u -si—I Differentiating, with respect to the two unknown reactions, x and y, we have: — fix V AE dx) = E T= XaX P lAE J = S \ — X a X (a* + Py + y) and similarly dy = o AE = LJ^EXPX(«* + + Y) The difficulty most commonly experienced in practice is that summation of the terms (1) and (2) leads to two simultaneous equations that are practically iden tical, and therefore almost insoluble. The reason for this will be made clearer by referring to Table 5, which shows a specimen of the strain energy calculations, carried out in the orthodox manner. The table applies to the aircraft under consideration, and gives the strain energy figures for the top longerons in terms of the two unknowns, x and y. It will be noticed that all the terms in x and y are comparable in magnitude, and that they are nearly equal at the forward end of the fuselage, where they have the greatest effect on the final calcula tions. This, of course, is inevitable, whenever the loads throughout the rear fuselages are expressed in terms of two similar and adjacent " unknowns " at the stern end. This point will be referred to again later. Various methods have been proposed for overcoming this difficulty. The method suggested below is believed to be new. It has the advantage of simplicity, and it involves no additional labour of any kind in the course of the calculations. Consider the rear fuselage wedge, AB CcdD. The following diagram (Fig. 2) shows the load system in terms of the two unknown reactions x and y. It will be found more convenient to apply the end- couple at C, c (i.e., 1.50a;) in the plane of the top plane truss, instead of in a true horizontal plane. This leads to the following system of reactions. (Fig. 3.) The proposed method of treatment is simply to replace the variables x and y by x and u, where x + y = u. Then 1.0667a: + 1.20y = 1.20w - 0.1333a:. Fig. 4, below, shows the load system supplied to bulkhead CcdD in terms of the two new unknowns, x and u. In the proposed method of treatment, the load P in any member of the fuselage, is found directly in terms of the unknowns, x and u. Thus: P = ax + bu + c where a, b and c are constants. Then with the usual notation ^ = O = EJ dx \ TyKa X (ax + bu + c) - du IAE X b X (ax + bu + c) I As explained above, the method now consists in determining the load in every member of the fuselage structure directly in terms of x and «, and in carrying out the normal strain energy calculations in terms of these variables. The resultant load system to be applied to the plan and side trusses of the fuselage is indicated in Fig. 5 below. (In every case the loads shown are in the plane of the truss concerned.) The following tables give the strain energy calcula tions for the longerons and wires of the rear fuselage structure. The contents of the tables are as follow: — Table I. Summary of longeron loads in terms of x and u. Table II. Strain energy calculations for top longerons in terms of x and u. 530 e
Sign up to
Flight Digital Magazine
Flight Print Magazine
Airline Business Magazine
E-newsletters
RSS
Events
