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Aviation History
1937
1937 - 1409.PDF
MAY 27, 1937 33 THE AIRCRAFT ENGINEER SUPPLEMENT TO FLIGHT — cos(^j — <fir)] = F. For a number of tangential loads, end load = Fj -f- F2 -f- . . . Fw and shear and B.M. are everywhere zero. Application of Preceding Theorem to the Frame Problem. First we consider the monocoque structure divided into panels bounded by consecutive stringers and frames. Then we estimate the buckling stresses of the panels each side of the frame considered, allowing for the stabilising effect of tension due to bend, and we average these fore and aft. Then we estimate the shear stresses in each panel allowing for the effect of body taper, and again average the stresses fore and aft. Then tension field stress = i(fs — fscr) = ft, where fscr is the average buckling stress of a panel in shear, and ft is the tension field stress. This assumes that the principal compressive stress remains constant after buckling, while the tension stress increases. Frames to that previously considered, the only B.M. being due to the fact that the neutral axis of the frame is inboard of the skin (see later). Similarly, the normal force due to the longitudinal curvature is given Stringers ft 4= mean tension field stress foV panels X Si V F1 = ft1«lxt F2 = J ''2-ft1)xlxt F3 = nft3-ft2)KlKt F4 = i(fl3-ft4]«lxr F5 = Uf»4-fi5)xlxt F6=i(ft5)xlxf ® - X I X t 2 Divide the frame into a number of equal elements of lengths (ds). The stringer spacing is suitable. Assuming the number of stringers to be large, the length A-A will be loaded by curvature effects of the area with double shading in Fig. 6. The total tension force on this strip in the ft I ft direction of the frame is given by—— X t x —-=. \/2 V2 where t is the skin thickness. The force normal to the • ft ds • frame due to this tension is — x / X t x ^7—where RT IS 2 1<T the transverse radius of curvature of the frame. The end ft load in the frame due to the tension field ==— x I X t 2 = (fs — fscr)l x t which in general is a variable since fs and/or fscr varies, and we have a tangential force applied at each stringer (see Fig. 7). If the tangential forces are given by F, the normal Fds forces are given by — and we have a system similar by f J 2 x ds KL longitudinal radius of curvature. ft stringer due to tension fields is — where RL — The compression in the X ds x t and the outward normal force due to this is— x ds x t x 77- This exactly 2 RL * balances the inward normal force from the skin. Let h be the distance from the skin to the neutral axis of the frame. Then at the point of application of each tangential force F we have an offset moment F X h. We can now do a strain energy calculation on the frame to include the effect of continuity, remembering that the B.M. is only due to the applied couple F x h (see Fig. 8). Complete Rings It should be noted that the method of applying tangential forces to the frames is only strictly correct, for a monocoque section open top and bottom. Where the monocoque • section is a complete ring instead of having tangential forces, it is possible for the tension in the skin, parallel to the frames, to continue over the top and bottom, and to be reacted by tension from the other side. This would necessarily be the case if the frames were not riveted to the skin. In this case there is no bend in the frames due to F xl, only uniform end load equal to F. The tension in the skin parallel to the frames is now constant and equal to one-half the greatest value of ft, while the shear along and perpendicular to the body axis, and the tension along the body axis, vary to accommodate changes in shear over the section. The difference in stresses computed on this basis and on the basis of applying tangential forces will be (assuming fixing in the latter case) about 25 per cent. Since the design stress on any particular type of frame is best found from a test on a portion of a typical monocoque, analysis of the test by either of the above methods can be made, and providing the same method is adhered .to in application to fuselage design, no error will result. In the case of torsion, since the shear per inch run is constant round the section, and providing the thickness of the skin and spacing of the stringers is approx. constant and varying stability due to variation of curvature is small, the tension field stress will be constant; and so will the tension stress parallel to the frames. In this case there will definitely be no bending due to F x h, and the frames are under uniform compression F given by F = -r— where Q • torque, A = area of enclosed section, / = frame spacing, and Qj = buckling torque. If the tension field stress is high and the stringers are flexible, a line drawn on the skin, parallel to the folds, and terminated by consecutive frames will lose its curva ture and become straight. We now have a break in the direction of such a line, at the frames ; but the inward X /
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