1942 - 0094.PDF

34 ^ _^W tA-^^ FT"TGHT. Ta " ^ l R C R A f T ENGINEER FLIGHT, January 8th, 1941 AIRCRAFT/SECTIONS The Importance oj^J^rsionaTa^fei/ as Flexural Rigidity in Sfee/ Alloys, /Aluminium AjjfisKand Magnesium Alloys E. Vk THOMAS^h.D.,/M.Sc., A.M.I.C.E., A.M.I.Struct.E. I N early structural design\strutsjwere env^geda£*ngid members of robust prnpIWi on <v a n rl fi\£b£m&ato resist direct crushing. The advent "of inild steel and standardisation of structural sections produced compound riveted stanchions in which the metal was distributed with a view to maximum flexural rigidity. In built-up welded sections the process was carried a stage farther, and further economy achieved in the distribution of the metal. With the development of aircraft sections the ratio of strength to weight became still more important, and a search began for high strength alloys resulting in lighter and thinner sections. It is this latter factor of thinness that has resulted in metal now being distributed to give torsional as well as flexural rigidity, as demonstrated in the corru- gated sections of modern aircraft. The need for the consideration of flexural and torsional rigidity, in addition to direct crushing, can be simply demonstrated thus : Consider a long and narrow strip of metal supported at the ends with end loading applied axially. Such a long strut will deform in a typical " Euler " curve, the bending being resisted by the flexural rigidity of the section. If the long strip is wide and the load still applied via the ends, wrinkling or twisting occurs, such deformation being resisted by the torsional rigidity of the section. In the standard sections such as angle, tee and channel the outstanding leg or flange will behave similarly, but the liability to twist will be increased since one long edge of the " strip'" will be supported. It is thus clear that any formula for the design of aircraft sections should incorporate flexural and torsional factors. Ratio of Flexural and Torsional Rigidities The importance of considering torsional rigidity is indi- cated in Fig. 1, where the ratio of flexural to torsional rigidity is plotted against an increasing value of breadth to thickness of the outstanding leg of a simple angle section Fig. 1. Relation between bit and EI NC, showing how the ratio EI/NC increases beyond B.S. range. The flexural rigidity is taken as proportional to EI, where E is the Modulus of Elasticity and I is the least moment of inertia ; and the torsional rigidity is taken as proportional to NC, •where N is the Modulus of Rigidity and C is the torsional constant. In Fig. 1, bjt represents the ratio of breadth to thickness of the outstanding leg. In the British Standard range of equal angle sections the ratio of bjt does not exceed 16, and the ratio of EI/NC is 85. By taking bjt as 32, that is to say twice the range of the British Standard sections, the value of EI/NC is 335. The ratio of flexural to torsional rigidity has increased fourfold, thus exhibiting a marked deficiency in the torsional rigiditv of the thinner sections. Standard Sections In the standard sections such as angle, channel and tee, the outstanding leg being thin will tend to deform under a ol II I IX IX Fig. 2. Typical T, angle and channel sections. I HORIZONTAL SECTION AT HALF HEIGHT - -fK end loading. Since such a leg is supported along one long edge, the deformation of the leg may be considered as (a) bending about an axis of least moment of inertia, as XX in Fig. 2, and (6) twisting about a centre of twist, as point O. The determination of the centre of twist will depend on the relative stiffness of the component rectangles of which the section may be considered formed. Determination of Crippling Stress Referring to Fig. 3, the general problem may be stated thus : Consider a strut of length " L," ends hinged, and let the area "a" be a small part of the cross section of the structural member. Then this typical longitudinal fibre will deform to a curve such as V = 8 . sir. — as shown in the elevation. The shorten- ing in length of the member due to this flexure is p " per unit area, the work done on this small longitudinal fibre is. AREA'a' 77* ELEVATION and if the end loading is r/YY = \ . p.a. -1. (H 3- dx. j o \dx, This work will be stored as flexural and torsional strain energies. The flexural strain energy is EI f L A^>'y 2 JOWV the bending occurring about an axis as XX, see Fig. 2. The moment of inertia will "be given by the expression — . t % . dr. The torsional strain energy is 2 \Q\dx ) in which C is the torsional constant for the section, and #j is the twist at any dd point x from the end. The value of —- 1 dx " " AREA'a' HORIZONTAL SECTION AT HEIGHT X Fig- 3-

1942 - 0094.PDF

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