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Aviation History
1934
1934 - 1409.PDF
MARCH 29.1934 21 THE AIRCRAFT ENGINEER SUPPLEMENT TO FLIGHT In the relevant references, formulae covering the case of beams having struts flexible in the plane of the web sheets are quoted. In general, however, it is preferable to secure the struts to the sheet, thus securing the greatest rigidity, the proportionate increase in the strength of the struts obtained by this means is indicated below (Fig. 6 and equation 18) while the whole stiffness of the girder is raised by such fixing ; the formulae for flexible struts are therefore not given. In addition to the stresses arising from the force calculated from equations 1, 2 and 3, bending stresses are also set up in the flanges due to the pull of the web sheet on these parts. The stress at the point A is given as (Ref. 10, page 5) /A=/,,.(V/V) = /»1/(1 - cot a tan 8)» (15) hL,(KV) /»/( cotatan 8)s (16) where/,,, = (Sw/kxt) 1/sin a cos a (17) In the above, the boom angles 8 and y are assumed equal. The strength of the vertical secured to the skin is derived by means of Fig. 6. The elastic support given to the verticals, results in what is, in effect, a reduction of the slenderness ratios or a virtual reduction of lengths of those members Vk I. e c. z \1\ \ —_ — e to >* Appendix HI: Figs 1 to 6. The bending moment is a maximum at the points of attach- ment of the web struts and is MF= Sd^Uh . tan a (11) If the resistance of the flanges to bending is small then the pull of the central parts of the web becomes ineffective (Fig. 3), it is then necessary to evaluate the expression wd= l-25isin ^ [l/(lt+Ic)h] (12) where 1/ and I,, are the moments of inertia of the tension and compression flanges about their own centroidal axes, and from Fig. 5 to obtain a value for the constant CV Then a new bending moment M*F= CiMp can be derived (13) In the case of flexible flanges, the equation (1) gives only the average stress in the web sheet, the max. stress is /max = /average X 1/^2 the value of C2 also being obtained from Fig. 5. In most wing constructions the spars taper, thus part of the shear is taken on the flanges direct, the amount taken by the web being the difference (Siu) of the total shear and the vertical components of the flange forces (Fig. 4). Wagner gives this case special treatment as indicated in Ref. 10, page 1, et seq. The main fact established is that the web stress vanes over the depth of the girder. At the same time the stress is constant along the length of any wave, thus the stress at the point A on section AB (Fig. 4) is the same as at A1 and the stress at point B is the same as at B1. and the virtual length I1 is given by »=C3Z (18) C3 being obtained from Fig. 6. Using this effective length and the loads V or V» the strength of the member as a strut can be obtained from the " strut curve," allowance being made for the " effective width " of attached material. 17 P.B.S., Vot. 105. On the stability under shearing forces of a flat elastic strip. B. V. Southwell. 18 Uuckling of thin plates in compression. R. & M. No. 1554. H. L. Cox. 19 Strength in shear of thin curved sheets of Alclad. N.A.C.A. Technical Note No. 343. O. M. Smith. 20 Strength tests of thin-walled duralumin cylinders in torsion. Technical Note 427. E. E. Lundquist. 21 P.E.S., Vol. 121. The strength of tubular struts. A. Robertson. 22 Z.F.M., 28/9/29. The buckling of corrugated sheet in shear. S. Berg- mann and H. Reissner. 25 D.V.i,., 6/3/31. Buckling tests on panels of corrugated sheet. E. Seydel. PIETZKER, NOT PESCA In the account of the discussion of Mr. Pollard's paper published in FLIGHT last week, Mr. Langley was made to refer to Pesca's theory. Some of our readers may have been puzzled by this unfamiliar name. The author to whom Mr. Langley referred was Henr Pietzker. Reference to Pietzker's theory is made in A.It.C It. & M. No. 1553, but there is a misprint in the reference. The analysis of Sir John Biles' experi- ments on H.M.S. Wolf in the light of Pietzker's theory was published in the Proc. Inst. Naval Architects in 1925, and not, as printed in R. & M. 1553, in 1905. 306 e
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