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Aviation History
1936
1936 - 1114.PDF
APRIL 30, 1936 27 THE AIRCRAFT ENGINEER SUPPLEMENT TO FLIGHT 462s THE STRESSING OF MONOPLANE WINGS Extension of Method to Non-straight " R" Line, Spars Still Parallel By HAROLD N. HORNE (Continued from p. 19) . THE method will now be extended to cover the case when the " R " line is not straight. (Reference Fig- *)• (1) The values of " R " at points along the span arc calculated and plotted as shown. (2) Draw an " R " line composed of two (or more) straight lines through the points so calculated. (3) Commencing at the tip draw the flexural lines for uniform and taper loading for the portion A.B. following the rules as for the previous example. (4) To obtain the flexural lines for the portion B.C. proceed as follows :— (a) Produce C.B. until it meets the ZT ZT axis at P. (b) From P draw lines of 2 and 3 times the slope of the portion of the " R " line B.C., over the same portion of the wing. (c) Join the lines obtained for the portion A.B. to those obtained for the portion B.C. by lines parallel to the ZT ZT axi>. W) Interpolation between the flexural lines so obtained for the type of loading under consideration will give the corresponding flexural line. Correction for Discontinuity If the values of M/i for the two spars are now obtained ^ will be found that the spars would not deflect equally. This is due to the discontinuity at the point B. A correction for this is given, the proof of which will not w* included, being too lengthy, but it will be found that if applied, the correction gives the true values for shears, tf-M.s ancj deflections of the spars. the correction is to apply a concentrated torque at the P°"it B. (i.e.) a concentrated load on each spar. The correction for the front spar is 'dR dR -j— inboard — outboard ) dx dx J wher (equation 3) dR Dre w is the loading at x, and the values of ~ are the "opes of the two portions of the " R " line, the slope being positive when the distance from the rear spar to the " R " ti e|"'n^reasing when moving along the X X axis from the same° 1 rCX>t' ^e correc1tic,u fr>r the rear spar is the a cr, T e but OI opposite sign. This correction gives r.oi,?,'1 xant increment to the shear T,°Ldlscontinuity- curve inboard of the c v .^' 4-—The front and rear spars are parallel to the ax is. The " R " hne is shown as A.B.C. DIAGRAM OF PROPORTIONS FOR r ex. - 14' front- spar _l 1 i_ ROOT -9 -8 •I TIP ROOT The flexural lines for the two cases of parallel loading and taper loading are shown as A.D.E. and A.F.G. As before, interpolation between these latter, according to the type of loading under consideration, will give the flexural line. The shear curves for the two spars can now be obtained by applying the load along the flexural line and taking moments about either spar to obtain the in dividual spar loading. It is to be noted that when drawing the shear diagram the correction is to be included as a constant quantity added or subtracted according to which spar is under con sideration, the correction to commence at the point of discontinuity and to be applied over the rest of the wing inboard of that point. Integration of the shear curves gives the B.M. curves and as before it will be found that values for M/i at various points along the spars give the same value for each spar thus checking the flexural line. Non-parallel Spars To make the application perfectly general it will now be shown how the flexural line can be drawn when the spars are not parallel to each other Referring to the general equation to the " R " line— R IF COS 3 a F (equation 4) IR OF XX 1F COS8 oF + IR COS3 OR where 1F = moment of inertia of front spar. = moment of inertia of rear spar. = Inclination of the front spar to the X X datum. = Inclination of the rear spar to the X X datum. It must be noted that the values of " R " are ratios of the distance to the " R " line (measured from the rear spar) to the distance between the spars. When this is understood, it will be easy to understand the following procedure. (Reference Fig. 5 a and b)). 1. Calculate " R " from the above equation (No. 4). 2. Draw two lines parallel to the X X axis F.S. R.S.
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