FlightGlobal.com
Home
Premium
Archive
Video
Images
Forum
Atlas
Blogs
Jobs
Shop
RSS
Email Newsletters
You are in:
Home
Aviation History
1936
1936 - 1411.PDF
SUPPLEMENT TO FLIGHT 576^ 34 THE AIRCRAFT ENGINEER MAX 28, 1936 Equation (1) wr = R» <m fx , d 2R [x [x • u ivdx+ —— w (rf*)2 the previous article or in using the notation given in R. & M. 1617 (2). In the previous article it was shown that the fiexural line (r) could be drawn direct when the " R " line was straight for the two cases of (1) uniform loading along the span. (2) a loading of o at the tip and varying uniformly to the root. Interpolation between these two for the loading under consideration gives the flexural line. The same principle is now applied to obtain the load curves on the spars, to give pure flexure. When the " R " line is approximated by straight lines dR ' d2R — = constant and —— = o dx dx- Eqiution (1) then becomes- dR wr — Rw + 2 — dx wdx (Equation 1a) (r) is the ratio of the load on a spar to the total load on the wing at any section. It is seen, therefore, that this ratio is a variable according to the variation of w, with respect to x. For w — 1.0 (Uniform Load along the span). Equation (2) r = R + zx— is derived from Equation (la) dx and the curve for this ratio can be drawn direct. For w as a variable with x (A loading commencing with o at the tip and varying linearly to 1.0 at the root). Equation (3) r = R + x — is derived from Equation (1) dx This also can be drawn direct. ! C P LINE i 1 1 m«-fj» ' FLEX LINE FIG. 1. 1 1 i • and Re. Values of loads, wa, wb, and wc are obtained as follows— («•„) For uniform load along the wing. Draw from d, a line dg, of 3 times the slope of de. Produce fe to meet the yy axis. Draw a line j, k, which is 3 times the slope of hf, commencing at h, and drawn over the portion of the spar (e/). Join g to j, by a line, parallel to axis yy. This gives the (r) curve for spar (a) (See Equation 2). Similar constructions give the (r) curves for spars (b) and (c). In this example, the loading along the span being uniform (w = 1.0), the (r) curves and the load curves are the same, and need not, therefore, be re-drawn. If the load along the span had been tapered (Equation 3) the same procedure would be followed, but the slopes would be at twice the slope of the " R " line (see Equation 3). ROOT 9 -8 cy -V \^ ^s>-, 1 1 1 1 1 FIG.3. CORRECTED SHEARS IftEXURf) 1 t 1 ~~"--^ I TIP For any loading along the span between the above two limits, the values of (r) can be obtained by interpolation between the above, for the loading under consideration. The actual load along the spar is then the value of (r) found, for the type of load distribution along the wing, multiplied by the ordinates of the load curve, for the wing. Example Reference Fig. 1. This shows a wing with 3 spars (a) (b) (c). For simplicity, the spars are shown parallel and the loading will be taken as uniform along the span, but for non-parallel spars the following method is modified as was done for a two-spar wing. The values of I of the spars taken in the example are such as to give a discontinuity in the fiexural line so that the correction for this can be shown and applied, as was done for a two spar wing. Calculate the values— I« 16 Ic and Ic la + lb -j- Ic la + 16 -f- Ic la + 16 these are given in Table 1. These values are plotted in Fig. 2 and shown as Ra, R6, For a variable wing loading interpolation between the two, would give the requisite values for (r). It must be noted that for any loading except uniform, the (r) curves as found are to be multiplied at any point by the value of the,wing load curve at that point, to obtain the spar load curves. It will be seen, therefore, that this method enables the spar loadings for pure; flexure to be obtained quickly and easily for any type of*wing loading. Integration of the load curves so obtained gives the shear for each spar. Owing to the Hscontinuity in the load curves due to the abrupt change in the values of R at .5 of the span, a correction to the shear has to be applied. This correction is the same as for a two-spar wing and is as follows— The shear inboard of the point of discontinuity is to be increased or decreased by the following—• ,/dR , , dR = 1 2 w x2 [ — inboard — \dx dx outboard ^ x is the distance from the tip to the point of discontinuity. w is the spar loading at x. — is the slope of the R line and is positive when R dx
Sign up to
Flight Digital Magazine
Flight Print Magazine
Airline Business Magazine
E-newsletters
RSS
Events
