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Aviation History
1937
1937 - 2368.PDF
SUPPLEMENT TO FLIGHT d 10 THE AIRCRAFT ENGINEER AUGUST 26, 1937 Lateral Loading It remains to find the lateral loading applied to a short length of stringer oz due to the tensile stress F. If p is the radius of curvature of the shell at the point x, y, z, the normal load J)N applied to the stringer is <)N = q.t . —. oz. P The tangential load applied to the stringer is given by ftf, 2>T 2)1 t. 2)1. 2>z Substituting from equations (1) and (2) for the stress oq terms q and — into the above equations, gives JN and J)T in the forms 3N ^, 1 — = t. cl.— oz PL .*.***] and -—: oz t .ol i Vy-T . The lateral loading on the stringer is therefore r v y .dl Ps.*. Ps .t (3) (4) (5) (6) The loads applied by the stringers to the rings are approximately, N = P> . W« (7) T = Pr . Wt. (8 (ii) Shear Due to Torsion. By Batho's formula, if A is the area enclosed by the section the constant shear stress is given by , Q *1 11 2 . A . t. - o. Corresponding to equations (5) and (6) we obtain : w-=,-x. 7 ,g) and W( = o (10 Application (Hi) Application to Elliptical Section fuselage with Vertical Shear had V. Referring to Fig. (3) x —• b cos (f> y — a sin <j> Writing b2ja2 = 1 — e2 dl gives —= «(i — e2 sin2<^)s d4 Now equation (5) may be written W. -[ qo x • qo - V 4at V ¥ •e y.dl 0 *y2.dl 0 ],. t . d*yr dx 1 + dv dx 3/2 sin <j> i — e2sin2<£)» rf<£_ ^sin2<£(i — e2sin2<£)i djr b.p,.t. cos2.* 4- (1 - e2) sin24> 3/2 The integrals may be evaluated by expanding (1 — e2 sin V)* and integrating as many terms of the series as are necessary to obtain the required degree of accuracy. The integrated form is : W. = \qo 1: vt-a-^-H irat I -[-l--^--••] I b .Ps .t 3/2 a2 J cos2^ + (1 - e2) sin* 4, It remains to determine qo. Since the shear stress is clearly zero when </> = — .-. w„ = V.P, qo = o f e2 cos26 L 2 3 cos <j> ira' [1 - |-2- Is-4.-j X j cosV + (i -*2) sin2/] 3/2 .'. W„ = K„ (11) where K„„ is a function of e and <f>. Wt is given by a somewhat simpler expression for W, 1 Ps.!!. V.Ps . sin <f> •na' :. W, = - K(, . 3T V.Ps 5f! 64 ••] (12) Where K,„ is a function of e and <f>. It is convenient to neglect the minus sign in equation (12) since it merely indicates the direction in which the load W, is acting (i.e., in a direction opposite to increasing values oil). The coefficients K.nl> and K.th are determined in an exactly similar manner. Finally <f> is written in terms of 6. tan <j> = bja tan 6. Plotting the Curves Using this relationship the coefficients K„„, etc., are plotted against 8 as families of curves, each curve represent ing a particular value of b/a. It will be noticed in Figs, (5) and (7) that the lower portions of the curves coincide over the range of b\a values plotted. The curves actually vary very slightly in this region, but to avoid confusion the mean line only is plotted, the error introduced being negligible. (iv) Elliptical Section Fuselage with Torque Applied. The coefficients are readily derived for from equation (9). 2A p b P. W. Q 2-nab 0 2irbs cos2<f> + (1 - e*) sm24> (1 - e2)| '] 3/2 p. OP • w = K ^ ' 2-nb3 From equation (10) W, =0. cos20 + (1 - e2) sin2^ ,j3/2 (13) (v) Particular case of Circular Section fuselage under Direct Shear Loads. It is interesting to note that for the circle where bja = 1 equations (11) and (12) become
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