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Aviation History
1928
1928 - 0234.PDF
Bxreruatsm TO FLIGHT 22 MARCH 29, 1928 THE AIRCRAFT ENGINEER having sides of length 2a and 26, and thickness 2h, secured at the edges and acted on by edge thrust Pj per unit length in^the direction of side of length 2a, and P2 per unit length on the side of length 2b. The conditions of loading and the dimensions of the plate are shown in the following diagram. P, PER UNIT OF LENGTH P2 PER UNIT OF LENGTH The form of the solution is nnz(xw = W sin provided that 2a a) . nr.(y ^ b) -Sm~2b~- (1) where w is the displacement of a point on the plate at(.r(/) from the origin W is a constant. m and n integers (giving the number of corrugations or " waves " parallel to the sides of the plate) and D = - -—- this term is called by Prof. Love the " flexuralo 1—<J rigidity " of the plate. a is Poisson's ratio for the material of the plate. The above equation gives the critical thrusts. For example, if Px = P2 the critical value of V1 and P2 is £ Dn-2 \ — -\— j If we take the case of a box spar with a flat plate flange then P2 = 0 and n = 1. It is assumed that P1 is the only force acting on the plate. 1 IT 1 •- - = P. (3) &2J >/m)2 •- w Therefore for minimum Px (at critical equilibrium) a/m — b (obtained by differentiating V1 with respect to a'm and equating to zero). .. , EAV2 4 P, Consequently, 6(1 -a2) h- 3 (1 — a2)b- If the stress intensity is p, then Pj = p.z.h. ETT2 jh ,2 The second case is that of a thin tube under compressive end load. Three types of failure may occur, according to the dimensions of the strut: (1) The well-known failure caused by the induced stress exceeding the compressive yield of the material. (2) Failure brought about by elastic instability of the strut as a whole, causing bending of the structure line of the member. (3) Instability of the strut wall. (1) and (2) are fully investigated in numerous text-books on structures or strength of materials, and no further attention need by given to them here. It is only within comparatively recent years that the third case has received serious attention. In ordinary structural engineering the matter is of small importance, but in aircraft engineering the reverse is the case. 70 60 • a) i wSO v> UJ K v> 40 30 DEPTH OF FLANGE INS. 2 12 3 A- -5 6 7 [ s DELATION BETWEEN D )F SPAR FLANGE 8. STR )EVEL0PED FROM FLAN la,3b. 3c THE GftUGE THER DIMENSIONS AS HEWN ON THE DRAWINC y / 1 /1 II ( 11 IPTH GES MO ~1_~t_ ' J j1 RELATK DF MATI FIG.I. 8. SECTIO y. )N BET1 iRIAL If STRESS (VEEN T 4 FLANC DEVEL HIC »E 0 OPE WE FSP .0 ss N 01 -012 -014 016 -018 OZQ 022 024 026 THICKNESS OF MAT INS. Graph 1. Mr. R. V. Southwell obtained the formula E t / Z~i~ r> = —— — A/ ____^_ (5) where p is the stress intensity at which a tubular strut would collapse through elastic instability of the walls. E = Young's modulus, t = wall thickness, R = radius of tube, and — = Poisson's ratio.m RFrom this equation a value of—= 115 is obtained if p = 65 tons/sq. in. Equations (4) and (5) are shown plotted in Graph (1). E for steel has been taken as 12,500 tons per sq. in. ;, = O" >» >) *> 0"0h ,, ,, It has consistently been found that the ratios of t/R and 90 80 70 SO *D WI5" 10 JO 20 10 t R •001 -002 003 -0 1" ; > STRIP THICKNESS RADIUS OF TUBE 0+ -005 -006 0( RELATION BETWEEN CRITIC/! INTENSITY OF STRESS & RATK OF SEMI THICKNESS TO PLAT WIDTH FOB FLAT PLATE UND / y \y * •01 015 hI y / / / d. E ER_ r f •-— / t A )7 -00S 009 -0 \ -J- / t 1 / SIMILAR RATIO FOR TUBE. ABSCISSAE BEING WAL THICKNESS TO RADIUS RATIO 02 03 STRIP SEMI THICKNESS BREADTH OF STRIP •04 ( 3 5 Graph 2. 2126
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