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Aviation History
1939
1939 - 1738.PDF
JUNE I, 1939 19 THE AIRCRAFT ENGINEER SUPPLEMENT TO FLIGHT IOC 7 OA D J i / tfff J 1 /// §W> Zfy / /1/ '//<</ u* 0 I •£ OEft-ECTlON IN INi Fig- 5-Flexural Stiffness. 2000 z «j z M s 0 F © Ifitf 0/ h-J V /* «- <xni(S) T <^ ^ P J & ' I "2 '3 DEFLECTION IN IN. Fig. 6. Torsional Stiffness. Flexural Stiffness : It is proposed to assign arbitrary but more probable actual values to the elastic constants of birch-bakelite three-ply and spruce. These are given in Table 5. TABLE 5. ELASTIC CONSTANTS. Material. Birch-Bakelite Three-ply.. Spruce Young'3 Modu.us ^^ s-^- 10* lb./ n.1 Eo 1.75 1.75 fa ,5 E90 .96 Modulus of Rigidity^^ G,» .13:. G^ .658 Guo .135 135 The deflection of a composite beam of two materials may be calculated by engineers' bending theory if the area of the material of lesser E is reduced in the ratio of the two Es. That is, if an equivalent section in one material is formed. The application of this artifice may be extended to meet the case of a composite beam of more than two materials. In the uncovered framework the E of the spruce flanges is 1.75 x 10* lb./in.! and the longitudinal E of the ply webs is Ew = .96 x io« lb./in.* /. -JS « .55 Referring to the section A A in Fig. 1. Equivalent area of web of side beam is A m X 5 X .55 = -325 "»s.* 254 1 of flanges of one side beam J of web of one side beam 3 53 •r-i- x .55 X — = .675 ins.4 25.4 12 Total I of one side beam is I = 5.8 ins.* In the covered frameworks it is assumed that 5 inches of the compression side as well as all the tension side of the coverings are effective in bending. This is indicated on section C C in Fig. 1. The neutral axes of the equivalent sections are found and thence the I s. In Table 6 are given the flexural constants of the sections. = 5.127 ins.* Specimen. Uncovered Frame.. !li .. ft) .. r; TABLE 6. E/ltr lb. in.' or Srrnce. L75 1.70 1.75 1.75 FLEXURAL CONSTANTS of G10* lb. in.' fo.- Spruce .135 .135 .13") .135 E/10* lb.'in.' tor Ply Covering. _ .5 US M SECTIONS. Equivalen. I in Spruce of Section in.' 11.60 13.11 16.65 14.46 Equlvalcn A n Spruce of Webs in.' .05 .65 .65 .65 The deflection of a cantilever with concentrated end load is given by W/3 6 W/ 8 = -~ +-^r (1) 3EI 5 GA ; In this expression is included the shear deflection of the webs, the shear deflection of the flanges is negligible. / = 46J ins. S = W 19600 10" + W "640" io6 Substituting the I s from the above table and making W equal to 100 lb., the following deflections are obtained and compared with the test deflections of Table 3. This is done in Table 7. TABLE 7. CALCULATED FLEXURAL STIFFNESS AS A PERCENTAGE OF MEASURED STIFFNESS. Specimen. Uncovered Frame ... (1) ... (2) ... (3) ... Measured Deflection of Specimen for Load of 100 lb. .233 .214 .182 .£01 Calculate- Deflection of Specimen for Load of 100 lb. .£50 .223 .177 .205 Percentage Ratio of Stiffness. Calculated Measured. 107% 104% 07% 103% Torsional Stiffness (Uncovered Framework) : The loads on the side beams and on the end rib or cross beam are as shown in Fig. 3. The torques Q constitute a balanced system of internal forces. Strain Energy 0/ Side Beam. H M* 3 W*/ J 0 2EI 5 GA The second term of the expression is the shear strain energy of the web, the shear strain energy of the flanges is negligible. [I \\\(l-x) - Q]' ^ [ 3W»/ n 2EI 5GA "W«/s 1 iEI + Q*/ - WQ/* "1 + 3^ J 5GA (2) Strain Energy of Half Cross Beam d U.-I°'«l 'Q-Qz 2 GK QW 2 2 uK 4GK where K is the torsional constant of the cross beam. K = .2636c' where - = c In this case b — 5 ins. c = U = U, +U, ins. that is (2Q/ - W/*) + = o oy = o 2EI Length oi Beam • E of Spruce G of Spruce I of Side Beam A of Web K of Cross Beam Length of Cross Beam d =16 ins. substituting the above in equation (3) Q = 7.i6W Deflection of Side Beam 2GK = 46I ins. = 1.75 X 10* lb./in.1 = .135 x io6lb./in.* * (3) = 5.8 ins.' = .325 ins.8 = 5.65 ins.* 6 ==- substituting (4) 1 2EI — - Op 1 + 6 W/ 3 J 5GA in (5) together with the other values. 3885W (4) (5) o = io° when W = - = a zooo 16 - 125. this compares with 6 = .486 ins. 8 =* .422 ins. from test.
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