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Bruhn - Analysis And Design Of Flight Vehicles Structures Episode 2 Part 10

Tham khảo tài liệu 'bruhn - analysis and design of flight vehicles structures episode 2 part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | ANALYSIS AND DESIGN OF FLIGHT VEHICLE STRUCTURES A23 11 mnrs _ GJ Ln Lm 1 I1 Al J A. únbm Unbn bn t ni -Lfli Lf 9 In the above derivation the torsional stiffness GJ at a representative section Is used. The stiffness Is obtained from Bredt s equation for the twist of a single cell thinwalled tube Eq. 13 Chapter A6 e T 41 4A G t from which by definition For box Ô-7-8-9 Gj _ - 34.3 Finally the stiffness matrices for the three boxes of the example become cf.eq. 9 For box 2-3-5-Ổ 0.000898 1 -1 1 1 -1 For box 3-4-Ổ-7 Here A is the area enclosed within the tube cross section by the median line of the tube wall and the Integration Is carried out around the tube perimeter index s gives distance along the perimeter . For the torque boxes encountered In delta wings it Is probably satisfactory to neglect the ds t contribution from the vertical webs It being small compared with the corresponding contribution from the cover sheets. In the example wing three boxes 2-3-S-6 3-4-Ổ-7 and Ổ-7-8-9 are to be used. These boxes are each 43 Inches square in plan and have average depths assumed here to be the uniform depths of the representative sections of 7.26 Õ.32 and 4.27 respectively. Fig. A23.ll shows the assumed representative cross section of box 2-3-Õ-Ổ and Its GJ calculation. i -ts.OSl hAV 7. 26 --------48 --------------- A 7. 26 X 48 348 in 3 Note rds _ 48 E J t 2 x.05i k8S x 10 G 276 ds t contribution of vertical webs neglected Fig. A23.11 Calculation of GJ for the Representative Section of Box 2-3-5-fi In similar fashion one finds For box 3 4-Ổ-7 GJg ỵ 53.3 For box Ổ-7-8-9 1 -1 -1. 1 QcJ 0.000310 -1 -1 1 1 1 1 -1 -1 1 -1 -1 1 A23. 5 Complete wing Stiffness Matrix The stiffness matrix for the composite wing now may be obtained by forming the sum of the complete stiffness matrices for the beam elements and the torque boxes. For this purpose a large matrix table 13 laid out and entries from the Individual stiffness matrices are transferred into the appropriate locations. Wherever