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Aircraft structures for engineering students - part 7

Tính toán và phác hoạ sự phân bố của dòng chảy cắt do một lực lượng cắt theo chiều dọc của S, hoạt động thông qua các trung tâm S cắt và lưu ý các giá trị chính. Cũng cho thấy rằng khoảng cách của các trung tâm cắt từ mũi của phần này là TS = 1 / 2 (1 + a / b). Một m. q2 = q4 = 3bSY/2h (ba), q3 = phân phối 3SY/2h | 352 Open and closed thin-walled beams Calculate and sketch the distribution of shear flow due to a vertical shear force Sy acting through the shear centre s and note the principal values. Show also that the distance s of the shear centre from the nose of the section is s z 2 l a b . Ans. q2 4 3bSy 2h b a q2 3Sy 2h. Parabolic distributions. P.9.15 Show that the position of the shear centre s with respect to the intersection of the web and lower flange of the thin-walled section shown in Fig. p.9.15 is given by 45a 97 77s 46a 97 Fig. P.9.15 P.9.16 Figure p.9.16 shows the regular hexagonal cross-section of a thin-walled beam of sides a and constant wall thickness t. The beam is subjected to a transverse shear force s its line of action being along a side of the hexagon as shown. Find the rate of twist of the beam in terms of Í a s and the shear modulus G. Plot the shear flow distribution around the section with values in terms of S and a. Fig. P.9.16 Problems 353 Ans. ảỡ áz 0A92S Gta2 clockwise qi 0.52S a q2 q ồATS a q3 q2 ữ.YlS a q4 q6 0A3S a q5 0A8S a Parabolic distributions q positive clockwise. P.9.17 Figure p.9.17 shows the cross-section of a single cell thin-walled beam with a horizontal axis of symmetry. The direct stresses are carried by the booms Bỵ to B4 while the walls are effective only in carrying shear stresses. Assuming that the basic theory of bending is applicable calculate the position of the shear centre s. The shear modulus G is the same for all walls. Cell area 135000 mm2. Boom areas Bỵ Bậ 450 mm2 B2 B3 550 mm2. Wall Length mm Thickness mm 12 34 500 0.8 23 580 1.0 41 200 1.2 Ans. 197.2mm from vertical through booms 2 and 3. Fig. P.9.17 P.9.18 A thin-walled closed section beam of constant wall thickness t has the cross-section shown in Fig. p.9.18. Fig. P.9.18 354 Open and dosed thin-walled beams Assuming that the dữect stresses are distributed according to the basic theory of bending calculate and sketch the shear flow distribution for a vertical