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Aircraft structures for engineering students - part 10

Chiếc máy bay đối xứng cứng nhắc nối khung 1234567, thể hiện trong hình. P.12.4, là cố định hỗ trợ cứng nhắc 1 và 5 và được hỗ trợ bởi các con lăn nghiêng 45 "so với chiều ngang tại các nút 3 và 7. Nó mang một điểm P tải thẳng đứng tại nút 4 và tải một w thống nhất phân phối cho mỗi đơn vị chiều dài trên khoảng 26 Giả sử EI độ bền uốn cho tất cả các thành viên, | Problems 535 P.12.4 The symmetrical plane rigid jointed frame 1234567 shown in Fig. p. 12.4 is fixed to rigid supports at 1 and 5 and supported by rollers inclined at 45 to the horizontal at nodes 3 and 7. It carries a vertical point load p at node 4 and a uniformly distributed load w per unit length on the span 26. Assuming the same flexural rigidity El for all members set up the stiffness equations which when solved give the nodal displacements of the frame. Explain how the member forces can be obtained. Fig. P.12.4 P.12.5 The frame shown in Fig. p.12.5 has the planes xz and yz as planes of symmetry. The nodal coordinates of one quarter of the frame are given in Table P.12.5 i . In this structure the deformation of each member is due to a single effect this being axial bending or torsional. The mode of deformation of each member is given in Table P.12.5 ii together with the relevant rigidity. Fig. P.12.5 536 Matrix methods of structural analysis Table P.12.S i Node X y z 2 0 0 0 3 L 0 0 7 L 0.8L 0 9 L 0 L Table P.12.5 ii Member Effect Axial Bending Torsional 23 El 37 - - GJ 0.8E7 29 EA 6 2 - - Use the direct stiffness method to find all the displacements and hence calculate the forces in all the members. For member 123 plot the shear force and bending moment diagrams. Briefly outline the sequence of operations in a typical computer program suitable for linear frame analysis. Ans. 529 5 28 a 2J 6 tension M3 M PL 9 hogging M2 2PL 9 sagging SF12 -SF23 P 3 Twisting moment in 37 PL 18 anticlockwise . P.12.6 Given that the force-displacement stiffness relationship for the beam element shown in Fig. p. 12.6 a may be expressed in the following form 12 6 -12 6 1 El 6 4 6 2 e L py 2 -12 6 12 6 v2 . M2ỊL J . -6 2 6 4. obtain the force-displacement stiffness relationship for the variable section beam Fig. p. 12.6 b composed of elements 12 23 and 34. Such a beam is loaded and supported symmetrically as shown in Fig. p. 12.6 c . Both ends are rigidly fixed and the ties FB CH .