tailieunhanh - Aircraft Structures 3E Episode 10

Tham khảo tài liệu 'aircraft structures 3e episode 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 346 Open and closed thin-walled beams Derive expressions for the vertical and horizontal components of the deflection of the beam midway between the supports B and D. The wall thickness t and Young s modulus E are constant throughout. Ans. u ữAMWl3 Ea3 t v Ea31. A uniform beam of arbitrary unsymmetrical cross-section and length 21 is built-in at one end and simply supported in the vertical direction at a point half-way along its length. This support however allows the beam to deflect freely in the horizontal X direction Fig. . For a vertical load w applied at the free end of the beam calculate and draw the bending moment diagram putting in the principal values. Ans. Mc 0 Wl -Wl 2. Linear distribution. Fig. A beam simply supported at each end has a thin-walled cross-section shown in Fig. . If a uniformly distributed loading of intensity w unit length acts on the beam in the plane of the lower horizontal flange calculate the maximum Problems 347 direct stress due to bending of the beam and show diagrammatically the distribution of the stress at the section where the maximum occurs. The thickness t is to be taken as small in comparison with the other cross-sectional dimensions in calculating the section properties Ixx Iyy and IXy. Ans. cr mai 7 3 13w 2 384a2í ƠZẠ wl2 96c t ơZĩ2 wl2 48a2t A thin-walled cantilever with walls of constant thickness t has the crosssection shown in Fig. . It is loaded by a vertical force w at the tip and a horizontal force 2W at the mid-section both forces acting through the shear centre. Determine and sketch the distribution of direct stress according to the basic theory of bending along the length of the beam for the points 1 and 2 of the cross-section. The wall thickness Í can be taken as very small in comparison with d in calculating the sectional properties Ixx IXy etc. Ans. ƠZẠ mid-point td2 crzl built-in end iJ2 ƠZ2 mid-point td2 Ơ-2 built-in end Wl td2 Fig. .