The three-cell structure shown

The three-cell structure shown below uses stiffeners connected with shear panels. Note that the curved panel between stiffeners 1 and 3 is semi-circular. The structure is under the action of forces and moments as shown. Assume the shear panels do not carry any direct stress. The material properties are: E = 72 GPa, G = 28 GP, y = 270 MPa, Ocy = 240 MPa, ty = 170 MPa. (a) Calculate the shear flow (N/mm) in each panel and determine the critical margin of safety in shear (not buckling or any other mode) (50%) (b) Re-size the thickness (mm) of the shear panels to reduce the cross-sectional area to achieve the following design requirements (10%): 1. area fraction AlAo less than 0.30 2. all margins of safety greater than or equal to 0.0 3. no panel thickness less than 0.2015 mm The area fraction is calculated as Al Ao, where A is the cross-sectional area of all panels combined, and Ao is the cross-sectional area of all panels using thicknesses as shown in the figure below. In re-sizing the panels, you should consider that the beam cross-section dimensions and stiffener areas are fixed, and that only the panel thicknesses can be varied. You should only consider failure due to shear (not buckling or any other mode). 0.7L 0.3L 2 0.5D 1 MAC dimensions in mm areas in mm MTE 200 0.5D I II III area = 679 3 4 Booms 1, 3: Booms 2, 4, 5: area = 48 750 1 1500 L=153KN D=21KN Mac = 19 kN m MTE = 3.8 kN m panel thickness (1) t = 1.5 mm for all panels except t1-3 = 5 mm

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