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In this project we consider collapse of plates due to in-plane loading. We analyze three problems: buckling of biaxially compressed plates, response of biaxially compressed plates in the presence of initial imperfections, and design of stringer-reinforced plates subject to compression. Problem 1. Determine allowable combinations of compressive and tensile loads applied along the xand y-axes for the simply supported plate with dimensions prescribed in your variant (three thickness values given in Table 1 should be considered). Consider all possible modes of failure, i.e. both buckling as well as the loss of strength (the factor of safety is equal to 1.0). Fig. 1. Plate subject to biaxial compression (in the solution you should consider the case of biaxial compression as well as the case where one of the applied stress resultant is tensile, while the other is compressive). 1 Problem 2. Determine allowable combinations of compressive loads applied along the x- and y-axes for the plate with the dimensions prescribed in your variant if the anticipated amplitudes of the initial imperfection are specified as 1/10, 1/4 and 1/2 the plate thickness (accordingly, you have three curves for allowable applied stress resultants on the N N x y − plane). Assume the most unfavorable shape of the initial imperfection with one half-wave along both x- and y-axes. You can use only the first thickness value prescribed in your project. Vary N and N x y throughout the entire range of possible compressive values. Compare your solution to that for Problem 1 to assess the effect of initial imperfections on the plate. Problem 3. Determine the required thickness of the reinforced plate as a function of the spacing between the stringers that are oriented along the direction of the compressive load (see Fig. 2a for the orientation of the stringers and x-axis), if the buckling compressive stress resultant Nx of the unreinforced plate in your variant must be increased by a factor of 2. The length and total width of the plate (a and b) should be taken as in Table 1. The thickness of the unreinforced plate corresponds to case 3 in Table 1. The distance between the stringers varies in the range from b/4 (three stringers) to b/2 (one stringer). The intermediate case of two stringers should also be considered. We do not specify the cross section of the stringers but assume that they provide simple support to the plate. Initial imperfections are negligible. Consider both modes of failure of the section of the plate between the parallel stringers, i.e. buckling and the loss of strength. The chosen thickness must prevent either mode of failure, while also providing the lightest (thinnest) possible structure. Thicknesses less than 2.5 mm are disallowed. 2 Comment 1: Each section of the plate between parallel stringers is considered simply supported and their mutual interaction is disregarded. This is a common approach in industry. Comment 2: The analysis is conducted only for the sections of the plate between two parallel stringers (called “subpanels” in Fig. 2a). Other possible modes of failure that we do not consider here include buckling or loss of strength of stringers (those are unlikely in a properly designed structure). The other possible failure mode is buckling of the entire reinforced plate including both the sections between the stringers and the stringers themselves. The classical solution to this problem was originally developed by the Russian school of mechanics in the beginning of the twentieth century. However, the complexity of such solution makes it unattractive so that today a relevant analysis is conducted using FEA. The solution you present in the project is conservative, neglecting the interaction between global and local buckling and the mutual effect of adjacent subpanels, i.e. it is acceptable only at the preliminary design phase

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