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Structural Calculation of Rectangular Plates with Different Support Conditions of Four Edges
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    Abstract:

    For a rectangular thin plate with different support conditions of four edges, a double Fourier series with additional terms was taken as the deflection function, and linear algebraic equations for solving the undetermined coefficients were derived. A unified structural calculation formula was obtained for the plate with any combination of simply supported, clamped, and free edges. The non-convergence of a series solution of bending moment at a point where a concentrated load is applied was discussed. In addition, the aspect ratio problem that needs to be achieved when simplifying a two-way plate is also discussed. The results show that the bending moment at the point can be calculated through the finite difference method using the deflection value, where a differential step length of 10 mm was selected. A plate with two opposite edges supported and two other edges free, and a plate with one edge clamped and the other three edges free, can be taken as a one-way plate. A plate with all four edges supported can be treated as a one-way plate with two ends clamped, one end simply supported and the other end clamped, or two ends simply supported if its aspect ratio reaches 2∶1, 2.5∶1, or 4.5∶1, respectively. A plate with three edges supported and the last edge free can be seen as a one-way plate with two ends clamped (and one end simply supported and the other end clamped), or two ends simply supported if its aspect ratio gets 1∶1 or 2∶1, separately; this type of plate can also be simplified as a cantilevered one-way plate at an aspect ratio of no less than 6∶1. A plate with two adjacent edges supported and the other two edges free can be taken as a cantilevered one-way plate if its aspect ratio reaches 2∶1 when the two supported edges are all clamped, or if the aspect ratio reaches1.5∶1 when one edge is clamped and an adjacent edge is simply supported.

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  • Online: January 16,2024
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