Determination of critical design parameters of rectangular plates under uniformly distributed lateral load
Date
2023-06
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Publisher
Federal University of Technology, Owerri
Abstract
This study investigated the critical design parameters of classical rectangular plates under uniformly distributed lateral load. The study used Kirchhoff’s hypotheses on total strain energy, work energy principle, kinematics, stress deflection relationship, and constitutive relationship to derive the third-order total potential energy functional for an isotropic rectangular thin plate with small deflection. External work was substituted into the third-order total potential energy functional, and the general equation of a classical rectangular plate under pure bending was obtained. The plate general equation was minimized with respect to deflection to obtain the equilibrium of forces governing equation of thin rectangular plates. The resistant forces were solved with Split-deflection approach and the solution gave the general polynomial deflection equation. Satisfying the boundary conditions of the plate with respect to the general polynomial deflection equation gave the peculiar deflection equation. The general polynomial deflection equation was simplified and substituted into the plate governing equation to obtain the amplitude of the deflection function. A close integral was performed on the shape function for various boundary conditions with respect to the general stiffness equation, which gave the peculiar stiffness and non-dimensional deflection coefficients of a plate with varying aspect ratios ranging from (0.1 ≤ α ≤ 2.0) with 0.1 intervals. The plate boundary conditions considered in this work are SSSS, CCCC, CSCS, CCSS, CSSS and CCCS (where S stands for simply supported edge and C stands for clamped edge). Limit state conditions, such as ultimate limit state of stress and serviceability limit state of deflection were satisfied and the critical design parameters for thickness (tc) and lateral imposed load (qic) were obtained. Numerical examples were performed with the critical design equations, and results were presented for critical design thickness suitable to withstand a given set of loads and critical design-imposed loads a given thickness can withstand for several boundary conditions such as SSSS, CCCC, CSCS, CCSS, CSSS, and CCCS. The aspect ratios considered for these examples are 1, 1.5, and 2. The percentage difference results from the center deflection for various boundary conditions with varying aspect ratios of the present study were around equivalent with respect to those obtained from Ibearugbulem et al. (2014), and the results are within the acceptable limit in engineering. With the presented critical design parameters (qicD,tcD, qicE, tcE), it was concluded that this can be used in the determination of a suitable plate thickness from a specified lateral load and also the critical lateral imposed load a specified plate thickness can withstand under specified conditions of operation.
Description
This thesis is for the award of Master of Engineering (M.ENG) in Structural Engineering
Keywords
Stiffness, lexural rigidity, aspect ratio, pure bending, shape function, maximum deflection, critical thickness, critical impose load, strain energy, deflection limit State, elastic limit State., Department of Civil Engineering
Citation
Ilesanmi, A. (2023). Determination of critical design parameters of rectangular plates under uniformly distributed lateral load (Unpublished Master's Thesis). Federal University of Technology, Owerri, Nigeria