ORIGINAL RESEARCH ARTICLE | Oct. 16, 2024
Use of a Refined Theory for Three-Dimensional Bending Analysis of Isotropic Rectangular Thick Plates
Bertram, D.I, Onwuka, D.O, Ibearugbulem, O.M, Okere, C.E
Page no 168-178 |
DOI: https://doi.org/10.36348/sjce.2024.v08i08.001
In this paper, a refined plate theory (Alternative II theory) is presented for the three-dimensional bending analysis of an Isotropic thick plate. The theory has similarity to the first order shear deformation theory but requires no shear correction factors. The kinematics equations were developed based on the Alternative II Refined plate theory. Thereafter, using a complete three-dimensional constitutive relation, the total potential energy was developed. A governing equation and two compatibility equations were obtained by the variation of the total potential energy with respect to displacement and rotations respectively. Solving the governing and compatibility equations, a polynomial displacement function was obtained. The stiffness coefficients were then obtained using the displacement function. Thereafter, the equations for the in-plane normal and shear stresses, transverse normal and shear stresses as well as the lateral displacement were developed using the stiffness coefficients and the displacement function. Numerical values of the lateral displacement parameters were determined for a rectangular plate of aspect ratio 2.0, 1.0 and 0.5 for span to thickness ratios of 20, 10 and 7.14286. Also, numerical values of the lateral displacement and stresses were determined for a square plate for span to thickness ratios of 4, 10, 100 and 1000. The results from this work were compared with the work of previous researchers using simple percentage difference. It was observed that refined plate theories overestimate the lateral displacement of a plate. Hence, three-dimensional analysis is recommended for thick plate analysis.
In this study, the strength effect of partially substituting Portland Cement (PC) with epoxy-resin in making concrete was examined. A mix ratio of 1:1.87:2.67 (PC: sand: granite chippings) at water-cement ratio of 0.5 targeting a strength of 30N/mm2 was adopted. The epoxy resin was mixed with hardener at a proportion of 1:0.5 and this mixture was used to replace PC at 10% intervals starting from 0% to 40%. Six cubes were cast for each mix ratio and were cured in water at room temperature for 28 days. The first set of samples were treated by heating them in an oven to a temperature of 1000C for 1 hour before testing in compression while, the other set were not treated. Results showed that as the quantity of epoxy resin in the concrete enlarged the compressive strength values reduced. But a rise was observed at 30%. All concrete produced were structural in nature except for the heated 40% specimen. An optimal replacement strength of 32.10 N/mm2 at 30% inclusion (unheated) and lowest strength of 18.63 N/mm2 at 40% replacement (heated) were obtained. The heated samples experienced further reduction in their compressive strength values. An 8.94% drop in strength was observed between the maximum replacement values for the heated and unheated samples at 30%. In conclusion, epoxy resin concrete can be used for structural works at replacement levels up to 40%. However, if the concrete will be exposed to increased temperature of 1000C, then an optimal replacement level of 30% is recommended.