FLEXURAL STRENGTH OF OPTIMIZED GRANITE PARTIALLY SUBSTITUTED BY PALM KERNEL SHELL CONCRETE USING SCHEFFE’S THEORY

Abstract

This work was carried out to develop mathematical model that can predict the response (modulus of rupture) of Granite-palm kernels shells aggregate concrete using Scheffe’s method of optimization. Scheffe considered experiment with mixtures in which the desired property depends on the proportions of the constituent materials present as atoms of the mixture. A simplex lattice which can be described as a structural representation of lines joining the atoms of a mixture can be used as a mathematical space in model experiments involving mixtures by considering the atoms as the constituent components of the mixture. Concrete Beams were casted consisting of thirty (30) different mix ratios. The first fifteen (15) mix ratios were used to determine the coefficients of the model and the second fifteen (15) mix ratios were used to validate the model. The beams were cured for 28 days before testing. The values of responses (Results) determined from the models agreed with the corresponding values that were obtained from the experimental results. The formulated models were tested for adequacy using F – statistic test and were found to be adequate. The batch with the point (A1) , with mix ratio of 0.52:1:1.47:2.75:0.36 (water: cement: sand: Granite: palm kernel shells). 5% replacement of palm kernel shells has the highest  Flexural strength of 3.8N/mm2, followed by point A2, A3 and A1,2 with modulus of rupture 3.4N/mm2, 2.9N/mm2 and 2.8N/mm2 respectively, The formulated models can predict all possible combinations of mix proportions if the value of modulus of rupture is given. Conversely, it can determine the modulus of rupture if a mix proportion is specified

Keywords: Optimization, Strength, Aggregates, Proportions, Models, Design and Samples