OPTIMIZATION OF PALM NUT FIBRE CONCRETE USING SCHEFFE’S THEORY

APPENDIX

REFERENCE

  

 

It is important to ensure that inputs or investments are at a minimal production level so as to obtain maximum gains or outputs. The method which consists of this maximization and minimization process is termed optimization (Orie et al., 2009). In the optimization process, the quantity or property under study is known as the objective function. The variables are referred to as the quantities or raw materials whose linear interactions will generate the objective function. Often the space of variability of the variables is not universal as some conditions limit them. These conditions are called constraints (Mama et al., 2011). The function is called the objective function and the specified requirements are known as the constraints of the problem. Concrete on its own does not make a good structural material; there are too many sources of tension stresses which it cannot resist by itself so in most situation we add a reinforcement to improve the strength. When the concrete is reinforced, it becomes a composite material in this case the concrete guides against compressive strength while the reinforcement is against tensile stress (Okere et al., 2014).

The failure type in concrete is altered from brittle to ductile failure where we can observe the formation of crack before the total loss of strength.  This action help you to recognize a potential catastrophe and hopefully manage it before it explode. Sometimes we hope to make a concrete structure of complicated or complex geometry where the use of the conventional rebar will not work; in this case the use of fiber reinforced concrete is highly recommended. Fiber are like micro reinforcement and when the FRC beam is loaded, the beam fall apart under failure load, but it will be held together by thin fibers. Fibers make the concrete stronger and also makes it hold the load longer after failure limit is reached. If we look at the cracks developed at the FRC beam, we can see the fibers doing an important job to give the concrete post-cracking strength also known as toughness. In statistics, Scheffe’s method is a technique for evaluating the significant levels to account for multiple comparison in a linear regression analysis. The method is a multiple single-step assessment method which applies to set of estimates among the factor level means of all possible contrast (Scheffé, 1958). Oil palm fiber is an important lignocellulose raw material for the preparation of cost-effective and environment-friendly composite materials.  Nowadays using fibers for composite materials like concrete is gaining popularity in several engineering applications majorly because it avails an environmental and economic advantage in terms of waste management and reuse. The use of palm nut fiber as a fifth component concrete was evaluated in this study using Scheffe’s theory; the optimum and minimum level combination of the mixture components was obtained. 

Structural concrete are made with specified materials for specified strength. Several attempts have been expended in the course to optimize the concrete mixture design using either the empirical/experimental methods or analytical /statistical methods. Empirical/experimental methods involve an extensive series of tests, sometimes conducted on a trial-and-error basis, and the optimization results are often applicable only to a slim range of local materials. In order for the number of exhaustive trials to be reduced before the optimum combination is established, use of analytical and statistical techniques which would enhance the rationalizing of the initial trial mixes into a logical and analytical process. This statistical method is very helpful in tracing of the optimum mixture combination based on a details of specific weight functions of the combination components and basic formula resulting from previous experimental experiences without engaging into laborious, time wasting and expensive works. The construction firms depend on conventional building materials namely; sand, gravel, cement and water for production of concrete. Due to economic instability and inflation, the cost of these conventional materials is very high and increasing; as a result of this, the infrastructural development has been hindered greatly. To tackle this challenge, reuse of solid wastes as a fifth component to the already existing conventional materials. These solid wastes are cheaper to obtain and locally available, this makes it a better option as it will enhance sustainable development.

The aim of this research is to optimize the palm nut fibre reinforced concrete using Scheffe’s methods. The specific objectives are;

This work is limited to the formulation of model equations for the optimization of flexural and compressive strength properties of five component concrete. Namely: water, fine aggregate, cement, coarse aggregate and palm nut fiber using Scheffe's second order optimization theory. In this research, palm nut fiber is used as the fifth component in the concrete mix proportion and not for replacement. The mechanical properties investigated will be limited to flexural and compressive strength and all tests are carried out on hardened specimens