Advances in Engineering & Scientific Research. Research Article FACTORIAL DESIGN AND OPTIMIZATION OF THE WEIGHT OF THE CUBE (KG) IN CONCRETE MIXTURE

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1 Open Access Scientific Publisher Research Article FACTORIAL DESIGN AND OPTIMIZATION OF THE WEIGHT OF THE CUBE (KG) IN CONCRETE MIXTURE ABSTRACT Ejikeme Ifeanyi R 1, Ezeliora Chukwuemeka Daniel 2 1 Commissioner for Transport, Anambra State, Nigeria 2 Department of Mechanical Engineering, Nnamdi Azikiwe University Awka, Anambra State, Nigeria Correspondence should be addressed to Ezeliora Chukwuemeka Daniel Received August 10, 201; Accepted August 1, 201; Published September 0, 201; Copyright: 201 Ezeliora Chukwuemeka Daniel et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Cite This Article: Ifeanyi R, E., Daniel, E.(201). Factorial Design and Optimization of the weight of the cube (kg) in Concrete Mixture. Advances in Engineering & Scientific Research, 1(1).1-1 This research work focused on the design, and optimization of the concrete mixture using factorial analysis. Data were collected for the concrete mixture proportion to observe the ratio of the mixture content. Factorial design analyses were used to design the concrete mixture. It was also used to optimize the concrete mixture of the variables. The results were discussed and were also recommended for concrete mixture. KEY WORDS: Optimization, Factorial Design, Concrete Mix, Response Surface Modelling and Analysis of Variance. INTRODUCTION INTRODUCTION TO CONCRETE MIXING The successful placement of concrete is dependent upon careful mixing, the proper equipment, and adequate transportation. This will define, analyze, and demonstrate the importance of each in the overall process of placing concrete. BATCHING AND MIXING CONCRETE Mixing concrete is simply defined as the "complete blending of the materials which are required for the production of a homogeneous concrete" [1]. This can vary from hand to machine mixing, with machine mixing being the most common. However, no successful mixture can be achieved without the proper batching of all materials. Batching is the "process of weighing or volumetrically measuring and introducing into the mixer the ingredients for a batch of concrete" [2]. Quality assurance, suitable arrangement of materials and equipment, and correct weighing of the materials are the essential steps that must be completed before any mixing takes place. The objective of the stud is to design, analyze and to optimize the weight of cube in concrete mixture content. CONCRETE MIXER A concrete mixer (also commonly called a cement mixer) is a device that homogeneously combines cement, aggregate such as sand or gravel, and water to form concrete. A typical concrete mixer uses a revolving drum to mix the components. For smaller volume works portable concrete mixers are often used so that the concrete can be made at the construction site, giving the workers ample time to use the concrete before it hardens. An alternative to a machine is mixing concrete by hand. This is usually done in a wheelbarrow; however, several companies have recently begun to sell modified tarps for this purpose [3]. 1

2 TYPES OF CONCRETE Advances in Engineering & Scientific Research There are many types of concrete, designed to suit a variety of purposes coupled with a range of compositions, finishes and performance characteristics [4]. MIX DESIGN between, the "slump" for easy mixing and placement and ultimate performance []. A mix is then designed using cement (Portland or other cementitious material), coarse and fine aggregates, water and chemical admixtures. The method of mixing will also be specified, as well as conditions that it may be used in. Modern concrete mix designs can be complex. The choice of a concrete mix depends on the need of the project both in terms of strength and appearance and in relation to local legislation and building codes []. The design begins by determining the requirements of the concrete. These requirements take into consideration the weather conditions that the concrete will be exposed to in service, and the required design strength. The compressive strength of a concrete is determined by taking standard melded, standard-cured cylinder samples. This allows a user of the concrete to be confident that the structure will perform properly. Various types of concrete have been developed for specialist application and have become known by these names. Concrete mixes can also be designed using software programs. Such software provides the user an opportunity to select their preferred method of mix design and enter the material data to arrive at proper mix designs []. Many factors need to be taken into account, from the cost of the various additives and aggregates, to the trade-offs The research method used is the analyses and optimization of the weight of cube in concrete mixture. Data, Analyses and Results Table 1: Level of factors and test for weight of cube kg 2 Level of factors and test Xnar Highest level (+) Xim Lowest level (-) Xer Central Level (0) average Interval of Change Δ X 1 = C Cement kg/m X 2 = w water content kg/m 3 X 3 = Fa fine paragraph kg/m X 4 = Ca coarse Aggregate kg/m Density of the Cube Kg/M Test No X 1 X 2 X 3 X 4 Y

3 Factorial Fit: Y3 versus X1, X2, X3, X4 Estimated Effects And Coefficients For Y3 (Coded Units) Term Effect Coef SE Coef T P Constant X X X X X1*X X1*X X1*X X2*X X2*X X3*X X1*X2*X X1*X2*X X1*X3*X X2*X3*X S = PRESS = * R-Sq = 81.42% R-Sq(pred) = *% R-Sq(adj) =.41% 3

4 Analysis of Variance for Y3 (coded units) Source DF Seq SS Adj SS Adj MS F P Main Effects X X X X Way Interactions X1*X X1*X X1*X X2*X X2*X X3*X Way Interactions X1*X2*X X1*X2*X X1*X3*X X2*X3*X Residual Error Lack of Fit Pure Error Total

5 Obs StdOrder Y3 Fit SE Fit Residual St Resid * X * X * X * X * X * X * X X denotes an observation whose X value gives it large leverage.

6 Estimated Coefficients for Y3 using data in uncoded units Term Constant X X X X X1*X X1*X Coef X1*X X2*X X2*X X3*X X1*X2*X E-0 X1*X2*X4 X1*X3*X E E-0 X2*X3*X Least Squares Means for Y3 Mean SE Mean X X X X1*X X1*X X1*X X2*X X2*X X3*X

7 X1*X2*X X1*X2*X X1*X3*X X2*X3*X

8 Predicted Response for New Design Points Using Model for Y3 Point Fit SE Fit 9% CI 9% PI (.903, ) (.80, ) (.33,.933) (.4440, 8.093) X (.4903,.39) (.3,.8482) (.4903,.39) (.3,.8482) (.033,.433) (.9440,.93) X (.33,.8033) (.2840,.8993) X (.903,.9029) (.480, ) (.903,.9029) (.480, ) (.383,.8133) (.2940,.9093) X (.133,.33) (.0440,.93) X (.423,.311) (.349,.8410) (.433,.91) (.314,.81910) (.30,.9081) (.439, ) (.3209,.000) (.23082,.84014) (.483,.9133) (.3940, ) X (.130,.9) (.34,.81222) (.903, ) (.80, ) (.4903,.39) (.3,.8482) (.433,.91) (.314,.81910) (.423,.311) (.349,.8410) (.38189,.80023) (.2901,.8919) (.383,.8133) (.2940,.9093) X (.32,.01) (.234,.92) (.12,.348) (.41384,.8912) (.130,.9) (.34,.81222) X denotes a point that is an outlier in the predictors. Values of Predictors for New Observations 8 New Obs X1 X2 X3 X

9 Term Percent Advances in Engineering & Scientific Research Figure 1: Effects Plot for Y Normal Plot of the Standardized Effects (response is Y3, Alpha = 0.0) Effect Type Not Significant Significant Factor Name A X1 B X2 C X3 D X Standardized Effect 2 3 Figure 2: Effects Pareto for Y3 D AB ABC AD ABD C B BD BC AC ACD BCD A CD 0.0 Pareto Chart of the Standardized Effects (response is Y3, Alpha = 0.0) Standardized Effect Factor Name A X1 B X2 C X3 D X4 9

10 Mean Frequency Residual Percent Residual Advances in Engineering & Scientific Research Figure 3: Residual Plots For Y Normal Probability Plot Residual Plots for Y3 0.1 Versus Fits Residual Fitted Value Histogram 0.1 Versus Order Residual Observation Order Figure 4: Main Effects Plot for Y3... X1 Main Effects Plot for Y3 Data Means X X3 X

11 Figure : Interaction Plot for Y3 Interaction Plot for Y3 Data Means X X X2 X2 X X X4 X Figure : Cube Plot (data means) for Y3 Cube Plot (data means) for Y X X1 X X

12 Figure : Contour Plots of Y3 Contour Plots of Y X2*X1 20 X3*X X3*X1 20 X4*X X4*X1 20 X4*X3 Y3 < > 12 Hold Values X1 23. X2 X3 2 X Figure 8: Surface Plots of Y3 Surface Plots of Y3.8 Y X1 X2 12 Y X3 20 X1.8 Y X X1 Hold Values X1 23. X2 X3 2 X Y3 9 3 X X3. Y X X2. Y X X

13 Table 2: Factorial Design table for weight of cube kg S/N FITS3 RESI3 COEF3 EFFE E E E E E E E RESPONSE OPTIMIZATION Parameters Goal Lower Target Upper Weight Import Y3 Target X1 = 20 X2 = X3 = 88. X4 = Y3 =.140, desirability = Composite Desirability = X1 = X2 = X3 =

14 X4 = 1380 Advances in Engineering & Scientific Research X1 = X2 = Y3 =.139, desirability = Composite Desirability = X1 = 23. X2 = X3 = 2 X4 = Y3 =.14, desirability = Composite Desirability = X1 = X2 = X3 = X4 = Y3 =.44, desirability = Composite Desirability = X1 = X2 = X3 = X4 = Y3 =.1820, desirability = Composite Desirability = X3 = X4 = 9.30 Y3 =.131, desirability = Composite Desirability = X1 = 20 X2 = X3 = X4 = 1380 Y3 =.14, desirability = Composite Desirability = X1 = X2 =.0034 X3 = 90 X4 = Y3 =.149, desirability = 0.99 Composite Desirability = 0.99 X1 = X2 =.0 X3 = X4 = 93

15 Y3 =.140, desirability = Advances in Engineering & Scientific Research X3 = 14.8 Composite Desirability = X1 = X2 =.833 X3 = X4 = 93 Y3 =.144, desirability = Composite Desirability = X1 = X2 =.0003 X3 = X4 = 93 Y3 =.140, desirability = Composite Desirability = X1 = X2 =.83 X3 = X4 = 93 Y3 =.8812, desirability = Composite Desirability = X1 = X2 =.0193 X4 = 93 Y3 =.14, desirability = Composite Desirability = X1 = X2 = X3 = X4 = Y3 =.14, desirability = Composite Desirability = X1 = X2 =.93 X3 = X4 = Y3 =.14, desirability = Composite Desirability = X1 = X2 =.0184 X3 = 90 X4 = 93 Y3 =.14, desirability = Composite Desirability =

16 X1 = X2 =.03 X3 = X4 = Advances in Engineering & Scientific Research Global Solution X1 = X2 =.0193 X3 = 14.8 X4 = 93 Y3 =.14, desirability = Composite Desirability = Y3 =.14, desirability = Composite Desirability = Figure 9: Optimization Plot Optimal D High Cur Low X1 X2 X3 X [.0] [.019] [14.84] [93.0] Composite Desirability Y3 Targ:.14 y =.14 d = DISCUSSION AND CONCLUSION From the result, a factorial design model was developed to show the new observed independent variables. It was observed that the coefficient of determination (R-sq) of the model developed was 81%. This shows a good correlation of both the dependent and independent variables. Further analyses were made to sow the effect of each of the independent variable to the model and the interaction of the independent variable. However, contour plots were also used to show the impact of the independent variables while the surface plot shows the area of the variables (both dependent and independent variables). Furthermore, an optimization response technique was also applied to observe the global response or the optimum response of both the dependent and independent variables.in conclusion, the application of the factorial design technique shows us a means of designing and optimizing the weight of the cube in concrete mixture. This will help and also serve as a guide line for standard concrete mixture. The research work is also recommended for wider use and applicability for concrete mixture in establishments. REFERENCES [1] Mindess, Sidney and J. Francis Young. Concrete. New Jersey: Prentice-Hall, Inc., 1981.

17 [2] Kosmatka, Steven H. And William C. Panarese. Design and Control of Concrete Mixtures(13 th Edition). Illinois Portland Cement Association, [3] Hunker, Henry L. (2000). Columbus, Ohio: A Personal Geography. Ohio State University Press. p. 19. ISBN [4] "Historic concrete recipes in ancient times, demonstrated by Colin Richards, experimental archaeologist". Channel.nationalgeographic.com Retrieved [] "Ultra High Performance Fibre-Reinforced Concretes." Association Francaise de Genie Civil, [] American Shotcrete Association Homepage. Shotcrete.org. Retrieved on [] An Investigation Into The Feasibility Of Timber And Limecrete Composite Flooring. Istructe.org. Retrieved on