Class 8 Rs Aggarwal Rational Number

[Kristin Banyas]

3Without actually performing the king division, State whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:

19. In each case, state whether the following numbers are rational or irrational. If they are rational and expressed in the form p/q, where p and q are coprime integers, then what can you say about the prime factors of q?

Which of the following statements are true and which are false?

(i) Every whole number is a rational number.

(ii) Every integer is a rational number.

(iii) 0 is a whole number but it is not a rational number.

Which of the following statements are true and which are false?

(i) lies to the left of 0 on the number line.

(ii)lies to the right of 0 on the number line.

(iii) The rational numbersandare on opposite sides of 0 on the number line.

(iv) The rational numberlies to the left of 0 on the number line.

(i) Which rational number is its own additive inverse?

(ii) Is the difference of two rational numbers a rational number?

(iii) Is addition commutative on rational numbers?

(iv) Is addition associative on rational numbers?

(v) Is subtraction commutative on rational numbers?

(vi) Is subtraction associative on rational numbers?

(vii) What is the negative of a negative rational number?

In this study, optimization of durability properties of the concretes was performed by using Taguchi method and Anova analysis. The durability performance of the concretes was evaluated using measurements of rapid chloride ion permeability, freezing-thawing resistance and sorptivity tests. The degree of freezing-thawing resistance was assessed the change of weight, ultrasonic pulse velocity (UPV) and flexural strength after 300 cycles. The use of fly ash improved the rapid chloride ion permeability and sorptivity of concrete. The best resistance to chloride ion permeability was obtained from a combination of type of class C fly ash content of 102 kg/m3 with PC content of 332 kg/m3. There was a remarkable reduction in the UPV after the specimens are subjected to freezing-thawing cycles. The amounts of flexural strength loss have been measured in the range of 6.70 - 29.83%. The use of type of class C fly ash positively affected freezing-thawing resistance of concrete. The Anova analysis indicated that the cement dosage has an utmost importance on the sorptivity level, chloride ion permeability and ultrasonic pulse velocity loss. Furthermore, the fly ash percentage has an utmost importance on the weight loss and flexural strength loss.

En este estudio, la optimizacin de la durabilidad de las propiedades de los hormigones se realiz utilizando el mtodo Taguchi y anlisis Anova. El rendimiento de la durabilidad de los hormigones fue evaluado utilizando medidas de permeabilidad rpida a los iones de cloruro, pruebas de resistencia a la congelacin-descongelacin y de capacidad de absorcin de agua por capilaridad. En el grado de resistencia a la congelacin- descongelacin se evalu el cambio de peso, la velocidad del pulso ultrasnico (UPV) y la resistencia a la flexin despus de 300 ciclos. El uso de la ceniza mejor la rpida permeabilidad de los iones de cloruro y la capacidad de absorcin de agua por capilaridad del hormign. La mejor resistencia a la permeabilidad del ion de cloruro fue obtenida de una combinacin de tipo de ceniza clase C de 102 kg/m3 con un contenido de PC de 332 kg/m3. Hubo una notable reduccin en la UPV despus de que las muestras se sometieran a ciclos de congelacin y descongelacin. Las cantidades de fuerza flexible perdidas han sido medidas en el rango de 6.70 a 29.83%. El uso del tipo de ceniza clase C afect positivamente a la resistencia de la congelacin y descongelacin del concreto. El anlisis de Anova indic que la dosis de cemento tiene una importancia mayor sobre el nivel de la capacidad de absorcin de agua por capilaridad, la permeabilidad del ion de cloruro y la prdida de velocidad del pulso ultrasnico. Adems, el porcentaje de ceniza tiene una importancia mayor en la prdida de peso y en la prdida de la fuerza flexible.

Fly ash is commonly used in blended cements, and is a by-product of coal-fired electric power plants (Alonso & Wesche, 1992). Two general classes of fly ash can be defined: low-calcium fly ash (ASTM Class F) produced by burning bituminous or anthracite coal; and high-calcium fly ash (ASTM Class C) produced by burning lignite or sub-bituminous coal (Nochaiya, Wongkeo, & Chaipanich, 2010). Class F is categorized as a normal pozzolan, a material consisting of silicate glass, modified with iron and aluminum. Type of class F requires Ca(OH)2 to form strength-developing products (pozzolanic reactivity), and therefore is used in combination with Portland cement, which produces Ca(OH)2 during its hydration. It lowers the heat of hydration and improves the durability properties of concrete when used in concrete as a cement replacement. It also conduces to concrete strength by pozzolanic and filler effects (Papadakis, 1999). The current worldwide production of coal ash is estimated about 700 million tones per year of which at least 70% is fly ash. There are 19 thermal power plants actively working in Turkey but type of class F fly ash is obtained only from Catalagzi Thermal Power Plant, FA of all other plants is type of class C. The annual fly ash production is about 20 million tones which is more than the rest of all industrial wastes in Turkey. Although FA is a valuable mineral additive for blended Portland cement and concrete, only about 4% of the total available FA is used for this purpose in Turkey (Yazici, Aydin, Yigiter, & Baradan, 2005). Particularly, due to the energy demand, the production rate of FA is expected to increase in the future (Felekoglu, 2006).

In severe environments, durability is a key function for materials which are used (Soroushia, Nagi, & Okwuegbu, 1992; Alexander & Magee, 1999). The freezing and thawing durability is especially important for a porous brittle material such as concrete when it is subjected to lower temperatures in cold environments (Cai & Liu, 1998). Frost damage, a progressive deterioration is a major concern when concrete is used in colder regions which starts from scaling or surface separation and ends up with complete collapse. The deterioration proceeds as freezing-thawing cycles are repeated, and the material gradually loses its strength and stiffness. In addition, increasing irreversible expansion is stimulated. So, the freezing and thawing action could be looked upon as one of the complex fatigue process. Now, there are increasing needs for concrete to be used for the lack of very cold substances. So, it is essential a rational evaluation of deterioration is in designing more reliable structures and minimizing possible damage (Shang, Song, & Qin, 2008).

The use of Taguchi and Anova methods in concrete technology has become widespread in recent years to optimize properties of concrete (Tanyildizi, & Sahin, 2015; Mohebi, Behfarnia, & Shojaei, 2015; Tanyildizi, 2018, Jafari, Tabatabaeian, Joshaghani, & Ozbakkaloglu, 2018; Tanyildizi, 2013; Tanyildizi et al., 2008; Tanyildizi, 2014). Tanyildizi and Sahin (Tanyildizi & Sahin, 2015) applied Taguchi method for optimization of concrete strengthened with polymer after high temperature. They reported that Taguchi analysis indicated the optimum parameters for ultrasonic pulse velocity and the compressive strength of concrete. Also, Anova analysis showed that the most effective parameters on the compressive strength and ultrasonic pulse velocity of concrete. Mohebi et al investigated abrasion resistance of alkali-activated slag concrete designed by Taguchi method and they declared that Taguchi method could be an effective and suitable design of experiment method for optimizing alkali-activated slag concrete parameters to achieve the maximum compressive strength and abrasion resistance (Mohebi et al., 2015). Tanyildizi also investigated long-term microstructure and mechanical properties of polymer-phosphazene concrete exposed to freeze-thaw. The effects on experimental results of each factor were determined using Anova. The results obtained using Anova analysis showed that cement dosage had made the most effective parameter (Tanyildizi, 2018). Jafari et al. (2018) used Taguchi and Anova methods to optimize the mixture design of polymer concrete. They reported that the optimum mix design of polymer concrete was determined using Taguchi and Anova methods.

The objective of this study is to investigate the effect of the use of type of class C fly ash as partial replacement of cement in various percentages on concrete properties. Several properties related to durability were determined such as chloride ion permeability resistance, sorptivity and particular attention was put on the resistance of the concrete mixes to the freezing and thawing cycles based on ASTM C 666. Taguchi method and Anova analysis were used to optimize durability properties of the concretes containing type of class C fly ash.

In this study, CEM I 42.5 R Portland cement and type of class C fly ash were used as binding materials. Their chemical compositions and properties are shown in Table 1. Type of class C fly ash was obtained from power plants in Turkey. Specific gravity of the cement used was 3.12 g/cm3. Initial and final setting times of the cement were 210 and 265 min, respectively. Crushed limestone aggregates with a maximum size of 16 mm were used as coarse aggregates. The specific gravity and water absorption of the crushed limestone aggregate was 2.70 and 0.31% respectively. Ordinary river sand with specific gravity of 2.61 and water absorption of 1.59% was also employed. A uniform grading of aggregate mixture was prepared. The fineness modulus of the mixture is 4.09. Volume percentages of aggregates were kept constant in all mixtures which means that aggregate quantities changed for each series but volume percentages of aggregates were kept constant for all aggregates in each series.

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