Advances in Materials Science and Engineering

Volume 2015 (2015), Article ID 580638, 12 pages

http://dx.doi.org/10.1155/2015/580638

## Effect of Cylinder Size on the Modulus of Elasticity and Compressive Strength of Concrete from Static and Dynamic Tests

^{1}R&D Center, JNTINC Co. Ltd., 9 Hyundaikia-ro 830 beon-Gil, Bibong-Myeon, Hwaseong, Gyeonggi-do 18284, Republic of Korea^{2}Department of Architectural Engineering, Dong-A University, 37 Nakdong-Daero 550 beon-Gil, Saha-gu, Busan 49315, Republic of Korea^{3}Department of Safety Engineering, Incheon National University, 119 Academy-ro, Yeonsu-gu, Incheon 22012, Republic of Korea^{4}Department of Civil Engineering, Chungnam National University, 99 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of Korea

Received 1 June 2015; Revised 23 August 2015; Accepted 2 September 2015

Academic Editor: Santiago Garcia-Granda

Copyright © 2015 Byung Jae Lee 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.

#### Abstract

The primary objective of this study is to investigate the effects of cylinder size (150 by 300 mm and 100 by 200 mm) on empirical equations that relate static elastic moduli and compressive strength and static and dynamic elastic moduli of concrete. For the purposes, two sets of one hundred and twenty concrete cylinders, 150 by 300 mm and 100 by 200 mm, were prepared from three different mixtures with target compressive strengths of 30, 35, and 40 MPa. Static and dynamic tests were performed at 4, 7, 14, and 28 days to evaluate compressive strength and static and dynamic moduli of cylinders. The effects of the two different cylinder sizes were investigated through experiments in this study and database collected from the literature. For normal strength concrete (≤40 MPa), the two different cylinder sizes do not result in significant differences in test results including experimental variability, compressive strength, and static and dynamic elastic moduli. However, it was observed that the size effect became substantial in high strength concrete greater than 40 MPa. Therefore, special care is still needed to compare the static and dynamic properties of high strength concrete from the two different cylinder sizes.

#### 1. Introduction

The elastic modulus of concrete is of great interest for design of new structures and condition assessment of existing structures. In structure design, there are requirements for serviceability of concrete structures such as maximum permissible deflections and allowable story drift for high-rise buildings in general building codes [1, 2]. is a fundamental parameter for calculating the static and dynamic behavior of structural elements (e.g., deflection, side sway of tall buildings, and vibration of concrete elements). Furthermore, is a good indicator of degree of concrete deterioration: more degradation results in lower . Therefore, is popularly used for condition assessment of concrete structures such as building components, pavements, and bridge decks [3].

Elastic modulus of concrete is directly measured by the static uniaxial compressive test in accordance with ASTM C469 [4], which is called static elastic modulus. In practice, is generally determined from compressive strength based on design codes rather than on the direct measurement. ACI 318 committee [1] proposes an empirical equation that relates and :where is compressive strength of concrete in MPa and is a unit weight of concrete in kg/m^{3} (for 1440 ≤ ≤ 2560 kg/m^{3}) for a value of less than 38 MPa [5]. Furthermore, ACI 363 committee [6] proposes a different equation for linking and for a value of between 21 MPa and 83 Mpa:For both normal strength and high strength concrete, the Comité-Euro-International du Béton and the Fédération Internationale de la Précontrainte (CEB-FIP) Model code and Eurocode 2 suggests an empirical equation relating and as follows:However, it has been reported that the simple code equations may not always produce accurate compared to the value based on direct measurements [7, 8]. In fact, there was no standard test method for determining when the equation adopted by ACI 318 [1] was developed: consequently, there was a substantial variation according to the definition of elastic modulus of concrete (i.e., initial, tangent, or secant modulus) [5]. Furthermore, the code equations (see (1)–(4)) do not take into account the critical parameters such as the type of coarse aggregates, mineral admixtures, and size of test specimens for compressive strength of concrete.

Elastic modulus of concrete can be determined by dynamic test methods such as ultrasonic pulse velocity and resonance frequency tests [9]. The resulting elastic modulus is commonly referred to as dynamic elastic modulus , which is larger than static elastic modulus [10]. There are several empirical equations that relate and . Lydon and Balendran [11] proposed the following empirical relationship between and :The British testing standard BS8100 Part 2 [12] provides another empirical equation for as follows:It is noteworthy that this equation does not apply to concrete containing more than 500 kg/m^{3} or to lightweight aggregate concrete [10]. A more general relationship was proposed by Popovics [13] for both lightweight and normal concrete, taking into account the effect of a unit weight of concrete:However, values for a given concrete predicted by different empirical equations do not agree with each other. In fact, it is known that the value of may vary significantly according to test methods and size and type of test specimens [7]. Therefore, it is difficult to select a correct equation that produces the least error for different dynamic tests and test specimens.

Requirements for the cylinder size of concrete are described in ASTM C192 [14] and ASTM C31 [15], which are adopted by general building code [1] and other ASTM standards for measuring compressive strength, static elastic modulus, and dynamic elastic moduli of concrete. Even though dimensions are not stipulated in a specification, test method, or practice, the concrete cylinder should have a diameter at least three times nominal maximum aggregate size and the height-to-diameter ratio of 2. In practice, maximum aggregate size ranges between 12.5 mm and 25 mm; therefore, a size of 100 by 200 mm cylinder is accepted by the standard tests method. The use of 100 by 200 mm cylinders has many advantages against using larger specimens (e.g., 150 by 300 mm cylinders) because it facilitates handling in practice and needs smaller space and reduces construction wastes. For dynamic elastic modulus, the frequency equations in ASTM C215 [16] are supposed to produce the same value of when test cylinder has the same diameter-to-height ratio without regard to cylinder sizes: however, different size of cylinder may produce inelastic effect and dispersion and consequently affect a value of . For static tests, a number of researchers [17–24] have observed that the size of cylinders affects compressive strength and elastic modulus of concrete. In summary, the cylinder size may affect the accuracy of the empirical equations that relate compressive strength and static elastic modulus (see (1)–(3)) and dynamic and static elastic moduli (see (4)–(6)). However, it is difficult to quantitatively say the size effect due to scarcity of experimental data comparing various empirical equations for estimating static elastic modulus of concrete from compressive strength and dynamic elastic modulus of concrete .

The primary objective of this study is to investigate the effect of cylinder size (100 by 200 mm and 150 by 300 mm) on empirical equations that relate static and dynamic elastic moduli of concrete and static elastic modulus and compressive strength of concrete. For the purposes, a series of experimental studies was performed in the laboratory, which is described in Section 2. Main experimental variables in this study include the cylinder size (100 by 200 mm and 150 by 300 mm cylinders), concrete ages at the test (4, 7, 14, and 28 days), and compressive strength (20, 30, and 40 MPa). The results (i.e., experimental variability, compressive strength, and static and dynamic elastic moduli) from various static and dynamic test methods are compared in Section 3. For a comparison, the experimental results in this study were compared with database collected from the literature.

#### 2. Experimental Program

##### 2.1. Preparation of Specimens

For experimental studies, two sets of one hundred and twenty concrete cylinders with different sizes (100 by 200 mm and 150 by 300 mm cylinders) were prepared in the laboratory. Concrete used in this study has the same mix proportions of Type I Portland cement, river sand, crushed granite with maximum size of 25 mm, and mineral admixtures (fly ash and granulate-furnace slag), except for three different water-to-binder ratios (W/B), 0.3, 0.35, and 0.45. Specific concrete mix proportions are summarized in Table 1. Concrete was cast in two standard plastic molds with dimensions of 100 by 200 mm and 150 by 300 mm and placed in a curing chamber within 30 minutes. Plastic molds were removed after 24 h and specimens were cured in a water pond. A series of static and dynamic tests were conducted at different ages: 4, 7, 14, and 28 days. One day before testing, ten 100 by 200 mm and 150 by 300 mm cylinders for each test series were taken out of a water pond and air-cured in a constant temperature-and-humidity room.