Advances in Materials Science and Engineering

Volume 2016, Article ID 2815247, 10 pages

http://dx.doi.org/10.1155/2016/2815247

## Flexural Strength Evaluation of Reinforced Concrete Members with Ultra High Performance Concrete

^{1}Research Institute of Industrial Science, Hanyang University, 17 Haengdang-Dong, Seongdong-Gu, Seoul 04763, Republic of Korea^{2}Department of Fire and Disaster Prevention Engineering, Kyungnam University, Gyeongsangnam-do 51767, Republic of Korea^{3}Department of Architectural Engineering, Hanyang University, 17 Haengdang-Dong, Seongdong-Gu, Seoul 04763, Republic of Korea

Received 25 September 2015; Revised 5 December 2015; Accepted 7 December 2015

Academic Editor: Stefano Sorace

Copyright © 2016 Baek-Il Bae 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

Flexural strength evaluation models for steel fiber reinforced ultra high strength concrete were suggested and evaluated with test results. Suggested flexural strength models were composed of compression stress blocks and tension stress blocks. Rectangular stress block, triangular stress block, and real distribution shape of stress were used on compression side. Under tension, rectangular stress block distributed to whole area of tension side and partial area of tension side was used. The last model for tension side is realistic stress distribution. All these models were verified with test result which was carried out in this study. Test was conducted by four-point loading with 2,000 kN actuator for slender beam specimen. Additional verifications were carried out with previous researches on flexural strength of steel fiber reinforced concrete or ultra high strength concrete. Total of 21 test specimens were evaluated. As a result of comparison for flexural strength of section, neutral axis depth at ultimate state, models with triangular compression stress block, and strain-softening type tension stress block can be used as exact solution for ultra high performance concrete. For the conservative and convenient design of section, modified rectangular stress block model can be used with strain softening type tension stress block.

#### 1. Introduction

Usually, flexural strength of normal strength concrete members is designed using rectangular stress block parameters. Current design codes provide the rectangular stress block parameters for simplified design methodology. However, these stress blocks are determined by tests of reinforced concrete columns and they have apparent limitations. Rectangular stress block can be used because the shape of stress-strain relation of concrete is similar to the trapezoid. However, shape of stress-strain relationship of concrete changed into triangle as increase of compressive strength of concrete. For this reason, rectangular stress block parameters depend on the compressive strength of concrete. For example, the current ACI code [1] suggests that higher value of compressive strength of concrete can be used as 0.85 times the specified compressive strength of concrete. And the depth of rectangular stress block has the lower bound of 0.65 at 76 MPa of compressive strength of concrete. Ultimate strain of concrete is suggested by value of 0.003. These values are determined from test results of normal strength concrete. However, depending on the compressive strength, mechanical properties and failure type of concrete are changed.

Generally, after experiencing peak stress, sudden drop of load resistance can be observed. Ultra high strength concrete also failed with this failure mode. Making brittle failure of ultra high strength concrete matrix more ductile, under compression, steel fiber can be included in the matrix. Inclusion of steel fiber can change the explosive failure of ultra high strength concrete and provide higher tensile strength and deformability. So steel fiber is usually used for ultra high strength concrete matrix.

Ultra high performance concrete usually has much higher compressive strength and tensile strength than normal strength concrete, generally ranging from 100 to 200 MPa. Shape of stress distribution in compression side of section and tensile strength of concrete shall be considered in section design. Design guidelines for ultra high performance concrete suggested the way to design the section of member suggested stress-strain relation. However, stress-strain relation for ultra high performance concrete needs specific test results not using stress blocks or assumptions. Therefore, in this study, various types of compression and tension stress block combinations were evaluated with experimental result and previous research results for easy and safe design of ultra high performance concrete members.

#### 2. Review of Current Design Codes for Flexural Strength of Ultra High Performance Concrete

Reinforced concrete members using normal strength concrete are designed with an assumption that stress distribution can be shaped with rectangle and concrete cannot transfer the tensile stress. However, these assumptions cannot be applied to flexural strength calculation of ultra high performance concrete members. Since ultra high performance concrete has much higher compressive strength than normal strength concrete and usually reinforced with steel fiber, shape of stress distribution in compression side will be changed and tensile stress distribution in tension side should be considered, in order to calculate the flexural strength of section. Some of design guidelines for high strength concrete or steel fiber reinforced concrete have different assumptions for flexural strength calculation. They can be categorized into two groups: one uses stress block parameters and the other uses specified stress-strain relation of concrete.

Current design code ACI318 [1] suggests that flexural strength of reinforced concrete section can be calculated by

In this equation, , depth of rectangular stress block, can be determined by using stress block parameter . For compressive strength of concrete between 17 and 28 MPa, 0.85 can be used as the value of . shall be decreased linearly a rate of 0.05 for each 7 MPa of compressive strength of concrete above 28 MPa of compressive strength of concrete. The smallest value of is 0.65.

As can be seen in ACI318 [1], current design code provisions did not consider the effect of steel fiber. Some of design guidelines suggested the way to calculate flexural strength of steel fiber reinforced concrete section. ACI 544 committee [2] provides the flexural strength equations by adopting research results of Henager and Doherty [3], especially for rectangular section memberwhere is nominal flexural strength of section, is yield strength of steel rebar, is effective depth of section, is depth of stress block, is height of section, , is strain in tension side, , is neutral axis depth, and tensile strength of steel fiber reinforced concrete can be calculated usingwhere is length of steel fiber, is diameter of steel fiber, is percent by volume of steel fiber, and is bond efficiency factor.

Imam et al. [4] suggested the modified ACI 544 [2] model which can be used as steel fiber reinforced concrete with high strength matrix. Imam et al. investigated the bond stress between steel fiber and matrix. They suggested that tensile stress block height coefficient should be changed into 0.02. According to this modification, tensile strength can be calculated using where means volume fraction of steel fiber () and is fiber factor (1.0~1.2). Moment capacity of section can be determined according to ACI 544 [2], (2).

Lim et al. [5] suggested that stress block parameters should be reevaluated with change of matrix and steel fiber. They use as 0.90 because steel fiber can provide more ductility under compression either. Tensile strength of steel fiber reinforced concrete can be determined using where is steel fiber orientation factor, is length efficiency factor, is average ultimate bond stress at the fiber-matrix interface, and is the ratio of the fiber cross-sectional area to its perimeter. Since Lim et al. [5] developed their model with plasticity approach, they use whole area over the neutral axis as compressive stress block. Neglecting cover thickness and considering tensile stress block in tension side of section, neutral axis depth can be calculated usingwhere is compressive strength of concrete, is width of section, and is yield strength of reinforcement. From (6) internal moment arm can be calculatedwhere is effective depth of section. Using (5), (6), and (7) flexural capacity of section can be calculated by using

Although stress block approach is easy to use for flexural strength calculation, it cannot consider the difference of concrete with higher strength matrix or other characteristics. Flexural strength calculation models for normal strength concrete and steel fiber reinforced concrete were illustrated in Figure 1. The main difference between normal strength concrete model and steel fiber reinforced concrete model is existence of tensile stress block. Difference among steel fiber reinforced concrete models is the range of tensile stress distribution. However, they are not exact models because stress distribution might be changed with compressive strength of matrix and tensile stress distribution is more comprehensive than used in Figure 1.