International Journal of Polymer Science

Volume 2018, Article ID 6274287, 14 pages

https://doi.org/10.1155/2018/6274287

## Crack Width and Load-Carrying Capacity of RC Elements Strengthened with FRP

Department of Reinforced Concrete Structures and Geotechnics, Vilnius Gediminas Technical University, LT-10223 Vilnius, Lithuania

Correspondence should be addressed to Justas Slaitas; tl.utgv@satials.satsuj

Received 7 March 2018; Revised 16 May 2018; Accepted 7 June 2018; Published 11 July 2018

Academic Editor: Young Hoon Kim

Copyright © 2018 Justas Slaitas 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 present study focuses on a prediction of crack width and load-carrying capacity of flexural reinforced concrete (RC) elements strengthened with fibre-reinforced polymer (FRP) reinforcements. Most studies on cracking phenomena of FRP-strengthened RC structures are directed to empirical corrections of crack-spacing formula given by design norms. Contrary to the design norms, a crack model presented in this paper is based on fracture mechanics of solids and is applied for direct calculation of flexural crack parameters. At the ultimate stage of crack propagation, the load-carrying capacity of the element is achieved; therefore, it is assumed that the load-carrying capacity can be estimated according to the ultimate crack depth (directly measuring concrete’s compressive zone height). An experimental program is presented to verify the accuracy of the proposed model, taking into account anchorage and initial strain effects. The proposed analytical crack model can be used for more precise predictions of flexural crack propagation and load-carrying capacity.

#### 1. Introduction

Retrofitting of existing structures is one of the main challenges for civil engineers today. One of the most advantageous material types for strengthening is fibre-reinforced polymers (FRP) due to their corrosion resistance and high strength to low weight ratio [1–5]. Anticorrosion properties are particularly relevant in aggressive environments, for example, bridge structures [6]. Strength properties could be used even more efficiently and economically by prestressing the FRP material [7, 8]. However, the effectiveness of strengthening can be compromised by loss of composite action, which can be delayed by using the additional anchorage [9]. There is a large quantity of researches made on the behaviour of the joint of concrete and FRP material [10–14], and the bond stiffness-reduction techniques are proposed [15–17], but none of the researches analysed by the authors was applied for prediction of concrete crack propagation. In accordance with design provisions [18, 19], the cracks in concrete open when a limiting tensile strain of concrete is reached; therefore, the crack width can be calculated by multiplying the mean values of a difference between tensile reinforcement and concrete strains with crack spacing. The researchers working on cracking phenomena of FRP-strengthened structures are trying to correct the empirical formulas to calculate crack spacing given by the design norms [20–22]. A different approach is proposed in this paper, that is, a crack model for direct calculation of flexural crack parameters which neglect the crack spacing. At the ultimate stage of crack propagation, the load-carrying capacity of the element is achieved. Therefore, it is assumed that the load-carrying capacity can be estimated according to ultimate crack depth (directly measuring concrete’s compressive zone height). The experimental program is presented to verify the accuracy of proposed crack propagation model, taking into account anchorage and initial strain effects. An extended database is used for comparison of numerical and experimental results of crack width under service load and load-carrying capacity of the element. In total, 98 RC beams, strengthened with externally bonded (EBR) and near surface-mounted (NSM) carbon fibre-reinforced polymer (CFRP) and glass fibre-reinforced polymer (GFRP) sheets, plates, strips, and rods were tested. The experimental results were collected from different scientific publications.

#### 2. Analytical Model

##### 2.1. Crack Width according to Design Standards

In this chapter, the estimation methods of the crack width and the mean crack spacing proposed in design standards [18, 19] are presented. The crack width of a RC structure can be calculated by following equation proposed in EC2 [18]. where is the maximum crack spacing and and are the mean strains in reinforcement and in concrete between cracks, respectively.

The mean value of crack spacing can be defined as follows [18]: where is a coefficient which evaluates the bond properties of the bonded reinforcement: 0.8 for high bond bars and 1.6 for bars with an effectively plain surface (e.g., prestressing tendons); is a coefficient which takes into account the distribution of strain: 0.5 for bending and 1.0 for pure tension.

Assuming stabilized cracking, the characteristic value of the crack width of FRP-strengthened RC structures is calculated according to fib bulletin 14 [19] recommendations: where is a tension-stiffening coefficient and is the reinforcement strain in the fully cracked state.

The mean crack spacing, taking into account the effect of both the internal and the external reinforcement, can be calculated as [19]
where is a mean value of concrete tensile strength; is an effective area of concrete’s tensile zone; and are the areas of steel and FRP reinforcements, respectively; and are the elasticity modules of steel and FRP reinforcements, respectively; and are the bond perimeters of steel and FRP reinforcement, respectively; and are the mean bond stresses of steel and FRP reinforcement; and *ξ _{b}* is a bond parameter given as

Neglecting the tension-stiffening effect and initial strain, the characteristic crack width is as follows [19]: where is the acting moment in a cross-section, is a ratio of the effective area in tension, and is the equivalent reinforcement ratio.

Hence, a denser cracking and the smaller crack widths are obtained for RC beams strengthened with FRP; the crack widths estimated by the methodology proposed in [19] were used for further analysis.

##### 2.2. Proposed Methodology

###### 2.2.1. Crack Width

In accordance with Jokūbaitis and Juknevičius and Jokūbaitis et al*.*’s [23, 24] proposed crack development model for RC structures, a flexural reinforced concrete element crack has two peaks; one leads to the crack spread toward the beam neutral axis, and the other refers to the tensile reinforcement. The width of the crack apex closer to the neutral axis is critical for further crack spread. The bond strength of concrete and reinforcements, which is equal to the tensile strength of concrete (), stresses of FRP, and steel reinforcements ( and , respectively), resist crack propagation. Parts of the element separated by the crack rotates about the intersection point of the crack surface and neutral axis (see Figure 1(a)).