Analytical Approach of Tension Stiffening Contribution of GFRP-Members

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1 Journal of Applied Science and Engineering, Vol. 18, No. 1, pp. 1 8 (2015) DOI: /jase Analytical Approach of Tension Stiffening Contribution of GFRP-Members Khalfallah S. Ecole Nationale Polytechnique, Ville Universitaire, Ali Mendjali, Constantine, Algeria Abstract To calibrate the tension stiffening effect of reinforced concrete member subjected to tensile forces, an analytical approach is presented. The tension stiffening behaviour is a primordial task in reinforced concrete mechanic field. In this model, an analytical relationship of stress-strain law in the cracking range is developed. The bi-linear relation used in CEB model doesn t represent faithfully the post-cracking behaviour of reinforced concrete structures. For this concern, a parabolic branch is selected in the post-cracking phase possessing as asymptotic line to the stress-strain line of the bare bar that minimizes the tension stiffening effect in ultimate load level. This assumption is taken into account for many considerations: material nonlinearities, the bond character and the tension stiffening effect. Analytical results are shown and compared with experimental data for direct tensile load. Obtained results show a well concordance to ward experimental data. More, the influence of concrete strength, reinforcement ratio and bar diameter on tension stiffening is studied and commented. Key Words: Analytical Model, Tension Stiffening, Nonlinear Analysis, Tensile Members, Bar Diameter, Reinforcement Ratio, Strength of Concrete 1. Introduction The intact concrete between adjacent cracks can still carry tensile stresses after cracking occurs in reinforced concrete structures. This phenomenon known as the tension stiffening effect is generated due to the bond between reinforcing bars and surrounding concrete. Since 80s, the international organizations of structural mechanic have recommended designers to consider tension stiffening effect in computing mechanics of serviceability of reinforced concrete (RC) structure deflections. The tension stiffening phenomenon depends on many factors, such as: member dimensions, the reinforcement ratio, re-bars diameter and mechanical properties of materials used Khalfallah [1] and Sooriyaarachchi et al. [2]. This effect can provide a well representation of the cracking effect of RC structures under monotonic loading. *Corresponding author. Khalfallah_s25@yahoo.com This effect occurs in the region characterized by the formation of cracking of concrete and yielding of longitudinal reinforcement of the structural behaviour. The introduction of the tension stiffening contributes to stiff the behaviour of RC structures and it becomes the main objective of the cracked concrete contribution. In literature, various models integrating tension stiffening effect have already been proposed in the design of RC structures. In this case, we can distinct the model of Branson [3] that the tension stiffening effect is incorporated using an equivalent moment of inertia of the cracked beam section. This model is largely used by designers to compute RC and FRP reinforced beam deflections. However, other models are presented using a modification on constitutive laws of steel or the sectional area obtaining an effective area of the section. These models have also been proposed to nonlinear analysis of pull-out tests and bent beams, indifferently. In this scope, we can illustrate various works published in the litera-

2 2 Khalfallah S. ture: Gilbert and Warner model [4], Choi and Cheung [5] and the CEB manual design model [6]. And among those that modify the sectional area, such as: ACI-440 [7] and Behfarnia [8]. Recently, many complex models based on the bond-slip mechanisms between concrete and reinforcing bars have been published: Khalfallah [1], Gupta and Maestrini [9], Kwak and Song [10], Ferreti and Savoia [11]. These models present some limitations in applications because these approaches depend on the distribution of bond along the reinforcement axis and it follows series of complex integrations of the second differential equation of bond. Unlike, previous attempts have already been drawn to represent more realistically tension stiffening effects assuming the modifications taken in the expression of steel stresses. Based on this concept, this work introduces a novel tension stiffening model applied to tensile members. The proposed model uses a parabolic curve to describe the post-cracking region of tensile stress-strain relationship of reinforcing bars improving the CEB-tension stiffening model [6]. This assumption is taken into a consideration due to many parameters having an influence on the member response. Among these parameters, we can tell: the nonlinear behaviour on concrete due to the cracking of concrete, the relative motion between concrete and steel bars engendering a friction effect and the property of the tension stiffening phenomenon that stiff more the RC member. Finally, the influence of concrete strength, reinforcement ratio and bar diameter on the tension stiffening is studied of glass fibber-reinforced polymer reinforced concrete members. 2. The CEB Model [6] The CEB-model developed for tensile RC members uses the tension stiffening phenomenon through an increase in reinforcement stiffness. The mechanism of cracking of RC members subjected to monotonic tensile loading is shown in Figure 1. The Figure 1 shows different ranges of the structural behaviour of RC members: (I) un-cracking concrete, (II) cracking concrete and (III) yielding of reinforcement. The CEB model adopts a stress-strain relationship of reinforcing bars in terms of an average strain of un-cracked section and that of totality cracked one, respectively. The average strain of reinforcement is expressed in the cracking region by: (1) With s2 is the strain of bare bar and s is the difference between the totality cracked section and the partially cracked reinforced concrete one (Figure 1). In the CEB manual design [4], the steel strain increment s based on experimental results is proposed, as: (2) s2 and sr are stresses in bare bar and that correspond to the cracked section level, respectively. The strain increment smax is the maximum tension stiffening contribution between strains s1 and s2, which occur at the beginning of the cracking process. An efficient tension stiffening model for nonlinear analysis of reinforced concrete member has been published by Stramandinoli et al. [12] in which the relationship (1) has been developed as a function of the uncracked section strain s1 and the full cracked of the member s2. (3) The CEB model presents a consistent theory of the Figure 1. The tension stiffening behaviour.

3 Analytical Approach of Tension Stiffening Contribution of GFRP-Members 3 post-cracking behaviour of RC members under pure tension. The corresponding curve is characterized with a bilinear branch law selected in the cracking of concrete region. 3. The Proposed Model A novel expression that describes the tension stiffening behaviour for structural members is proposed in this section. The model is based on the modification of the stress-strain formula of reinforcing bars as shown below. The concrete is assumed to behave like a linear-elastic material until the tensile strength of concrete is reached. When the applied load, N, is relatively small, the strains in steel and concrete maintain a single value and materials behave together. In this phase, the strain of each component is then given by: (4) E s and E c are elastic modulus of reinforcing bars and concrete before cracking, of concrete, respectively. A s and A c are the reinforcement area and member cross section and N is the tensile applied load. Until the formation of the primary crack of concrete, components of the composite material change its behaviour due to the initiation and propagation of cracks. At this point, the stress value of reinforcing bars is computed based on the notion of the cracked section, where the maximum stress in the concrete under tension reaches its strength one. The value of the un-cracked concrete range can be evaluated considering that concrete and GFRP-bars behave together. (5) which is founded on the bi-linear law in the cracking range, seems that this approach cannot represent well the structural behaviour of RC tensile members. For this raison, a novel expression improving the CEB model is proposed. For many reasons, the nonlinearity made the dominance on the structural response, to be aware: the heterogeneous composition of concrete and the intervention of others phenomena, such as: the tension stiffening effect, the bond adherence and the dowel action.et. Basing on this concept, in the post-cracking region, a polynomial expression is formulated until yielding of reinforcing bars takes place. The stress-strain relationship of the bare bar is assumed as asymptotic straight of the curve representing the expression developed minimizing the tension stiffening in the cracking region of the member behaviour. After cracking, the stress in the reinforcement steel between the once cracking and the yielding of reinforcement is then expressed using the mathematical establishments of this concept by: (6) where cr and sr are the cracking strain and the strain in reinforcement in state II with totally cracked section without any concrete contribution corresponding to the stress sr, respectively. The corresponding strain can be drawn from the equation (6) in the following form: where s = N EA s s (7) The tension stiffening contribution in the cracking range of concrete can be evaluated by: = A As c is the reinforcement ratio, = E Es c and f t is the tensile strength of concrete. The modification that can be added to the CEB model, (8) Particularly, the maximum tension stiffening can be deduced as (Figure 1):

4 4 Khalfallah S. (9) The applied load, N, can be divided between concrete and reinforcing bars: (10) With ct is the tensile stress in concrete. In the other manner, the equation (10) can be written as: (11) Using equations (7) and (8), the relation (11) can be written as: (12) f t is the tensile strength of concrete. The novel expression of tensile concrete behaviour can be done with: (13) To trace the stress-strain of concrete taking into account the tension stiffening behaviour, the value of s2 = N taken as a variable is computed by varying the Es As applied load until the yielding of reinforcement. From obtained values of s2, the stress in concrete is then considered using the equation (13). 4. Validation of the Model The proposed model has been compared to experimental results of tensile RC members experimentally studied by Sooriyaarachchi et al. [2]. Geometries and material properties are reported in Tables 1 and 2, respectively. Sooriyaarachchi et al. [2] tested RC members strengthened by GFRP-bars and loaded with tensile applied force. The experimental study is devoted to analyse the influence of concrete strength, reinforcement ratio and bar diameter on the RC member response. In the experimental work, Sooriyaarachchi et al. [2] have chosen GFRP-bars for the reinforcement presenting relatively low stiffness compared with steel reinforcement to make prediction of deflections and particularly at service loads. This selection of type reinforcement category can deal an important deflection or strain of tested members and more quantify the tension stiffening contribution in the global response of members. Experimental study aims to analyze the influence of Table 2. Material properties used in [2] Property GFRP-Bar 13 mm 19 mm Concrete strength Grade 50 Grade 90 Strength (MPa) Stiffness (GPa) Tensile strength (MPa) Table 1. Details of the test specimens [2] Specimen Concrete strength (MPa) Diameter D (mm) Dimension b*d*l (mm) Reinforcement ratio % C50/13/ *100* C50/13/ *150* C50/13/ *200* C90/13/ *100* C90/13/ *150* C50/19/ *150* C50/19/ *200* C90/19/ *150* C90/19/ *200*

5 Analytical Approach of Tension Stiffening Contribution of GFRP-Members 5 the reinforcement ratio; it s very important to appreciate how the area of concrete around bars contributes to calibrate tension stiffening effect. Figures (Figures 2 3) compare the tension stiffening effect of different reinforcement ratios tested in this study [2]. The experimental work taken involved testing two grades of concrete and obtained results are plotted in separate graphs (Figures 2 and 3) show for grade C50 concrete whilst Figures 4 5 show for grade C90 concrete. It s very clear from obtained results that the tension stiffening increases with a decrease of reinforcement ratio. For the same quality of concrete (C50) used, the tension stiffening effect is more quantified for under-reinforced concrete sections but it s below-estimated for overreinforced concrete ones. The rebar stress at cracking concrete level is 100 MPa for = 1.26% but it s about 200 MPa for = 0.32%. The quantity of reinforcement area delays the apparition of cracks. The previous remark is again verified when a concrete feature (C90) is so used. In addition, the amount of steel used delays significantly the cracking phenomenon. In this concept, moving from 1.26% to 0.32%, the rebar stress increases from 100 MPa to 230 MPa. The rebar stress at cracking of concrete level is about 100 MPa for concrete class C50 but it s evaluated to 250 MPa for concrete class C90. It is absolutely clear that the quality of the concrete affects the tension stiffening option. The quality of concrete is primordially characterized by its tensile strength. The concrete strength delays the apparition of cracks that are the main effect of the tension stiffening creation. In explicitly, we can say that the diameter of the bar has an influence on the tension stiffening. Figures (6, 7, 8, and 9) allow to show the influence of the bar diameter on the tension stiffening contribution. The Figure 10 shows the influence of reinforcment ratio on the the tension stiffening option. Very clear that the Figure 2. Rebar stress-strain of concrete C50 with = 1.26%. Figure 4. Rebar stress-strain of concrete C90 with = 1.26%. Figure 3. Rebar stress-strain of concrete C50 with = 0.32%. Figure 5. Rebar stress-strain of concrete C90 = 0.56%.

6 6 Khalfallah S. Figure 9. Rebar stress-strain of concrete C90 with = 19 mm. Figure 6. Rebar stress-strain of concrete C50 with = 13 mm. Figure 10. Influence of reinforcement ratio on the tension stiffening. Figure 7. Rebar stress-strain of concrete C90 with = 13 mm. influes primirdially on the tension stiffening contribution. The influence remains considerably until the ultimate load. From Figure 12, the diameter of bars used to reinforce GFRP-members hasn t any significant effect of bars size on the tension stiffening contribution. 5. Conclusions Figure 8. Rebar stress-strain of concrete C50 with = 19 mm. quantity of reinforcement ratio influes on the tension stiffening contribution. This influence is more pronounced at the firstly cracking level and decreases as the loading increases. The Figure 11 plots strength concrete curves to quantify the tension stiffening effect. The quality of concrete In this study, a novel tension stiffening analytical model for reinforced concrete members is presented. An analytical expression is used to describe the concrete tensile stress-strain curve in the cracking range of the member behaviour. The work presented can be divided in two parties. Firstly, the study presents the validity of the analytical approach illustrated in above sections and examines the influence of many parameters on the tension stiffening behaviour. In general, the model presents an improvement compared with experimental data obtained by Sooriyaarachchi and Pilakoutas [2].

7 Analytical Approach of Tension Stiffening Contribution of GFRP-Members 7 5. The proposed tension stiffening model can be easily implemented in finite element analysis based on crack models. References Figure 11. Influence of concrete strength on the tension stiffening. Figure 12. Influence of diameter bar on the tension stiffening. Secondly, to calibrate the tension stiffening contribution, the analysis appears the local behaviour of concrete between cracks. The reinforcing ratio, the concrete strength and bar size of diameter are studied to present their influence on the tension stiffening behaviour. Conclusions can be drawn from this analysis are: 1. Concrete strength and reinforcing ratio having an influence effect on the tension stiffening effect. 2. There is no significant influence on the tension stiffening behaviour using different bar diameter. 3. High concrete strength and bar size can provide an important ultimate load of reinforced concrete members. 4. The analysis requires the introduction of the bond characterization between concrete and reinforcement bars to more understand this aspect for accurate predictions of tension stiffening effect. The positivity of this assumption can deal to quantify more tension stiffening and bond effects on RC member response. [1] Khalfallah, S., Tension Stiffening Bond Modeling of Cracked Flexural Reinforced Concrete Beams, Journal of Civil Engineering and Management, Vol. 14, No. 2, pp (2008). doi: / [2] Sooriyaarachchi, H., Pilakoutas, K. and Byars, E., Tension Stiffening Behavior of GFRP-Reinforced Concrete, American Concrete Institute, Special Publication, Vol. 230, pp (2005). [3] Branson, D. E., Design Procedure for Computing Deflection, ACI Journal Vol. 65, No. 8, pp (1968). doi: /7508 [4] Gilbert, R. I. and Warner, R. F., Tension Stiffening in Reinforced Concrete Slabs, Journal of the Structural Division ASCE, Vol. 104, No. 2, pp (1978). [5] Choi, C. K. and Cheung, S. H., Tension Stiffening Model for Planar Reinforced Concrete Members, Computers and Structures, Vol. 59, No. 1, pp (1996). doi: / (95) [6] CEB Model. Cracking and Deflection Bulletin d information N 158. Paris, France (1985). [7] ACI Committee 440, Guide for the Design and Construction of Concrete Reinforced with FRP Bars (ACI 440.1R-03), American Concrete Institute, p. 42 (2003). doi: /40753(171)158 [8] Behfarnia, K., The Effect of Tension Stiffening on the Behaviour of R/C Beams, Asian Journal of Civil Engineering (Building and Housing), Vol. 10, No. 3, pp (2009). doi: /40753(171)158 [9] Gupta, A. and Maestrini, S. R., Tension Stiffening Model for Reinforced Concrete Bars, Journal of Structural Engineering ASCE, Vol. 116, No. 3, pp (1990). doi: /(ASCE) (1990)116: 3(769) [10] Kwak, H. G. and Song, J. Y., Cracking Analysis of RC Members Using Polynomial Strain Distribution Function, Engineering Structures, Vol. 24, pp. 455

8 8 Khalfallah S. 468 (2002). doi: /S (01) [11] Ferretti, D. and Savoia, M., Non-Linear Model for R/C Tensile Members Strengthened by FRP-Plates, Engineering Fracture Mechanics, Vol. 70, pp (2003). doi: /S (02) [12] Stramandinoli, R. S. B. and La Rovere, H. L., An Efficient Tension Stiffening Model for Nonlinear Analysis of Reinforced Concrete Members, Engineering Structures, Vol. 30, pp (2008). doi: /j.engstruct Manuscript Received: Feb. 27, 2013 Accepted: Jan. 26, 2015