Nonlinear Analysis on Torsional Strengthening Of Rc Beams Using Cfrp Laminates

: This research is devoted to investigate the behavior and performance of reinforced concrete beams strengthened with externally bonded Carbon Fiber Reinforced Polymer (CFRP) laminates under the effect of torsion. In this study a theoretical analysis has been conducted using finite element code ANSYS. Six previously tested beams are used to investigate reinforced concrete beams behavior under torsion, two of them are solid and the rest are box-section beams. Also, two beams are without CFRP reinforcement, which are used as control beams for the strengthened one


INTRODUCTION
The repair and retrofitting of existing structures has become a major part of construction activity in many countries. To a large extent, this can be attributed to the aging of the infrastructure. Some of the structures are damaged by environmental effects, which include the corrosion of steel, variations in temperature and freeze-thaw cycles. There are always cases of construction-related and design-related deficiencies that need correction. Many structures, on the other hand, need strengthening because the allowable loads have increased or new codes have made the structures substandard. This last case applies mostly to seismic regions, where new standards are more stringent than the old. A new class of structural material known as Fiber Reinforced Polymer (FRP) has become a viable alternative to steel plates. FRP composites can be defined as composite materials consisting of high-strength fibers embedded in a polymer matrix.
Previously, FRP composites have been used, almost exclusively, in aviation and aerospace industries due to their high costs. Recently, the fall in the prices has led to their gradual introduction in the civil construction industry. The stiffness and strength of a composite is generally governed by the embedded fibers. In addition to binding the fibers together, the surrounding matrix acts as a protection against environmental damage. The advantages of composite materials in comparison with traditional construction materials such as steel, wood and concrete are that they are non-corrosive, nonmagnetic, resistant to various types of chemicals, of high strength and lightweight. Fiber reinforced polymer (FRP) has shown great promise as a state-of-the-art material in flexural and shear strengthening as an external reinforcement. However, little attention is paid to torsional strengthening in terms of both experimental and numerical research.

BACKGROUND
In 2003, Taljsten publishes the results of pilot tests conducted on five reinforced concrete beams strengthened with both CFRP and GFRP. The dimensions of the members are 150mm wide by 600mm deep and 6000mm long. It is concluded that strengthening in torsion with externally-bonded FRP was feasible, but continuity of the FRP reinforcement around the section with proper anchorage was critical. Only the torque-twist response of the tests was reported. Salom et al. (2004) present a study that describes an experimental program on the torsional strengthening of reinforced concrete spandrel solid beams using composite laminates. The variables considered in the study include fiber orientation, composite laminates, and effect of anchoring system. The study proved that the FRP laminates could increase the torsional capacity of concrete beams by more than 70%. Allawi, A. (2006) studies the behavior and performance of nine reinforced concrete members strengthened with externally bonded CFRP laminates in torsion. Two different software have been used, DIANA and P3DNFEA software, to model the tested beams by using FEM. Comparisons of the finite element method results with experimental data show that the maximum difference is 8.2% and 7.3% for cracking and ultimate torque, respectively, when confinement and expansion effects is included in the analysis. While, a difference of 14.3% and 22.7% is obtained for cracking and ultimate torque, respectively, when neglecting these effects.
Al-Mahaidi and Hii (2004Hii ( , 2005Hii ( , and 2006) study the behavior and performance of six medium scale reinforced concrete beams. Two specimens were solid sections, while the rest were box-sections strengthened with externally bonded CFRP laminates in torsion. The experimental results show that the bonding of CFRP laminates to beams causes an increase up to 40% and 78% in both cracking and ultimate strengths, respectively compared to the control specimens. DIANA software is used to study numerically tested beams and compare finite element results with experimental outcomes. Good agreement with experiments in terms of torque-twist behavior, steel and CFRP reinforcement responses, and crack patterns is achieved.

OBJECTIVE
The main objective of the present study is to investigate the behavior of reinforced concrete beams that have been strengthened by using Carbon Fiber Reinforced Polymers under the effect of torsion forces. Finite element program ANSYS 11.0 is used to model experimentally the tested beams in torsion so that numerical results can simulate tested beams in torque-twist behavior. The torsional behavior of the reinforced concrete beams having different number of CFRP layers, different concrete compressive strength and U-wrap for the CFRP configuration is investigated.

VERIFICATION OF THE FINITE ELEMENT IDEALIZATION
The validity and accuracy of the finite element idealization are studied and checked by analyzing concrete beams that have been tested experimentally by Hii and Al-Mahaidi (2006). Six reinforced concrete beams are adopted in this study. Four of these beams are strengthened by using CFRP in torsion, while the other two beams are without strengthening and are used as control beams. The material properties and specimen details of the adopted beams in the main experimental program are shown in Tables 1, 2

Finite Element Idealization Of The Beams
The six concrete beams are modeled using 8-node brick elements (SOLID 65) for the concrete. The reinforcing bars are modeled using 2-node element (LINK 8), and the CFRP strips and the epoxy layer are modeled by using (MEMBRANE 41) and spring elements, respectively. The loading arm is modeled using (SOLID 45) elements, as shown in Fig. 4 and

Boundary Conditions
For the loaded end, a pivot support which is fixed in the lateral and vertical directions is placed. The use of a pivot support allows twist of the crosssection under applied torque. The pivot is free to move in the longitudinal direction to allow elongation or shortening of the beam. During the preliminary analyses, localized concrete crushing around the pivot support is observed. To overcome this, the concrete brick elements around the support are assigned linear elastic properties to distribute the reaction loads uniformly. At the fixed end, the elements at the support are fixed in the longitudinal, vertical and lateral directions.
The constraints reflect the fixity provided by the steel collar in experiments. Loading on the model is achieved by a point load on the loading arm at an eccentricity of 855mm from the centerline of the beam. As accurate stress and strain results from the loading arm are not needed, the use of linear elastic properties ensures no premature termination of analyses occurred from stress concentrations with point loads.

Finite Element Results Verification
A comparison between the numerical and experimental results has been made to verify the accuracy of the numerical models. The results of the solid beam CS1, as shown in Figs. 5, 6, and 7, are chosen to validate finite element results with respect to experimental work. These figures show the relationship between the torque and the angle of twist, the beam extension, and the strain in the stirrups for this beam. These figures reveal that the general behavior for the tested beams in torsion is well established by the adopted numerical model.

PARAMETRIC STUDY
The parametric study is carried out to investigate the behavior of reinforced concrete solid and box section beams having: • Different values of concrete compressive strength.
• Different number of CFRP layers.
• U-wrap CFRP sheets effect is investigated in comparison to fully wrapped sheets.  Table 7 shows the values of the concrete strength used in the parametric study, while Fig. 8 shows the effect of increasing ( on the angle of twist of the solid beam, whereas its effect on the longitudinal extension and strain are shown in Figs. 9 and 10, respectively. As for the boxsection beam, the effect of variation is presented in Figs. 11, 12 and 13. Table 8 shows the differences in the ultimate torque among these cases.

Effect of the number of CFRP layers
The effect of the number of CFRP layers is considered in this study. Different number of layers is used, namely 3, 4 and 5 layers. Two beams are chosen to be tested against this effect, a solid beam and a box-section beam. Table 9 shows material properties for CFRP strips used in the parametric study.
Figs. 14, 15 and 16 show these effects for the solid beam, whereas Figs. 17, 18 and 19 show these effects for the box-section beam. Concrete compressive strength for the adopted beams is 56.4 MPa. Also, CFRP sheets spacing for both beams is 0.50D. From the figures presented below, it is obvious that when the number of layers is increased the ultimate torque also increased so as for the angle of twist and other factors. Table 10 shows the effect of increasing the number of CFRP layers on torsion behavior for both solid and box-section beams.

Effect of CFRP U-wrap style
Two beams have been chosen to investigate this effect. A solid and a box-section beam are tested numerically under U-wrap style for CFRP strips. The results are compared with the fully wrapped beams under the same conditions. Also, a comparison has been made for the two beams (solid and box-section) to investigate the effect of wrap style on them. Concrete strength for the adopted solid and box-section beams is 56.4 MPa, also two layers of CFRP laminates with 0.50D spacing is applied.
The results show that the full-wrap is more viable and bears greater loads than the U-wrap and the solid beam is better than the box-section beam. Figs. 20, 21 and 22 show these effects for the solid beams, whereas Figs. 23, 24 and 25 show these effects for the box beams.

Figs. 26, 27
and 28 show a comparison between solid and box beams under U-wrap. Table 11 show the effect of the wrap style on the torque strength for the two beams.

CONCLOSIONS
From the numerical analysis carried out in this study, the following conclusions are shown: 1. When comparing the Numerical and experimental results, it is evident that ANSYS finite element models underestimate the angle of twist and the ultimate torsional strength of the adopted beams, especially for the box-section specimens. However, the general behavior for the tested beams is well established.
2. The numerical results revealed that using CFRP laminates generally increases the ultimate torque capacity of the strengthened beams.
3. The ultimate torque at failure is found to increase as the compressive strength of the concrete is increased, Consequently, increasing concrete compressive strength from 25 MPa to 56.4 MPa shows the following : • An increase of about 63.6% in the ultimate torque for the solid beam.
• An increase of about 81.8% in the ultimate torque for the box-section beam.
4. The ultimate torque at failure is found to increase as the number of CFRP layers applied is increased. Increasing the number of CFRP layers from 2 to 5 shows the following :  • Salom, P. R., Gergely, J. and Young, D. T.