Finite Element Model Updating of Damaged Concrete Beams Reinforced with GFRP Bars Using Modal Test Data

1. Damage in reinforced concrete beams causes a reduction in stiffness. Since the elastic modulus of Glass Fiber Reinforced Polymer (GFRP) bars is lower than that of steel bars, concrete beams reinforced with GFRP bars have a lower stiffness after cracking. The finite element model should be updated for analyzing the structure after being damaged. Experimental dynamic measurement can be used for damage assessment of structures. Flexural stiffness reduction due to cracking of reinforced concrete beams is simulated by reducing the elastic modulus [1].This paper presents a practical and user-friendly damage identification technique for estimating the stiffness of FRP reinforced concrete beams using the genetic algorithm and vibration test results. The identification is based on the finite element model updating involving an optimization process in which the objective function is defined as the difference between the analytical and corresponding experimental modal data.2. Methodology2.1. Experimental study:A total of 10 RC beam specimens with the length of 2.3 m (the distance between two supports was 2 m) strengthened with GFRP bars, were manufactured. Width and height of the beam cross section were 150 mm and 200 mm, respectively. Three concrete mixtures with cylindrical compressive strength of 20, 38 and 64 MPa were used in this study. Three specimens had lap-spliced bars. Splice length and the amount of transverse reinforcement in splice zone had been designed based on the equation represented by Esfahani and Kianoush [2].3. In Fig. 3, it is observed that with increasing load and more severe damage, the peak of the FRF curve takes place in lower frequency and the structural natural frequencies decrease. In Fig. 4, with increasing in load level, relative variations of frequency are raised. The greatest loss in frequency is caused mainly by the load step L1 and the intensity of frequency drops is reduced in L2 and L3 steps. Variation of the modal curvature has been used as a damage index [4]. According to Fig., it is illustrated that after damage, the slope of mode shapes grows. Fig.6 compares the values of moment of inertia predicted by the genetic algorithm in specimens B-1 and B-7. Specimen B-1 with concrete compressive strength of 20 MPa reinforced with two 10 mm diameter GFRP tension reinforcement has degradation in the moment of inertia far greater than specimen B-7 with concrete strength of 64 MPa and three GFRP bars with a diameter of 16 mm and one 10 mm.4. By comparing the values of moment of inertia estimated by the genetic algorithm with cracking status of the beam specimens, it is concluded that the aforementioned program predicts the stiffness distribution of damaged beams with good accuracy. The program evaluates the moment of inertia in specimens with lower concrete strength and longitudinal reinforcement ratio as being less than the values related to the specimens with higher concrete strength and reinforcement ratio. These results indicate that the process of stiffness updating is logical.