2019 Convention Article




  • 1. Introduction

  • 2. Background of Related Literatures

  •   2.1 Research and Development of Bridge Rehabilitation Techniques

  •   2.2 Ductility Defined using Load-Displacement Curve

  • 3. Finite Element Modeling

  • 4. Discussion of Results

  •   4.1 Finite Element Results

  •   4.2 Seismic Performance Evaluation

  •   4.3 Summary of Results

  • 5. Conclusion

1. Introduction

Bridges are one of the most critical and important structures in the transportation systems that are constantly subjected to different kinds of loadings. At times of natural disasters, transportation systems must withstand the calamities in order to sustain transport connections and communication for better crisis management. One of the most commonly encountered and destructive natural calamities is earthquake, thus, the seismic performance of the bridges should be strictly observed, especially the seismic performance of existing bridges.

The majority of existing bridges were built based on old building codes and structural manuals. Old bridges constructed from old structural standards assumed less service loads, which made them vulnerable to structural damages resulting to possible poor performance during an earthquake. In addition to that, most of the existing bridges were made from reinforced concrete that are constantly exposed to hostile physical and chemical conditions. This aggressive environment contributes to the progressive damage of reinforced concrete which made the structure susceptible to the fatigue behavior of concrete, exposing the reinforcing steel to rust and corrosion.

The minor damages in the concrete element such as cracks and spalling in column of the bridges affects the confinement of concrete to the structure, thus, leading to brittle failure of the column that could result into serious failure or worse, total collapse of the structure. The column of bridges is one of the main structural members of the bridge that resist lateral seismic forces and vertical forces, thus, the performance and reliability of the column is vital regarding the performance of the entire structural system. Therefore, in order to prevent the brittle failure, it is essential to enhance the ductility of the columns, thus, increasing the performance and reliability of existing bridges.

Ductility criteria of a concrete column member is a one of the most important parameters in evaluating the seismic performance of the structure. In order to increase this type of criteria, confinement or external strengthening of concrete column structures could be provided in order to increase the ductility criteria. Therefore, in this paper the seismic performance of the structure was evaluated using the calculated ductility. The progressive development of computer simulations was utilized using a finite element software, ABAQUS (2013), to numerically evaluate and observe the relationship of ductility of the structure with respect to length-to-height ratio and width-to-span ratio of CFRP.

2. Background of Related Literatures

2.1 Research and Development of Bridge Rehabilitation Techniques

Researchers and engineers have been interested in the continuous development of bridge rehabilitation techniques since the mid 1980’s. According to the study of Saadatmanesh et al. (1996), Özcan et al. (2008)Ye et al. (2003) and Rashid and Mansur (2005), the problem with the columns constructed based on old codes faces poor detailing of starter bars and inadequate lateral reinforcement that leads to seismic performance deficiency. Forces induced by seismic loads that result into shear forces are mainly resisted by lateral reinforcement, if properly designed, buckling of the longitudinal bars and sudden loss of bond could be prevented. Therefore, existing columns with inadequate lateral reinforcement must be provided by external confinement to enhance the ductile behavior of the structure.

Many techniques have been implemented into the retrofit design process mainly based on experimental testing of scaled-down models of bridge structures. Previous researches, such as study of Priestley et al. (1984), Chai et al. (1991), and Sun et al. (1992) in University of California in San Diego have indicated that strengthening of columns by using steel jackets significantly improves the performance and ductility of a column. However, rehabilitation techniques that utilize steel and concrete, such as section enlargement of columns, confinement by concrete covers, and attachment of steel jackets are time consuming and difficult in execution of construction methodologies, therefore, considering the disadvantages of existing materials, a study for new material is necessary to develop new techniques.

Since then, researchers have conducted experimental tests to find an effective and economical alternative material for bridge rehabilitation. Priestley et al. (1992) presented the study of column seismic retrofit using Fiberglass/Epoxy, Yamasaki et al. (1993) investigated the use of Fiber Reinforced Polymers (FRP) bars to retrofit concrete bridges, and Ehsani et al. (1993) analyzed the use of glass fiber reinforced polymer (GFRP) bars by circumferentially wrapping the columns around the plastic region. After years of study using FRP bars and straps as retrofit materials, Toutanji (1999) extended the study to FRP sheets and presented a structural model for the behavior of GFRP and CFRP confined concrete columns using large-scale samples in experiments. The researches presented that the use of FRP as a material for retrofit provided desirable results in increasing the performance of the structure.

The desirable properties of FRP make it to be an appropriate substitute material for rehabilitation techniques of existing bridges. FRP is superior to resist corrosion, good adhesion to concrete, has high strength-to-weight ratio, capability of vibration absorption, and moisture resistance. In addition to that, Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures (ACI, 2002), reported that FRP has thermal expansion coefficient of close to concrete and steel which made it to be a suitable material for externally strengthening reinforced concrete. Although FRP laminates, bars and straps are generally more expensive than concrete and steel, research of Katsumata et al. (1988) and Teng et al. (2002) revealed that the use of CFRP and GFRP is approximately 20 % less cost than steel considering construction methodology.

In the recent years, development of computers and various finite element software has progressed and provided accurate results. Numerous researchers had corresponded to experimental tests in the previous decades and conducted numerical experiments through finite element simulations. In 1999, Tedesco et al. (1999) assessed a FRP laminate-repaired bridge by finite element method, Wang and Restrepo (2001) reported that good agreement of results was observed between the numerical and analytical results using a short-term assessment of axial load-deformation of reinforced columns confined with GFRP and steel, Monti et al. (2001) and Pantelides and Gergely (2002) presented formulae for calculation of required FRP wrapping thicknesses and provided design and analysis techniques for seismic retrofit of concrete members by FRP.

Due to popularity and the increasing demand of research matter, more and more researches with parametric studies have been conducted to optimize the application of retrofit materials to bridge columns. Experimental and analytical parametric studies were made to establish relationship of column and retrofit materials. In 2013, Taghia and Bakar (2013) studied parametric studies and assessed the relationship of varying cross-section of reinforced short column and varying CFRP layers based on finite element analysis. Studies of varying reinforcing materials were also made. Pateriya et al. (2015) presented a numerical analysis of compressive strength of columns reinforced with varying materials using steel, GFRP and CFRP and Han et al. (2016) conducted experimental tests on reinforced concrete evaluating the performance between CFRP, steel plate and fiber steel composite plates (FSC). Varying shape of FRP reinforcement were also studied such as the study of Zeng et al. (2018) which investigated the behavior and three-dimensional finite element modeling of circular concrete columns partially wrapped with FRP strips.

2.2 Ductility Defined using Load-Displacement Curve

Ductility of a concrete bridge column is an important design factor to consider in seismic performance of the structure. The ductility of the structure is critical in aspect of dissipation of seismic energy during earthquake, therefore, the reliability of existing bridges is enhanced by improving ductility.

In 1994, Jeong (1994) developed energy based method using load- displacement curve. This method defines the ductility of a structure using concept of energy by the relating any two of inelastic, elastic, and total energy as shown in the ductility indices on Fig. 1. In order to determine the slope that distinguishes elastic energy from inelastic energy, the slope, S, is calculated as:

$$S=\frac{P_1S_1+(P_2-P_1)S_2+(P_3-P_2)S_3}{P_3}$$ (1)

where, slopes S1, S2, S3, were obtained through analytical calculation and the loads, P1 andP2, were the intersection points of extended slopes and P3 as the ultimate load. The inelastic, elastic and total energies were calculated through numerical integration and in this paper, the ratio of inelastic energy to total energy is considered.

Fig. 1.

Energy Index

$$Energy\;Ratio(ER)=\frac{Inelastic\;Energy(E_i)}{Total\;Energy(E_t)}$$ (2)

It is suggested by Grace et al. (1998) that the structure having an energy ratio of greater than 75 % is classified to be ductile, and semi-ductile behavior of energy ratio ranging from 70~74 %.

3. Finite Element Modeling

Finite element program ABAQUS was chosen to simulate the model. The software has wide variety of modelling capability and has concrete damage plasticity (CDP) option that captures the real behavior of concrete. Rodríguez et al. (2013) recommended that the use of CDP model exhibits good behavior for concrete under monotonic, cyclic and dynamic loading.

The simulated structure was analyzed under three (3) model cases, the initial case, the change in height of CFRP (length- to-height ratio or wrapping height), and the change in thickness of CFRP (width-to-span ratio or relative wrapping thickness). In order to account for the effect of change in height of CFRP, the cross-section of the circular concrete bridge pier was constant and the thickness of the CFRP and set 2mm. In order to evaluate the effect of change in thickness of CFRP, the cross-section of the circular concrete bridge pier were to set to a fixed dimension and the height of the CFRP were set to height of ¼ of the column. Fig. 2 demonstrates the finite element model cases and Tables 1 and 2 show the corresponding nomenclature of ratio with respect to each case analysis.

Fig. 2.

Nomenclature of Parametric Models

Table 1. Nomenclature of Length-to-Height Ratio Cases

Case Profile Analysis Designation Length (m) Height (m) Ratio Percentage (%)
Initial CFRP_0 0 1.65 0 0
Length-to-Height CFRP_25 0.4 1.65 0.25 25
CFRP_50 0.825 1.65 0.50 50
CFRP_75 1.24 1.65 0.75 75
CFRP_100 1.65 1.65 1.0 100

Table 2. Nomenclature of Width-to-Span Ratio Cases

Case Profile Analysis Designation Width (m) Span (m) Ratio Percentage (%)
Initial CFRP_0 0 0.4 0 0
Width-to-Span CFRP_1 mm 0.001 0.4 0.0025 0.25
CFRP_2 mm 0.002 0.4 0.0050 0.50
CFRP_3 mm 0.003 0.4 0.0075 0.75

The dimensions of the structure were taken from experimental specimens subjected to real life hydraulic actuator as shown in Fig. 3(a). In order to avoid creating unnecessary elements, the foundation of the structure was not modelled and changed into encased boundary condition to account for the footing. Fig. 3(b) shows the schematic design of the numerical model. A three- dimensional finite element was modelled as shown in the Fig. 4, having C3D8R hexahedral elements for concrete structure as S4R shell elements for CFRP.

Fig. 3.

Model Configuration Setup

Fig. 4.

Boundary and Loading Conditions of Meshed Numerical Model

In this study, numerical models were subjected to gravity loading and dynamic loading were applied until failure of the structure. Fig. 4 illustrates the direction and location of dynamic loading which is positioned in the middle of the loading cap in order to equally distribute the loads. Tie constraint option was used in defining the interaction between CFRP and concrete structure. CFRP was tied to concrete in order to force the nodes to behave in the same translations. The assumed values of the mechanical properties of the materials were listed in Tables 3 and 4 while the dynamic loading is shown in Fig. 5.

Table 3. Material Properties of CFRP

Density (kg/m3) Young's Modulus (MPa) Poisson's Ratio Yield Stress (MPa) Plastic Strain
1500 2.35 0.3 344 0

Table 4. Material Properties of Concrete

Angle (°)
Eccentricity fbo/fco Kc Viscosity
2400 28 0.2 36 0.1 1.16 0.667 0
Compressive Behavior Compressive Damage Tensile Behavior Tensile Damage
Stress (MPa)
15 0 0 0 3 0 0 0
23 0.003 0.2 0.000333 2 0.0002 0.2 0.0002
29 0.00055 0.3 0.0007 1.5 0.0003 0.3 0.0003
33 0.00147 0.4 0.0013 1.2 0.0004 0.4 0.0004
25 0.0066 0.45 0.002 1 0.0005 0.5 0.0005
22 0.008 0.5 0.003 0.8 0.0008 0.6 0.0008
20 0.009 0.6 0.0043 0.5 0.001 0.8 0.001
10 0.01 0.8 0.007 0.4 0.002 0.7 0.002
0.9 0.01 0.2 0.003 0.9 0.003
0.1 0.005 0.99 0.005

Fig. 5.

Applied Dynamic Loading

The values of CFRP were taken from the experimental study of Han et al. (2016) and the values of concrete properties were taken from the study of Senturk and Pul (2017). Senturk and Pul (2017) published a calibrated concrete damage plasticity parameter by performing a standard cylinder test on ABAQUS using a f’c=30 MPa concrete. Table 4 listed the parameters of concrete material where fb0/fc0 is the ratio of strength in biaxial state (fb0) to strength in uniaxial state (fc0) and Kc, is the ratio of the distances between the hydrostatic axis and respectively the compression meridian and the tension meridian in the deviatoric cross section. Fig. 6 shows the graph of tensile and compressive stress-strain for the numerical model of concrete.

Fig. 6.

Stress-Strain Curve of Simulated Concrete

4. Discussion of Results

The stress-strain and load-displacement hysteresis curve were investigated through finite element results and the ductility of the structure were obtained by numerical integration.

4.1 Finite Element Results

After performing finite element analysis, an element within the plastic hinge section of the column was evaluated as shown in Fig. 7. The structure without CFRP reinforcement was compared to CFRP with increasing thickness and wrapping ratio. Fig. 8 and Table 5 show the effect of increasing the length-to-height ratio of CFRP to stress-strain of the structure. It shows that the use of CFRP improves the performance of the structure in terms of stress-stain. In addition to that, it was observed that the increase of height in CFRP significantly enhanced the behavior of the column than the increase of thickness of CFRP.

Fig. 7.

Evident Deformation at Plastic Hinge Region

Fig. 8.

Comparison of Stress-Strain Curve without CFRP to Structure with CFRP

Table 5. Comparison of Stress according to CFRP Ratio

Case Ratio Stress (kPa)
Yield Ultimate
Initial 0 1143.66 1980.51
Length-to-Height Ratio 0.25 2171.50 2303.76
0.50 2246.91 2507.11
0.75 2926.41 3049.41
1.00 2979.74 3211.01
Width-to-Span Ratio 0.0025 1651.31 2227.48
0.0050 2246.91 2507.11
0.0075 2280.45 2301.23

Load-displacement hysteresis curve was also analyzed and compared with respect to length-to-height ratio. The follow figures, Figs. 9, 10, and 11 shows the individual load-displacement hysteresis curve and skeleton curve of the original structure, and the cases of varying length-to-height ratio and width-to-span ratio. Figs. 12 shows the comparison of hysteresis curve of structure without CFRP to Fig. 12(a), structure with varying wrapping ratio, and Fig. 12(b), structure with varying wrapping relative thickness. Fig. 13 displays the combined skeleton curve. Based from the finite element results, Fig. 13(a) illustrates that the base shear of the structure and the displacement increases as length-to-height ratio increases. In addition to that, it could be observed from Fig. 13(b) that the combined skeleton curve with respect to change in width-to-span ratio indicates that there is insignificant change in the load-displacement of the structure as the thickness of the CFRP is being increased. Tables 6 and 7 present the base shear and deformation as the length-to-height ratio and width-to-span ratio varies. Based from the results, it was observed that the increase of thickness in CFRP is capable of slightly improving the performance of the structure but not as significant as change in length-to-height ratio.

Fig. 9.

Load-Deflection Curve of Concrete Column without CFRP

Fig. 10.

Individual Load-Deflection Hysteresis Curve and Skeleton Curve with Varying Length-to-Height Ratio

Fig. 11.

Individual Load-Deflection Hysteresis Curve and Skeleton Curve with Varying Width-to-Span Ratio

Fig. 12.

Comparison of Load-Deflection Hysteresis Curve with and without CFRP

Fig. 13.

Comparison of Load-Deflection Skeleton Curve with and without CFRP

Table 6. Comparison of Base Shear according to CFRP Ratio

Case Ratio Load (kN)
Yield Ultimate
Initial 0 30090.35 31785.50
Length-to-Height Ratio 0.25 38880.75 39965.20
0.50 53500.31 55626.30
0.75 86912.82 109029.60
1.00 113832.49 138392.00
Width-to-Span Ratio 0.0025 39369.27 39814.20
0.0050 38880.75 39965.20
0.0075 39466.61 40466.60

Table 7. Comparison of Displacement according to CFRP Ratio

Case Ratio Displacement (mm)
Yield Ultimate
Initial 0 9.854 29.969
Length-to-Height Ratio 0.25 12.482 31.730
0.50 18.876 58.294
0.75 30.641 75.597
1.00 61.460 120.486
Width-to-Span Ratio 0.0025 9.785 31.312
0.0050 12.482 31.730
0.0075 9.609 32.821

4.2 Seismic Performance Evaluation

The ductility of the structure was evaluated using numerical analysis. The elastic, inelastic and total energy were obtained through numerical integration. Table 8 lists the ductility of the structure according to change in wrapping ratio and relative thickness of the reinforcement. Based from the results, each of the specimen confined by CFRP reduced the risk in brittle failure, thus, improving the seismic performance of the structure. In particular, the increase of length-to-height ratio of the reinforcement significantly contributed to the enhancement of ductility of the structure than the increase of width-to-span.

Table 8. Comparison of Ductility according to CFRP Ratio

Case Ratio Ductility (%)
Initial 0 77.921
Length-to-Height Ratio 0.25 88.549
0.50 90.149
0.75 91.812
1.00 91.917
Width-to-Span Ratio 0.0025 84.781
0.0050 88.549
0.0075 89.186

4.3 Summary of Results

The discussion in this section summarizes the relationship of length-to-height ratio of the CFRP to the overall performance of the structure. Fig. 14(a) to Fig. 14(d) show that the same increasing trend was observed in general, the response of the circular concrete column strengthened with CFRP improved as the height of the reinforcement increased. The increasing trend indicates that as the ratio of length-to-height increases, the capacity in stress, load, deflection and ductility of the structure also increases. Table 9 summarizes the performance of the structure under the change in length-to-height ratio and it was found out that the full confinement, length-to-height ratio of 1:1, exhibits significant improvement in the seismic performance of the structure.

Fig. 14.

Effect of Increasing Length-to-Height Ratio to the Performance of the Structure

Table 9. Performance of the Structure according to Change in Length-to-Height Ratio

CASE Stress (kPa) Load (kN) Displacement (mm) Energy Ratio (%) Remarks
Yield Ultimate Yield Ultimate Yield Ultimate
0 1143.66 1980.51 30090.35 31785.20 9.854 29.969 77.921 Ductile
0.25 2171.50 2303.76 38880.75 39965.20 12.482 31.730 88.549 Ductile
0.50 2216.91 2477.11 53500.31 55626.30 18.876 58.294 90.149 Ductile
0.75 2926.41 3049.41 86912.82 109029.60 30.641 85.597 91.812 Ductile
1.00 2979.74 3211.01 113832.49 138392.00 61.460 120.486 91.917 Ductile

The relationship of increasing thickness of the reinforcement and general behavior of the structure is discussed in this section. Fig. 15(a) to 15(d) show that there is only slight improvement in the performance of the circular concrete column as the thickness of the CFRP increases. Based from the graphs of Fig. 15, there is a seemingly flat slope trend observed as the width-to-span ratio moves from 0.0025 to 0.0075. This gradual incline indicates that there is only slight improvement in the performance of the structure as the thickness of the CFRP is being increased. Table 10 summarizes the behavior of the structure with respect to change in width-to-span ratio.

Fig. 15.

Effect of Increasing Width-to-Span Ratio to the Performance of the Structure

Table 10. Performance of the Structure according to Change in Width-to-Span Ratio

CASE Stress (kPa) Load (kN) Displacement (mm) Energy Ratio (%) Remarks
Yield Ultimate Yield Ultimate Yield Ultimate
0 1143.66 1980.51 30090.35 31785.50 9.854 29.969 77.921 Ductile
0.0025 1651.31 2227.48 39369.27 39814.20 9.785 31.312 84.781 Ductile
0.0050 2171.50 2303.76 38880.75 39965.20 12.482 31.730 88.549 Ductile
0.0075 2280.45 2301.23 39466.61 40466.60 9.609 32.821 89.186 Ductile

5. Conclusion

The following conclusions are drawn based by means of the results of the conducted finite element analysis. The main aim of this paper was to optimize the application of CFRP. The performance of a circular concrete column was analyzed according to the of change in length-to-height ratio and width-to-span ratio of CFRP.

(1)For the change of length-to-height ratio, it was found out that using CFRP as reinforcement with ratio of 0.25 to 1.0 could increase the ductility of the circular concrete column from 78 % ranging up to 89~92 %. In this regard, the continuous use of CFRP throughout the length of circular concrete structure showed significant improvement in the base shear, stress capacity, lateral deformation and ductility. Furthermore, this proves that the full confinement of the structure using CFRP or the length-to-height ratio of 1.0 is the optimum wrapping ratio of CFRP.

(2)The change of width-to-span ratio indicated that the increase in the thickness of CFRP also increases the ductility of the structure. It was found out that from the ductility of the original structure, 78 %, it could be improved ranging from 85 % up to 89 % with a wrapping thickness ratio of 0.0025 to 0.0075. However, the effect of increasing the thickness of CFRP to the overall performance structure tends to be insignificant. It was observed that the increase of thickness of the confining material could enhance the structure, however, there is only slight improvement in the behavior of the structure

(3)For circular concrete columns, increasing the wrapping height of external confinement developed significant improvement than increasing the wrapping thickness of CFRP. The increase in wrapping height provided more confinement to reduce the brittle failure and to increase the ductility and earthquake resistance of circular bridge pier columns.


This research is supported by the Ministry of Land, Transportation and Maritime Affairs (19SCIP-B146946-02) and National Research Foundation (NRF-No.2019R1F1A1060708), Republic of Korean.

본 논문은 2019 CONVENTION 논문을 수정·보완하여 작성되었습니다.



ABAQUS (2013). Standard user's manual, Version 6.7, Hibbit, Karlsson and Sorensen, Inc.


ACI 440.2R-02 (2002). Guide for the design and construction of externally bonded FRP systems for strengthening concrete structures, American Concrete Institute.


Chai, Y. H., Priestley, M. J. N. and Seible, F. (1991). "Seismic retrofit of circular bridge columns for enhanced flexural performance." ACI Structural Journal, Vol. 88, No. 5, pp. 572-584. DOI: 10.14359/2759.


Ehsani, M. R., Saadatmanesh, H. and Tao, S. (1993) "Bond of GFRP rebars to ordinary- strength concrete." International Symposium on Fiber-Reinforced-Plastic Reinforcement for Concrete Structures, ACI-SP-138, Vol. 138, pp. 333-346, DOI: 10.14359/3930.


Grace, N. F., Soliman, A. K., Abdel-Sayed, G. and Saleh, K. R. (1998). "Behavior and ductility of simple and continuous FRP reinforced beams." Journal of Composites for Construction, Vol. 2, No. 4, pp. 186-194. DOI: 10.1061/(ASCE)1090-0268(1998)2:4(186).


Han, K. B., Cho, D. Y. and Kim, J. S. (2016). "Seismic performance evaluation and improvement for damaged reinforcement concrete piers using a fiber steel composite plate." JVE International Ltd. Journal of Vibroengineering, Vol. 18, No. 7, pp. 4574-4582, DOI: 10.21595/jve.2016.17422.


Jeong, S. M. (1994). Evaluation of ductility in prestressed concrete beams using fiber reinforced plastic tendons, Ph.D. Thesis, University of Michigan, Ann Arbor, Mich.


Katsumata, H., Kobatake, Y. and Takeda, T. (1988). "A study on strengthening with carbon fiber for earthquake-resistant capacity of existing reinforced concrete columns." Proceedings of the 9th. World Conference Earthquake, Tokyo, Japan.


Monti, G., Nisticò, N. and Santini, S. (2001). "Design of FRP jackets for upgrade of circular bridge piers." Journal of Composites for Construction, Vol. 5, No. 2, pp. 94-101. DOI: 10.1061/ (ASCE)1090-0268(2001)5:2(94).


Özcan, O., Binici, B. and Ozcebe, G. (2008). "Improving seismic performance of deficient reinforced concrete columns using carbon fiber-reinforced polymers." Engineering Structures, Vol. 30, No. 6, pp. 1632-1646. DOI: 10.1016/j.engstruct.2007.10.013.


Pantelides, C. and Gergely, J. (2002) "Carbon-fiber-reinforced polymer seismic retrofit of RC bridge bent: Design and in situ validation." Journal of Composites for Construction, Vol. 6, No. 1, pp. 52-60, DOI: 10.1061/(asce)1090-0268(2002)6:1(52).


Pateriya, R., Akhtar, S. and Rajvaidya, N. (2015). "Analysis of compressive strength of columns reinforced with steel & FRP bars." International Journal of Recent Development in Engineering and Technology, IJRDET, Vol. 4, No. 6, pp. 1-5.


Priestley, M. J. N., Seible, F. and Fyfe, E. (1992). "Column seismic retrofit using fiberglass/epoxy jackets." Proceedings of Advanced Composite Materials in Bridges and Structures, Canadian Society for Civil Engineering, Sherbrooke, Québec, Canada. pp. 287-298.


Priestley, M. J. N., Seible, F., Xiao, Y. and Verma, R. (1984). "Steel jackets retrofitting of reinforced concrete bridge columns for enhanced shear strength - Part 2: Test results and comparison with theory." ACI Structural Journal, Vol. 91, No. 5, pp. 537-551.


Rashid, M. A. and Mansur, M. A. (2005). "Reinforced high-strength concrete beams in flexure." ACI Structural Journal, Vol. 102, No. 3, pp. 462-471, DOI: 10.14359/14418.


Rodríguez, J., Martinez, F. and Marti, J. (2013). "Concrete constitutive model, calibration and applications." Proceeding Conference 2013 SIMULIA Community Conference, Conference: SIMULIA Community Conference, Vienna, Austria.


Saadatmanesh, H., Ehsani, M. R. and Jin, L. (1996). "Seismic strengthening of circular bridge pier models with fiber composites." ACI Structural Journal, Vol. 93, No. 6, pp. 639-647.


Senturk, M. and Pul, S. (2017). "Finite element analysis for obtaining structural performance of bridge pier interacting with soil" Proceeding Conference SMAR 2017 - Fourth Conference on Smart Monitoring, Assessment and Rehabilitation of Civil Structures, Zürich, Switzerland.


Sun, Z., Seible, F. and Priestley, M. J. N. (1992). "Diagnostics and retrofit of rectangular bridge columns for seismic loads." Proceedings of the 8th U.S.-Japan Bridge Engineering Workshop, Chicago, USA, pp. 282-296.


Taghia, P. and Bakar, S. (2013). "Mechanical behaviour of confined reinforced concrete-CFRP short column- based on finite element analysis." World Applied Sciences Journal, Vol. 24, No. 7, pp. 960-970. DOI: 10.5829/idosi.wasj.2013.24.07.1156.


Tedesco, J. W., Stallings. J. M. and El-Mihilmy, M. (1999). "Finite element method analysis of a concrete bridge repaired with fiber reinforced plastic laminates." Computers and Structures, Vol. 72, No. 1-3, pp. 379-407. DOI: 10.1016/S0045-7949(99)00010-3.


Teng, J. G., Chen, J. F., Smith, S. T. and Lam, L. (2002). FRP strengthened RC Structures, John Wiley & Sons, New York, USA.


Toutanji, H. (1999). "Stress-strain characteristics of concrete columns externally confined with advanced fiber composite sheets." ACI Materials Journal, Vol. 96, No. 3, pp. 397-404. DOI: 10.14359/639.


Wang, Y. C. and Restrepo J. I. (2001). "Investigation of concentrically loaded reinforced concrete columns confined with glass fiber-reinforced polymer jackets." ACI structural journal, Vol. 97, No. 3, pp. 377-385. DOI: 10.14359/10226.


Yamasaki, Y., Masuda, Y., Tanano, H. and Shimizu, A. (1993). "Fundamental properties of continuous fiber bars." International Symposium on Fiber-Reinforced-Plastic Reinforcement for Concrete Structures, ACI-SP-138, pp. 715-730. DOI: 10.14359/3952.


Ye, L. P., Zhang, K., Zhao, S. H. and Feng, P. (2003). "Experimental study on seismic strengthening of RC columns with wrapped CFRP sheets." Construction and Building Materials, Vol. 17, pp. 499-506. DOI: 10.1016/S0950-0618(03)00047-3.


Zeng, J., Guo, Y., Li, L. and Chen, W. (2018). "Behavior and three-dimensional finite element modeling of circular concrete columns partially wrapped with FRP strips." Polymers, Vol. 10, No. 3. DOI: 10.3390/polym10030253.

페이지 상단으로 이동하기