Nonlinear Analysis for Shear Performance of Circular Cross-sectional RC Beams
Reinforcing by Carbon Fiber Reinforced Polymer
Civil Engineering: Yan Haoran
Supervisor: Associate Prof. Tomohiro Miki
1. Introduction
Fiber-reinforced-polymer (FRP) bars are considered alternatives to conventional steel bars for reinforced concrete structuresin severe environments. There are some experimental studies introducing the shear performances of circular cross-sectional
carbon FRP (CFRP) RC beams with different reinforcement type, shear reinforcement ratio and sectional dimension. However,there are still rooms that influence shear performances not mentioned in the experimental study, such as the bond properties
between the CFRP reinforcement and surrounding concrete. This study aims to investigate the following three points; 1.
Reproduce the experiment of circular cross-sectional CFRP RC beams by carry out finite element analysis to evaluate the shear
performance, 2. Comparing analytical results with experimental results in order to evaluate how bond properties affect theshear performance of circular cross-sectional CFRP RC beams, and 3. Evaluate the effect of the bond model with different
parameters on the internal concrete strain distribution.
2. Analytical Model
The specimens used in this study were mainly those of Mohamed et al (2017).
The section diameter of the specimens is 500 mm and the total length is 3000 mm.
Figure 1 shows the finite element mesh of analytical model, the model is divided
to grid by size of 50 mm. The RC specimen with circular section was modeled inthree dimensions and the crack model based on total strain was used to simulate
concrete with compression strength of 36 N/mm2. For CFRP bars and spirals, thelinear elastic model was used. The Von Mises model was used to model steel
reinforcement with yield strength of 460 N/mm2.

Fig. 1 Analytical model

The shear performance of the circular CFRP reinforced concrete beams wasevaluated by finite element analysis. The load in analysis has been set as
displacement control with step of 0.2 mm. The Newton-Raphson method is usedas the iterative calculation method.
3. Sensitivity Analysis of Bond Model Parameters
The sensitivity analysis for the bond model parameters was performed.
Through comparing analytical results with experimental results, we evaluate howbond properties affect the shear performance of circular cross-sectional CFRP RCFig. 2 Bond model with different surface
condition

beams. This research focused on the analytical results of shear performance suchas load carrying capacity, load-displacement relationship, crack patterns, andconcrete strain distribution.
In the chapter 3, four series of bond property models were used for analysis, as
shown in Fig. 2, 3, 4 and 5. The parameters of these bond models include
different surface conditions, different maximum shear stress, different initialshear stiffness and different post-peak softening parts.
 The bond model with smooth surface in analysis, leading to the decrease ofFig. 3 Bond model with different
maximum bond stressmaximum load and stiffness of the specimens. As the smooth surface bondmodel shows larger relative bond slip compare with the sand-coated bond
Keywords：Nonlinear analysis, Circular CFRP RC beams, Bond property model, Internal concrete strain distribution

model, the crack patterns and concrete strain distribution show more obvious
crack at the area where bond slip is occurred.
 The bond model with low maximum shear stress will reduce the maximum
load and stiffness of the specimen, while the bond model with high maximum
shear stress will reduce the maximum load but increase the stiffness.
 The bond model with low initial shear stiffness results in a soft
load-displacement stiffness after the formation of diagonal crack.

Fig. 4 Bond model with different initialshear stiffness

4. Discussion on Internal Strain Distribution of Concrete
In this research, the analytical results of three vertical sections at different
positions are used to evaluate the internal strain distribution of concrete. The
results of different bond models are compared. Through the comparison, the effectof the bond model with different parameters on the internal concrete strain
distribution of circular cross sectional CFRP RC beams under the same load level

Fig. 5 Bond model with different
softening parts

is evaluated.
For the bond models with different parameters, the analytical results indicatethat the main difference in the internal concrete strain distribution is the maximum
value of strain. The analytical results of all specimens indicate that the maximum
value of internal concrete strain corresponding to the cross section decreases withthe decrease of the distance from the cross section to the surface.
5. Conclusion
1) The bond property model of CFRP bars has a great effect on the shear

Fig. 6 Load-displacement relationshipperformance of circular cross-sectional CFRP RC beams. The analyticalresults indicate that the maximum load and the displacement at which themaximum load of the specimens with shear reinforcement is reached are
significantly increased when the sand-coated bond model is used. It can beconcluded that the contribution of shear reinforcement to load carrying
capacity can be reproduced by using appropriate bond model in the analysis.
2) The analytical results of the crack patterns and the concrete strain distribution

Fig. 7 Cracking patterns

show more obvious diagonal shear cracks with sand-coated bond model isused. It is indicated that the bond model can make the specimens tend to failwith diagonal tensile failure.
3) The bond models with smooth surface condition, low maximum shear stressand low shear stiffness will show a large maximum value of the internal
concrete strain. However, for the case that the specimen BC with low shear
stiffness bond model, the maximum value of internal concrete strain is smaller

Fig. 8 Internal concrete strain
distribution

than that of the high shear stiffness bond model.
4) As the decrease of the distance from the cross section to the surface of specimen, the distance between the center of thecross section and the longitudinal reinforcement of top and bottom side also decreases. This seems to increase theresistance during the formation of diagonal crack, leading to the decrease in the maximum value of internal concrete strain.
References
1) Mohamed HM, Ali AH, Benmokrane B. (2017) Behavior of circular concrete members reinforced with carbon-FRP bars
and spirals under shear. J Compos Construct, 21(2): 04016090.