Debonding failures often govern the behaviour of FRP shear-strengthened concrete beams and prevent such beams from attaining their full load capacity. Consequently, the proper
Figure 4: Line interface element*
Figure 2.29: Discrete crack description [Lee et al., 2001]
modelling of the FRP/concrete interfacial behaviour is essential for developing accurate numerical simulations. For this purpose, appropriate interface elements are required that must be able to capture the interfacial nonlinearities, including slip, and account for all possible failure modes. To date, some key studies that have considered the FRP/concrete interfacial behaviour are those of Lee et al. [2001]; Wong and Vecchio [2003]; Lee [2003].
Theses studies lead to good predictions of the overall load-deflection response and load ca- pacity enhancements. However, they do not address the complete details of FRP debond- ing (i,e., slip profiles along the FRP/concrete interface).
In finite element analysis, two approaches can be adopted to simulate the debonding.
In the first approach, debonding is simulated by modelling the cracking and failure of the concrete elements adjacent to the adhesive layer. This approach, which is referred to as the mesoscale model, utilized a very fine mesh with element sizes (0.2 - 0.5 mm) being one order smaller than the thickness of the fracture layer of the concrete [Lu et al., 2005].
This method generally requires large computational resources. In the second approach, interface elements are utilized to predict the nonlinear behaviour between the FRP and concrete [Lee et al., 2001; Wong and Vecchio, 2003; Lee, 2003].
In the work of Lee et al. [2001], predefined discrete shear cracks based on the ac- tual major shear crack pattern observed from experiments were proposed to simulate the debonding failure of the FRP composites (Figure 2.29). To simplify the modelling, the crack pattern was idealized into several straight lines. The CFRP strips were bonded to the web over the shear crack. This was performed by an additional layer of elements over the concrete elements with both the CFRP and concrete elements sharing typical nodes;
i.e., perfect bond was assumed.
2.9. NUMERICAL MODELLING
BOND ^ STRESS
Umax • -
BOND ^ STRESS
SaH SLIP (a)
F i g u r e 2.30: Constitutive relationships for bond interface: (a) elastic-plastic; and (b) linear elastic [Wong and Vecchio, 2003]
RWOA-1 (FE-EP)
RWOA-1 (exp)
20 40 MID-SPAN DEFLECTION (mm)
60
F i g u r e 2.31: Load-deflection curves for RWOA specimens [Wong and Vecchio, 2003]
T h e Wong and Vecchio [2003] model is perhaps considered to be the pioneering model in implementing FRP/concrete interface elements for shear strengthened beams. Two bond-slip models were proposed to simulate the interfacial behaviour: elastic, and elastic- plastic models (Figure 2.30). These models were based on the characteristics of the ad- hesive layer and neglected the characteristics of the F R P laminates and concrete. After doubling the concrete compressive strength while keeping the strain at peak stress un- changed [Wong, 2001], the numerical model was shown to give reasonable results in terms of ultimate load capacity. The numerical model was more accurate when the elastic- plastic bond relationship was applied. T h e linear elastic bond relation led to a premature shear failure. The predicted load-deflection curves, along with the comparisons against the experimental results, are plotted in Figure 2.31 and show very good agreement. The authors conclude that more clearly defined constitutive relations must be developed for the F R P / c o n c r e t e interface elements to further improve the modeling capabilities.
Perfect bond
Perfect j *- "J bond % ' t
Concrete "" '*/
element CFRP i element ;
\
Concrete element bond
(a) m Figure 2.32: Modelling of FRP/concrete interface behaviour at: (a) web; (b) flange [Lee, 2003]
A three-dimensional finite element model was developed by Lee [2003] in order to obtain overall strength improvement predictions for shear-strengthened beams. The slip between the concrete and FRP strips was modelled using structural interface elements.
Furthermore, since the CFRP strips were well anchored in the flange and soffit of the beam, perfect bond between the two surfaces was assumed at these locations, as shown in Figure 2.32. In that study, the bond-slip behaviour between the concrete and CFRP plates was established based on experimental results of shear-lap specimens. Furthermore, to correctly and accurately model CFRP debonding failure due to shearing failure of the concrete layer, a fine mesh was employed for the concrete layer lying between the outer surface and the steel stirrups. A linear elastic behaviour was used for the steel reinforcements since failure was observed to occur without any steel yielding. Overall, the numerical predictions were very close to the experimental loading capacities.
2.10 S u m m a r y
The latest advancements in using FRP composites to increase a beam's shear carrying capacity was reviewed and the behaviour of shear-strengthened beams was studied. In this manuscript, the published factors affecting the shear-strengthened beams were ad- dressed and the contradiction of certain parameters was observed. Among the parameters influencing such beams are beam dimensions (.i.e., steel stirrups, concrete strength, size
Slip modelled
2.10. SUMMARY
Table 2.2: Review of structural modelling of shear-strengthened beams
Kali akin etal.(1996)
Arduini etal. (1996) Malek and Saad- atmanesh(1998)
Kachlakev et al. (2001)
Al-Mahaidi et al. (2001) Lee et al. (2001)
Lee(2003)
Wong and Vecchio (2003) Santhakumar and Chandrasekaran (2004)
Elyasian et al. (2006)
Program type
ABAQUS software In-house code ABAQUS
software ANSYS sofware DIANA software DIANA software DIANA sofware In-house
code ANSYS sofwatre ANSYS software
Structural modelling Concrete
elements
8-node brick 8-node
brick 4-node plane stress 8-node brick
(SOLID65) 8-node plane stress
8-node plane stress 8-node brick
(HX24L) 4-node plane stress
brick (SOLID65) 8-node cubic
(SOLID65)
Steel elements
3-D bar
NA*
2-node bar 2-node (LINK8)
3-node truss 3-node
truss 3-node
truss
truss
truss (LINK8-3D)
3-D spar (LINK8)
FPvPs elements
4-node shell
NA
4-node shell 4-node (SOLID46)
8-node plane stress
8-node plane stress 4-node plane stress (Q8MEM)
truss elements
SOLID46
shell (SHELL43)
Interface elements
No
No
No
No
No
Yes
2-node interface
2-node interface
No
No It is not available at the reference
Table 2.3: Review of material modelling of shear-strengthened beams
Kaliakin et al(1996)
Arduini etal(1996) Malek and Saad-
atmanesh (1998) Kachlakev etal.(2001) Al-Mahaidi et al (2001) Lee (2003)
Wong and Vecchio (2003) Santhakumar and Chandrasekaran (2004)
Elyasian et al (2006)
Material modelling Concrete
model
ABAQUS concrete
nonlinear behavior
ABAQUS concrete
ANSYS concrete
DIANA concrete
DIANA concrete
nonlinear behavior
ANSYS concrete
ANSYS concrete
Steel model
elast ic-perfectly plastic
elastic-perfectly plastic
NA
elast ic-perfectly plastic
elast ic-perfectly plastic
linear elastic
elast ic-perfectly plastic
NA
uniaxial tension- compression
FRPs model
linear elastic isotropic
linear elastic isotropic
NA
linear elastic orthotic pic
elastic-perfectly plastic isotropic
linear elastic orthotic pic
linear elastic isotropic
NA
elastic
Interface model
No
No
No
No
No
Mod. shear- lap specimens
elastic- plastic
No
No
Mesh sensitivity
Yes
No
No
Yes
N o
N o
N o
Yes
N o
Parameters studied
Concrete strength, FRP elastic modulus of elasticity and plate thcikness
No
Plate thickness, fibres orientation angle, steel stirrups spacing
No
No
No
No
No
Fibre orientation angle, concrete strength, tensile steel and
steel stirrups spacing The shear-lap test was modi fied for shear-strengthened beams