of strengthening or repairing the existing structure and does not allow for bonding the plate in the form of a closed continuous loop around the whole cross section of the beam. Based on the available experimental data, side-bonded plates are very vulnerable to premature failure. Full wrapping is the most effective technique but it is not adopted in the field since most beams are cast monolithically with a slab, and U-jacket is lying in between.
Therefore, full wrapping should be used whenever is possible, followed by U-jacketing.
Since shear strengthening often forms a key part of an effective strengthening strategy for reinforced concrete structures, numerous shear strengthening studies have been carried out since the 1990s (e.g. Uji [1992]; Al-Sulaimani et al. [1994]; Chajes et al. [1995];
Alexander and Cheng [1996]; Araki et al. [1997]; Arduini et al. [1997]; Sato et al. [1997b];
Hutchinson et al. [1997]; Triantafillou [1997]; Chaallal et al. [1998a,b]; Khalifa et al. [1998];
Malek and Saadatmanesh [1998a,b]; Fanning and Kelly [1999]; Deniaud and Cheng [2001a];
Kachlakev and McCurry [2000]; Khalifa and Nanni [2000]; Triantafillou and Antonopoulos [2000]; Khalifa and Nanni [2002]; Pellegrino and Modena [2002]; Taljsten [2003]; Wong and Vecchio [2003]; Adhikary and Mutsuyoshi [2004]; Bousselham and Chaallal [2004a];
Teng et al. [2004]; Cao et al. [2005]; Carolin and Taljsten [2005]; Zhang and Hsu [2005];
Bousselham and Chaallal [2006b]; Pellegrino and Modena [2006]; Leung et al. [2007]; Monti and Liotta [2007]; Mosallam and Banerjee [2007]; Lee and Al-Mahaidi [2008]).
2.4 Shear Behaviour of Reinforced Concrete Beams
2.4.1 Shear Behaviour of RC Beams without F R P Strengthen- ing
The shear behaviour of un-strengthened reinforced concrete beams was reviewed in ASCE [1998] and Kong and Evans [1990]. Shear is an important but controversial topic in structural concrete design. In design, it is generally desirable to ensure that the ultimate strengths are governed by flexure rather than by shear; except in seismic design. Small deflections and little warning characterize shear failures before the occurrence of failure.
It is now known that the shear resistance mechanism of a simply supported reinforced concrete beam is not a function of a single variable. The mode of diagonal failure has been found by experiment to be strongly based upon the shear-span/effective depth ratio,
Shekr-u<R^n-ô4on t'W\urằl Mi>n*ra Sttt-njtili Simigth
. J . . . . . i _ _J. J_- i.._
I 2 -> J S 6 Knliii of Nht-ar Span In lltam IK-plh. o/rf
Figure 2.12: Variation of shear strength with shear-span/effective depth ratio [Mosallam and Banerjee, 2007]
as illustrated in Figure 2.12. The shear behaviour of a beam is governed by some secondary parameters, such as:
• concrete strength
• tension steel
• aggregate type
• beam size.
The shear strength of a beam is substantially increased by the use of shear reinforce- ment. The shear reinforcement increases the ductility of the beam and considerably limits the crack width a n d reduces the likelihood of a sudden and catastrophic failure. The general principle of design of shear assumes t h a t concrete provides t h e primary shear re- sistance of the beam and t h a t the shear force in excess of the concrete shear resistance has to be resisted by the internal shear reinforcement. Before diagonal cracking, it is assumed the external applied force produces few stresses in t h e web reinforcement. When the di- agonal crack forms, any web bar which intersects t h e diagonal crack will suddenly carry a portion of t h e shear force. Web bars not intersected with t h e diagonal crack remain slightly stresses. As t h e external applied force is increased, t h e most stressed stirrups start to yield. If the crack continues to widen, the neighbouring stirrups reach their yield
2.4. SHEAR BEHAVIOUR OF REINFORCED CONCRETE BEAMS
limit and start to deform until all the stirrups crossing the cracks start to yield. The shear strength carried by the web reinforcement remains stationary at the yield value and the subsequent increase of the external force will be carried by the concrete shear strength.
When the diagonal crack widens, the aggregate interlock becomes less effective and the dowel action of the tension reinforcement increases rapidly. Failure of the beam finally occurs either by the dowel splitting of the concrete along the longitudinal reinforcement or by crushing of the concrete in the compression zone. Reinforced concrete beams without transverse steel fail with one principal diagonal crack whereas those with steel stirrups fail with a diagonal cracked area.
2.4.2 Shear Behaviour of F R P Shear-Strengthened RC Beams
The available evidence from experiments indicates a basic difference in the mode of failure of a reinforced concrete beam strengthened in shear with externally bonded FRP plates from that of a beam reinforced with internal steel stirrups [Swamy et al., 1999; Khalifa et al., 1998; Triantafillou and Antonopoulos, 2000; Teng et al., 2002]. In the case of beams with internal steel stirrups, the shape and position of the latter ensure sufficient anchorage, and failure is determined by the tensile strength of the links. By contrast, for beams reinforced with externally bonded FRP plates, the failure criterion is governed primarily by the anchorage efficiency, rather than by the tensile strength of the FRP plates.
2.4.2.1 Shear Failure Controlled by FRP Rupture
This type of failure occurs most often with a diagonal shear tension crack. Vertical flexural cracks originating from the tensile face occur first. A crack near the support may propagate towards the loading point and may become an inclined crack. In some cases, a diagonal crack may appear abruptly. The sudden formation of a diagonal crack causes an abrupt load transfer to a localized region of the FRP intersecting the diagonal crack. As the width of the diagonal crack increases, the maximum strain in the FRP strips eventually reaches its maximum strain, which often occurs at a strain lower than the ultimate strain of the FRP [Triantafillou and Antonopoulos, 2000; Teng et al., 2002].
Figure 2.13: Shear rupture failure of the FRP sheets [Carolin and Taljsten, 2005]
The failure is initiated at the most highly stressed point in the FRP strip intersected by the shear crack. When the FRP strip reaches its ultimate tensile strength, then rupture of the FRP plates propagates along the diagonal shear crack in the concrete, leading to total failure of the beam in a brittle manner. After rupture of the first strip the stresses redistribute to the other fibres and so on until all strips are broken. Figure 2.13 shows the rupture failure of FRP plates. Partial debonding of the FRP sheets from the beam sides often occurs prior to rupture in most cases whilst only the FRP plates remain bonded to the top and bottom face of the beam. However, the eventual failure is due to the rupture of the FRP strips. The results show that the FRP strips do not close the cracks, but help to delay the occurrence and propagation of cracks. All of the beams with full wrapping of the FRP composites around the beam and some with U-jackets fail in this mode. The tensile strength of the FRP can always be fully utilized if there is a sufficient bond length, which is called the effective bond length. Beyond this length there is no further transfer of load to the FRP. The effective bond length is based on the concrete strength, modulus of elasticity, and thickness of the FRPs [Chajes et al., 1995; Triantafillou, 1998; Triantafillou and Antonopoulos, 2000; Deniaud and Cheng, 2000; Li et al., 2001; Taljsten and Carolin, 2001; Teng et al., 2002; Carolin and Taljsten, 2005].
2.4.2.2 Shear Failure Controlled by FRP Debonding
A shear-strengthened reinforced concrete beam may fail due to the debonding of the FRP plates from the sides of the beam. This kind of failure occurs when the concrete
2.4. SHEAR BEHAVIOUR OF REINFORCED CONCRETE BEAMS
(a) (b) Figure 2.14: Shear debonding failure of the FRP sheets in: (a) U-wrap [Khalifa and Nanni, 2000], (b) side-bonded [Pellegrino and Modena, 2002]
surface strength is too low, the epoxy used has low shear strength or the length of the F R P strips is not sufficient to transfer the shear forces between the reinforcement and the concrete. After the formation of the shear crack along the depth of the beam and with the increase of the external applied load, the debonding initiates at the F R P plates crossing the crack. T h e debonding is initiated above and below the shear cracks at the areas where the development length is not sufficient, with a concrete layer attached to them. T h e bonded area progressively decreases as debonding of F R P s proceeds outwards away from the shear crack location towards both ends of the strip. T h e studies reveal that strips intercepting the shear crack close to the end have small areas of debonding.
Those intercepting the shear crack near mid-height show greater areas of debonding. This results in an instantaneous increase in the load carried by the vicinity, which leads to a rapid propagation of the debonding of the F R P sheets over the shear cracks, combined with beam failure. In some cases, the load is not able to increase beyond the first peak reached at the failure of the first strip. In other cases, the maximum load may occur after a few strips have already failed. Consequently, first strip failure does not correspond to the ultimate shear capacity. The deflection of beams failing in this mode is usually very limited. Figure 2.14 presents shear-debonding failure of F R P sheets. Available test results indicate t h a t all beams strengthened with side-bonded F R P s , and many beams strengthened with U-jackets, fail in this mode [Khalifa and Nanni, 2000; Taljsten and Carolin, 2001; Teng et al., 2002]. A diagram of the shear behaviour of a reinforced concrete beam is shown in Figure 2.15.
Beam with no FRP strengthening
Diagonal- tension failure
Shear-tension failure
6>a/d<2.5
RC BEAM
FRP-Strengthened beam
Shear-compression failure
FRP rupture failure
2.5>a/d<l
FRP debonding failure
Completely wrap U-wrap Side-bonded
Figure 2.15: Diagram of the shear behaviour of reinforced concrete beams