was reported as ±0.015 mm. The measured twists are illus-
trated in Fig. 3, which correspond well to conventional
measurements. The main focus in this paper is on the slip
behaviour and strain development of the CFRP reinforce-
ment. More details about the setup and other aspects of the
photogrammetry investigation can be found in Hii and Al-
Mahaidi [8].3.1. Slip behaviour between CFRP reinforcement
and concrete
Photogrammetry was used to determine slip between the
CFRP laminates and concrete surface at various points
along the CFRP strip. It is reasonable to assume that the
relative movement of the concrete surface adjacent to the
CFRP strip was representative of the concrete layer under-
neath. Since load in the CFRP was mainly carried in the
principal fibre direction, only slip in this direction is consid-
ered. The scope was narrowed to the CFRP strips which
ruptured first as being representative for analysis. Two sep-
arate slip profiles on each side of the CFRP strip along the
beam depth were obtained. The reference point of the beam
depth was taken to be the edge of the north-top face in
Fig. 6 (FH050D2).
At low load levels, i.e. before the formation of cracks in
the vicinity, the amount of slip is negligible. Subsequently,
localized areas of slip would form in the vicinity of the tor-
sional cracks. This is first observed at torque levels of
20.1 kN m, 25.7 kN m, 23.8 kN m, and 77.7 kN m for
beams FH075D1, FH050D1, FH050D2, and FS050D2,
respectively. This is expected so to satisfy the deformation
compatibility requirement between the CFRP laminates
and concrete; otherwise infinite CFRP strains would have
to develop at the crack which is not physically feasible.
As the applied torque was increased, the slip values
increased and gradually propagated from the crack loca-
tion. The torque levels which showed marked increases in
slip values correspond closely to the loads where the devel-
opment of crack widths was significant [8]. The slip
between CFRP and concrete would decrease as measure-
ments were taken further from the cracks. Generally, the
shape of the slip profiles along the beam depth is
exponential.
As observed by Pham and Al-Mahaidi [9], debonding
between the CFRP laminate and concrete generally initi-
ates when slip exceeds 0.05 mm. However, it is difficult to
define the exact torque level where this occurs, as the local-
ized debonded portions were extremely sensitive to the for-
mation of cracks in the vicinity. As the torque level
increased, large portions of the CFRP strips clearly deb-onded. In comparing Fig. 6a and b, the locations on the left
and right sides of the CFRP strip where debonding initi-
ated for beam FH050D2 are at different depths. The same
observation could be made for the rest of the strengthened
beams. This is due to the inclined torsional cracks crossing
the CFRP reinforcement at an angle. The non-uniform
width along the length of the crack also explains the
uneven debonded zone across the width of the CFRP strip.
A plot of the average bond-slip development of the crit-
ical CFRP strip with torque is shown in Fig. 7 for all the
strengthened beams. The average slip was obtained by
averaging the slip of all the points along and on both sides
of the critical CFRP strip. At low load levels, the average
slip is small. At higher torque levels, the average slip
exceeds 0.05 mm, which is defined as the initiation of mac-
rodebonding. The exact torque values where this occurs are
44.0, 38.2, 39.3, and 71.7 kN m for beams FH075D1,
FH050D1, FH050D2, and FS050D2, respectively. No
trends between the amount of CFRP reinforcement and 钢筋混凝土桥梁英文文献和中文翻译(3):http://www.youerw.com/fanyi/lunwen_4466.html