r - The Hong Kong Polytechnic University

ond-slip parameters calculated using Lu et al.’s (2005b) bi-linear bond-slip model are: δ f = 0.16 mm; τ f = 3.5
MPa; and G f = 0.28 N/mm. These parameters may also be obtained using other models such as Seracino et al.
(2007). Key points in the load-displacement response are marked as O, A and B in Figure 6. The curve OA
represents the S–R state of the interface, with point A representing the initiation of debonding. The plateau AB
represents the D–S–R state, with point B representing the end of the D-S-R state when the softening front
reaches mid-span. The curve starting from B onwards (dotted line in Figure 6) refers to the D–S state which
has little practical significance as discussed above.
20
Bending moment (kNm)
16
12
8
4
O
•
A
B
• •
0
0.0 0.3 0.5 0.8 1.0 1.3 1.5
Relative displacement at the left plate end (mm)
Figure 6 Load-displacement response of the bonded joint in CMR
FLEXURAL DEBONDING TEST DATABASE
A large database containing 67 RC beams with the flexural strengthening plate terminated in a CMR and which
failed due to flexural debonding has been assembled from an extensive literature survey.. The database includes
54 steel plated beams, 9 CFRP plated beams, 2 GFRP plated beams and 2 C-GFRP plated beams. All the beams
failed due to flexural PED failure either by concrete cover separation or interfacial failure or a combination of
these two modes. Geometric and material parameters for the beams can be found in Oehlers and Moran (1990),
Oehlers (1992), Mohammed Ali et al. (2001), Smith and Teng (2003) and Yao and Teng (2007). Measured
debonding moments and debonding moments predicted by the expressions derived earlier are presented in Table
1. It is seen that these tests cover a wide range of important parameters: (1) elastic modulus of plate E 2 = 8.8-257
GPa; (2) nominal thickness of plate t 2 = 0.165-32 mm; (3) cube strength of the concrete f cu = 25-59 MPa; (4)
split tensile strength of the concrete f t = 2.55-4.9 MPa; (5) elastic modulus of concrete E 1 = 20-32 GPa; (6) axial
stiffness of plate per unit width E 2 t 2 = 37.6-3150 (x10 3 ) N/mm; (7) effective axial stiffness of beam per unit
width E 1 d e = 2.4-7.1 (x10 6 ) N/mm; (8) flexural rigidity of the cracked plated RC beam section (EI) c,p = 0.83-6.7
(x10 12 ) Nmm 2 ; (9) flexural rigidity of the cracked un-plated RC beam section (EI) c,0 = 0.38-4.7 (x10 12 ) Nmm 2 ;
(10) width ratio of beam to plate α w = 1.0-4.8; (11) internal tensile reinforcement steel ratio ρ s = 0.44-5.40 %;
(12) interfacial fracture energy G f = 0.25-0.88 Nmm/mm 2 ; and (13) interfacial bond strength τ f = 2.7-6.8
N/mm 2 .
The formulation of the present theoretical model includes the adhesive thickness t a , but the results are
insensitive to the value selected. The predictions from the theoretical model presented in the rest of the paper do
not include the effect of adhesive parameters. Not all concrete properties such as f t , f cu and cylinder strength f c
were available for many test beams. In such cases, the relationships provided in BS 8110 (1997) and ACI 318-08
(2008) have been used to calculate the missing properties from those available.. Compression reinforcement is
ignored in all calculations.
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