r - The Hong Kong Polytechnic University

Figure 1 Flexural-strengthened RC beam with plate terminated in CMR
ASSESSMENT OF PEELING AND SHEAR EFFECT FROM ADHESION ANALYSIS
Higher interfacial shear and normal (peeling) stresses are introduced between the beam and the plate at the plate
end {τ(0) and σ(0) respectively} when the beam is loaded. The PED failure is usually due to the combination of
these two stresses, but their relative significance depends on the geometry, material and loading of the plated
beam. A simplistic assessment of these stresses based on an elastic adhesion analysis using Narayanamurthy et
al.’s (2010) model for a plate terminated within the CMR reveals that their magnitude is primarily influenced by
the shear stiffness of the adhesive and the axial stiffness of the plate, Figure 2.
Shear to normal interfacial
stress ratio τ (0)/σ (0)
5
4
3
2
Ea/ta=0.5 GPa/mm
Ea/ta=1 GPa/mm
Ea/ta=2 GPa/mm
Ea/ta=5 GPa/mm
Ea/ta=10 GPa/mm
1
0.0 0.6 1.2 1.8 2.4 3.0
Axial stiffness of plate E 2 t 2 (GPa-m)
Figure 2 Interfacial shear-to-normal stress ratio at the plate end in a beam with plates terminating in the CMR
Figure 2 shows that the peak interfacial shear stress is several times greater than the peak interfacial normal
stress over a wide range of these two parameters. For practical values of adhesive and plate stiffnesses, the peak
shear stress exceeds the peak normal stress by between 50% and 500%. Therefore, it may be reasonable to
assume that the Mode-2 shear fracture dominates in flexural debonding, and Mode-1 tension fracture is
neglected in the following analysis for simplicity. The accuracy of the model will be assessed with a test
database.
INTERFACIAL SHEAR BEHAVIOUR
Bonded Joint Model
Consider a simply supported RC beam with a span of l under four point bending (Figure 1). It is strengthened in
flexure by adhesive bonding of an FRP or steel plate of length L within the CMR. The PED in this beam may be
analysed by investigating the plated segment between the major flexural cracks at each end of the plate. Cracks
between the two ends of the plate are neglected but their effects on the axial and flexural stiffnesses can be
easily taken into consideration by using cracked section values in the analysis. The segment is idealised as a
bonded joint and is subjected to identical axial forces N 1 (0) and bending moments M 1 (0) on both sides as shown
in Figure 3. End faces of the plates are unstressed. The adhesive is assumed to have a constant thickness and the
bond stress is assumed to be constant through its thickness. The adherends are assumed to behave linearly. The
left (x = 0) and right (x = L) crack locations are referred as left end and right end respectively. The moment at
the left is equal to that at the right in the case considered in this study (Figure 3).
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