Analysis of Energy Relea Rates of Interface Crack in FRP - Strengthened RC Beams under Three Point Bending
Date of Submission:
Date of Acceptance:
Corresponding author:
Telephones:
Fax:
E-mail:
Abstract:
法家代表To investigate the propagation behavior of interface crack in reinforced concrete (RC) beam strengthened with fiber reinforced polymer (FRP), a theoretical study was conducted to anal
yze the stress field around the interfacial crack tip in this paper. Take into account the effect of the major flexural crack, a mechanical analysis model was established for the interface crack tip of the strengthened beam under three-point bending. Combined with the mechanical analysis model, a theoretical derivation of the energy relea rates for the interface crack in the strengthened beam was prented bad on the fracture mechanics theory. Results showed that the energy relea rates of the interface crack in the strengthened beam under three-point bending decrea with the increa of the interface crack length.
Keywords: Fiber reinforced polymer (FRP)；Crack；豹纹美甲Energy relea rates；Interface; Strengthen
1. INTRODUCTION
Fiber reinforced polymer (FRP) has been extensively applied to strengthen concrete structures in recent years. This material is of interest to rehabilitation engineers becau of the high-strength/weight ratio, ea of handling and application, the elimination of the n
eed for heavy equipment, a faster construction rate and the fact that they do not corrode 1,2. However, many studies showed that concrete-FRP debonding usually occur in the reinforced concrete (RC) members strengthened with FRP 3-5. Debonding results in the lost of the high-strength characteristics of FRP and the reduction of strengthened efficiency. The modes of debonding mainly include intermediate crack (IC) debonding and plate end debonding, and IC debonding usually occurs in the RC beams flexurally strengthened with FRP. With regard to the failure behavior of IC debonding, general rearchers firstly analyzed the interface stress, and then propod prediction models by regarding the critical slip value or the shear stress as the criterion of debonding 4,5. Nevertheless, the studies did not investigate the stress field around interfacial crack tips after the formation of the interface crack and the propagation behavior of the interface crack, which is just the key issue to study the interface fatigue lives of FRP strengthened beams. Although some studies have been directed to investigate the propagation behavior of the interface crack in concrete member strengthened with FRP 6-8, the studies almost were carried out on the simple pull tests of FRP-to-concrete joint
s. It should be noted that the stress state of the interface in a simple pull test is pure shear, which is different from that in a bending specimen. In addition, a few of rearchers focud on the stress field around the interfacial crack tip of the double-bond bending members, but their studies were not considered the effects of the flexural cracks 9-11. It should be mentioned that for the most part of concrete structures, the in-rvice components usually work with flexural cracks. Therefore, further studies on the coupling behavior between the interface cracks and the flexural cracks need to be carried out. In this study, the main objective is to derive the stress field of interface crack tip by a mechanical analysis model considering the effect of the major flexural crack, and analyze the relationship between the energy relea rates and the interface crack length.
2. THEORETICAL DERIVATION
Many studies have reported that the concrete-FRP interface cracks propagation dominates in IC debonding failure mode when the RC beams strengthened with FRP are subjected to bending loads. IC debonding of the strengthened beams under three-point b
ending has the feature that interface cracks initiate from the root of the major flexural crack and propagates towards the free end of the plate, as shown in Fig. 1.
经贸局2.1. Mechanical analysis model
The strengthened beam model as shown in Fig. 2 is subject to three-point bending, where the major81年属啥 flexural crack is on the mid-span ction. The interface cracks 直肠癌能治好吗initiated the root of the major flexural crack are assumed to be a symmetric distribution. The RC beam is described with the geometry of length L, height路得记 h1, width b and the distance from the steel center to the bottom of beam hs. The length and thickness of FRP laminates are l and h2, respectively. The length of the interface crack and the height of the major crack are respectively denoted by a and h, and w denotes the flexural crack width on the bottom of beam. The coordinate system as shown in Fig. 2 is adopted with its origin located at the tip of the interface crack.
The schematic illustration of the element between the flexural cracked ction and the ction of the interface crack tip is shown in Fig. 3a), and the mechanical analysis model
of the element in terms of two layers is shown in Fig. 3b), where layer 1 is RC beam and layer 2 is FRP. Fig. 3b) shows moment手疼怎么缓解 M, shear force Q, axial force N in each layer, where the subscripts denote the ction location and the superscripts denote the layer number, and 保育员培训心得q(x) denotes the distributed interaction force between FRP and RC beam. In the following analysis, two assumptions have been ud: (1) the curvatures of both layers are the same; (2) the shear stress between FRP and RC beam after the formation of the interface crack are neglected.
2.2. Deflection analysis
Consideration of force equilibrium of the strengthened beam in Fig. 2 gives
