Abstract

Shear strength reduction due to the size effect in internal bonded steel reinforced concrete beams were dealt with a semi empirical relationship, which were developed based on the experimental results. Size effect for other reinforced materials such as bonded and un-bonded FRP reinforcement cannot be developed statistically due to limited numbers of existing experimental results. Therefore, in the current work, a new ‘generalised characteristic length’ was developed theoretically in order to determine the size effect in reinforced concrete beams irrespective of bond condition and material properties of reinforcement. The model is developed based on mode I fracture crack bridging effect of concrete. The crack bridging effect can be applied to both bonded internal and un-bonded external reinforcement. To validate the crack bridging effect of concrete, a series of mode I three-point bending experiments was undertaken.

The proposed generalised characteristic length depends on the concrete material, the shape of the beam, the shape of the stress distribution in the fracture process zone and the force in the reinforcement. It was identified that the generalised characteristic length varies as the crack propagates. The generalised characteristic length was compared with existing experimental results for beams with or without longitudinal reinforcement. Based on the experimental validation, it was shown that the generalised characteristic length can be applied to beams which fail due to the propagation of a vertical or inclined crack. Moreover, it was concluded that the size effect reduction factor depends on the crack bridging force in the reinforcement across a crack which implicitly depends on the bond properties between the reinforcement and concrete, the type of reinforcement and the area of reinforcement.