Keywords: reinforced concrete, T-beams, shear deformations, shear damage, deflections, gravity loads.

When a reinforced concrete member is subjected to an increasing load, its response is initially linear-elastic up to the initiation of cracking. Be that flexural or shear cracking, the response thereafter will deviate from the linear-elastic behaviour. If the load level attained is reasonably high, the member will sustain a certain amount of damage. Upon subsequent re-loading the behaviour is expected to depend primarily upon the extent and type of damage inflicted.

If certain sections of the member had experienced some level of damage, then the behaviour of the whole member will be dependent upon the type and extent of damage. For example, if a member is loaded within the elastic limits of the materials used then upon unloading, no permanent damage will be experienced. However, if any section of the member is loaded beyond the elastic limits of the materials, then the member is expected to experience some sort of damage at these locations. Upon subsequent re-loading and depending upon the type and extent of formerly inflicted damage, the ability of the section to attain its ultimate capacity and/or the expected ultimate ductility can be influenced.

In this paper, the experimental behaviour of eight pre-damaged half-scale T-shaped simple beams with a cantilever overhang is studied. The specimens had a simple span of with a cantilever overhang of . The beams had variable slab widths and different flexural and shear reinforcement ratios. The beams were tested at the Structures and Materials Testing Laboratory of the Dept. of Civil Engineering in Helwan University, Cairo, Egypt. All eight specimens were pre-damaged near the internal support by first loading the tip of the cantilever until the sectional capacity was attained at the section near the support. The beams experienced extensive shear damage at these locations. A single monotonically increasing gravity point load was subsequently applied to the simple beam at mid span. Thus, the effect of damage at one of the supports on the behaviour, ultimate capacity, mode of failure and deflections of simple beams could be studied. In essence, parameters to be investigated and monitored included the ultimate attainable capacities, the modes of failure, the reported-versus-computed deflections and the effectiveness of the compression slabs. Accordingly, deflections as well as reinforcement strains are reported for the re-loaded beams at different load stages.

The experiments revealed valuable information regarding the increased deflections of the simple beam as well as the effectiveness of the compression slab acting integrally with the section. Comparison between the experimental observations and code provisions for ultimate capacity and deflections of the beams are presented and discussed. Possible effects of damage on the behaviour of the re-loaded beams are evaluated.

Special emphasis was placed in comparing the actual deflections with the theoretically computed ones. Two sets of analyses were performed:

1. In the first set, the deflections were computed using the full T-section dimensions as well as a rectangular section having a width equals to the web width. For both shapes of cross-sections, the deflections were computed using the ACI recommended modulus of rupture and a reduced modulus of rupture .

2. In the second set, the deflections were computed for two phases:

   a)

   Phase (a) was concerned with calculating the deflections prior to achieving the yield loads of the beams. This was done by integrating the curvatures at several sections along the length of the beam. Following ACI code provisions, the modulus of elasticity of the concrete was determined as the initial tangent modulus. This was assumed to be constant for the different load stages. For the steel reinforcement, an elastic-perfectly plastic stress- strain curve was assumed. Cracking of the concrete sections was taken into account by interpolating the curvature at each section between the uncracked and a fully cracked section condition. To investigate the effectiveness of the slab on the deflections of the simple beam, the calculations were performed using different widths of the slab. The effect of shear damage was ascertained by comparing the actual deflections to the theoretically calculated flexural deflections.

   b)

   In phase (b), the idealized bi-linear moment-curvature diagrams were computed using the actual nonlinear material properties. The deflections due to flexural deformations were then calculated using the Moment-Area Method. The purpose here was to compute the deformations due to plastification in the beam's plastic hinge zone. This study revealed that in the post yield phase, flexural deformations dominated the behaviour and that the effects of shear damage were much less pronounced in this phase.

Results of both sets of analyses were then compared with the experimentally reported deflections. As mentioned earlier, the purpose here was to study the effects of pre- damage on the capacities and deflections of the beams. Another target to be achieved was to evaluate the effectiveness of the technique suggested for modelling the effects of damage inflicted on the beams. The experiments as well as the analysis indicated the following: The deflections were not affected by the flange widths possibly due to the lack of continuity in the perpendicular directions. Better agreement between the experiments and the analysis was achieved by using the reduced modulus of rupture. The effect of shear pre-damage significantly influenced the deflections in the phase prior to reaching the yield load of the beams. The ultimate capacity of the beams was not affected by the damage inflicted due to pre-loading. Flexural deformations dominated the behaviour in the post-yield phase of loa

The deflections were not affected by the flange widths possibly due to the lack of continuity in the perpendicular directions. Better agreement between the experiments and the analysis was achieved by using the reduced modulus of rupture. The effect of shear pre-damage significantly influenced the deflections in the phase prior to reaching the yield load of the beams. The ultimate capacity of the beams was not affected by the damage inflicted due to pre-loading. Flexural deformations dominated the behaviour in the post-yield phase of loading.

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