ALBERT

Description / Table of Contents: Summary Non linear methods for computing deflections of reinforced concrete linear structures in cracked stage are now spreading rapidly. In some latest reinforced concrete codes and manuals, the basic assumption regarding such calculations lies in the relationship between the mean steel (or concrete) strain and the steel strain in a fully cracked section. The authors have established a state-of-the-art for such relationships. All proposed formulas can practically be written in the following form: $$\varepsilon _m = \varepsilon _s - \vartriangle \varepsilon ,$$ where εm stands for the mean steel and concrete strain, εs the steel strain in a cracked section and where Δθ represents the tension stiffening effect of concrete lying between the cracks. Various propositions have been made for the relationship between Δθ and the steel stress (e.g. constant, linear, hyperbolic,…); other important factors too are the strength of concrete in tension and the reinforcement ratio. Considering that little experimental evidence supports the various propositions, an experimental program on thirteen reinforced concrete prisms (ties) subjected to uniaxial tension was carried out. The influence of the reinforcement ratio is especially studied. Careful assessment of the validity of previous formulas is made. A new bilinear relationship between the tension stiffening effect and the steel stress is proposed for analytical calculations.

Description / Table of Contents: Summary This paper reports the results of experimental research focusing on two possible methods to enhance the service load behaviour of ordinary reinforced concrete structural elements, i.e. the use of steel-fibre concrete and the use of high-strength concrete. The programme involved the testing of nine reinforced concrete beams with rectangular cross-section (b=25 cm, h=15 cm) and span L=140 cm. The reinforcement ratios considered (ρ=0.33, 0.52 and 0.75%) are usual for slabs, for which the deflection limit state may often become a design factor. For each reinforcement ratio, we tested a beam in ordinary concrete (BN; 32 MPa), a beam in high-strength concrete (BHP; 60 MPa) and a beam in fibre-reinforced concrete (BF; 38 MPa; fibre content 0.4 vol%). We also tested a fibre-reinforced concrete beam with no bar reinforcement (BRF; ρ=0) to determine the material properties of fibre concrete that we needed to compute the carrying capacity of the BF beams. Test results show that the use of high-strength concrete seems more effective than the use of fibre concrete to reduce the deflections at service load level. BF beams are slightly stiffer than the BHP beams for higher loading levels (stabilized cracking phase of BN and BHP beams) for the two lowest reinforcement ratios. The carrying capacity of the BF beams is greater than the carrying capacity of the BN beams; the difference in carrying capacity may be estimated on the safe side with a simple prediction model, and is significant (experimentally 32%) for the lowest reinforcement ratio. However, the ultimate load behaviour of the BF beams is far less satisfactory than the ultimate load behaviour of the BN and BHP beams. For the BF beams, we observed the concentration of all inelastic deformations at failure in a single cracked section and the ductility factor varied between 1 and 2.8 compared with 4.5–6.3 for the BN beams and 8.7–10.6 for the BHP beams. The ultimate load behaviour of the BHP beams was quite satisfactory, with the largest number of cracks equally spaced and equally open and the largest deformation capacity. We conclude from these tests that the tensile properties of cracked fibre-reinforced concrete are too limited to reach the level of deformation that is required in safe reinforced concrete design and that the use of steel fibres as complementary reinforcement of rebars should be avoided.