Analytical approach for the evaluation of minimum fibre factor required for steel fibrous concrete beams under combined shear and flexure

• Proposed approach concludes to cubic formula that calculates fibre factor required.
• Estimation of fibre factor to satisfy pre-set strength and ductility requirements.
• Steel fibres can be used without or with a minimum or desirable amount of stirrups.
• Validation established by predictions in a database of 256 beams from literature.
• Diagrams-design charts are plotted using this procedure as parametric analysis tool.

The use of steel fibres as shear resistance mass reinforcement has been well-documented and the possibility of partially or even fully replacing of stirrups with steel fibres has been examined. However, issues of common engineering practice about the optimum content of steel fibres in shear-dominated fibrous concrete beams have not yet been fully clarified. This study presents an analytical approach to the aforementioned question. The proposed methodology is initially based on the calculations of the flexural and shear capacities of a steel fibrous concrete element and to the concept that a pure flexural response should be achieved. The target of this method is to evaluate the minimum fibre factor, F, required in order that a fibrous concrete beam to satisfy pre-set strength and ductility requirements. The well-known fibre factor expresses the effect of both the volume fraction and the geometrical characteristics of the used steel fibres and its calculation is achieved by a concluding cubic formula derived from the proposed procedure. Steel fibres can be used either as the only shear reinforcement or in combination with a minimum or a desirable amount of stirrups. A database of 256 tested beams collected from 17 existing works around the world is used to establish the validity of the proposed approach. Comparisons between experimental data and predicted results derived from the analytical procedure showed a very good agreement. Two numerical examples of a typical shear-critical beam and a rather short edge-loaded cantilever slab that illustrate the application of the described method are also presented herein. Further, analytical curves and design charts have been plotted by the implementation of the proposed approach as an analysis tool for parametrical study. The influence of the concrete strength, the span-to-depth ratio, the tension steel longitudinal reinforcement and the amount of the provided stirrups on the value of the fibre factor has also been investigated and discussed.