A direct procedure for determining the reinforcement of transition-zone reinforced concrete beam sections

Current design of transition-zone reinforced concrete beam sections is performed using tables, charts, trial and error, and iterative procedures. This is due to changes that the American Concrete Institute (ACI) introduced in the ACI code in 2002. This paper presents several direct procedures for the design of transition-zone reinforced concrete beam sections.The procedures are based entirely on the concept of reinforcement ratios as opposed to strains and/or geometric section parameters. A complete formulation based on reinforcement ratios to analyze and design reinforced concrete beam sections was first introduced in Orozco (2015). Also in reference Orozco (2015), a direct procedure for the design of transition-zone rectangular sections was introduced. This procedure entails the solution of a quadratic equation that produces the reinforcement ratio and the strength reduction factor that corresponds to the design. In the present paper, an improved version of this direct procedure that avoids the use of cumbersome constants and results in a cleaner quadratic equation is introduced. As an alternative to this direct procedure, an iterative approach that uses a general formula for the calculation of the reinforcement ratio and an equation for the strength reduction factor is also presented. Finally, a direct procedure for the design of transition-zone T-sections is also introduced. Numerical examples using the new formulations and procedures are presented at the end of the paper. The numerical tests performed indicate that the new design procedures produce results that are exactly equivalent to those of current design practices but are more accurate and require less computational effort.