Design of RC sections with single reinforcement according to EC2-1-1 and the rectangular stress distribution

Nowadays, the design of concrete structures in Europe is governed by the application of Eurocode 2 (EC2). In particular, EC2-Part 1-1 deals with the general rules and the rules for concrete buildings. An important aspect of the design is specifying the necessary tensile (and compressive, if needed) steel reinforcement required for a Reinforced Concrete (RC) section. In this study we take into account the equivalent rectangular stress distribution for concrete and the bilinear stress-strain relation with a horizontal top branch for steel. This chapter presents three detailed methodologies for the design of rectangular cross sections with tensile reinforcement, covering all concrete classes, from C12/15 up to C90/105. The purpose of the design is to calculate the necessary tensile steel reinforcement. The first methodology provides analytic formulas and an algorithmic procedure that can be easily implemented in any programming language. The second methodology is based on design tables that are provided in Appendix A, requiring less calculations. The third methodology provides again analytic formulas that can replace the use of tables and even be used to reproduce the design tables. Apart from the direct problem, the inverse problem is also addressed, where the steel reinforcement is given and the purpose is to find the maximum bending moment that the section can withstand, given also the value and position of the axial force. For each case analytic relations are extracted in detail with a step-by-step procedure, the relevant assumptions are highlighted and results for four different cross section design examples are presented.