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A Few Practical Formulas for the Design of Reinforced Concrete Flexural Members

In this paper, a series of formulas corresponding to the so-called Unified Design Method (UDM) characterizations of tension-controlled, compression-controlled, and, transition-zone beam sections are presented. The formulas are in terms of reinforcement ratios and completely avoid the use of strain limits and/or t d c/ ratios. Many of the formulas presented here are well known and established, but a few are new. In particular, a formula for the compression-controlled reinforcement ratio limit is introduced and a direct design procedure for transition-zone sections is developed and described. It is hoped that the formulas and ideas presented in this paper will prove useful both for the instructor in the classroom, and for the practicing structural engineer. Somewhat detailed derivations of most of the formulas in the paper are presented and several numerical examples to illustrate their use are provided at the end of the paper.