Reinforced Concrete Beam Sections Under Biaxial and Axial Force: An Exact Solution

Abstract:
This paper introduces a fundamentally clear approach to analyze and design reinforced concrete T, L and rectangle beam sections under biaxial bending and axial compression or tension force. For the first time since 1844, the paper shows how a given set of design requirements can be met exactly in a unified method using closed form solution and the concept of modular programming. The new approach provides an exact solution to the mechanics equations by direct integration of the normal stresses over the concrete and steel areas. To computerize this approach, the concept of modular programming was found suitable and attractive for such application. The advantages of the new approach include rigorous calculations; resolving the disadvantages and shortcomings of the published pertinent numeric methods such as lack of accuracy, numeric instability, and non-convergences, and meeting the needs for simple and fast computational tools for the daily design and educational practices. Also, the paper provides details of the computer formulation for the closed form solution. To demonstrate its validity and viability, eleven numeric applications are presented covering a broad spectrum of diverse problems some of which were solved manually in the literature by prominent scholars.