This paper presents a non-iterative reinforced concrete design methodology that can be used to design structural components such as beam-columns, walls and slabs of reinforced concrete structures subjected to combined axial force and bending moment. The paper demonstrates that the required reinforcing area of a demand point (paired axial force and bending moment) on the interaction diagram can be accurately computed by 1) constructing two non-dimensionalized capacity curves approximated by a combination of polygon segments that are expected to bound all possible design cases including the demand point, 2) dividing the area enclosed by the lower- and upper-bound capacity segments into several four-sided capacity polygons, 3) locating a capacity polygon where the demand point is located and identifying associated lower- and upper-bound capacity segments, 4) identifying a capacity segment that passes through the demand point by linear interpolation from the given two bounding segments, and finally 5) determining the required reinforcing area for the demand point by linear interpolation between the minimum and maximum reinforcing ratios associated with the pre-defined lower- and upper-bound capacity segments, respectively. This essentially eliminates a cumbersome need to perform iterative trial and error solutions to obtain the required reinforcing area for the combined axial force and moment concrete design. Illustrative design examples per ACI 349 and ACI 359 are presented within the paper.
Non-Iterative Reinforced Concrete Design Methodology for Combined Axial Force and Bending Moment
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Jung, S, Harrold, J, & Alchaar, N. "Non-Iterative Reinforced Concrete Design Methodology for Combined Axial Force and Bending Moment." Proceedings of the ASME 2012 Pressure Vessels and Piping Conference. Volume 8: Seismic Engineering. Toronto, Ontario, Canada. July 15–19, 2012. pp. 77-86. ASME. https://doi.org/10.1115/PVP2012-78372
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