Amending the Traditional ‘ACI Commentary Jc Method' and Other Sources
Downloads
This article aims to amend the traditional formulas for polar moment of inertia suggested in Section R8.4.4.2.3 of ACI 318-19 and other sources. The authors claim that these formulas have been incorrectly derived as far back as 1960s due to an incorrect implementation of Steiner's theorem (parallel axis theorem) for sections spanning in three-dimensional space. To support the claim, a formal proof using elementary calculus is presented in order to obtain the correct formulas with mathematical rigor. Then, the implications of using the traditional formulas versus the correct ones are investigated with the solution of a design problem related to a combined footing.
Doi: 10.28991/CEJ-2023-09-11-015
Full Text: PDF
[2] ACI Committee 318-63. (1963). Building code requirements for structural concrete (ACI 318-63). American Concrete Institute (ACI), Michigan, United States.
[3] ACI. (2021). The Reinforced Concrete Design Handbook A Companion to ACI 318-19. American Concrete Institute (ACI), Michigan, United States.
[4] Collins, M. P., & Mitchell, D. (1997). Prestressed concrete structures. Response Publications, Ontario, Canada.
[5] CIS. (2022). Reinforced concrete slab design manual for ETABS (Version 20). Computers & Structures, California, United States.
[6] Clarke, L. A., & Cope, R. J. (1984). Concrete slabs: analysis and design. CRC Press, London, United Kingdom. doi:10.1201/9781482292794.
[7] Darwin, D., & Dolan, C. W. (2021). Design of concrete structures (16th Ed.). McGraw-Hill Education, New York, United States.
[8] Stasio, J., & Buren, M. P. (1960). Transfer of Bending Moment Between Flat Plate Floor and Column. ACI Journal Proceedings, 57(9), 299–314. doi:10.14359/8022.
[9] Dolan, C. W., & Hamilton, H. R. (2019). Prestressed Concrete: building, design, and construction. Springer, Cham. Switzerland. doi:10.1007/978-3-319-97882-6.
[10] Islam, S. (1973). Limit design of reinforced concrete slabs: openings and slab-column connections. Ph.D. Thesis, University of Canterbury, Christchurch, New Zealand.
[11] Lin, T. Y., & Burns, N. H. (1981). Design of prestressed concrete structures. (3rd Ed.). John Wiley & Sons, Hoboken, United States.
[12] McCormac, J. C., & Brown, R. H. (2015). Design of reinforced concrete. (10th Ed.). John Wiley & Sons, Hoboken, United States.
[13] Naaman, A. E. (2004). Prestressed concrete analysis and design: fundamentals. (2nd Ed.). Techno Press, Michigan, United States.
[14] Nawy, E. G. (2009). Prestressed concrete: a fundamental approach (5nd Ed.). Pearson Education, New Jersey, United States.
[15] Park, R., & Gamble, W. L. (1999). Reinforced concrete slabs. (2nd Ed.). John Wiley & Sons, Hoboken, United States.
[16] PTI. (2006). Post-Tensioning Manual (6th Ed.). Post-Tensioning Institute, Arizona, United States.
[17] Wight, J. K., & MacGregor, J.G. (2012). Reinforced concrete: mechanics and design (6th Ed.). Pearson Education, New Jersey, United States.
[18] Zhou, Y. (2019). Seismic Performance Assessment and Nonlinear Modeling Parameters for Slab-Column Connections. Ph.D. Thesis, College Station, United States.
- Authors retain all copyrights. It is noticeable that authors will not be forced to sign any copyright transfer agreements.
- This work (including HTML and PDF Files) is licensed under a Creative Commons Attribution 4.0 International License.
