Amending the Traditional ‘ACI Commentary Jc Method’ and Other Sources

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