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Mathematical Framework for Computing Polar Moments of Inertia for Use with Traditional 'ACI Commentary Jc Method'.

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Title: Mathematical Framework for Computing Polar Moments of Inertia for Use with Traditional 'ACI Commentary Jc Method'.
Authors: Esquivel, Hugo1, Lin, Guang2
Source: ACI Structural Journal. May2026, Vol. 123 Issue 3, p111-121. 11p.
Subjects: Moments of inertia, Mathematical analysis, Geometric shapes, Structural design, Mathematics
Abstract: This paper presents a robust mathematical framework for computing centroidal polar moments of inertia in a standardized manner, applicable to both regular- and irregular-shaped sections, for use with the traditional "ACI Commentary Jc Method." The paper also showcases with mathematical rigor why, for over 60 years, the standard (traditional) expressions used to compute polar moments of inertia for planar sections embedded in three-dimensional (3-D) space have been incorrectly derived, and explores the implications of not adopting the correct expressions in design. The mathematical framework for computing polar moments of inertia is developed using advanced calculus, and primitive sections are integrated into the formulation to derive with ease the necessary expressions for the most common sections used in design, namely rectangular, circular, C-shaped, L-shaped, and regular polygon-shaped sections. Finally, a numerical example is provided to demonstrate the practical implementation of the proposed mathematical framework. [ABSTRACT FROM AUTHOR]
Copyright of ACI Structural Journal is the property of American Concrete Institute and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: This paper presents a robust mathematical framework for computing centroidal polar moments of inertia in a standardized manner, applicable to both regular- and irregular-shaped sections, for use with the traditional "ACI Commentary Jc Method." The paper also showcases with mathematical rigor why, for over 60 years, the standard (traditional) expressions used to compute polar moments of inertia for planar sections embedded in three-dimensional (3-D) space have been incorrectly derived, and explores the implications of not adopting the correct expressions in design. The mathematical framework for computing polar moments of inertia is developed using advanced calculus, and primitive sections are integrated into the formulation to derive with ease the necessary expressions for the most common sections used in design, namely rectangular, circular, C-shaped, L-shaped, and regular polygon-shaped sections. Finally, a numerical example is provided to demonstrate the practical implementation of the proposed mathematical framework. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of ACI Structural Journal is the property of American Concrete Institute and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.14359/51749378
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      – Code: eng
        Text: English
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        PageCount: 11
        StartPage: 111
    Subjects:
      – SubjectFull: Moments of inertia
        Type: general
      – SubjectFull: Mathematical analysis
        Type: general
      – SubjectFull: Geometric shapes
        Type: general
      – SubjectFull: Structural design
        Type: general
      – SubjectFull: Mathematics
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      – TitleFull: Mathematical Framework for Computing Polar Moments of Inertia for Use with Traditional 'ACI Commentary Jc Method'.
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              Text: May2026
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              Y: 2026
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