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Aerospace Engineering

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Oct 30, 2023

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Moment of Inertia of Composite Areas Structures I R. Taher Moment of Inertia of Composite Areas 1 Warning The information contained in this lecture is protected by intellectual property laws. The content may be used only by the students enrolled in this course. Do not reproduce, transmit, publish, rewrite, sell or post the content on internet sites without a written permission from the instructor teaching this course. Moment of Inertia of Composite Areas 2 Textbook Reading • Simplified Structural Analysis and Design for Architects, Revised 2 nd Edition, by Rima Taher, published by Cognella, 2021. • Chapter 5 Centroids and Moment of Inertia Moment of Inertia of Composite Areas 3 • Transfer Formula • Example • Moment of Inertia of Composite Areas • Example • Practice Problems Moment of Inertia of Composite Areas 4 Transfer Formula • The previous formulas can be used to calculate the moment of inertia with respect to an axis passing through the centroid of the area in question. • A transfer formula must be used to calculate the moment of inertia about an axis parallel to the centroidal axis. Moment of Inertia of Composite Areas 5 • For example, to calculate the moment of inertia of the shown rectangular area with respect to the axis a-a which is parallel to X-X, this transfer formula must be used: • A: rectangular area in question • d: perpendicular distance between the two axes Moment of Inertia of Composite Areas 6

Example • Determine the moment of inertia of this rectangular area with respect to the axis (a-a) which is parallel to the axis (X-X) and located as shown in the figure. Moment of Inertia of Composite Areas 7 • Calculate the moment of inertia about the centroidal axis (X-X): Moment of Inertia of Composite Areas 8 • Apply the transfer formula: Moment of Inertia of Composite Areas 9 Moment of Inertia of Composite Areas • To find the moment of inertia of a composite area: 1- Divide the area into simple areas. 2- Calculate the moment of inertia of the simple areas about the axis in question. 3- Add the moments of inertia of the components to get the total moment of inertia for the composite area. Moment of Inertia of Composite Areas 10 Example • Determine the moment of inertia of the T-section with respect to its horizontal and vertical centroidal axes. Moment of Inertia of Composite Areas 11 Solution • The first step is to determine the location of the centroid which was done in the previous lecture. • The centroid is located as shown along the vertical axis of symmetry and at 1.5 in from the base of the flange. Moment of Inertia of Composite Areas 12

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