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Advanced Statics Lecture 19: Principal Moments, Inertia, & Homework Assignments

In Lecture 19 of the Statics course, we cover key concepts related to Principal Moments of Inertia, Principal Axes, and Mohr's Circle, emphasizing their importance in mechanics. Students are assigned homework from Chapters 4 and 9, including problems for double integration techniques and application of the product moment of inertia and torsional stiffness concepts. Additional resources will be provided on the Angel platform. Homework is due Friday, October 24. This lecture is crucial for understanding the mechanics of composite sections and section properties.

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Advanced Statics Lecture 19: Principal Moments, Inertia, & Homework Assignments

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  1. ME 221 StaticsLecture #19Sections 9.7 - 9.9 Lecture 19

  2. Homework #7 • Chapter 4 problems: • 52, 53 & 54 • Chapter 9 problems: • 2, 3, 4, 11, 23, 29 & 32 • Use double integration for 2, 3, 4 & 11 • Due Friday Lecture 19

  3. Homework #8 • Chapter 9 problems: • 42, 43, 50 & 55 • Chapter 5 problems: • 11, 13, 16, 20, 24 & 25 • Additional information to be on Angel • Due Friday, October 24 Lecture 19

  4. Last Lecture Principal Second Moments Product Moment of Inertia Principal Axes Mohr’s Circle

  5. Mechanics Nomenclature Polar Moment of Inertia = Torsional Stiffness Second Moment of Area = Bending Stiffness

  6. y x Product Moment of Inertia • Basic section with two axes of symmetry • Composite sections - product parallel axis theorem Lecture 19

  7. -Ixy • draw circle center (Ixx + Iyy)/2 x • draw point (Ixx , Ixy) and the circle IMIN Ixx IMAX 2b x Ixx, Iyy Iyy • use geometry to find IMAX , IMIN and b x Ixy +Ixy (Ixx+Iyy)/2 Mohr’s Circle for Principal Inertia Angles in Mohr’s circle are twice those in the section analyzed. Lecture 19

  8. Chapter 9 Example Lecture 19

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