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ME 221 Statics Lecture #19 Sections 9.1 - 9.6 Exam #2 Review

This lecture covers moments of area and serves as a review for Exam 2. It includes examples and problems from Chapter 4 and Chapter 9, focusing on double integration and centroids of composite bodies. The exam topics include calculating moments, cross products, moment of a force, moment of a couple, equivalent force systems, center of mass, centroids, and distributed loads on beams.

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ME 221 Statics Lecture #19 Sections 9.1 - 9.6 Exam #2 Review

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  1. ME 221 StaticsLecture #19Sections 9.1 - 9.6Exam #2 Review 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 Wednesday, October 23 Lecture 19

  3. Exam 2 • Friday, October 18 • More on the exam later in the hour Lecture 19

  4. x dA y r Moments of Area • Characterizes the way area is distributed about the centroid • Always a positive value with units of in4, mm4, ft4, m4, etc. • Moment of inertia Lecture 19

  5. y y y dx dy x x x a dx dx dy Example dA=dxdy dIx=y2dA dIy=x2dA dA=(a-x)dy dIx=y2dA dA=ydx dIy=x2dA use horizontal element for value in x use vertical element for value in y Lecture 19

  6. y x y x Moments of Basic Shapes • Rectangle Common values found in table 9.1, p451 • Circular Lecture 19

  7. y r x Polar Moment The polar moment is the second moment about the z-axis Note that: Ixx + Iyy = JOz Lecture 19

  8. y x’ C d x Parallel Axis Theorem The centroid of the area MUST be one of the axes used in the parallel axis theorem. Lecture 19

  9. Radius of Gyration An alternate, equivalent way to represent the moment of an area Lecture 19

  10. Example Lecture 19

  11. ME 221 Exam 2 Topics • Chapter 3 • Calculating moments • Cross products • Moment of a force about an axis • Moment of a couple • Equivalent force systems Lecture 19

  12. ME 221 Exam 2 Topics • Chapter 4 • Center of mass • Centroids of lines, areas and volumes • Centroids of composite bodies • Distributed loads on beams Lecture 19

  13. Lecture 19

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