1. ME 221Lecture 171 ME 221 Statics Lecture #19 Sections 9.1 - 9.6 Exam #2 Review

2. ME 221Lecture 172 Homework #6 Chapter 4 problems: –2, 4, 10, 11, 18, 24, 39, 42, 43 & 47 –Due Today

3. ME 221Lecture 173 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, October 17

4. ME 221Lecture 174 Exam 2 Friday, October 10 More on the exam later in the hour

5. ME 221Lecture 175 Moments of Area Characterizes the way area is distributed about the centroid Area Moment of Inertia (Second moment of an area) –Always a positive value with units of in 4, mm 4, ft 4, m 4, etc. dA y x r

6. ME 221Lecture 176 Example dx dy x y dA=dxdy dI xx =y 2 dA dI yy =x 2 dA dx x y dA=(a-x)dy dI xx =y 2 dA dA=ydx dI yy =x 2 dA dx dy x y a use horizontal element for value in x use vertical element for value in y

7. ME 221Lecture 177 Moments of Basic Shapes Rectangle x y Circular x y Common values found in table 9.1, p451

8. ME 221Lecture 178 Polar Moment The polar moment is the second moment of area about the z-axis (resistance to torsion) x y r Note that: I xx + I yy = J Oz

9. ME 221Lecture 179 Parallel Axis Theorem MUST The centroid of the area MUST be one of the axes used in the parallel axis theorem. y d x x’ C

10. ME 221Lecture 1710 Radius of Gyration An alternate, equivalent way to represent the moment of an area Distance to where the area is concentrated

11. ME 221Lecture 1711 Example

12. ME 221Lecture 1712 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

13. ME 221Lecture 1713 ME 221 Exam 2 Topics  Chapter 4 Center of mass Centroids of lines, areas and volumes Centroids of composite bodies Distributed loads on beams