ME 221Lecture 191 ME 221 Statics Lecture #19 Sections Exam #2 Review

ME 221Lecture 192 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

ME 221Lecture 193 Exam 2 Friday, October 18 More on the exam later in the hour

ME 221Lecture 194 Moments of Area Characterizes the way area is distributed about the centroid Moment of inertia –Always a positive value with units of in 4, mm 4, ft 4, m 4, etc. dA y x r

ME 221Lecture 195 Example dx dy x y dA=dxdy dI x =y 2 dA dI y =x 2 dA dx x y dA=(a-x)dy dI x =y 2 dA dA=ydx dI y =x 2 dA dx dy x y a use horizontal element for value in x use vertical element for value in y

ME 221Lecture 196 Moments of Basic Shapes Rectangle x y Circular x y Common values found in table 9.1, p451

ME 221Lecture 197 Polar Moment The polar moment is the second moment about the z-axis x y r Note that: I xx + I yy = J Oz

ME 221Lecture 198 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

ME 221Lecture 199 Radius of Gyration An alternate, equivalent way to represent the moment of an area

ME 221Lecture 1910 Example

ME 221Lecture 1911 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

ME 221Lecture 1912 ME 221 Exam 2 Topics  Chapter 4 Center of mass Centroids of lines, areas and volumes Centroids of composite bodies Distributed loads on beams

ME 221Lecture 1913