ME 221Lecture 151 ME 221 Statics Lecture #15 Section 4.5

ME 221Lecture 152 Homework #5 Chapter 3 problems: –48, 51, 55, 57, 61, 62, 65, 71, 72 & 75 –Due Today Homework #6 Chapter 4 problems: –2, 4, 10, 11, 18, 24, 39, 42, 43 & 47 –Must use integration methods to solve –Due Wednesday, October 8

ME 221Lecture 153 Quiz #4 Monday, October 6 Exam #2 Friday, October 10

ME 221Lecture 154 Last Lecture: Centroids of Areas & Volumes

ME 221Lecture 155 Centroid of Composite Bodies Basic shapes are added together to get the composite centroid –We look these up in Table 4.2 –This table will be supplied on future exams Problems

ME 221Lecture 156 Area Centroids This case is representative of line and volume centroids. Divide total area into simple shapes (rectangles, semi-circles) Add up simple shapes x y xcxc ycyc + + = x3x3 y3y3 A3A3 y2y2 x2x2 A2A2 y1y1 x1x1 A1A1

ME 221Lecture 157 May Also Use Subtraction x y xcxc ycyc = - y2y2 x2x2 A2A2 y1y1 x1x1 A1A1

ME 221Lecture 158 Composite Centroid of an Area Geometric center of the area –Summation of the pieces (holes are negative) –Where:

ME 221Lecture 159 Composite Centroid of a Volume Geometric center of the volume –Average of the first moment over entire volume –Where:

ME 221Lecture 1510 Examples