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ME 221 Statics Lecture #16 Section 4.5 ME 221 Lecture 16 1 Homework #6 • Chapter 4 problems: – 10, 11, 18, 24, 39, 42, 43 & 47 – Must use integration methods to solve – Due Monday, October 14 ME 221 Lecture 16 2 Quiz #4 • Wednesday, October 9 ME 221 Lecture 16 3 Last Lecture: • Centroids of Areas, Volumes & Lines ME 221 Lecture 16 4 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 221 Lecture 16 5 Area Centroids This case is representative of line and volume centroids. Divide total area into simple shapes (rectangles, semi-circles) Add up simple shapes y A2 x1 x2 A1 y1 ME 221 + y2 A3 + = xc x3 Lecture 16 yc y3 x 6 May Also Use Subtraction A1 x2 x1 y1 ME 221 y A2 = y2 Lecture 16 yc xc x 7 Composite Centroid of an Area • Geometric center of the area – Summation of the pieces (holes are negative) 1 xc xiAi A i – Where: 1 yc yiAi A i A Ai i ME 221 Lecture 16 8 Composite Centroid of a Volume • Geometric center of the volume – Average of the first moment over entire volume 1 xc xiVi V i 1 yc yiVi V i – Where: V Vi 1 zc ziVi V i i ME 221 Lecture 16 9 Examples ME 221 Lecture 16 10