Lecture 15 sect 4.5

# Lecture 15 sect 4.5 - (rectangles semi-circles Add up...

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ME 221 Lecture 15 1 ME 221 Statics Lecture #15 Section 4.5

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ME 221 Lecture 15 2 Homework #5 Chapter 3 problems: Due Today Homework #6 Chapter 4 problems: Must use integration methods to solve Due Wednesday, October 8
ME 221 Lecture 15 3 Quiz #4 Monday, October 6 Exam #2 Friday, October 10

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ME 221 Lecture 15 4 Last Lecture: Centroids of Areas & Volumes
ME 221 Lecture 15 5 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

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ME 221 Lecture 15 6 Area Centroids This case is representative of line and volume centroids. Divide total area into simple shapes

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Unformatted text preview: (rectangles, semi-circles) Add up simple shapes x y x c y c + + = x 3 y 3 A 3 y 2 x 2 A 2 y 1 x 1 A 1 ME 221 Lecture 15 7 May Also Use Subtraction x y x c y c =-y 2 x 2 A 2 y 1 x 1 A 1 ME 221 Lecture 15 8 Composite Centroid of an Area • Geometric center of the area – Summation of the pieces (holes are negative) – Where: ∑ = i i i c A x A x 1 ∑ = i i i c A y A y 1 ∑ = i i A A ME 221 Lecture 15 9 Composite Centroid of a Volume • Geometric center of the volume – Average of the first moment over entire volume – Where: ∑ = i i i c V x V x 1 ∑ = i i i c V y V y 1 ∑ = i i V V ∑ = i i i c V z V z 1 ME 221 Lecture 15 10 Examples...
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Lecture 15 sect 4.5 - (rectangles semi-circles Add up...

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