ME 221 Statics
Lecture #15
Section 4.5
ME 221
Lecture 15
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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 221
Lecture 15
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Quiz #4
• Monday, October 6
Exam #2
• Friday, October 10
ME 221
Lecture 15
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Last Lecture:
• Centroids of Areas & Volumes
ME 221
Lecture 15
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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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Lecture 15
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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 15
yc
y3
x
6
May Also Use Subtraction
A1
x2
x1
y1
ME 221
y
A2
=
y2
Lecture 15
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
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Lecture 15
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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
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Examples
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Lecture 15
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