Old Lecture 15 sect ..

```ME 221 Statics
Lecture #15
Section 4.3
ME 221
Lecture 15
1
Homework #5
• Chapter 3 problems:
– 48, 51, 55, 61, 62, 65, 71, 72 &amp; 75
– May use MathCAD, etc. to solve
– Due today
ME 221
Lecture 15
2
Homework #6
• Chapter 4 problems:
– 10, 11, 18, 24, 39, 42, 43 &amp; 47
– Must use integration methods to solve
– Due Monday, October 14
ME 221
Lecture 15
3
Quiz #4
• Wednesday, October 9
ME 221
Lecture 15
4
Last Lecture:
• The concepts of distributed loads, centroids
and center of gravity were presented.
ME 221
Lecture 15
5
Centroid of an Area
• Geometric center of the area
– Average of the first moment over the entire area
1
xc   xdA
AA
– Where:
1
yc   ydA
AA
A   dA
A
ME 221
Lecture 15
6
Centroid of an Area
• Is then defined as an integral over the area.
• Integration of areas may be accomplished
by the use of either single integrals or
double integrals.
ME 221
Lecture 15
7
Centroid of a Volume
• Geometric center of the volume
– Average of the first moment over entire volume
1
xc   xdV
VV
1
yc   ydA
AA
– In vector notation:
ME 221
Lecture 15
1
zc   zdV
VV
1
rc   rdV
VV
8
Examples
ME 221
Lecture 15
9
```