Chapter 5.1-5.5: Distributed Forces: Centroids and Centers of Gravity

Statics Lecture 29: Center of Gravity

Statics Lecture 30: Centroid of an Area

Statics Lecture 31: Centroid of composite areas

Statics Lecture 32: Mass Moment of Inertia and Area Moment of Inertia

 

 Statics Lecture 33: Area Moment of Inertia -- Calculation

Statics Lecture 34: Area Moment of Inertia -- Composite Areas

wiki list of centroids:

http://en.wikipedia.org/wiki/List_of_centroids

http://www.engineering.com/Library/ArticlesPage/tabid/85/articleType/ArticleView/articleId/109/Centroids-of-Common-Shapes.aspx

centroids:

http://en.wikipedia.org/wiki/Centroid

 

5.2: Start in 2D

Divide plate into n small elements, each with weight "W".

element n = 1 (x1, y1)

element n = 2 (x2, y2) etc.

Total weight:

Moments about x and y axis:

 or: 

Center of Gravity of a wire:

** Center of gravity "G" is not usually located on the wire.

Similar to:


Just divide above by thickness and specific weight:

Centroid of an Area
Define coordinates for the center of gravity of a homogeneous plate:

For homogeneous wire:

5.4  First Moments of Areas and Lines

   

Symmetrical objects:

5.5  Composite Plates and Wires

 1st moment of composite area:

Pay attention to your signs!

Probs 5.1-5.33

Examples:

Find the centroids of the areas:

HW Problems:

x=19.27, y=26.6

x=92, y=23.3

x=3.2, y=2.0

56.7°