1. ME221Lecture 81 ME 221 Statics Lecture #8 Section 4.5-4.6

2. ME221Lecture 82 Homework #3 Chapter 3 problems: –48, 55, 57, 61, 62, 65 & 72 Chapter 4 problems –2, 4, 10, 11, 18, 24, 39 & 43 –Due Today

3. ME221Lecture 83 Homework #4 Chapter 4 problems: –52 & 54 Chapter 9 problems –2, 11 & 32 –Due Monday, June 14 MatLab Group Problems –4.13 – plot as a function of R with 0º < α < 45º –4.51 – plot as a function of l –4.60 – plot the equivalent force and point of action –Due Monday, June 14

4. ME221Lecture 84 Quiz #4 Today Quiz #5 Wednesday, June 16

5. ME221Lecture 85 Last Lecture: Centroids of Areas & Volumes

6. ME221Lecture 86 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 for shapes other than rectangles, circles and triangles

7. ME221Lecture 87 Area Centroids This case is also representative of line and volume centroids. Divide total area into simple shapes (rectangles, semi-circles) Add simple shapes x y xcxc ycyc + + = x3x3 y3y3 A3A3 y2y2 x2x2 A2A2 y1y1 x1x1 A1A1

8. ME221Lecture 88 May Also Use Subtraction x y xcxc ycyc = - y2y2 x2x2 A2A2 y1y1 x1x1 A1A1

9. ME221Lecture 89 Composite Centroid of an Area Geometric center of the area –Summation of the pieces (holes are negative) –Where:

10. ME221Lecture 810 Composite Centroid of a Volume Geometric center of the volume –Average of the first moment over entire volume –Where:

11. ME221Lecture 811 Examples

12. ME221Lecture 812 Distributed Loads Distributed loads on beams –Application of equivalent load

13. ME221Lecture 813 Beams Beams can be loaded by a point load or a distributed load P w(x) Replace the distributed load with an equivalent concentrated force. x dx L The equivalent force is the sum of all the forces.

14. ME221Lecture 814 Equivalent Load Location The equivalent load is placed at the centroid of the distributed load. w(x) xcxc L To find reaction loads: replace distributed load with equivalent load at centroid W

15. ME221Lecture 815 Example

16. ME221Lecture 816 Quiz #4