1. Lecture 33: Frames and Machines
ENGI 1313 Mechanics I
Lecture 33: Frames and Machines

2. Chapter 33 Objectives
to illustrate the analysis of frames and machines by example

3. Example 33-01
The compound beam is pin supported at B and supported by rockers at A and C. There is a hinge (pin) at D. Determine the reactions at the supports.

4. Example 33-01 (cont.) What FBD to Analyze? Member DC 7kN Dx Dy Cy 16kNBx Dx Ay By Dy

5. Example (cont.)
Member DC
7kN Dy Cy Dx
16kN
6kN Dx Dy Bx By Ay

6. Example 33-01 (cont.) Member ABD What equilibrium equation? 7kN Dy CyDx
16kN
6kN Dx Dy Bx By Ay

7. Example (cont.)
Member ABD
7kN Dy Cy Dx
16kN
6kN Dx Dy Bx By Ay

8. Example 33-02
Determine the horizontal and vertical components of force at each pin. The suspended cylinder has a weight of 80 lb.

9. Example 33-02 (cont.) Where to Start? Structural characteristics
Pulley
Two-force member DC
Two-force member EB
No. Why? W W

10. Example 33-02 (cont.) Draw FBD What FBD to Analyze? Member ABC Ex Ey WBx By W Ax Bx W
FCD By

11. Example (cont.)
What Equilibrium Equation? W Ax Bx W
FCD By

12. Example (cont.)
Find Bx to Help Solve for Unknowns Ex Ey W Bx By

13. Example (cont.)
Find Ax W Ax Bx W
FCD By

14. Example 33-03
The link is used to hold the rod in place. Determine the required axial force on the screw at E if the largest force to be exerted on the rod at B, C, or D is to be 100 N. Also, find the magnitude of the force reaction at pin A. Assume all surfaces of contact are smooth.

15. Example (cont.)
Any Structural Characteristic?
Concurrent forces

16. Example (cont.)
FBD
Assume 1 N unit load at Ex Ay Ax Ex
45 NB

17. Example (cont.)
Equilibrium Analysis Ay Ax Ex
45 NB

18. Example (cont.)
Equilibrium Analysis Ay Ax Ex
45 NB

19. Example (cont.)
Equilibrium Analysis of Cylinder Ay Ax Ex
45 NB

20. Example (cont.)
Equilibrium Analysis of Cylinder Ay Ax Ex
45 NB

21. References Hibbeler (2007)