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

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

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.

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

Example 33-01 (cont.) Member DC 7kN Dy Cy Dx 16kN 6kN Dx Dy Bx By Ay

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

Example 33-01 (cont.) Member ABD 7kN Dy Cy Dx 16kN 6kN Dx Dy Bx By Ay

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

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

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

Example 33-02 (cont.) What Equilibrium Equation? W Ax Bx W FCD By

Example 33-02 (cont.) Find Bx to Help Solve for Unknowns Ex Ey W Bx By

Example 33-02 (cont.) Find Ax W Ax Bx W FCD By

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.

Example 33-03 (cont.) Any Structural Characteristic? Concurrent forces

Example 33-03 (cont.) FBD Assume 1 N unit load at Ex Ay Ax Ex 45 NB

Example 33-03 (cont.) Equilibrium Analysis Ay Ax Ex 45 NB

Example 33-03 (cont.) Equilibrium Analysis Ay Ax Ex 45 NB

Example 33-03 (cont.) Equilibrium Analysis of Cylinder Ay Ax Ex 45 NB

Example 33-03 (cont.) Equilibrium Analysis of Cylinder Ay Ax Ex 45 NB

References Hibbeler (2007) http://wps.prenhall.com/esm_hibbeler_engmech_1