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**Lecture 33: Frames and Machines**

ENGI 1313 Mechanics I Lecture 33: Frames and Machines

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

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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.

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

Bx Dx Ay By Dy

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

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**Example 33-01 (cont.) Member ABD What equilibrium equation? 7kN Dy Cy**

Dx 16kN 6kN Dx Dy Bx By Ay

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

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

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**Example 33-02 (cont.) Where to Start? Structural characteristics**

Pulley Two-force member DC Two-force member EB No. Why? W W

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**Example 33-02 (cont.) Draw FBD What FBD to Analyze? Member ABC Ex Ey W**

Bx By W Ax Bx W FCD By

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

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

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

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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.

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Example (cont.) Any Structural Characteristic? Concurrent forces

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

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

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

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

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

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**References Hibbeler (2007)**

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Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland ENGI.

Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland ENGI.

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