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Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland ENGI 1313 Mechanics I Lecture 33:Frames and Machines

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ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng. 2 Chapter 33 Objectives to illustrate the analysis of frames and machines by example

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ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng. 3 Example 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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ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng. 4 Example (cont.) What FBD to Analyze? Member DC 16kN DxDx DyDy BxBx ByBy AyAy 6kN DxDx 7kN CyCy DyDy

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ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng. 5 Example (cont.) Member DC DxDx 16kN6kN DxDx DyDy BxBx ByBy AyAy 7kN DyDy CyCy

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ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng. 6 Example (cont.) Member ABD What equilibrium equation? DxDx 16kN6kN DxDx DyDy BxBx ByBy AyAy 7kN DyDy CyCy

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ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng. 7 Example (cont.) Member ABD DxDx 16kN6kN DxDx DyDy BxBx ByBy AyAy 7kN DyDy CyCy

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ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng. 8 Example Determine the horizontal and vertical components of force at each pin. The suspended cylinder has a weight of 80 lb.

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ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng. 9 Example (cont.) Where to Start? Structural characteristics Pulley Two-force member DC Two-force member EB No. Why? W W

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ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng. 10 Example (cont.) Draw FBD What FBD to Analyze? Member ABC W W W F CD BxBx EyEy ExEx ByBy BxBx ByBy AxAx

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ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng. 11 Example (cont.) What Equilibrium Equation? W W F CD ByBy BxBx AxAx

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ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng. 12 Example (cont.) Find B x to Help Solve for Unknowns W BxBx EyEy ExEx ByBy

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ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng. 13 Example (cont.) Find A x W W F CD ByBy BxBx AxAx

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ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng. 14 Example 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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ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng. 15 Example (cont.) Any Structural Characteristic? Concurrent forces

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ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng. 16 Example (cont.) FBD Assume 1 N unit load at E x AxAx AyAy ExEx NBNB 45

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ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng. 17 Example (cont.) Equilibrium Analysis AxAx AyAy ExEx NBNB 45

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ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng. 18 Example (cont.) Equilibrium Analysis AxAx AyAy ExEx NBNB 45

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ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng. 19 Example (cont.) Equilibrium Analysis of Cylinder AxAx AyAy ExEx NBNB 45

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ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng. 20 Example (cont.) Equilibrium Analysis of Cylinder AxAx AyAy ExEx NBNB 45

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ENGI 1313 Statics I – Lecture 33© 2007 S. Kenny, Ph.D., P.Eng. 21 References Hibbeler (2007) mech_1

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