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Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland spkenny@engr.mun.ca ENGI 1313 Mechanics I Lecture 23:Equilibrium of a Rigid Body

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ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 2 Mid-Term Thursday October 18 Material:Chapter 1 to 4.5 inclusive Time:830am-945am Location:EN 2043, EN 1040, EN 2007, EN 1001, EN 1003 & EN 1054 Seating arrangements http://www.engr.mun.ca/undergrad/schedule.php

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ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 3 Quiz #4 Week of October 22-26 Section 4.6 through 4.10 Excluding “Reduction to a Wrench”

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ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 4 Chapter 5 Objectives to develop the equations of equilibrium for a rigid body to introduce the concept of the free-body diagram for a rigid body to show how to solve rigid body equilibrium problems using the equations of equilibrium

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ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 5 Lecture 23 Objectives to identify support reactions to establish the free-body diagram for a rigid body in 2-D to develop the equations of equilibrium for a 2-D rigid body

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ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 6 Recall – Particle Equilibrium (L10) Concurrent Force Systems F1F1 F2F2 F3F3 V = 0, v +Y +X 2 Equations Solve for at most 2 Unknowns

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ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 7 Rigid Body Equilibrium Forces are Typically not Concurrent Potential moment or couple moment

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ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 8 Recall – Particle FBD (L10) +Y +X = 30 F AB W = F AC = mg F AD W = (255 kg)(9.806m/s 2 ) = 2.5kN A

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ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 9 Rigid Body FBD What is it? Sketch or diagram illustrating all external force and couple vectors acting on a rigid body or group of rigid bodies (system) Purpose? A visual aid in developing equilibrium equation of motion

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ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 10 Rigid Body FBD (cont.) What is the procedure? Draw isolated or “free” outlined shape Establish idealized model Establish FBD Show all forces and couple moments External applied loads Rigid body self-weight Support reactions Characterize each force and couple Magnitude Sense Direction

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ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 11 Rigid Body FBD (cont.) Drilling Rig 200 kg suspended platform on derrick tower Drill Rig Idealized Model Rigid Body FBD

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ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 12 Rigid Body FBD (cont.) Cantilever Beam 100 kg beam Idealized Model Rigid Body FBD

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ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 13 Support Reactions Newton’s 3 rd Law External loads Support specific characteristics Translation prevented support reaction force Rotation prevented support couple moment

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ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 14 Common Structural Supports Cable

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ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 15 Common Structural Supports (cont.) Roller

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ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 16 Common Structural Supports (cont.) Pin

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ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 17 Common Structural Supports (cont.) Fixed

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ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 18 Example 23-01 Foot Pedal FBD Spring force is 30 lb Foot Pedal Idealized Model Rigid Body FBD

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ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 19 Example 23-02 Dump Truck FBD 5000 lb dumpster supported by a pin at A and the hydraulic cylinder BC (short link) G W = 5000 lb 20 30 B F CB AyAy AxAx Rigid Body FBD

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ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 20 Comprehension Quiz 23-01 Internal forces are _________ shown on the free body diagram of a whole body. A) always B) often C) rarely D) never Answer: D

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ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 21 Comprehension Quiz 23-02 The beam and the cable (with a frictionless pulley at D) support an 80 kg load at C. In a FBD of only the beam, there are how many unknowns? A) 2 forces and 1 couple moment B) 3 forces and 1 couple moment C) 3 forces D) 4 forces Answer: C AyAy AxAx F BD

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ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 22 Example 23-03 Draw the free-body diagram of the beam supported at A by a fixed support and at B by a roller. Explain the significance of each force on the diagram.

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ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 23 Example 23-03 (cont.)

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ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 24 Example 23-04 Draw the free-body diagram of the automobile, which is being towed at constant velocity up the incline using the cable at C. The automobile has a mass M and center of mass at G. The tires are free to roll. Explain the significance of each force on the diagram.

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ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 25 Example 23-04 (cont.)

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ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 26 Textbook Problems

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ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 27 Textbook Problems

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ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 28 Textbook Problems

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ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 29 Textbook Problems

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ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 30 References Hibbeler (2007) http://wps.prenhall.com/esm_hibbeler_eng mech_1

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