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

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  

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 19 Example 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

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

ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 21 Comprehension Quiz 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

ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 22 Example 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.

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

ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 24 Example 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.

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

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

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

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

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

ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng. 30 References Hibbeler (2007) mech_1