ENGI 1313 Mechanics I Lecture 23 Equilibrium of

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

Mid-Term n Thursday October 18 Material: Ø Time: Ø Location: Ø Chapter 1 to 4. 5 inclusive 830 am-945 am EN 2043, EN 1040, EN 2007, EN 1001, EN 1003 & EN 1054 • Seating arrangements ¨ http: //www. engr. mun. ca/undergrad/schedule. php Ø 2 © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 23

Quiz #4 Week of October 22 -26 n Section 4. 6 through 4. 10 n Ø 3 Excluding “Reduction to a Wrench” © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 23

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

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

Recall – Particle Equilibrium (L 10) n Concurrent Force Systems +Y V = 0, v F 1 +X F 3 F 2 2 Equations Solve for at most 2 Unknowns 6 © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 23

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

Recall – Particle FBD (L 10) +Y FAB A = 30 FAD +X W = FAC = mg W = (255 kg)(9. 806 m/s 2) = 2. 5 k. N 8 © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 23

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

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

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

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

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

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

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

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

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

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

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

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

Comprehension Quiz 23 -02 n 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? Ø Ø n 21 A) 2 forces and 1 couple moment B) 3 forces and 1 couple moment C) 3 forces Ax D) 4 forces Answer: C © 2007 S. Kenny, Ph. D. , P. Eng. FBD Ay ENGI 1313 Statics I – Lecture 23

Example 23 -03 n 22 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. © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 23

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

Example 23 -04 n 24 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. © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 23

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

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

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

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

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

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