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ENGI 1313 Mechanics I

ENGI 1313 Mechanics I . Lecture 23: Equilibrium of a Rigid Body. 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 Mechanics I

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  1. ENGI 1313 Mechanics I Lecture 23: Equilibrium of a Rigid Body

  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

  3. Quiz #4 • Week of October 22-26 • Section 4.6 through 4.10 • Excluding “Reduction to a Wrench”

  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

  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

  6. +Y V = 0, v F1 +X F3 F2 Recall – Particle Equilibrium (L10) • Concurrent Force Systems 2 Equations  Solve for at most 2 Unknowns

  7. Rigid Body Equilibrium • Forces are Typically not Concurrent • Potential moment or couple moment

  8. Recall – Particle FBD (L10) +Y FAB A  = 30 FAD +X W = FAC = mg W = (255 kg)(9.806m/s2) = 2.5kN

  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

  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

  11. Rigid Body FBD (cont.) • Drilling Rig • 200 kg suspended platform on derrick tower Drill Rig Idealized Model Rigid Body FBD

  12. Rigid Body FBD (cont.) • Cantilever Beam • 100 kg beam Idealized Model Rigid Body FBD

  13. Support Reactions • Newton’s 3rd Law • External loads • Support specific characteristics • Translation prevented   support reaction force • Rotation prevented   support couple moment

  14. Common Structural Supports • Cable

  15. Common Structural Supports (cont.) • Roller

  16. Common Structural Supports (cont.) • Pin

  17. Common Structural Supports (cont.) • Fixed

  18. Example 23-01 • Foot Pedal FBD • Spring force is 30 lb Foot Pedal Idealized Model Rigid Body FBD

  19. G B FCB 30 20 Ax W = 5000 lb Ay Example 23-02 • Dump Truck FBD • 5000 lb dumpster supported by a pin at A and the hydraulic cylinder BC (short link) Rigid Body FBD

  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

  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 FBD Ax Ay

  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.

  23. Example 23-03 (cont.)

  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.

  25. Example 23-04 (cont.)

  26. Textbook Problems

  27. Textbook Problems

  28. Textbook Problems

  29. Textbook Problems

  30. References • Hibbeler (2007) • http://wps.prenhall.com/esm_hibbeler_engmech_1

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