Basic Mechanical Engineering – ME 101 Textbook: Engineering Mechanics- STATICS

1. Basic Mechanical Engineering – ME 101 Textbook: Engineering Mechanics- STATICS 12th E, R. C. Hibbeler

2. Fundamental Concept of Forces (Left): Three forces on the hook at A. Since these forces all meet at a point, then for any force analysis, we can assume the hook to be represented as a particle. (right): Steel is a common engineering material that does not deform very much under load. Therefore, we can consider this railroad wheel to be a rigid body acted upon by the concentrated force of the rail.

3. Vector Addition of Forces(Parallelogram Law)

4. Addition of Several Forces The resultant force on the hook requires the addition of F1+F2, then this resultant is added to F3.

5. Coplanar Force Resultants • The resultant force of the four cable forces acting on the supporting bracket can be determined by adding algebraically the separate x and y components of each cable force. This resultant force produces the same pulling effect on the bracket as all four cables.

6. Right-Handed Coordinate System • A rectangular coordinate system is said to be right-handed if the thumb of the right hand points in the direction of the positive z-axis when the right-hand fingers are curled about this axis and directed from the positive x towards the positive y axis.

7. The resultant force acting on the bow the ship can be determined by first representing each rope force as Cartesian vector and then summing the i, j and k components.

8. Position vector • If an x,y,z coordinate system is established, then the coordinates of points A and B can be determined. From this position vector r acting along the cable can be formulated. Its magnitude represents the length of the cable, and its unit vector, u=r/|r|, gives the direction defined by α,β,γ.

9. Force directed along a line • The force F acting along the chain can be represented as a Cartesian vector by establishing x,y,z axes and first forming a position vector r along the length of the chain and the force can be determined. Finally, the magnitude of the force is combined with its direction, F=Fu

10. Dot Product

11. Free-Body Diagram

12. Free-Body Diagram

13. Coplanar Force Systems

14. Conceptual Examples

15. Free-Body Diagram Exercise (Engineering Mechanics –Statics 5th e, by J.L.Meriam and L.G.Kraige)

16. Three-Dimensional Force Systems

18. Moment of a Force

19. Examples

20. Principle of Moment

21. Equivalent Couples

22. Example

23. Simplification of a Force and Couple System

24. Support Reactions • As a general rule, if a support prevents the translation of a body in a given direction, then a force is developed on the body in that direction. Likewise, if rotation is prevented, a couple moment is exerted on the body. • Three ways to support a horizontal member: • Roller (it only prevents the beam from translating in the vertical direction) • Pin (it can prevent translation of the beam in any direction (Fx, Fy)) • Fixed Support (it prevents both translation and rotation of the beam- force and couple moment must be developed on the beam at its point of connection).

25. Equilibrium of A Rigid Body

28. Typical Examples of Actual Support

29. Weight & Center of Gravity • When a body is subjected to a gravitational field, then each of its particles has a specified weight. For the entire body it is appropriate to consider these gravitational forces to be represented as a system of parallel forces acting on all the particles contained with the boundary of the body. • We refer to this force resultant as the weight W of the body and to the location of its point of application as the center of gravity. • Also when the body is uniform, the center of gravity will be located at the body’s geometric center or centroid.

30. Selection of a Model- Steel Beam • (a): the steel beam is to be used to support the roof joists of a building. Building code requirements are used to specify the roof loading which results in a calculation of the joist loads F.

31. Selection of a Model-Lift Boom • It is supported at A and by the hydraulic cylinder BC, which can be approximated as a weightless link. The weight of the boom and the location of its center of gravity G are determined.

32. Example: Draw the free-body diagram of the foot lever. The operator applies a vertical force to the pedal so that the spring is stretched 1.5 cm and the force in the short link at B is 20N.

33. Example: Two smooth pipes, each having a mass of 300kg, are supported by the forks of the tractor. Draw the free-body diagrams for each pipe and both pipes together.

34. Example: Draw the free body diagram of the unloaded platform that is suspended off the edge of the oil rig. The platform has a mass of 200kg.

35. Two and Three Force Members: Many mechanical elements act as two or three force members, and the ability to recognize them in a problem will considerably simplify an equilibrium analysis.

36. Back-Hoe • A hydraulic excavating machine consisting of a tractor having an attached hinged boom, with a bucket with movable jaws on the end of the boom. • (www.dictionary.com)

37. Example: Two and Three Force Members (A Hanged Lamp) http://web.mit.edu/4.441/1_lectures/1_lecture15/1_lecture15.html

38. Exercise 5-9 (pg. 182)

39. Exercise 5-10 (pg. 182)

40. Exercise 5-11 (pg. 182)

41. Exercise 5-12 (pg. 183)

42. Exercise 5-13 (pg. 183)