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Basic Mechanical Engineering – ME 101 Textbook: Engineering Mechanics- STATICS 12 th E, R. C. Hibbeler. Fundamental Concept of Forces
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Basic Mechanical Engineering – ME 101 Textbook: Engineering Mechanics- STATICS 12th E, R. C. Hibbeler
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.
Addition of Several Forces The resultant force on the hook requires the addition of F1+F2, then this resultant is added to F3.
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.
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.
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.
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.
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
Free-Body Diagram Exercise (Engineering Mechanics –Statics 5th e, by J.L.Meriam and L.G.Kraige)
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).
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.
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.
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.
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.
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.
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.
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.
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)
Example: Two and Three Force Members (A Hanged Lamp) http://web.mit.edu/4.441/1_lectures/1_lecture15/1_lecture15.html
