static-lec1,2,3 - Engineering mechanics "Static" lecture 1...

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Engineering mechanics "Static" lecture 1 Force System Before dealing with a group or system of forces, it is necessary to examine the properties of a single force in some detail, A force has been define as an action of one body on another. In dynamics we will see that a force is defined as an action which tends to cause acceleration of a body. A force is a vector quantity, because its effect depends on the direction as well as on the magnitude of the action. Thus, the forces may be combined according to the parallelogram taw of vector addition. The action of the cable tension on the bracket in Fig.1a is represented in the side view,.Fig.2b, by the force vector P of magnitude P. The effect of this action on the bracket depends on P, the angle θ , and the location of the point of application A. changing any one of these three specifications will alter the effect on the bracket, such as the forces in one of the bolts which secure the bracket to the base, or the internal the complete specification of the action of a force must include its magnitude, direction, and point application, and therefore we must treat it as a fixed vector. 1 External and internal Effects We can separate the action of a force on a body into two effects, External and internal , for the bracket of Fig.2 the effects of P external to the bracket are the reactive forces(not shown) exerted on the bracket by the foundation and bolts because of the action of P. forces external to a body can be either applied. forces or reactive forces. The effects of P internal to the bracket are the resulting internal forces and deformations distributed throughout the material of the bracket. The rotation between internal forces and internal deformations depends on the material properties of the body and is studied in strength of materials, elasticity, and plasticity. Figure 1
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Principle of transmissibility When dealing with the mechanics of a rigid body, we ignore deformations in the body and concern ourselves with only the net external effects of external forces. In such cases, experience shows us that it is not necessary to restrict the action of an applied force to a given point. For example, the force P action on the rigid plate in Fig.2 may be applied at A or at B or at any other point on its line of action, and the net external effects of P on the bracket will not change. The external effect are the force exerted on the plate by the bearing support at 0 and the force exerted on the plate by the roller support at C. This conclusion is summarized by the principle of transmissibility, which states that a force may be applied at any point on its given line of action without altering the resultant effects of the force external to the rigid body on which it acts. Thus, whenever we are interested in only the resultant external effects of force, the force may be treated as a sliding vector, and we need specify only the magnitude, direction, and line of action of the force, and not its point of application. Figure 2
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This note was uploaded on 02/04/2010 for the course ME mechanics- taught by Professor M1 during the Spring '10 term at École Normale Supérieure.

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static-lec1,2,3 - Engineering mechanics "Static" lecture 1...

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