engineering mechanics-static-lec5

engineering mechanics-static-lec5 - Lecture 5 Equilibrium...

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Lecture 5 Equilibrium Static deals primarily with the description of the force conditions necessary and sufficient to maintain the equilibrium of engineering structures. When body is equilibrium, the resultant of all forces acting on it is zero. Thus, the resultant force R and the resultant couple m are both zero, and we have the equilibrium equations These requirements are both necessary and sufficient conditions for equilibrium. All physical bodies are three-dimensional, but we can treat many of them as two-dimensional when the forces to which they are subjected act in a single plane or can be projected onto a single plane. When this simplification is not possible, the problem must be treated as three System Isolation And The Fee- body Diagram Before we apply Eqs.3/1, we must define unambiguously the particular body or mechanical system to be analyzed and represent clearly and completely all forces actins oz the body. Omission of a force which acts on the body in question, or inclusion of a force which does not act on the body, will give erroneous results. A mechanical system is defined as a body or group of bodies which can be conceptually isolated from all other bodies. A system may be a single body or a combination of connected bodies. The bodies may be rigid or non rigid. The system may also be an identifiable fluid mass, either liquid or gas, or a combination of fluids and solids. In statics we study primarily forces which act on rigid bodies at rest, although we also study forces actins on fluids in equilibrium. Once we decide which body or combination of bodies to analyze, we then treat this body or combination as a single body isolated from all surrounding bodies. This isolation is accomplished by means of the free body diagram, which is a diagrammatic representation of the isolated system treated as a single body. The diagram shows all forces applied to the system by mechanical contact with other bodies, which are imagined to be removed If appreciable body forces are present. Such as gravitational or magnetic attraction, then these forces must also be shown on the free-body diagram of the isolated system. Only after such a diagram has been carefully drawn should the equilibrium equations be written. Because of its critical importance, we emphasize here that Before attempting to &aw a free-body diagram, we must recall the basic characteristics of force. These chrematistics were described in Art. 2/2, with primary attention focused on the vector properties of force. Forces can be applied either by direct physical contact or by remote action. Forces car be either internal or external to the system under consideration. Application of force is accompanied by reactive force, and both applied and reactive forces may be either concentrated or distributed. The principle of 34
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transmissibility permits the treatment of force as a sliding vector as far as its external effects on a rigid body are concerned. We will now use these force characteristics to develop conceptual models of isolated mechanical systems.
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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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engineering mechanics-static-lec5 - Lecture 5 Equilibrium...

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