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Unformatted text preview: 1 DRAWING FREE-BODY DIAGRAMS Almost every problem in Mechanics of Materials will involve drawing one or more free-body diagrams and it is crucial that you learn how to do this correctly and reliably. A free-body diagram is a picture of an object showing the external forces acting on it. An external force is one that is exerted on the object by something that is not itself part of the object. 1. The crucial first step is to decide what is the object you are drawing. Draw the geometrical picture first before you even think about what forces are going to act on it. In this way, you separate the object from the rest of the universe and the forces that you then place on the drawing are those exerted by the rest of the universe on the object. These external forces will typically comprise (i) prescribed external forces such as the weight of the object and forces ‘deliberately’ exerted on it by an external agency and (ii) reaction forces generated at the supports — i.e. the places where the object is physically connected to the rest of the universe. 2. Reaction forces can be developed whenever local motion of the object is pre- vented and the nature of the reaction forces can be decided from the degrees of freedom of motion that are prevented. For example, if the object is pinned to the ground, the location of the pin is prevented from translating horizontally or vertically, so in general horizontal and vertical reactions will be required. However, rotation about the pin is not prevented, so there will be no moment at the pin. In placing these reactions on the diagram, put on all the forces that can be applied by the supports and label them with symbols (e.g. R 1 ,R 2 , or A x ,A y , etc.). Don’t try to decide what forces will actually act on the object at this stage. Also, it doesn’t matter which direction you place these forces. If they are later found to be negative it simply means they act in the opposite direction to that in your drawing, but that is fine.to that in your drawing, but that is fine....
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This note was uploaded on 10/05/2011 for the course MECHENG 211 taught by Professor ? during the Fall '07 term at University of Michigan.

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