Tutorial on Free-body diagrams

Tutorial on Free-body diagrams - FREE-BODY DIAGRAMS Almost...

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FREE-BODY DIAGRAMS Almost every problem in Mechanics of Materials will involve draw- ing one or more free-body diagrams and it is crucial that you learn how to do this correctly and reliably. You need to reach a level of competence in this procedure such that you have absolutely no doubt that your di- agram is correct. Anything less than this opens you up to the risk that you will waste a whole lot of subsequent analytical work. This document is intended to help you to acquire this level of competence. The first section explains the basic principles underlying the drawing of free-body diagrams and reduces the process to a set of rules that you should follow carefully. These rules are illustrated by an example. In the second section, you will find three example problems for you to work on yourself. After you have given each of these examples your best shot, but not before , you should turn the page to see a selection of previous student attempts at these problems. Study these carefully and identify which you think are strictly correct in view of the procedure you have learned. Refer back to the first section to remind yourself of this procedure where necessary. In the final section, we give explanations of which sample diagrams are incorrect and why. Please restrain your impulse to look at this until you have really given the previous questions your absolutely best shot! Imagine these questions were on a take-home examination with no time limitation and that your answers were to be a substantial part of the course grade. The answers will be much more useful to your learning if you have struggled with the process seriously before you look at them.
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DRAWING FREE-BODY DIAGRAMS 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 — these will typically be the forces shown in the original drawing for the problem — and (ii) reaction forces generated at the supports — i.e. the places where the object is physically connected to the rest of the universe. Notice that you must expect reaction forces at all points where the object that you draw touches or is connected to something that you don’t draw. 2. Reaction forces can be developed whenever local motion of the object is prevented
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Tutorial on Free-body diagrams - FREE-BODY DIAGRAMS Almost...

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