The conditions for equilibrium are, generally speaking, the resultant force or the summation of the forces acting is 0, and the summation of the individual moments about some point is also equal to 0. However, I have to calculate where that single force the line of action of that single force. So in this way I can replace a force, a system of forces by a single force with no moment. In other words, the distance here of my resu, single resultant force is equal to the moment, the result in moment divided by the resultant force. And if I want this to be a single force here, then I have to, for this system to be in equilibrium, the moment of my resultant force about the point O, in other words, R times d, must be equal to the summation of the individual moments. So let's suppose that my single force here is R. Now we can go further than that and replace this force system by a single force acting at some point. And these are the formulas which are given in the reference handbook above.
#EQUILIBRIUM 3D STATICS PLUS#
So, in other words, the resultant force is just the summation of the forces which are acting, in this case, F1 plus F2 plus F3, and the resultant moment is the sum of the moments of the individual forces about that point. So, therefore, my equivalent system consists of the resulting force here, r, which is the summation of all of those forces passing through some point O here, plus a resultant moment M0, which is the sum of the moments of all of those individual forces about the point. So, to have those two systems be truly equivalent, I need to add a resultant moment.
Because, if I look at this point O here, each of these forces have a moment about that force. However, if I move all those forces through a single point like that, then we can see that this is not going to be an equilibrium. So, if I want to replace that by a single force, then the single resultant is just the summation of those forces, F1 plus F2 plus F3. Let's suppose we have a body here which is acted on by three forces, F1, F2, and F3, and we'll assume that these forces do not all pass through a single point. Now, generally speaking we can replace a system of forces by a single force through some point, and a moment. So for example the x component of the resultant force is equal to the summation of the x components of the individual forces, and the y component is equal to the summation of the y components of the forces. And again, we can form this resultant by simply adding up the components of the forces in the x and y directions. Or, more generally, the summation overall of the forces which are acting, which is the equation given in the reference handbook here. So, in this case, let's suppose we have two forces here, F1 and F2, then the resultant force is simply the vector sum of those forces. The resultant is similarly, simply the sum of the forces which is acting, or which are acting on an object. So firstly resultants and equilibrium, and here is the section over on the right hand side from the reference handbook.
#EQUILIBRIUM 3D STATICS FREE#
And, in particular in this segment, we'll look at sigma, systems of forces and resultants, the conditions for equilibrium, drawing free body diagrams, analyzing pulleys, and analyzing problems involving friction. And, these are the subjects or the topics we'll look at. In all cases, basic ideas and equations are presented along with sample problems that illustrate the major ideas and provide practice on expected exam questions.Time: Approximately 3 hours | Difficulty Level: MediumĬontinuing our discussion of statics, now, I want to talk on the idea of equilibrium. These are moments of inertia, centroids, and polar moments of inertia of simple and composite objects.
Finally, we analyze the geometrical properties of lines, areas, and volumes that are important in statics and mechanics of materials.
#EQUILIBRIUM 3D STATICS HOW TO#
The concept and major characteristics of trusses are discussed, especially simple trusses, and we show how to analyze them by the method of joints and the method of sections. Then how to analyze pulleys and compute static friction forces and solve problems involving friction. We show how to draw a meaningful free body diagram with different types of supports. We discuss the concept of equilibrium of a rigid body and the categories of equilibrium in two dimensions. Then the meaning and computation of moments and couples. We discuss the main characteristics of vectors and how to manipulate them. Then we consider systems of forces and how to compute their resultants. We first discuss Newton’s laws and basic concepts of what is a force, vectors, and the dimensions and units involved. This module reviews the principles of statics: Forces and moments on rigid bodies that are in equilibrium.
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