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Lecture 5 part I

# Lecture 5 part I - LECTURE 5 DISTROBUTED FORCES CENTROIDS...

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1 LECTURE 5 DISTROBUTED FORCES: CENTROIDS AND CENTER OF GRAVITY PART I CONTENTS INTRODUCTION CENTERS OF GRAVITY AND MASS CENTROIDS OF VOLUMES, AREAS, AND LINES THEOREMS OF PAPPUS AND GUILINUS † : weekend reading using the same effort as for your homework

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2 INTRODUCTION Concurrent force systems are dealing with particles with negligible size and shape. And noncurrent force systems are dealing with bodies with definite size and shape. In rigid bodies with definite size and shape, as we consider the points of application of the applied forces, the area of the rigid body will have important effect on the effect of the applied forces. Previously , we are dealing with the magnitude, direction, including orientation and sense, of the force as a vector. Now , we are concerning about the point of application of the force vector. When a particle is a primary concern, a concentrated force can be represented as a simple vector quantity with a magnitude, a direction, a line of action, and in some instances a point of application. However, when the areas over which the loads are applied become significant with respect to the size of the body , the assumption of a concentrated force is no longer valid. In this circumstance, a distribute load should be used instead of a concentrated load. A distributed load can act on the body along a line (Fig. 5-1 a ), over a surface (Fig. 5-1 b ), or through the entire body (Fig. 5-1 c ). a ) Line force b) surface force c) body force Fig. 5-1 Distributed forces along a line, on the surface, and through the body
3 A distributed force at any point is characterized by its intensity and its direction . A force distributed over an area and acting normal to the surface is known as pressure . Internal distributed forces in solids may or may not act normal to the surface of interest. The units for pressure are force per unit area (lb/in 2 . or N/m 2 ). Forces distributed over the volume of the body are measured in unit force per unit volume (lb/in 3 . or N/m 3 ). Analogous to the moment produced by the force, moments of area , masses , volumes are also encountered in engineering application. For instance, considering the moment of an area A about the y -axis as shown in Fig. 5.1, since an area is a distributed quantity, its moment of area, defined as the product of the area of the element and the distance of the element w.r.t.

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Lecture 5 part I - LECTURE 5 DISTROBUTED FORCES CENTROIDS...

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