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## Engineering Mechanics: Statics

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**Engineering Mechanics: Statics**Chapter 5: Distributed Forces**Introduction**‘Concentrated’ force does not exist, since every force applied mechanically is distributed over a finite contact area. When the applied region is not negligible, we must account for the actual manner the force is distributed Three categories: Line distribution (N/m) Area distribution (N/m2, Pa) Volume distribution or body force (N/m3)**Centers of Mass**Body force due to gravitational attraction of the earth (weight) is the most commonly encountered distributed force This section treats the determination of the point in a body through which the resultant gravitational force acts. Center of gravity Apply the principle of moments (The moment of the resultant force W equal the sum of the moments about the same axis of the force dW acting on all particles) Center of mass**Centers of Massand Centroids**In vector form where and The density r of a body is its mass per unit volume, thus , etc. • When the density r of a body is uniform throughout, the expressions define purely geometrical property of the body and the term centroid is used.**Centroids**• Centroid of lines • Centroid of areas • Centroid of volumes • In a homogeneous body, center of mass always lies on a plane of symmetry! • Since the moments due to symmetrically located elements will always cancel.**Choice of Element for Integration**• Order of element • Continuity • Discard higher-order term (integration of ydx instead of ydx+1/2dydx) • Choice of coordinate system • Centroidal coordinate of element**Sample Problem 5/2**Determine the distance from the base of a triangle of altitude h to the centroid of its area**Sample Problem 5/5**Locate the centroid of the volume of a hemisphere of radius r with respect to its base.**Composite Bodies**• When a body can be divided into several parts whose mass centers are easily determined, we use the principle of moments and treat each part as a finite element of the whole**Sample Problem 5/6**Locate the centroid of the shaded area. 120 40 40 30 20 50 Dimensions in mm 20 20 30**Problem 5/57**The rigidly connected unit consists of a 2-kg circular disk, a 1.5-kg round shaft and a 1-kg square plate. Determine the z-coordinate of the mass center of the unit.