2009+6-GeometricProperties - Introduction to Solid...

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Statics:The Next Generation Mehta & Danielson Lecture Notes for Section 9.1-9.2 1 SJTU Introduction to Solid Mechanics -Vm211 Chapter 6 Geometric Properties and Distributed Loadings Chapter 6 Geometric Properties and Distributed Loadings SJTU Introduction to Solid Mechanics -Vm211 CENTER OF GRAVITY AND CENTROID Objective : a) Understand the concepts of center of gravity, center of mass, and centroid. b) Be able to determine the location of these points for a system of particles or a body. SJTU Introduction to Solid Mechanics -Vm211 APPLICATIONS To design the structure for supporting a water tank, we will need to know the weights of the tank and water as well as the locations where the resultant forces representing these distributed loads are acting. How can we determine these weights and their locations? SJTU Introduction to Solid Mechanics -Vm211 One concern about a sport utility vehicle (SUVs) is that it might tip over while taking a sharp turn. One of the important factors in determining its stability is the SUV’s center of mass . APPLICATIONS SJTU Introduction to Solid Mechanics -Vm211 Should it be higher or lower for making a SUV more stable? How do you determine its location? APPLICATIONS SJTU Introduction to Solid Mechanics -Vm211 CONCEPT OF CG CG and CM CM The center of gravity (G) is a point which locates the resultant weight of a system of particles or body. From the definition of a resultant force, the sum of moments due to individual particle weight about any point is the same as the moment due to the resultant weight located at G. For the figure above, try taking moments about A and B. 3m 4N 1m A B 1 N 3 N G
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