2009+6-GeometricProperties

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 AB 1 N 3 N G
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Statics:The Next Generation Mehta & Danielson Lecture Notes for Section 9.1-9.2 2 SJTU Introduction to Solid Mechanics -Vm211 Also, note that the sum of moments due to the individual particle’s weights about point G is equal to zero. Similarly, the center of mass is a point which locates the resultant mass of a system of particles or body. Generally, its location is the same as that of G. CONCEPT OF CG and CM 3m 4N 1m AB 1 N 3 N G SJTU Introduction to Solid Mechanics -Vm211 CONCEPT OF CENTROID The centroid C is a point which defines the geometric center of an object. The centroid coincides with the center of mass or the center of gravity only if the material of the body is homogenous (density or specific weight is constant throughout the body). SJTU Introduction to Solid Mechanics -Vm211 CONCEPT OF CENTROID If an object has an axis of symmetry, then the centroid of object lies on that axis.
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This note was uploaded on 08/09/2011 for the course EE 211 taught by Professor Liuxila during the Summer '09 term at Shanghai Jiao Tong University.

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

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