![]() ![]() ![]() Then if you move the area so that the centroid is no longer at the origin of the coordinate system you need to add an additional moment of inertia to the centroidal moment of inertia based on the parallel axes theorem. They are published for many basic shapes. Those are the values shown in the figure to the left. Generally though you start with the centroidal moments of inertia (figure at the left). Since the there are an infinite number of possible locations of the rectangle, there are an infinite number of moments of inertia each unique to the specific location of the area with respect to the axes. The moment of inertia of the area is with respect to the xy axes. But the rectangle can be located anywhere in the xy plane. It only applies to the two figures below. To say there are 2 moment of inertias for a rectangle is misleading. Then when they say the moment of inertia "with respect to an axis collinear with the base" they probably mean the moment of inertia with respect to an axis that is collinear with the base (collinear with the x-axis). See the figure at the left below where C indicates the location of the centroid. This is a guess on what they mean, but for a rectangle in the xy plane, I suspect the statement "one with the axis" means the moment of inertia of the rectangle with respect to the centroidal axis (x and y), that is, when the centroid of the rectangle is at the origin of the xy coordinate system so that the centroidal axes are the same as the x-y axes. I find the quoted statement poorly worded. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |