In Chapter XII is presented the material on curved bars which previously appeared in the second volume of this book. That material has been entirely rewritten and new material added. I t is hoped with these major changes as well as the innumerable minor changes through-out the entire text that the volume will be not only more complete but also more satisfactory as a textbook in elementary courses in strength of materials.
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Nature menu. The determination Of a body or centroid of a section is equivalent to determining the resultant Of a number of like, parallel forces. These forces are vertical and they can be Replaced by a single vertical resultant of magnitude equal to the total weight Of the body and acting at the centre of gravity of the body. Consider the plate lying horizontally. The Plan view is as shown with the weight forces acting vertically downwards at Right angles to the page. X and Y are to the horizontal plane and intersect at a convenient origin O.
The small element shown has an area dA and is located at a distance x From the Y axis and distance y from the X Axis.
It should be obvious that for a Square, rectangle and circle, the centroid will be central as shown below. Now look at the triangle shown in figure d above. Furthermore, fibres far away from the neutral axis are stressed more Heavily than those near to the neutral axis, fibres lying on the neutral axis Are neither in tension or compression.
The location of the neutral axis of a plane area is an important geometric property of the area. To determine the coordinates of centroid point of intersection of two or more neutral axis in different directions of the plane area, let us refer to figure 2. A differential element of area dA, with coordinates x and y, is shown in the figure.
The total area is defined as the following integral. If an area is symmetric about an axis the centroid must lie in that axis because the first moment about an axis of symmetry equals zero. For example, the centroid of single s Cec Theory - Hydrogeology Documents. Strength of Materials - of Materials Author: Owner Subject: Strength of Materials Keywords: engineering mechanics, strength of materials, mechanics of materials Documents. Unit 1.
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