. The strength of materials; a text-book for engineers and architects. rallel to x x, then the distance from the twolines will determine its position. In connection with the centroid it should be noted thatthe position of the centroid depends solely on the shape ofthe figure, and not on the position of the axes about whichmoments are taken. As in the case of forces, we have positiveand negative moments in areas, the moment being positivewhen the given element of area is above or to the right of thegiven axis, and negative when it is below or to the left. First Moment about Line through Centroi
. The strength of materials; a text-book for engineers and architects. rallel to x x, then the distance from the twolines will determine its position. In connection with the centroid it should be noted thatthe position of the centroid depends solely on the shape ofthe figure, and not on the position of the axes about whichmoments are taken. As in the case of forces, we have positiveand negative moments in areas, the moment being positivewhen the given element of area is above or to the right of thegiven axis, and negative when it is below or to the left. First Moment about Line through Centroid.—Nowconsider the first moment of an area about a line c c, Fig. 80,through the centroid. The moments of elements of area abovethe line such as that at P will be positive, and the momentsof elements of area below the line such as that at p will benegative. Now in this case c J is zero, and therefore A x c j will also 166 THE STRENGTH OF :\IATERIALS be zero, and therefore we have the rule that the first momentof any area about a line tlirough its centroid is PosiTio:?^ OF Centroid with Axes of Symmetry.—Supposean area has an axis of s}Tnmetry Y Y, Fig. 81. Then this line y
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