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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク First moment of area ： ウィキペディア英語版 First moment of area The first moment of area, sometimes misnamed as the first moment of inertia, is based in the mathematical construct moments in metric spaces, stating that the moment of area equals the summation of area times distance to an axis (× ''d'') ). It is a measure of the distribution of the area of a shape in relation to an axis. First moment of area is commonly used to determine the centroid of an area. ==Definition== Given an area, ''A'', of any shape, and division of that area into ''n'' number of very small, elemental areas (''dAi''). Let ''xi'' and ''yi'' be the distances (coordinates) to each elemental area measured from a given ''x-y'' axis. Now, the first moment of area in the ''x'' and ''y'' directions are respectively given by: :$$ S_x = A \bar y = \sum_^n = \int_A y dA and :$$ S_y= \sum_^n = \int_A x dA . The SI unit for first moment of area is a cubic metre (''m''3). In the American Engineering and Gravitational systems the unit is a cubic foot (''ft''3) or more commonly inch3. The static or statical moment of area, usually denoted by the symbol ''Q'', is a property of a shape that is used to predict its resistance to shear stress. By definition: $Q\_\; =\; \backslash int\; y\_i\; dA$, where * ''Q''''j,x'' - the first moment of area "j" about the neutral ''x'' axis of the entire body (not the neutral axis of the area "j"); * ''dA'' - an elemental area of area "j"; * ''y'' - the perpendicular distance to the element ''dA'' from the neutral axis ''x''. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「First moment of area」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.