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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 Theorem of three moments ： ウィキペディア英語版 Theorem of three moments In civil engineering and structural analysis Clapeyron's theorem of three moments is a relationship among the bending moments at three consecutive supports of a horizontal beam. Let ''A,B,C'' be the three consecutive points of support, and denote by ''l'' the length of ''AB'' by $l\text{'}$ the length of ''BC'', by ''w'' and $w\text{'}$ the weight per unit of length in these segments. Then〔J. B. Wheeler: An Elementary Course of Civil Engineering, 1876, Page 118 ()〕 the bending moments $M\_A,\backslash ,\; M\_B,\backslash ,\; M\_C$ at the three points are related by: :$M\_A\; l\; +\; 2\; M\_B\; (l+l\text{'})\; +M\_C\; l\text{'}\; =\; \backslash frac\; w\; l^3\; +\; \backslash frac\; w\text{'}\; (l\text{'})^3.$ This equation can also be written as 〔(Srivastava and Gope: Strength of Materials, page 73 )〕 :$M\_A\; l\; +\; 2\; M\_B\; (l+l\text{'})\; +M\_C\; l\text{'}\; =\; \backslash frac\; +\; \backslash frac$ where ''a''1 is the area on the bending moment diagram due to vertical loads on AB, ''a''2 is the area due to loads on BC, ''x''1 is the distance from A to the center of gravity for the b.m. diagram for AB, ''x''2 is the distance from C to the c.g. for the b.m. diagram for BC. The second equation is more general as it does not require that the weight of each segment be distributed uniformly. ==Derivation of Three Moments Equations == Mohr's Theorem can be used to derive the Three Moment Theorem (TMT). 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「Theorem of three moments」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.