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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 Direct integration of a beam ： ウィキペディア英語版 Direct integration of a beam Direct integration is a structural analysis method for measuring internal shear, internal moment, rotation, and deflection of a beam. For a beam with an applied weight $w(x)$, taking downward to be positive, the internal shear force is given by taking the negative integral of the weight: : $V(x)\; =\; -\backslash int\; w(x)\backslash ,\; dx$ The internal moment M(x) is the integral of the internal shear: : $M(x)\; =\; \backslash int\; V(x)\backslash ,\; dx$ = $-\backslash int\; (w(x)\backslash \; \backslash ,\; dx)\; dx$ The angle of rotation from the horizontal, $\backslash theta$, is the integral of the internal moment divided by the product of the Young's modulus and the area moment of inertia: : $\backslash theta\; (x)\; =\; \backslash frac\; \backslash int\; M(x)\backslash ,\; dx$ Integrating the angle of rotation obtains the vertical displacement $\backslash nu$: : $\backslash nu\; (x)\; =\; \backslash int\; \backslash theta\; (x)\; dx$ ==Integrating== Each time an integration is carried out, a constant of integration needs to be obtained. These constants are determined by using either the forces at supports, or at free ends. : For internal shear and moment, the constants can be found by analyzing the beam's free body diagram. : For rotation and displacement, the constants are found using conditions dependent on the type of supports. For a cantilever beam, the fixed support has zero rotation and zero displacement. For a beam supported by a pin and roller, both the supports have zero displacement. 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「Direct integration of a beam」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.