Meriam, Kraige & Bolton — Statics of Particles: Problem 2_73

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/73 Determine the equivalent force–couple system at the origin O for each of the three cases of forces being applied along the edges of a regular hexagon of width d. If the resultant can be so expressed, replace this force–couple system with a single force. Problem 2/73 Geometric Analysis of the Regular Hexagon For a regular hexagon of width (distance between opposite parallel sides): The side length is given by . The distance from the center to the midpoint of any side is . In the provided coordinate system, we assume the hexagon has two vertical sides at . The -axis passes through the top and bottom vertices. The unit vectors for forces directed counter-clockwise (CCW) along each side are: Top-Right slanted (): Top-Left slanted (): Left vertical (): Bottom-Left slanted (): Bottom-Right slanted (): Right vertical (): Each force acting along a side has a perpendicular lever arm of from the origin . A CCW force produces a moment . (a) Four forces on slanted edges ● Calculation Process 1. Determine Resultant Force : The forces are applied to the four slanted edges: Top- Right, Top-Left, Bottom-Left, and Bottom-Right. Assuming all arrows are in the CCW d ss= 3 d Oh= 2 d x= ± 2 d y S TR u = TR − i+ 2 3 j 2 1 S TL u = TL − i− 2 3 j 2 1 S L u = L 0i−1j S BL u = BL i− 2 3 j 2 1 S BR u = BR i+ 2 3 j 2 1 S R u = R 0i+1j Fh= 2 d O M=F⋅ 2 d R sense: 2. Determine Resultant Moment : Since all four forces are in the CCW sense, their moments ab