Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_176

⚡ Mecademy AIENG정역학 · ch5  Problem Statement The fresh-water side of a concrete dam has the shape of a vertical parabola with vertex at A. Determine the position of the base point B through which acts the resultant force of the water against the dam face C. Problem 5/176 (a) Determination of the Parabola Equation 1. Formula: Let the coordinate system have its origin at the bottom-left corner of the dam. Since the parabola has its vertex at and its shape in the diagram suggests a horizontal axis of symmetry (steeper at the bottom), the equation is of the form: 2. Substitution: From the diagram, point is at a height of from the base, so and . The top of the curved face is at the water surface, which is from the base. The horizontal distance from the vertical line through to this top point is . Thus, the top point is . 3. Calculation: 4. Result: The equation of the curved face is for . ● Final Conclusion: The parabolic face is defined by the relation in meters. b O(0,0) A x=k(y−y ) A 2 A6 m y = A 6 mx = A 0C 36 mA 27 m(27,36) 27=k(36−6) 2 27=k(30) 2 27=900k k= = 900 27 0.03 m −1 Cx=0.03(y−6) 2 6≤y≤36 x=0.03(y−6) 2 (b) Calculation of the Resultant Water Force Components 1. Formula: The horizontal force is the hydrostatic force on the vertical projection of the curved face: . The vertical force is the weight of the water column directly above the curved face: . 2. Substitution: Using specific weight of water , , , and . 3. Calculation: Horizontal Force: Vertical Force: 4. Result: