Meriam, Kraige & Bolton — Rigid Bodies: Equivalent Systems of Forces: Problem 3_57

⚡ Mecademy AIENG정역학 · ch3  Problem Statement The vertical and horizontal poles at the traffic-light assembly are erected first. Determine the additional force and moment reactions at the base caused by the addition of the three 100-lb traffic signals , , and . Report your answers as a force magnitude and a moment magnitude. Problem 3/57 (a) Additional Force Reaction at Base 1. Formula: The additional reaction force at the base must balance the sum of the added gravitational forces of the traffic signals: 2. Substitution: Each signal has a weight of acting in the negative -direction: 3. Calculation: The magnitude of the reaction force is: 4. Result: ● Final Conclusion: The addition of the three traffic signals results in an additional vertical reaction force of at the base . (b) Additional Moment Reaction at Base 1. Formula: The additional reaction moment at the base must balance the total moment produced by the signals about point : O BCD O R O R = O − F = ∑ i −(W + B W + C W ) D 100 lbz R = O −(−100k−100k−100k) lb R = O 300k lb R= = 0+0+300 222 300 lb R=300 lb 300 lbO O M O O M = O −( r × ∑ i W ) i 2. Substitution: From the diagram, defining the junction on the -axis at height , the position vectors and weight forces are: The total external moment from the signals is: 3. Calculation: Using cross product rules (, , ): The reaction moment is . The magnitude is: 4. Result: (to three significant figures) ● Final Conclusion: The additional moment reaction at the base has a magni