Meriam, Kraige & Bolton — Statics of Particles: Problem 2_49

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/49 The asymmetrical support arrangement is chosen for a pedestrian bridge because conditions at the right end do not permit a support tower and anchorages. During a test, the tensions in cables 2, 3, and 4 are all adjusted to the same value . If the combined moment of all four cable tensions about point is to be zero, what should be the value of the tension in cable 1? Determine the corresponding value of the compression force at resulting from the four tensions applied at . Neglect the weight of the tower. Problem 2/49 ● 1. Define the Coordinate System and Geometry We set point at the origin . Based on the provided diagram, we can determine the coordinates of the tower top and the cable anchor points and . The tower is tilted to the left of the vertical. The vertical height of above is . Coordinates of : The anchor points are on the bridge deck, which is at a height of above . Horizontal distances from the vertical line through : ● 2. Express Cable Tensions as Vectors F T OT 1 PO A O(0,0) AB,C,D,E OA5 ∘ AO H=16 ft+50 ft=66 ft A x = A −Htan5= ∘ −66tan5≈ ∘ −5.7743 ft y = A 66 ft 16 ftO y = B y = C y = D y = E 16 ft O x = B −22 ft x = C 30 ft x = D 30+35=65 ft x = E 65+35=100 ft The force exerted by each cable on point is , where is the unit vector from toward the anchor point . Cable 1 (A to B): Cable 2 (A to C): Cable 3 (A to D): Cable 4 (A to E): ● 3. Solve for using Moment Equilibrium The total moment about point must be zero.