Meriam, Kraige & Bolton — Rigid Bodies: Equivalent Systems of Forces: Problem 3_83

⚡ Mecademy AIENG정역학 · ch3  Problem Statement The vertical plane containing the utility cable turns 30° at the vertical pole . The tensions and are both 950 N. In order to prevent long-term leaning of the pole, guy wires and are utilized. If the two guy wires are adjusted so as to carry equal tensions which together reduce the moment at to zero, determine the net horizontal reaction at . Determine the required value of . Neglect the weight of the pole. Given Dimensions: , , , , . The utility cable segments have a sag angle of below the horizontal. The line of the guy wires on the ground makes a angle with the -axis. Problem 3/83 (a) Required value of tension in the guy wires 1. Formula: The total moment about the base must be zero for equilibrium: where is the moment from utility cable tensions and is the moment from guy wire tensions. 2. Substitution: First, find the horizontal resultant of the utility cables . Since the cable "turns" , the angle between the two tension vectors (pulling away from the pole) is . The utility moment magnitude is: The guy wire moment magnitude is the sum of moments from and : OC T 1 T 2 AD BET OO T OA=9 mOB=11 mOC=13 mOD=8 mOE= 10 m10 ∘ 15 ∘ x T O M = ∑ O M + OT M= Og 0 M OT T ,T 12 M Og F Uh 30 ∘ 180− ∘ 30= ∘ 150 ∘ F = Uh 2T cos(10)sin(30/2)= cable ∘∘ 2(950)cos(10)sin(15) ∘∘ M = UT OC⋅F = Uh 13⋅[2⋅950cos(10)sin(15)] ∘∘ M Og ADBE M = Og TOA +OB ( OD+OA 22 OD OE+OB 22 OE ) Substituting given values: 3. Calculation: Coefficient for guy wires: Sett