Static Triple Vector Load Calculator

AI Thread Summary
The discussion revolves around calculating the load on three lines (A, B, C) supporting a static weight (W) at different angles in both the x-y and z-planes. The user has successfully applied trigonometry for a two-rope system but struggles with the complexity of a three-rope setup. They are attempting to solve the problem using simultaneous vector equations but are encountering difficulties. The key equations for static equilibrium are presented, indicating that the sum of the vector components must equal zero in the horizontal plane and equal the weight in the vertical plane. Assistance is sought in resolving the calculations or visualizing the system for better understanding.
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Hi All,

I've been trying to figure out how to get this formula working for a few days now, and I *refuse* to give up.

There are three high points, with a line running down from each to a load W.
Each of the lines A,B,C are at different angles to each other (x-y plane), and each of the lines depart the load to the high points at different angles (z-plane).
The load is static, and there is no stretch or movement in the system.

By knowing only the angles of the lines and the weight of the load, how can I calculate the load on each line?


I have calculated this for a two rope system and it is simple trig, but for a three rope system I cannot seem to get it happening!
I've tried solving using trigonometry, but I keep getting stuck. Today I've been trying to solve simultaneous vectors, but I still can't seem to get it right.

If anyone has any clues, or could help I would greatly appreciate it.
I can also draw up a picture to show the system, if that helps.
 
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Some extra information that I've been trying to use for simultaneously solving is this;

If Vectors:
A=[Ai, Aj, Ak]
B=[Bi, Bj, Bk]
C=[Ci, Cj, Ck]


Then for the system to be static:
Ai + Bi + Ci = 0
Aj + Bj + Cj = 0
Ak + Bk + Ck = W
 
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