Here is a typical block up elevator machine arrangement with car and counterweight. The car is supported by cables that run over the driving machine sheave, onto a deflector sheave (frictionless) and then down to the counterweight. I am trying to find the most accurate way to analyze the reaction forces at the base of the block up assembly (red) acting on the supporting beam (blue). Obviously the car and counterweight cause tension in the cables that travel over both sheaves - where should this tension be applied? A coworker says I can simply idealize the cable tension as a point load directly on the blue beam at the locations they pass the supporting beam.

My instinct says this isnt the proper way to analyze this. I think I need to start by figuring out the reaction forces of the machine and deflector sheave onto the red beam they are both mounted to. However, I run into the problem that the cable tension is unequal from the car side to the counterweight side. I believe the cable tension on either side of the deflector sheave is equal, but the angle of the rope causes a force downward and towards the drive sheave on the deflector. How should I be analyzing the drive sheave? Am I overthinking this?

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