Consider the situation in which a piece of cord is looped over a pulley and both free ends are fixed to an object which exerts a 10 kN downward force.
Would the setup hold given a cord with a tensile breaking strength of 8 kN? My instinct says no, due to the fact that the portion of the rope going over the pulley is subjected to the full 10 kN force. This can be depicted easier with two pulleys side by side.
I ask because in rock climbing, a common method for building an anchor involves a loop of cord tied as depicted below. The top 3 carabiners are clipped to fixed points on the rock (bolts, camming devices, etc.) and the climbers then attach to the bottom "master point" below the figure-8 knot.
As you can see, each of the 3 "legs" of the anchor are an example of this pulley problem. I am concerned because in the climbing community, it is accepted as common knowledge that each of the 3 legs will be able to hold twice the rating of the cord (ignoring strength loss due to the figure-8 knot) due the two strands sharing the load.
Is this really the case? Or are the legs only capable of supporting up to the single strand tensile strength rating as I suspect?
I am interested in answers concerning both "perfect" frictionless pulleys as well as how a real world pulley (like a carabiner) would affect the outcome.