Re: So where do you run them?
Wow, where to begin.
First, ideal physics: Statics & Mechanics and all of that stuff. No friction, no material propeties, just idealized concepts that many engineers forget about until it bites them in the posterior. Let's look at an example that might help explain your pulley/strap problem. First find a 10 ft piece of rope and a friend. ( WARNING: No nooses please /w3tcompact/icons/laugh.gif) Now you and your friend start playing tug-of-war. Assume neither of you are winning. The two of you are now exerting a certain amount of force on the rope that is equally to the sum of the forces that each of you are applying. Now assume a sumo wrestler also wants to get into the act, but being from Japan he doesn't know how to play tug-of-war. He grabs the rope in the middle and starts to pull from the middle. He eventual pulls the both of you until you and your friend are side-by-side. At this point, your combined force directly oppose him and causes a stalemate. The force he exerts is equal to the sum of each of the forces that each of you are applying. Assuming his hands are frictionless, I'm sorry but it is required, then there is no change in force on the rope.
Example #2. O.K. The sumo wrestler's hands aren't really frictionless, so what does this mean. If his grip is strong enough, he basically turns the rope into seperate pieces by acting as a clamp. Now each section of rope is independent and only has the force applied by you OR your friend. The sumo wrestler still feels the force exerted by the both of you.
Real Physics: Material Properties & Safety Factors. Pen & Paper exercises get replaced by experimental testing and computer simulations. I'm on travel and I will be guessing at the following numbers. I think high tensile steel has yield strength of 70,000 lbs per square inch, and 1/2" grade 70 chain has a strength of approximately 7000 lbs. A 1/2" chain is about 1/3" square inches. So, divide 70,000 by 3 to get about 23000lbs. So why isn't the chain rated for 23,000lbs? A chain isn't a straight piece of material. It is bent and welded together to form a closed loop. A chain will normally break at the point of maximum curvature normally at the 1/4 and 3/4 positions. The bending of the steel creates residual stress and strain. The weld is also a high stress area. So I would assume that experimental testing probably resulted in chains break somewhere between 10,000 and 14,000lbs. Now to keep people alive, and the lawyers at bay, a safety margins between 1.25 and 2.0 depending on the industry, customer, and/or application are applied to lower the chain's rated strength to 7,000lbs. Any manufacturer's specification whether it's a chain or even a complex item like a FEL, basically says that barring any manufacturer's defect, for example: bad steel or weld, the item will perform with failing. That's why guys sometimes notice that their equipment is stronger than advertised. They are just taking it to the edge, where failure is much more likely.
Now my head hurts. /w3tcompact/icons/crazy.gif
