I'm attempting to set up the TRX in my house and wanted to know your opinion about my strategy for making a secure anchoring point. I inserted a sturdy hook on a support beam and clipped in a carabeener to it. Do you think it's safe enough to attach the suspension anchor to that carabeener? The hook is rated at over 250lbs. Let me know what you think.

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It's all relative to what you consider secure.  I have mine wrapped around a 4x4 support column where it meets the rafters in my garage and it works great, granted it's also designed to support the weight of a house so I'm pretty sure it'll work for all of my 170LB.  When you start dealing with ancillary attachments such as hooks and whatnot, you are creating another variable to the equation which can become a liability to your safety if you're not careful.  Even though your hook is designed to hold 250LB, a botched install or a poor mounting point on an aging rafter will quickly bring trouble.

I haven’t studied physics in years, so I might be explaining the following incorrectly.  I believe the weight of your body equates to the mass of your body multiplied by the acceleration of gravity.  I’m sure doing some atomic crunches won’t produce lots of load on your mount, however I would imagine something like the inertia of your body weight in the downward acceleration of a back extension will produce a load that has the potential to exceed your hook’s load capacity.  Imagine jumping up and down on a scale.

Having said that, I’m not really sure anybody on a forum can say for certain if your install is safe or not.  The idea sounds very doable, just make sure you use common sense and be careful as you are entrusting the weight of your body on it. 

Fitness Anywhere actually sells anchoring solutions for just such a problem. I weigh 220lbs and love my X-Mount. 

I have a large eye bolt in my training room that I have a TRX suspended from in exactly the way you describe. I am not sure what it was rated to but i stress tested it by adjusting the TRX so that I could hang by entire body weight off of it so that I was just a few inches off the ground over a mat. I proceeded to shock load it repeatedly and the hook didn't budge.

Most TRX exercises use only a percentage of your body weight so I felt that by shock loading it with my full weight I was stressing it significantly greater than I will when I train. To date it still is working fine.

If you are concerned there are a few ways to put something up that will be bomb proof.

1) Buy the "X" mount available on the website that is designed specifically for this. This is your best alternative.

If you are feeling more "do it yourselfy" there are a couple of other options

2) If your beam is exposed drill a hole through it and use a "U" bolt or thread chain or 7mm climbing cord through it to provide you with an anchor point to clip into.

3) Screw in an additional eye bolt to back up the first and equalize them using chain or 7 mm climbing cord that you can get at REI.

As I said I think that you will be fine but there are some other alternatives for you.