In response to the original question it depends on whether you mean "how many BHP will make it undriveable?" or "how many BHP will break it?". Sadly the answer to both is "it depends". Undriveable is an unmeasurable concept, F1 cars are pushing 800ish BHP through rear wheels in a 600 KG chassis at 200 MPH but few of we mere mortals would be able to drive it at all.
As for how much power it will take to break it, again "it depends". How heavy will it be and rather than BHP look at the torque the chassis has to contend with. If there's lots of torque ( think of Robo's V8 beast or my own V6 Cosworth job, not massive power but serious torque) and you are using soft sticky tyres and driving it in anger on track then there is a good chance of something breaking, probably the rear diff/suspension area for a guess.
Just my humble opinion, D.
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