The answer is that it would burn a hole right through. In this study, beams with 100 times fewer protons, 5 times less focused, and 15 times less energy per proton than the LHC were fired at copper and stainless steel targets. They made holes.
The other painful things they talk about in this video (synchrotron radiation, extreme vacuum, etc.) are also true.
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There was an explicit study of high-energy proton beams to answer exactly this question (replacing “hand” with “expensive machine component”):
http://cdsweb.cern.ch/record/858162
The answer is that it would burn a hole right through. In this study, beams with 100 times fewer protons, 5 times less focused, and 15 times less energy per proton than the LHC were fired at copper and stainless steel targets. They made holes.
The other painful things they talk about in this video (synchrotron radiation, extreme vacuum, etc.) are also true.