I have done this too!
In fact, I went to the same exact exhibit! At the Museum of Science and Industry. I went there at least twice. I’m a big Titanic fan, so I had to. And it really was great to touch a “piece of history”.
How to touch a piece of the Titanic
How I did it: We went to the Titanic exhibit in Tampa and they had the largest recovered piece of the titanic on display so I reached out and touched it with my hand. I got in trouble directly after.
Lessons & tips: I wouldn't recommend doing it. I got in trouble, but it was worth it to me, I'm a huge Titanic history buff.
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I visited the Titanic exhibits at the Museum of Science & Industry in Chicago. The exhibit stopped there twice. They had a 13-ton piece of the hull supported in literally a shallow sandbox, with no one guarding it. I wanted so badly to touch it that I almost stepped into the stand and did it. A year and a half later, we visited the new version of the exhibit, which had added more artifacts. I would have gone into the sand and touched it that time, but instead they had a piece of the hull in a box with a small hole in the top that you could reach in and touch. It was neat to touch a piece of history.

