strictfather I already excuse myself for the langauge.
Honestly even if you put her in one and she doesn't go on a rampage and destroy your and your wife's lives, it isn't guaranteed that it will even remotely solve the problem. It might even make everything worse.
"We asked her if there was some problem, if me and my wife could help her. "
Has it come to your mind that she might be in a problem so massive that she cannot talk about it with you?
You were these situations yourself, you or someone else fucked up and somthing went horribly wrong. now you got the mess on your hands but you cannot tell anyone because either you are too afraid or to proud to do so. I can think about a million situations a young girl in her age could have gotten herself into.
There are reasons why there are psychologists, that specialise in treating minors and teenagers, they have special methodes they can use to earn their trust. I strongly suggest you hire such a person to figure out what is wrong with her, especially before you put a belt on her. It might safe your relationship and her life.
Also why the hell a belt? If she is such a rebel she will figure out that it will take minutes to lockpick it or seconds to cut it open. The only way you can prevent her from doing such a thing, is my making her a Belt that cannot be open'd once locked, but that isn't really possible for various reasons.