It is a very technical tool, and it sure could use a bit more documentation for getting started, but it does what you're asking for.
You can set it up to run as a proxie and connect a browser. Then you record various sessions of typical browsing of the site you want to test and Tsung will save them in an xml format.
Based on these xml sessions you then setup a test plan for Tsung where you can define phases. The idea is to make the phases increasingly tough on the site with more and more users arriving per second.
Once you have the test plan you let Tsung loose on your servers and you will get some nice graphs and reports. If you made the later phases brutal enough you should get to see at what point the increasing traffic makes your site die and you will know wether that point is something that could realistically be reached during normal use...