This wont work with just PHP..
You can work with javascript to make a single page application.
There are many frameworks available.
Take a look at this question to see some that are available.
but you dont need a framework for this. This can also be done with pure javascript or with jquery.
I was just concerned that each time i press a link, the navigation bar will also be refreshed and wanted a way to just make things "smoother"
Here is a simple solution:
Add eventlisteners(click) to your buttons or links. In the callback make a ajax request to grab the file (or jquery load()), and fill a element with the response.