Typically a framework is released by a team experienced in building a type of application to give other less experienced developers a head start. If you are less experienced, then building a framework is probably not the best place to start.
For instance, A team that builds web applications might release their codebase as a framework (krakenjs, rails, django, etc..). A team that designs web sites might release their sass/less base as a framework (bootstrap, foundation). Building a framework without first building real applications is just putting the cart before the horse IMO.
"David Heinemeier Hansson extracted Ruby on Rails from his work on
Basecamp, a project management tool by 37signals (now a web
application company)." - http://en.wikipedia.org/wiki/Ruby_on_rails#History
"Django grew organically from real-world applications written by a Web development team in > Lawrence, Kansas, USA" - http://www.djangobook.com/en/2.0/chapter01.html#django-s-history
It would be more beneficial to build real applications, possibly using existing frameworks, then if you are successful, release the base of those projects as a new framework, or an extension to an existing one.
In contrast to frameworks, OOP is a more general programming approach that is used across many application types. You could have an OOP business module, an OOP GUI, etc...
For some references, see a list of books here: http://www.island-data.com/bookreviews/oobooks.html Then try to model small applications, for example if you are into animals, you could start with the classic Animal/Dog/Cat (http://www.inf.ed.ac.uk/teaching/courses/inf1/op/Lectures/pub/07-poly.handout-2x2.pdf), building your way to the PetStore. Choose whatever type of application keeps your interest and start building.
Just keep in mind that the web application, and your application, are probably separate concerns, and sometimes frameworks will actually sacrifice OOP design to get a web application up quickly, so be careful commingling the two.