If you mean build your own framework... NO. There's no reason to waste time on that garbage that defeats the entire reason CSS even exists. Just build the site directly in HTML/CSS without those nitwit crutches. In HTML, CSS or JavaScript I've NEVER seen a legitimate advantage in a framework that wasn't ridiculously and absurdly outweighed by the negatives. Developers are dumber for ANY of this garbage even existing, and much like a number of other web technologies the only way I can figure anyone could see a reason to even try and use them is if you never learned to build a website properly in the first place. (Of course just a "view source" on most sites is proof enough of the ineptitude we're seeing out of this halfwit bull) Though of course with HTML 5's audience being people who never embraced strict, grasped semantics or accessibility, and instead until recently were still sleazing out HTML 3.2 and slapping 4 tranny on it -- well, I guess I shouldn't be as surprised as I am by broken, outdated, bloated methodologies that read like a laundry list on how NOT to build a website. I've never seen a framework that wasn't half assed ****, I've never seen a site built with a framework that wasn't an inaccessible train wreck of idiocy, and I do not believe it is possible to make a framework that is worth a flying purple fish. Encouraging ANYONE to use a framework is one of the worst things that can be done in terms of producing a website of any actual value!
Why would anyone even think about crap like gumby when their home page does not even validate? The validator reports 16 errors including the use of obsolete elements and structural erros. It is bad enough to load in a bunch of trash, but if they cannot even do valid code then they are nothing but crap in a marketing wrapper just like the rest of the "easy to use" trash. Easy to use is real code written by real developers and the frameworks for novices belong in in a toy store catering to hobbyists. Professional developers don't need bloated garbage and don't use trash that gets in the way of quality, accessibility, usability, and security.
What I've come to expect when I see a HTML 5 doctype, after all it is basically the new HTML 3.2! Even with valid it's usually such a bloated non-semantic wreck of run-on sentences, endless classes for nothing, failing to leverage those allegedly semantic new tags properly, and static style/scripting in the markup it's shameful; see how most such folks end up with 10k of markup doing 5k's job on the 'lightweight' side, and 100k of markup doing 10k's job on the heavy side. Again, HTML 5 is certainly not meant for anyone who actually cared about validation, 4 Strict, separation of presentation from content, semantics or any of the other two or three dozen improvements of the past ten years; 5 seems to exist ENTIRELY for redundant semantics, pissing on logical document structure, loosening the structural rules to the point of making validation pointless, and on the whole setting coding practices back to the worst of the late '90's browser wars. See the absolutely idiotic halfwit nonsense like SECTION, ARTICLE, NAV, ASIDE and FOOTER, which are redundant to numbered headings and horizontal rules if you use them properly and if UA's other than Jaws and Opera 12/lower (as opposed to the useless steaming pile of crippleware known as Chrome with the Opera logo slapped on it any-old-way) got off their asses and implemented heading navigation.
Best way to make a responsive website would be using Bootstrap. You use the components (classes) in your design and Bootstrap makes the rest. You can also use premade Bootstrap templates and themes in your web page. Find them here: http://usebootstrap.com