I believe most of the eyeglasses won't get broken when you first put them on unless you get them from individual on the street. Most online optical stores offer cheap glasses with good quality. You can search them on your own in the web broswer, like google. Generally speaking, the online optical stores on the first web page are reliable and have high reputation. Try cheapglasses123.com or selectspecs.com which offer nice cheap eyeglasses with good quality. Good luck!
Just search cheap glasses in Google and they will comes out some famous online glasses shop. You can look it one by one and search reviews about these glasses shop. Those reviews will help you judge which online shop are reputable and reliable. And i heard that coastalcontacts.com is a reliable shop for buying good quality eyeglasses and firmoo.com is a good site for cheap glasses with good quality.