I would like to build a web scraper for a list of scientific papers libraries, what are the legal limits? I am a researcher, and I would like to scrape a list of scientific libraries sites such as Springerlink.com, ScienceDirect.com, IEEExplore digital library and so on, to analyse them for some purpose. In this task I'm interested in abstracts, and full text of publicly accessible papers, I would like to know the legal framework of this, since that I read before (but I don't remember where and how to find it again) that this is illegal, and if I do that any new request from my IP address to those sites will be rejected. It means that this task will be considered as a Denial of service attack.

To what extent this is true?
I am not a lawyer. This is a legal question. Get proper legal advice.
The legal framework is contract law, and intellectual property law. There may also be implications for other parts of the legal code if your scraping behaves like, or could be interpreted as, a denial-of-service attack or hacking.
Read each site's terms and conditions. Understand the contract of use for each site. Interpret each contract within the legal context of the contract's jurisdiction.
Take into account intellectual property law within your own country, and the publisher's country. You might also need to consider intellectual property law within the country where the web-server is located, too.
Do bear in mind that there have been recent attempts across several jurisdictions  to bring intellectual property within criminal, rather than civil law / contracts.
I am not a lawyer. This is a legal question. Get proper legal advice.