It's possible to find journals, articles, and books that CTU users have access to without using links from the Library web site (for example, in Google search results or footnotes of other materials you're using).
When trying to access a resource not found through Library links, you can the login options provided by the external site to see if CTU subscribes to its content. You cannot use your CTU credentials directly in the site's login screen, however. You'll need to look for an option to log in with your organization.
The format and procedure will vary from site to site (and not all sites offer it), but these are some common ways the login option you need may appear:
Here's how to log in with your CTU credentials for the LIbrary of Catholic Thought at the Theology & Religion Online database.
Step 1: Select Log In at the top right
Step 2: Click the link to log in via the Shibboleth Login Page
Step 3: Type Catholic Theological Union in the box that says Find your Organization (and click the orange link when you see it)
Step 4: You should see this screen next and be able to log in with your CTU credentials. Contact firstname.lastname@example.org if you need help with this page.
Step 5: Look for "Access Provided By Catholic Theological Union"
When you see this, you are logged in and have access to everything that CTU users have permission to use (but note that this may not include all the content offered by the site. Most sites have the option to restrict search results to only the content you can access).