What version of Premiere Elements are you using and on what computer operating system is it running?
You are not talking about atypical frame sizes if you have 1920 x 1080 video.
What is the frame rate of this Fraps 1920 x 1080 and are you dealing with a progressive or interlaced frame rate?
Lots of questions customized to what you are asking
a. Where are you seeing these black borders - in the Edit area monitor before export OR in viewing exported file?
b. What is your export choice - and what are the details of the export settings? Are you using the default export
settings of the preset or are you customizing the export settings under the Advanced Button of the preset?
Bottom line: if you have 1920 x 1080 source media, 1920 x 1080 project settings, 1920 x 1080 export settings, you
should not be seeing black borders anywhere in the workflow.
Is the black border issue your only issue with your workflow? From what you wrote, it appears to be. Please confirm and
give the details requested.