If you want to have the possibility to create expenses not only for a particular user but also for projects, set it in the security items. Click on the Plus button in your Tabs bar.
In All Tabs list click Security Items tab.
Find project_only_expenses on the security items list. If it is set to Yes, during expense creation user will see checkbox which give him possibility to add this expense as a project's expense.
If you want to change you can double click on the Access letter Y or N and change it.
You can also set the possibility to add expenses to public projects for a specific profile group by setting the security item 'can see public projects' to Yes. That will allow people with a specific profile to report expenses not only to projects to which they are added as participants but also to public projects on which they are not added.