To create a subsite in PWA; please follow these steps.
1. Click on Site Actions.
2. Click on New Site.
3. Select the Template.
4. Enter the Title.
5. While entering the URL; please enter only the last part. So for example if you want to use http://projects.contoso.com/demo1; then please enter demo1 only.
6. Your SharePoint Site for the Project has been created.