The is a lot of dereference between windows Authentication and FBA Authentication .If you have done the project in classic Authentication and want to convert it into Claims in the middle of the project then you open the SharePoint 2010 powershell command as administratior and run the below command
$ConvertApp=get-spwebapplication "URl"
$ConvertApp.useclaimsauthentication="True"
$ConvertApp.Update()
