Cannot open database “user_auth.mdf” requested by the login. The login failed. Login failed for user 'web_user'
If you created the database using SSMS, you should use the logical database name and not the file with the .mdf extension in your connection string.

Use 

Server=XYZ;Database=user_auth;User ID=web_user;Password=web_user 


for your connection string and let SQL Server worry about the file-related details.