Full backups do not truncate transaction logs. If you're in full or bulk logged recovery modes, only a log backup will truncate teh transaction log and make the space available.

Since you're in simple recovery, the transaction log should be truncated at chackpoints, but that doesn't mean that the file on disk shrinks, only that the space within the tran log is made available for reuse.

If you're not seeing that then something is preventing the removal of old log records. See what the value of Log_Reuse_Wait_desc is in sys.databases for that database.