Yesterday the LOC announced it is releasing it's first service on id.loc.gov which contains LCSH terms represented as RDF/XML, N-Triples and JSON.
The vocabulary is available for download, or can be searched online at http://id.loc.gov/authorities/
Here are some sample snapshots:
Search for "simple machines"
View for the topical term "Simple machines". Note you can export the term as RDF, N-Triples or JSON.
Each term has a "Visualization" tab which shows related, broader and narrower term relationships.