We've just pushed a new template to Viaduct which allows you easily deploy static websites to Viaduct. A static website is any folder which contains HTML files (plus any assets needed to serve them).
To get started, just ensure you have an index.html file in the root of your repository, and go ahead and deploy it to Viaduct in the usual way.
Static sites do not need to run any processes on our application servers and are completely powered by our front-end infrastructure. Therefore you'll only pay for the bandwidth needed to serve your application.