DavidW is correct regarding “The Roads Must Roll.” Asimov has stated repeatedly that he borrowed the idea from Heinlein. So you will probably find additional information in that story.
Asimov himself didn’t provide a detailed technical description how the strips and Expressways work. He discussed them in an editorial where he acknowledged that there are (unanswered) questions, and stated that it’s not necessary for an author to provide “engineering specifications.”
I, myself, in my robot novels have continually
running “Expressways”—a sort of perpetual railroad with an infinite number of never-ending coaches. In order to get on, people have to move up a series of strips, each moving parallel to the Expressway at a faster speed than the one before. Eventually, you get to the final strip which is moving at the speed of the Expressway. When you get to that strip, the Expressway is standing still relative to you and you simply get on. In getting off, you simply reverse the procedure. (I got the idea from Robert Heinlein’s “The Roads Must Roll,” so don’t bother writing to tell me that I did.[…])
In any case it wasn’t enough just to have the Expressways. A whole litany of questions arises. How do children use the “strips”? What about old people who are no longer entirely ambulatory, and what about wheelchair cases? What happens to the wind effect as you move up the strip? After all, each strip may travel slowly compared to the one before, but the speed relative to the atmosphere goes up as you move on. What about the noise of a continuous train? Doesn’t that drive people in the area crazy?
The reader is sufficiently interested in the story (I can hope) not to require very much explanation, but if you don’t explain at all then he is quite likely to think of such things and, assuming that you don’t, he will become irritated. If, however, you indicate that you are aware of such problems, you don’t have to give blueprints and engineering specifications. A few comments and the reader is satisfied.
From the editorial Surprise, Isaac Asimov’s Science Fiction Magazine, September 1988
You might find additional (non-canon) information in the short story “Strip-Runner” by Pamela Sargent, which is an homage to The Caves of Steel.