I have a connection in Washington, DC and did not check any of my luggage when I checked in.
At Frankfurt of course. First you clear immigration, then you walk through the baggage claim area and enter the customs area, picking the green or red lane depending on whether you have anything to declare (green if you don't, red if you do)
As you are arriving from outside the EU, you will land at Frankfurt, follow the queues to immigration control - then walk past the luggage carousels (as you don't have any checked in luggage), and then go through either the green (nothing to declare) or the red (goods to declare) lanes of customs before you can exit the terminal.
It does not matter if you have checked-in luggage or not, everyone always goes through immigration and customs.