I'm pasting this from the last time I answered it, so pardon the tone if it comes across wrong:
I'm a local and travel to DC all the time.
The city-based restrictions prohibition carry of any knife with a blade longer than 3" with intent to use unlawfully against another. However, DC cops are notoriously thick and often simply presume unlawful intent based on size alone in combination with whatever you did to piss them off enough to search you in the first place.
The law can be found here:
http://dccode.org/simple/sections/22-4514.html
Sometimes knife carry in DC becomes impractical for other reasons. Not only museums, but any federal building is likely to have security checkpoints and often metal detectors. These locations may limit you to a knife with a blade 2.5" or less (federal buildings) or may prohibit all sharp instruments entirely. Most of the public museums do not subject you to an intensive search though, and merely search your bag by hand. But it's hard to say which will do what, and procedure is subject to change. For example, Air & Space has metal detectors: they are not being used most of the time, but if the gov is on "alert" that weekend, they might decide to use them. So if you really don't want a hassle, it might be better to just leave all knives at the hotel/house.
Here's an additional pointer to relieve you of some hassles. Most museums do a visual bag check, which means they just have you unzip all the pockets and they poke them with a stick. Some even force you to check your bag at coat-check, like one of the art galleries. But the loophole is these particular guards at locations with no metal detectors are not allowed to check your physical body or any garment you are wearing (unless they see an item in plain site or you are already being arrested). So I wear a photographer's vest loaded with pockets. It is hilarious when my wife gets her little pink purse rooted through and they just wave me in my vest past. I don't actually carry any weapons in; it's just the principle of the thing; I dislike having my privacy invaded and the search are moronic, unnecessary and ineffectual. Plus I don't have to wait in line for the check in some cases.