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For instance:

3040a - Slope 45° 2 x 1 - without Bottom Tube

and

3040b - Slope 45° 2 x 1

Are both of these always interchangeable? If not, what are the cases where you would absolutely need no bottom tubes?

10

Parts with and without bottom tubes are nearly always interchangeable in normal building scenarios.

However, there is definitely a functional difference. Not having bottom tubes generally does the following:

  • Reduces clutch power. There's one less surface for the stud to produce friction against.
  • Allows for lots of different connection points along the bottom edge rather than just at both ends. This can be useful in places where you aren't always working in whole numbers of modules. For example, here's one way that you could build a wall at 45 degrees to what you would normally build by exploiting 1x2 bricks without bottom tubes:

45 degree wall

  • 1
    Accepting this answer just because it was the first and it has the most upvotes. All entries were great additions. Thanks to all participants! – Patrice Gahide Nov 16 '15 at 22:05
4

Are both of these always interchangeable?

Yes and no. They are 100% compatible with the standard LEGO building system, but you may be able to use the bottom-tubeless elements in arrangements that wouldn't work with a standard brick, and vice-versa.

If not, what are the cases where you would absolutely need no bottom tubes?

Bottom tubes were introduced into bricks to increase support and stability. Or, as @jncraton mentioned, "clutch power". Bottom tubes have been around for awhile, but the pieces without bottom tubes have been slowly dying off.

They've almost been completely discounted as of 2002, partly for those structural reasons. In fact, only 11 sets since 2002 have used them, compared to hundreds during or before 2002.

There's one exception to the lack of use of bricks without bottom tubes: Small translucent pieces used for decoration or to represent translucent materials, such as glass and water. These translucent bricks are still in popular use, because the lack of the center tube makes them appear more clear. Over 200 sets have used such pieces since 2002, primarily for glass and water representation.

So, there, it's not required, but it looks much nicer.

3

jncraton and CreationEdge have both explained what the tubes are for and mentioned two advantages to not having them: nicer-looking clear parts, and connections that aren't aligned with the system stud grid. The main advantage to having them is the clutch power it adds: in a 2x2 brick such as the slope with no tube, each stud touches two walls, but with a tube each stud also touches the tube, so 50% more clutch.

As I explained in this comment regarding a pizza tile that had a variant element with a tube, the tube is a useful attachment point. The inside of the tube is a stud-hole so you can put a stud there, and this can be used to great effect with the right pieces. In the case of the pizza element, a minifig hand can be placed in the tube to hold the pizza centrally from underneath. Similarly bricks with tubes can be placed on half-stud offsets from other bricks using the tubes.

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