Which LEGO joins are the strongest?

A first grader’s first science fair project

6 min readFeb 12, 2020

Broken LEGO creations are frustrating. It makes my LEGO-obsessed kid sad. How can he make his creations stronger? Can we identify the joins that are the strongest, or less likely to break when dropped from the height of a 7-year old’s hands?

For my son’s first science fair project, we sought to test the drop strengths of different joins between two 2x4 Lego bricks. We found some answers but wound up with others. In this post I share the story, and end with a request from Miles: Can anyone on the internet comment on the experiment, or help answer the remaining questions? Miles would like social media feedback to be a part of the final presentation. UPDATE: The project has been turned in!

Miles’ beginning hypotheses

More studs connecting two bricks make for a stronger joint.

The experiment

I suggested that the orientation of the bricks at the moment of impact would affect the results but acknowledged that they would be hard to control for. We decided that to overcome the effect of orientation, we would perform multiple drops, trusting that natural variation would randomly distribute its effects across the data. Given the constraints on the…uh…attention span constraints of our science team (and the presence of a 1-year old sister complicating the laboratory space), we determined that 10 drops would be a nice balance between achievability and statistical relevance.

So, the experiment plan was this.

Identify possible joins between the most common brick type: The 2x4 brick.
Drop them from a consistent height 10 times each and record how they perform. Do they break apart or stick together?
Rank the joins in terms of performance.

Joins we tested

1-stud corner-to-corner join. This and other joins below were modeled via https://www.mecabricks.com/.

2-stud combos: The stair, the T-shape, the L-shape.

4-stud combos: The deep stair, the wide stair, the L-shape, the T-shape, and the X-shape.

Note: We realized after the experiment that there are two join types we did not test. At this point, we do not expect that testing these joins would change the results of the experiment.

The 3-stud join and the 2-stud corner-to-corner join.

Drop details

We placed a piece of tape at the 4-foot mark of a door and dropped each piece from this same height. Miles squeezed the LEGO bricks tightly together before each drop. The joined bricks fell onto a quartz-composite entryway floor and were observed for their end condition.

An example of the starting position for each drop.

Drop results

Note: Names for joins in this picture differ from names used in this post. The post names are better descriptors.

1-stud join: None survived.
2-stud stair: 1 survived. (Notes: Lucky? Wow!)
2-stud L-shape: None survived.
2-stud T-shape: None survived. (Note: Ow! Hurt foot!)
4-stud wide-stairs: 1 survived. (Notes: Sweet! [Editor: This note may reveal a bias on the part of the notetaker that the joins survive.])
4-stud deep-stairs: None survived.

4-stud L-shape: 4 survived. (Notes: What the! Wow! Amazing! Holly macaral!)
4-stud T-shape: None survived
4-stud X-shape: None survived.
6-stud stair: 9 survived. (Notes: One drop had the wrong configuration and had to be repeated.)
8-stud stack: All survived.

This made the final ranking as follows, ordered for strength.

8-stud stack.
6-stud stairs.
4-stud L-shape.
2-stud stair, 4-stud wide stair
1-stud corner, 2-stud L-shape, 2-stud T-shape, 4-stud deep stairs, 4-stud T-shape, 4-stud T-shape.

An example of one of the drops hitting the floor. And of a need to paint the interior doors.

What did we learn from this first experiment?

Our original hypothesis was confirmed. Connections with more studs are more durable and resistant to breaking when dropped. But the most interesting things we learned from the experiment were not the original hypothesis, but unexpected patterns in the results.

There is a significant break between the 4-stud joins and the 6-stud joins. Four and below were prone to break and 6 and more were prone to survive.
The stair-shaped join survived more than other configurations.
Of the 4-stud joins, the L-shape survived much more than other joins.
The data isn’t as useful as we’d hoped. The 8-stud stack, while strong, limits the ability to build larger things. The 6-stud stair is strong, but, if it was joined in a regular-pattern construction, would be adjacent to a weak 2-stud stair join, and its benefits would be limited. That led us to conduct a second experiment regarding the 4-stud joins.

An additional experiment: Why did the 4-stud corner join perform so unexpectedly well? Are there other configurations of 3 bricks that work as well?

Miles had no hypothesis for this experiment. He wanted to just see which worked the best. We identified six configurations of three bricks where the joins where the 4-stud L-shape from the prior experiment.

2-layer: stair, rotor. 3-layer: spiral, zipper, bolt, and peacock.

We used the same drop technique and tracked the results.

In this case, there weren’t two possible results to track (survive or break apart), but three.

Survive (written as a green check on the chart)
One brick broke off (written as a red 1on the chart)
All bricks broke apart (written as a red 3 on the chart)

The ranked results are as follows.

Stair: 4 successes, 5 single splits, 1 total split.
Zipper: 1 success, 3 single splits, 6 total splits.
Rotor and spiral: 1 success, 2 single splits, 7 total splits.
Peacock: 5 single splits, 5 total splits.
Bolt: 4 single splits, 6 total splits.

What did we learn from this follow-on experiment?

With the stair doing so much better than other configurations, we had a mild suspicion that the more bricks sit alongside other bricks, the stronger the configuration. (This would suggest that the rotor would perform second best, but it didn’t, so a bit of a puzzler.)

Remaining questions

Though we have a basic confirmation of the hypothesis, we were left with a few remaining questions.

What accounts for the later results? Are there known principles of construction (or, we guess, physics) that would help us understand?
If we were to do it again (and weren’t constrained by attention spans) what would be an ideal number of drops?

Then an unsettling possibility occurred to us. Are our LEGOs getting weaker as we continue to drop them in the experiment? The test we did was left to right on the paper, and as you can see, the results seemed to get worse in the same order. To do a quick test of this, we re-ran the stair configuration drops. The results were completely different. Two single splits and three total splits. It’s the second column of drop results in the column, written in purple.

How could we test this possibility?
Has prior research been done on this?

Feedback

As mentioned in the intro, Miles is eager to hear from other experts who might be able to suggest reasons for why we see the results we do. So, if you have thoughts on the experiment, would you take a few moments to comment? If you know someone who might have some insight (structural engineer, or physicist, or LEGO fanatic with experience to share) could you share this with them? Thank you!