(A description of the measurements and results follows now; however, if you are just interested in results and implications, skip down to the "Conclusion" section.)
Let us first consider the forces that are relevant in the Lego Technic world. For most practical matters, we can assume that the beams are always strong enough when under compression or tension ("pushed and pulled"). It is usually bending that causes troubles, and that is what we will measure. Arguably, torsion (twisting) can play a role too, but let's keep that for the future posts. ☻
There are many methods to measure resistence to bending, and one of the simplest is to construct a simple bridge with a desired beam, push it down in the center with a known force, and measure the resulting descent.
|15L studless, and 16L studded beams - the mainstays of Technic constructions.|
In this case, two beams that are roughly equivalent were used for comparison - 16L studded, and 15L studless. The force applied on their center was 25 N (approx. the gravitational force of an object weighing 2.5 kg or 5.5 lbs), but as the aim of the experiment is to measure relative strength rather than absolute units, its amount is not that important as long as it is equal in all measurements.
Since the beams aren't symmetric in this case due to their axle holes, there is an important difference between resistances to bending from the side (along the same axis as the axle holes), and in the vertical axis. As many Technic builders already know, beams are significantly stronger vertically.
|Horizontal (top) and vertical (bottom) force application. Due to the construction of Technic beams, they will not yield same results.|
So, let's get down to measurements ― firstly with bending in the vertical plane (i.e. the force applied to the top of the brick). The studded 16L beam's center descended 0.8 mm, while the 15L studless did 1.5 mm. Studded is almost twice as strong! Applied to the side of the beams, the beams are, as expected, slightly weaker: the studded 16L's center descended 1.5 mm, while the amount for studless 15L was 2.5 mm. This time, the studless did not lose that heavily, which can be explained by the studded beams being taller but not wider than studless, however studless is still 67% weaker.
Let's add their weights into the account. A studded beam weighs 4.1 g, and a studless 3.1 g. Therefore, the latter is only 24% lighter than the former, much less than the difference in strength. Therefore, we can conclude that the studless beams, besides less strength, have a lower strength-to-weight ratio, too. Of course, our constructions do not consist of beams only, but they have an importantly high weight portion.
That's about the beams alone; however, beam connectors need to be taken in account as well, as the larger constructions depend on them too. So another batch of measurements was done, using two beams of various lengths, connected to form a total 16L size with different connectors, for easier comparison to the earlier results. Only the vertical measurements make sense here, as the horizontal disconnect the beams easily ― this problem has to be overcome with the construction itself in the model.
The first one consists of two 10L studded beams (having a 4L joint section), connected with two friction pins. Its descent amounts to 4 mm, suggesting that strength drops rapidly with small joints ― in this case, five times!
|Increasing the connection width dramatically increases overall strength.|
However, increasing the joint section helps significantly; two 12L studded beams with a section of 8L and four friction pins descended only 0.7 mm, providing even more strength than the full 16L beam! Reducing the number of pins of the latter configuration did a noticeable difference ― removing the inner two pins increased descent to 1.5 mm: half the strength, and in total, just like the 15L studless beam.
|It helps strength to keep the inner pins within the connected sections.|
Replacing the two remaining friction pins with the frictionless pins or a pair of 4L axles with bushings at the ends added further 0.2 mm to the descent: not a drama, but if you can choose, prefer friction pins to other methods whenever possible.
|Frictionless pins and axles are slightly weaker connectors than friction pins.|
▪▪ CONCLUSIONS ▪▪
▪ Studded beams are almost double as strong vertically and about two thirds stronger horizontally than the studless beams, despite being only a third heavier.
▪ Beam connections affect the total strength more widely than the differences between studded and studless.
▪ Widely and strongly joined beams (e.g. 8L, with 4 friction pins) do not reduce strength, but could even increase it.
▪ When connecting the beams widely, increasing the density of pins (as opposed to just the pins in the outermost holes) increases the strength, too.
▪ Narrow beam connections (e.g. 4L, with two friction pins) reduce overall strength several times, making the question whether it's the matter of studded or studless beams less important.
▪ Friction pins are better connectors than frictionless and axles, but the choice of pins is less important for general strength than the width of the beam connections and the type of beams themselves.
Hope you will find this useful!