a redditor's dilemma
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A Redditor’s Dilemma
How many Legos, stacked on top of the other, would it take to destroy the bottom brick?
Shortbushero
Science_man_29
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Experimental Setup
• 15 2x4 yellow Legos were bought from bricklink.com andweighed on an analytical balance and their dimensionsmeasured with calipers without any modification.
• Three of the Legos were chosen at random and their nubswere removed via a metal file.
• Compression tests were performed on an Instron 5567 with a50kN test cell.
• Acoustic emission tests measured with a Physical AcousticsPCI – 2 sensor, with the sensor attached to the front side of the top compression platen.
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Experimental Data – Dimensions and Mass
Dimensions -
Length: 31.79 mm
Width: 15.77 mm
Height (with nubs): 11.41 mm
Height (w/o nubs): 9.54 mm
Tolerance: 0.01 mm
Mass -
Highest: 2.2715 g
Lowest: 2.2492 g
Range: 0.0223 g
Average : 2.2576 g
St. Dev : 0.0077 g
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Experimental Results - Compression
02
4
6
8
1012
14
16
18
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
S t r e s s ( M P
a )
Strain (mm/mm)
Compressive Test - 0.1 mm/min
E1
E2
σy
Plastic deformation region
E1 = 192.997 MPa
E2 = 245.973 MPa
σy = 15.841 MPa
Max. Load = 7942 N
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Experimental Results - Compression
0
2
4
6
8
1012
14
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20
0 0.1 0.2 0.3 0.4 0.5
S t r e s s ( M
P a )
Strain (mm/mm)
Compressive Test - 1.5 mm/min
E1 = 280.34 MPa
E2 = 400.69 MPa
σy = 18.363 MPa
Max. Load = 9206 N
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Experimental Results - Compression
0
2
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1012
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0 0.1 0.2 0.3 0.4 0.5 0.6
S t r e s s ( M P a )
Strain (mm/mm)
Compressive Test - 2 mm/min
E1 = 279.75 MPa
E2 = 387.95 MPa
σy = 18.45 MPa
Max. Load = 9248 N
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Experimental Results - Compression
02
4
6
8
1012
14
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18
20
0 0.1 0.2 0.3 0.4
A x i s T i t
l e
Strain (mm/mm)
Compressive Test - 3 mm/min
E1 = 257.42 MPa
E2 = 348.30 MPa
σy = 18.19 MPa
Max. Load = 9120 N
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Experimental Results - Compression
0
2
4
6
8
1012
14
16
18
20
0 0.1 0.2 0.3 0.4 0.5
S t r e s s ( M
P a )
Strain (mm/mm)
Compressive Test - 5 mm/min
E1 = 238.78 MPa
E2 = 338.68 MPa
σy = 18.92 MPa
Max. Load = 9489 N
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Experimental Results - Compression
0
2
4
6
8
1012
14
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18
20
0 0.1 0.2 0.3 0.4 0.5 0.6
S t r e s s ( M P a )
Strain (mm/mm)
Compressive Test (nubless) - 1 mm/min
E1 = 394.14 MPaσy = 18.77 MPa
Max. Load = 9410 N
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Experimental Results - Compression
02
4
6
8
1012
14
16
18
20
0 0.1 0.2 0.3 0.4
S t r e s s ( M
P a )
Strain (mm/mm)
Compressive Test (nubless) - 3 mm/min
E1 = 417.44 MPaσy = 19.31 MPa
Max. Load = 9679 N
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Experimental Results - Compression
0
5
10
15
20
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
S t r e s s ( M
P a )
Strain (mm/mm)
Compressive Test (nubless) - 5 mm/min
E1 = 445.01 MPaσy = 20.06 MPa
Max. Load = 10058.2 N
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0
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02
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0 0.1 0.2 0.3 0.4 A m p
l i t u d e o f E m i s s i o n ( d B )
S t r e s s ( M P a )
Strain (mm/mm)
Acoustic Emission - 1 mm/min
Experimental Results – Compression with
Acoustic Emission
Elastic to plastictransition.
σy = 17.844 MPa
Max. Load = 8941 N
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010
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02
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1012
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0 0.1 0.2 0.3 0.4 0.5 A m p l i t u d e o f E m i s s i o n ( d B )
S t r e s s ( M P a )
Strain (mm/mm)
Acoustic Emission - 2 mm/min
Experimental Results – Compression with
Acoustic Emission
σy = 17.835 MPa
Max. Load = 8941 N
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Experimental Results – A Comparison
y = 400.92ln(x) + 8886.2R² = 0.9451
7500
8000
8500
9000
9500
10000
10500
0 1 2 3 4 5
M a x L o a d ( N
)
Compression Rate (mm/min)
Compression Rate vs. Max. Load
Normal Legos
Nubless Legos
~13% increase!
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Experimental Results – Qualitative Analysis
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Conclusions – How many Legos?
Compression Rate Legos Height (mi)
0.1 mm/min 358,602 (±1,227) 2.148 (±.007)
1.0 mm/min 407,163 (±1,393) 2.421 (±.008)
1.5 mm/min 415,674 (±1,422) 2.472 (±.008)
2.0 mm/min 417,582 (±1,429) 2.483 (±.008)
3.0 mm/min 411,803 (±1,409) 2.449 (±.008)
5.0 mm/min 428,467 (±1,466) 2.547 (±.009)
1.0 mm/min* 424,903 (±1,454) 2.527 (±.009)
3.0 mm/min* 437,039 (±1,495) 2.599 (±.009)
5.0 mm/min* 454,159 (±1,554) 2.701 (±.009)**
* - Denotes nubless legos
** - Mt. Everest is 5.49 miles at its tallest height
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Conclusions – Notable Points
Structural Integrity
• One can determine the relative density of a Lego
given its volume and mass. When done so, Legos
have 41.33% the density of acrylonitrile
butadiene styrene (ABS), yet they have
• 17.81% of ABS’ Young’s modulus
• 45.95% of ABS’ yield strength
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Conclusions – Failure Analysis
• Under high load, the weakest points on a Lego
are the sidewalls, which bulge outwards.
• Center, cylindrical supports are not affected
and remain (relatively) unchanged in
comparison to sidewalls.
• To reinforce Legos , add support “beams” from
center cylinder to outside walls. (See right)
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Summary
• One can stack upwards of 454,000 Legos on top of one
another until the bottom one breaks.
• This result is highly dependant on compression rate, and
follows a log scale.
• Nubless Lego can support ~13% more weight than their
normal counterparts. This provides a more realistic answer,
as Legos stack platen-on-platen rather than nub-on-nub.
• Although its high toughness and hardness make it attractive
as use for housing materials, its high thermal conductivity
and high flammability ultimately makes it unsafe.