A Redditor's Dilemma

8/4/2019 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



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.



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



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




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 - 1.5 mm/min

E1 = 280.34 MPa

E2 = 400.69 MPa

σy = 18.363 MPa

Max. Load = 9206 N




0

2

4

6

8

1012

14

16

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 - 2 mm/min

E1 = 279.75 MPa

E2 = 387.95 MPa

σy = 18.45 MPa

Max. Load = 9248 N




02

4

6

8

1012

14

16

18

20

0 0.1 0.2 0.3 0.4

A x i s T i t

l e

Strain (mm/mm)


E1 = 257.42 MPa

E2 = 348.30 MPa

σy = 18.19 MPa

Max. Load = 9120 N




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)


E1 = 238.78 MPa

E2 = 338.68 MPa

σy = 18.92 MPa

Max. Load = 9489 N




0

2

4

6

8

1012

14

16

18

20

0 0.1 0.2 0.3 0.4 0.5 0.6


Strain (mm/mm)

Compressive Test (nubless) - 1 mm/min

E1 = 394.14 MPaσy = 18.77 MPa

Max. Load = 9410 N




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)


E1 = 417.44 MPaσy = 19.31 MPa

Max. Load = 9679 N




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)


E1 = 445.01 MPaσy = 20.06 MPa

Max. Load = 10058.2 N



0

10

20

30

4050

60

70

80

02

4

6

8

1012

14

16

18

20

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 )


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



010

20

30

40

50

60

70

80

90

02

4

6

8

1012

14

16

18

20

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 )


Strain (mm/mm)

Acoustic Emission - 2 mm/min

Experimental Results – Compression with

Acoustic Emission

σy = 17.835 MPa

Max. Load = 8941 N



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!



Experimental Results – Qualitative Analysis



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



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



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)



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.

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A Redditor's Dilemma