User:ABielat/ENES-100/Project 3

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Week 9 Narrative
Calculations were performed to find the yield stress (fy) and the elasticity (E) of the PLA material from the tests performed to date. Elasticity (E) and yield stress (fy) were calculated and compared graphically and analytically to other popular structural materials. Data tables, graphs and calculations were updated for all data compiled to date. Load vs deflection curves were also be constructed for all recorded tests containing defection data.

Researching Project Page Design Calculations
The calculations on the Projects Page were researched to see what was done, how it was done and how it compares to the engineering and calculations approach performed to date.

 Project Page Elasticity Equation 

The equation is as follows:

E=(FL^3)/4wh^3d)

There is no mention of where this equation comes from, how it is derived or how it is used? After an hour or so of trying to figure it out I believe I was able to.

Staring with our deflection equation and focusing on a rectangular prism:

E = (Pl^3)/ (deflection tested * 48 * Ixx)

I believe that they are using the Ixx for a rectangular prism.

Ixx = bh^3/12

Plugging the Ixx for a rectangular prism we get:

E = (Pl^3)/ (d *48 * bh^3/12)

E = (Pl^3) / 4bh^3d = (FL^3)/4wh^3d)

So there equation comes from our derivation focusing on only rectangular prism.

1. This equation will not work on any shape other than a rectangular prism.

2. They did not derive the equation.

3. They did not say where is came from.

4. They did not produce a bending equation for the 3 point test to calculate fy.

 Project Page Bending Equation 

The equation is as follows:

fy = (FLc)/(12wh^3)

Once again, there is no mention of where this equation comes from, how it is derived or how it is used?

I will try to derive it from a two point bending cantilever.

M design = Pl --- for a cantilever with a concentrated load on the far end.

M alw = Ixx * fy/yc

Setting the moments equal to each other and solving for fy:

Pl = Ixx * fy/yc

Assume they are using a rectangular prism again.

Ixx = bh^3/12

Plug in Ixx and solve for fy:

Pl = bh^3/12 *fy/yc

fy = 12PLyc/bh^3 =not= (FLc)/(12wh^3)

I believe they tried to do this and made a math error with the 12, putting it in the denominator rather than the numerator.

So there equation is incorrect and comes from our derivation focusing on only rectangular prism.

1. There equation is wrong and will under estimate the yield stress by a factor of 144.

2. This equation will not work on any shape other than a rectangular prism.

3. They did not derive the equation.

4. They did not say where is came from.

5. They did not produce a elasticity equation for the 2 point test to calculate fy.

 Project Page Rope Bending Stress Equation 

The equation is as follows:

Bending Stress = Moment * Y/ I

This equation makes no sense at all!

1. There is no bending stress on the rope as it is in tension.

2. The stress in the rope has no bearing on the project specifically the mechanical properties of the PLA prism beams.

3. The stress in the rope = F/A--  but is not relevant to this project.

4. The formula they tried to use is for bending = Mc/I--  does not make sense for these ropes.

5. This equation is worse then useless as it will be counter productive to anyone trying to use it. It will only provide utter confusion and unexplainable results.

After evaluating the equations on the project page only the elasticity equation for the 3 point test is valid. It has major limitations as it is only valid for a rectangular prism. This was a good exercise as it validated all of the engineering equations we derived for this project. The equations I derived here are good for any shape and are properly derived and documented. This project will continue to use the equations I derived for all calculations.

Predicted Failure Engineering Calculations for Green Cylindrical Prism Beam with 10% Infill
The yield stress (fy) for all members of a specific PLA color and infill should be the same. All values will be averaged and extreme values will be eliminated such that our team will develop a working yield stress (fy) for future designs. As of now, the average yield stress for green PLA material with 10% infill is fy = 4,207 psi. Utilizing this average yield stress value (fy) when will be able to predict the Engineering Calculations for Green cylindrical Prism Beam with 10% Infill.

Given:

Length = 6.75 in

bearing = .625 in

span (l) = 5.5 in

diameter (d) = 0.5 in

radius (r) = 0.25 in

yc = 0.25 in

Ixx = (1/4)*pi*r^4

Ixx = (1/4)*pi*(0.25)^4

Ixx = 0.003068 in^4

Mmax = (Ixx/yc)* fy

fy = 4,207 psi = 33.67 MPa (from previous test)

Mmax = (0.003068/4)*4,207

Mmax = 51.63 in-lbs

Mdesign = Pl/4 (simply supported beam with single load at midpoint)

Set Mdesign = Max and solve for P

51.63 = Pl/4

P = 51.63*(4)/(5.5)

P = 37.5 lbs

Using the data base sample fy = 4,207 psi predicts that the  green PLA cylindrical prism beam (10% infill) with a diameter of 0.5 inch will fail at approximately 37.5 lbs. As more test are completed the fy value will be established allowing us to successfully engineer and predict test failures. Deflections will also be measured in future tests allowing us to establish elasticity (E) for the various PLA materials.

The actual failure was 30 lbs.

Deflection Engineering Calculations Red Cylindrical Prism Beam 10% Infill
Givens:

Span = 5.5 in

diameter (d) = 0.5 in

radius (r) = 0.25 in

Ixx = (1/4)*pi*r^4

Ixx = (1/4)*pi*(0.25)^4

Ixx = 0.003068 in^4

E = (Pl^3)/ (deflection tested * 48 * Ixx)

E = (15.0 lbs)*(5.5 in)^3 / [(6mm/(25.4mm/in))*48*(0.003068 in^4)]

E = 90,729 psi

The elasticity for each of the data points are calculated and shown in the table below. Moreover, the load vs deflection is plotted as seen below.



Deflection Engineering Calculations Red Pentagonal Prism Beam 10% Infill
Givens:

Span = 5.5 i

diameter (d) = 0.476 in

radius (r) = 0.238 in

yc = 0.238 in

Ixx = (1/4)*pi*r^4

Ixx = (1/4)*pi*(0.25)^4

Ixx = 0.00252 in^4

E = (Pl^3)/ (deflection tested * 48 * Ixx)

E = (22.5 lbs)*(5.5 in)^3 / [(7mm/(25.4mm/in))*48*(0.003068 in^4)]

E = 92,239 psi

The elasticity for each of the data points are calculated and shown in the table below. Moreover, the load vs deflection is plotted as seen below.



Deflection Engineering Calculations Green Cylindrical Prism Beam 10% Infill
Givens:

Span = 5.5 in

diameter (d) = 0.5 in

radius (r) = 0.25 in

Ixx = (1/4)*pi*r^4

Ixx = (1/4)*pi*(0.25)^4

Ixx = 0.003068 in^4

E = (Pl^3)/ (deflection tested * 48 * Ixx)

E = (22.5 lbs)*(5.5 in)^3 / [(7mm/(25.4mm/in))*48*(0.003068 in^4)]

E = 92,239 psi

The elasticity for each of the data points are calculated and shown in the table below. Moreover, the load vs deflection is plotted as seen below.



Deflection Engineering Calculations Green Pentagonal Prism Beam 10% Infill
Givens:

Span = 5.5 in

diameter (d) = 0.476 in

radius (r) = 0.238 in

Ixx = (1/4)*pi*r^4

Ixx = (1/4)*pi*(0.25)^4

Ixx = 0.00252 in^4

E = (Pl^3)/ (deflection tested * 48 * Ixx)

E = (7.5 lbs)*(5.5 in)^3 / [(2mm/(25.4mm/in))*48*(0.00252 in^4)]

E = 131,013 psi

The elasticity for each of the data points are calculated and shown in the table below. Moreover, the load vs deflection is plotted as seen below.



Deflection Engineering Calculations for Green Triangular Prism Beam with 10% Infill
Givens:

Span = 5.5 in

b = .5 in

h= .43 in

Ixx = 1/36*b*h^3

Ixx = 1/36*.43*.5^3

Ixx = 0.001104 in^4

E = (Pl^3)/ (deflection tested * 48 * Ixx)

E = (20.0 lbs)*(5.5 in)^3 / [(10mm/(25.4mm/in))*48*(0.00001104 in^4)]

E = 131,013 psi

The elasticity for each of the data points are calculated and shown in the table below. Moreover, the load vs deflection is plotted as seen below.



Summary of Results to Date
The following data table summarizes our testing and calculations to date (11-12-14).

A few of the data points seem to be outside the realm of what would be expected. Most notably, the Green Triangular prism beam with 10% infill as it's yield stress (fy) was way above the red triangular value as well as the average yield stress (fy) for the green PLA material. I suggest that we complete 2 more trials for prism beam for a total of 3 each and average the values. This will give our team much more accurate results and allow us to isolate odd-ball tests. This will not be possible for any of the red prism beams as the lab is out of red PLA material. Three total trials can be completed for the green PLA material and other colors that are available to produce. The results seem to be reasonable but still I believe there is some experimental error and three trials of each color we be very beneficial.

The published yield stress for PLA solid material is 7,300 psi. Our average value tested value for PLA material is 4,312 psi which is a very reasonable number considering we only have 10% infill compares to a solid specimen.

The published elasticity value for PLA solid material is 510,000 psi. Our average value tested value for PLA material is 106,388 psi which is a very reasonable number considering we only have 10% infill compares to a solid specimen.

The published density value for PLA solid material is 78 lb/ft^3. Our average value tested value for PLA material is 31.1 lb/ft^3 which is a very reasonable number considering we only have 10% infill compares to a solid specimen.

All in all our results make sense. I believe with 3 trials of each we can even improve upon our work to date.

Comparison of Common Material Modulus Elasticity's
The flowing table compares our PLA material Elasticity to common materials.



Clearly, the weakness of this PLA material is it's Modulus Of Elasticity (E) when comparing it to other popular construction materials. When comparing it to other materials such as wood, aluminum and steel, the E value for PLA material is virtually non-existent.

Comparison of Common Material Yield Stresses
The flowing table compares our PLA material yield stress to common materials.



On the other hand, PLA material does very well when comparing its yield strength to other materials. Even with only a 10% infill the PLA material test showed very respectable numbers when comparing it to other construction materials such as wood, aluminum and steel. Even with only 10% infill its fy values are very close to wood and aluminum.

Overall, the PLA material with 10% infill does very well when comparing its strength to other building materials. Buts weakness is clearly its low E numbers. Simply put, this product will not have the stiffness necessary to be competitive to the common building materials currently used today.

Engineering As-Built Drawings
The following engineering as-built drawing represents the cylindrical prism beams:



The following engineering as-built drawing represents the rectangular prism beams:



The following engineering as-built drawing represents the triangular prism beams:



Week 10 Narrative
Engineering Calculations were performed to find the yield stress (fy) and the elasticity (E) of the PLA material from the tests performed to date. Elasticity (E) and yield stress (fy) were calculated and compared graphically and analytically to other popular structural materials. Data tables, graphs and calculations were updated for all data compiled to date. Load vs deflection curves were also be constructed for all recorded tests containing defection data. Moreover, utilizing our data base of results to date, predictions were made from Engineering Calculations to the failure load (P) of the 3 test performed. This gives a real live Engineering application for the materials we are developing mechanical properties for. So fart he predictions have been pretty good, well within the error range of our experiment.

Test were performed, data collected and Engineering Calculations were performed for the following prism beams:


 * Yellow PLA Cylindrical Prism Beams with 10% infill
 * Yellow PLA Pentagonal Prism Beams with 10% infill
 * Green PLA Pentagonal Prism Beams with 10% infill

Summary of Results to Date
The following data table summarizes our testing and calculations to date (11-26-14).



 Overall Results 

Overall, the results to date make a lot of sense when compared to each other, published values of PLA material and other popular building materials. The table above summarizes and tabulates the 11 tests performed to date. Moreover, the results gives us working Mechanical Properties of the PLA material in the form of yield stress (fy) and elasticity (E) which allows us to predict the failure load of test before we preform them. This brings the project full circle, allowing us to perform real live Engineering similar to the engineering practiced everyday by structural and mechanical engineers.

When comparing the results to each other, the Red PLA material is the strongest with an average yield stress (fy) of 4,416.7 psi, followed by the green at 3,920.7 psi and the yellow at 3,035.3 psi. When comparing the elasticity (E), the green PLA material is first with an average 95,826 psi closely followed by red with an average value of 94,597 psi and yellow at a distant third with an average value of 80,275 psi. There are factories and variables that skew these results and they will be addressed as well below.

The published yield stress for PLA solid material is 7,300 psi. Our average value tested value for PLA material is 3,940.1 psi which is a very reasonable number considering we only have 10% infill compares to a solid specimen. The published elasticity value for PLA solid material is 510,000 psi. Our average value tested value for PLA material is 94,327 psi which is a very reasonable number considering we only have 10% infill compares to a solid specimen. All tested specimens to date have been with 10% infill which is significantly lower in strength (fy) and elasticity (E) than solid PLA prism beams. The results validated this and showed that our prism beams with 10% infill make sense. The source for the PLA published data can be found at http://plastics.ulprospector.com/generics/34/c/t/polylactic-acid-pla-properties-processing.

PLA material does very well when comparing its yield strength (fy) to other materials. Even with only a 10% infill the PLA material test showed very respectable numbers when comparing it to other construction materials such as wood, aluminum and steel. Even with only 10% infill its fy values are very close to wood and aluminum. This examined in full detail below as the values are plotted against popular building materials. Overall, the PLA material with 10% infill does very well when comparing its strength to other building materials. Buts weakness is clearly its low E numbers. Simply put, this product will not have the stiffness necessary to be competitive to the common building materials currently used today. This examined in full detail below as the elasticity (E) values are plotted against popular building materials. The published density value for PLA solid material is 78 lb/ft^3. Our average value tested value for PLA material is 29.0 lb/ft^3 which is a very reasonable number considering we only have 10% infill compares to a solid specimen.

 Variability/Error 

There are several sources of variability in the project to date. The first is PLA color which could affect its mechanical properties and that has been discussed above.

Shape:

Theoretically, the mechanical properties should be the same for each color regardless of shape. This would probably be true if our prism beams were 100% solid PLA material but they are only 10% infill. The 10% infill has a different affect on each shape as the Makerbot manufacturing process results in drastically different densities for the respective shapes. As a result this skews our results and creates some explainable inconsistency's between shapes. As seen from our data, the triangular shapes have the highest density's pushing 40 lb/ft^3. In contrast, the rectangular shapes have the lowest density in the low 20's lb/ft^3. This makes sense as the uniform nature of the rectangular prism is much easier to manufacture with the honey comb infill. The bottom line is that 10% infill is not the same with each shape which is a major source of our variability.

Printer:

Through testing, it is evident that there is a major difference between the densities of the parts produced by the 5th generation printer and the second. So much so that a column on the data table has been added to quickly distinguish which printer produced which part. The only part which was produced by both printers to date was the Green Rectangular Prism with 10% infill. The density of the 5th generation printer is 26.4 lb/ft^3 compared to only 22.6 lb/ft^3 for the 2nd generation 3D printer. This trend between the 2 printer is consistent throughout our data. Unfortunately. with all of the problems the lab had with the printers, our team had to take what we could get.

Rope Thickness:

Our compiled test data shows that there is also variation between test with the thickness of rope used to support the weight during the testing procedure. The rope thickness has also been added to the data table. I am fearful that the thinner rope is causing another failure mode other than bending on the specimens resulting in lower failure loads (P). In establishing mechanical properties, it is imperative that we induce a bending failure. I recommend that for future tests we only use the bigger rope. Failure modes will be closely monitored and documented so that a true bending failure is the testing goal for all tests.

Repeatably:

I suggest that we complete 2 more trials for prism beam for a total of 3 each and average the values. This will give our team much more accurate results and allow us to isolate odd-ball tests. This will not be possible for any of the red prism beams as the lab is out of red PLA material. Three total trials can be completed for the green PLA material and other colors that are available to produce. The results seem to be reasonable but still I believe there is some experimental error and three trials of each color we be very beneficial. Most importantly, 3 tests will allow our team to isolate the variables described above.

All in all our results make sense. I believe with 3 trials of each we can even improve upon our work to date.

Predicted Failure Engineering Calculations for Yellow Cylindrical Prism Beam with 10% Infill
The yield stress (fy) for all members of a specific PLA color and infill should be the same. All values will be averaged and extreme values will be eliminated such that our team will develop a working yield stress (fy) for future designs. As of now, the average yield stress for all PLA material with 10% infill is fy = 3,940 psi. Utilizing this average yield stress value (fy) when will be able to predict the Engineering Calculations for Yellow cylindrical Prism Beam with 10% Infill.

Given:

Length = 6.75 in

bearing = .625 in

span (l) = 5.5 in

diameter (d) = 0.5 in

radius (r) = 0.25 in

yc = 0.25 in

Ixx = (1/4)*pi*r^4

Ixx = (1/4)*pi*(0.25)^4

Ixx = 0.003068 in^4

Mmax = (Ixx/yc)* fy

fy = 3,940.1 psi (average of all test)

Mmax = (0.003068/4)*4,207

Mmax = 50.79 in-lbs

Mdesign = Pl/4 (simply supported beam with single load at midpoint)

Set Mdesign = Max and solve for P

50.79 = Pl/4

P = 50.79*(4)/(5.5)

P = 36.9 lbs

Using the average data base sample fy = 3,940.1 psi predicts that the  yellow PLA cylindrical prism beam (10% infill) with a diameter of 0.5 inch will fail at approximately 36.9 lbs.

The actual failure was 31 lbs.

Predicted Failure Engineering Calculations for Yellow Pentagonal Prism Beam with 10% Infill
The yield stress (fy) for all members of a specific PLA color and infill should be the same. All values will be averaged and extreme values will be eliminated such that our team will develop a working yield stress (fy) for future designs. As of now, the average yield stress for all PLA material with 10% infill is fy = 3,940 psi. Utilizing this average yield stress value (fy) when will be able to predict the Engineering Calculations for Yellow Pentagonal Prism Beam with 10% Infill.

Given:

Length = 6.75 in

bearing = .625 in

span (l) = 5.5 in

diameter (d) = 0.5 in

radius (r) = 0.25 in

yc = 0.25 in

Ixx = (1/4)*pi*r^4

Ixx = (1/4)*pi*(0.25)^4

Ixx = 0.00252 in^4

Mmax = (Ixx/yc)* fy

fy = 3,940.1 psi (average of all test)

Mmax = (0.00252/4)*3,940.1

Mmax = 41.72 in-lbs

Mdesign = Pl/4 (simply supported beam with single load at midpoint)

Set Mdesign = Max and solve for P

41.72 = Pl/4

P = 41.723*(4)/(5.5)

P = 30.34 lbs

Using the average data base sample fy = 3,940.1 psi predicts that the  yellow PLA pentagonal prism beam (10% infill) with a diameter of 0.5 inch will fail at approximately 30.34 lbs.

The actual failure was 20 lbs.

Predicted Failure Engineering Calculations for Green Rectangular Prism Beam with 10% Infill
The yield stress (fy) for all members of a specific PLA color and infill should be the same. All values will be averaged and extreme values will be eliminated such that our team will develop a working yield stress (fy) for future designs. As of now, the average yield stress for all PLA material with 10% infill is fy = 3,940 psi. Utilizing this average yield stress value (fy) when will be able to predict the Engineering Calculations for the Green Rectangular Prism Beam with 10% Infill.

Given:

Span = 5.5 in

P = 60 lbs

b = .5 in

h= .5 in

c = h/2 = .25 i

Ixx = 1/12*b*h^3

Ixx = 1/12*.5*.5^2

Ixx = 0.005208 in^4

Mmax = (Ixx/yc)* fy

fy = 3,940.1 psi (average of all test)

Mmax = (0.005208/4)*4,207

Mmax = 82.1 in-lbs

Mdesign = Pl/4 (simply supported beam with single load at midpoint)

Set Mdesign = Max and solve for P

82.1 = Pl/4

P = 82.1*(4)/(5.5)

P = 59.7 lbs

Using the average data base sample fy = 3,940.1 psi predicts that the green PLA rectangular prism beam (10% infill) with a base of 0.5 inch and height of .5 inch will fail at approximately 59.7 lbs.

The actual failure was 42 lbs.

Deflection Engineering Calculations Green Rectangular Prism Beam 10% Infill
Givens:

Span = 5.5 in

diameter (d) = 0.5 in

radius (r) = 0.25 in

Ixx = (1/4)*pi*r^4

Ixx = (1/4)*pi*(0.25)^4

Ixx = 0.003068 in^4

E = (Pl^3)/ (deflection tested * 48 * Ixx)

E = (22.5 lbs)*(5.5 in)^3 / [(5mm/(25.4mm/in))*48*(0. in^4)]

E = 76,067 psi

The elasticity for each of the data points are calculated and shown in the table below. Moreover, the load vs deflection is plotted as seen below.



Deflection Engineering Calculations Yellow Pentagonal Prism Beam 10% Infill
Givens:

Span = 5.5 i

diameter (d) = 0.476 in

radius (r) = 0.238 in

yc = 0.238 in

Ixx = (1/4)*pi*r^4

Ixx = (1/4)*pi*(0.25)^4

Ixx = 0.00252 in^4

E = (Pl^3)/ (deflection tested * 48 * Ixx)

E = (17.5 lbs)*(5.5 in)^3 / [(7mm/(25.4mm/in))*48*(0.00252 in^4)]

E = 87,342 psi

The elasticity for each of the data points are calculated and shown in the table below. Moreover, the load vs deflection is plotted as seen below.



Deflection Engineering Calculations Yellow Rectangular Prism Beam -Test 1 - 10% Infill
Givens:

Span = 5.5 in

diameter (d) = 0.5 in

radius (r) = 0.25 in

Ixx = (1/4)*pi*r^4

Ixx = (1/4)*pi*(0.25)^4

Ixx = 0.003068 in^4

E = (Pl^3)/ (deflection tested * 48 * Ixx)

E = (22.5 lbs)*(5.5 in)^3 / [(5mm/(25.4mm/in))*48*(0. in^4)]

E = 76,067 psi

The elasticity for each of the data points are calculated and shown in the table below. Moreover, the load vs deflection is plotted as seen below.



Bending Engineering Calculations Yellow Cylindrical Prism Beam 10% Infill
Givens:

Span = 5.5 in

P = 40 lbs

diameter (d) = 0.5 in

radius (r) = 0.25 in

yc = 0.25 in

Ixx = (1/4)*pi*r^4

Ixx = (1/4)*pi*(0.25)^4

Ixx = 0.003068 in^4

MDesign = Pl/4

MDesign = (31 lbs * 5.5 in)/4

MDesign = 42.63 in lbs

fy = (Mmax * c )/ Ixx

fy = (42.63 in*lbs * 0.25 in)/ 0.003068 in^4

fy = 3,473.4 psi = 23.95 Mpa

Bending Engineering Calculations Yellow Pentagonal Prism Beam 10% Infill
Givens:

Span = 5.5 in

P = 33 lbs

diameter (d) = 0.476 in

radius (r) = 0.238 in

yc = 0.238 in

Ixx = (1/4)*pi*r^4

Ixx = (1/4)*pi*(0.25)^4

Ixx = 0.00252 in^4

MDesign = Pl/4

MDesign = (20 lbs * 5.5 in)/4

MDesign = 27.5 in lbs

fy = (Mmax * c )/ Ixx

fy = (427.5 in*lbs * 0.238 in)/ 0.00252 in^4

fy = 2,597.2 psi = 17.91 Mpa

Bending Engineering Calculations Green Rectangular Prism Beam 10% Infill
Givens:

Span = 5.5 in

P = 60 lbs

b = .5 in

h= .5 in

c = h/2 = .25 in

MDesign = Pl/4

MDesign = (42 lbs * 5.5 in)/4

MDesign = 57.75 in lbs

fy = (Mmax * c )/ Ixx

Ixx = 1/12*b*h^3

Ixx = 1/12*.5*.5^2

Ixx = 0.005208 in^4

fy = (Mmax * c )/ Ixx

fy = (57.75 in*lbs * 0.25 in)/ 0.005208 in^4

fy = 2,772.0 psi = 19.11 Mpa

Comparison of Common Material Modulus Elasticity's
The flowing table compares our PLA material Elasticity to common materials.



Clearly, the weakness of this PLA material is it's Modulus Of Elasticity (E) when comparing it to other popular construction materials. When comparing it to other materials such as wood, aluminum and steel, the E value for PLA material is virtually non-existent.

Comparison of Common Material Yield Stresses
The flowing table compares our PLA material yield stress to common materials.



On the other hand, PLA material does very well when comparing its yield strength to other materials. Even with only a 10% infill the PLA material test showed very respectable numbers when comparing it to other construction materials such as wood, aluminum and steel. Even with only 10% infill its fy values are very close to wood and aluminum.

Overall, the PLA material with 10% infill does very well when comparing its strength to other building materials. Buts weakness is clearly its low E numbers. Simply put, this product will not have the stiffness necessary to be competitive to the common building materials currently used today.

Week 11 Narrative
Engineering Calculations were performed to find the yield stress (fy) and the elasticity (E) of the PLA material from the tests performed to date. Elasticity (E) and yield stress (fy) were calculated and compared graphically and analytically to other popular structural materials. Data tables, graphs and calculations were updated for all data compiled to date. Load vs deflection curves were also constructed for all recorded tests containing defection data. Moreover, utilizing our data base of results to date, predictions were made for Engineering Calculations of the failure load (P) of the four test performed. This gives a real life Engineering application for the materials we are developing mechanical properties for. So far the predictions have been pretty good, well within the error range of our experiment.

Test were performed, data collected and Engineering Calculations were performed for the following prism beams:


 * Yellow PLA Triangular Prism Beam with 10% infill
 * 2-Yellow PLA Rectangular Prism Beams with 10% infill
 * Green PLA Pentagonal Prism Beam with 10% infill

Summary of Results to Date
The following data table summarizes our testing and calculations to date (11-26-14).



 Overall Results 

Overall, the results to date make a lot of sense when compared to each other, published values of PLA material and other popular building materials. The table above summarizes and tabulates the 15 tests performed to date. Moreover, the results gives us working Mechanical Properties of the PLA material in the form of yield stress (fy) and elasticity (E) which allows us to predict the failure load of test before we preform them. This brings the project full circle, allowing us to perform real life Engineering similar to the engineering practiced everyday by structural and mechanical engineers.

When comparing the results to each other, the Red PLA material is the strongest with an average yield stress (fy) of 4,417 psi, followed by the green at 3,735 psi and the yellow at 2,357 psi. When comparing the elasticity (E), the green PLA material is first with an average 98,471 psi closely followed by red with an average value of 94,597 psi and yellow at a distant third with an average value of 69,164 psi. There are factors and variables that skew these results and they will be addressed as well below.

The published yield stress for PLA solid material is 7,300 psi. Our average value tested value for PLA material is 3,457 psi which is a very reasonable number considering we only have 10% infill compared to a solid specimen. The published elasticity value for PLA solid material is 510,000 psi. Our average value tested value for PLA material is 94,327 psi which is a very reasonable number considering we only have 10% infill compared to a solid specimen. All tested specimens to date have been with 10% infill which is significantly lower in strength (fy) and elasticity (E) than solid PLA prism beams. The results validated this and showed that our prism beams with 10% infill make sense. The source for the PLA published data can be found at http://plastics.ulprospector.com/generics/34/c/t/polylactic-acid-pla-properties-processing.

PLA material does very well when comparing its yield strength (fy) to other materials. Even with only a 10% infill the PLA material tests showed very respectable numbers when comparing it to other construction materials such as wood, aluminum and steel. Even with only 10% infill its fy values are very close to wood and aluminum. This examined in full detail below as the values are plotted against popular building materials. Overall, the PLA material with 10% infill does very well when comparing its strength to other building materials. But its weakness is clearly its low E values. Simply put, this product will not have the stiffness necessary to be competitive to the common building materials currently used today. This is examined in full detail below as the elasticity (E) values are plotted against popular building materials. The published density value for PLA solid material is 78 lb/ft^3. Our average value tested value for PLA material is 27.4 lb/ft^3 which is a very reasonable number considering we only have 10% infill compared to a solid specimen.

 Variability/Error 

There are several sources of variability in the project to date. The first is PLA color which could affect its mechanical properties and that has been discussed above.

Shape:

Theoretically, the mechanical properties should be the same for each color regardless of shape. This would probably be true if our prism beams were 100% solid PLA material but they are only 10% infill. The 10% infill has a different affect on each shape as the Makerbot manufacturing process results in drastically different densities for the respective shapes. As a result this skews our results and creates some explainable inconsistency's between shapes. As seen from our data, the triangular shapes have the highest density's pushing 40 lb/ft^3. In contrast, the rectangular shapes have the lowest density in the low 20's lb/ft^3. This makes sense as the uniform nature of the rectangular prism is much easier to manufacture with the honey comb infill. Moreover, the percent of infill versus the surface area of the different shapes varies adding to the variably in the comparative densities. The bottom line is that 10% infill is not the same with each shape which is a major source of our variability.

Printer:

Through testing, it is evident that there is a major difference between the densities of the parts produced by the 5th generation printer and the second. So much so that a column on the data table has been added to quickly distinguish which printer produced which part. The only part which was produced by both printers to date was the Green Rectangular Prism with 10% infill. The density of the 5th generation printer is 26.4 lb/ft^3 compared to only 22.6 lb/ft^3 for the 2nd generation 3D printer. This trend between the 2 printers is consistent throughout our data. Moreover, the 2nd generation printer is struggling to produce consistent parts particularly with the yellow PLA material. Unfortunately, with all of the problems the lab had with the printers, our team had to take what we could get. The following pictures show the deficiency of the yellow parts produced by the 2nd generation printer.



Rope Thickness:

Our compiled test data shows that there is also variation between test with the thickness of rope used to support the weight during the testing procedure. The rope thickness has also been added to the data table. I am fearful that the thinner rope is causing another failure mode other than bending on the specimens resulting in lower failure loads (P). In establishing mechanical properties, it is imperative that we induce a bending failure. I recommend that for future tests we only use the bigger rope. Failure modes will be closely monitored and documented so that a true bending failure is the testing goal for all tests.

Repeatably:

I suggest that we complete 2 more trials for prism beam for a total of 3 each and average the values. This will give our team much more accurate results and allow us to isolate odd-ball tests. This will not be possible for any of the red prism beams as the lab is out of red PLA material. Three total trials can be completed for the green PLA material and other colors that are available to produce. The results seem to be reasonable but still I believe there is some experimental error and three trials of each color we be very beneficial. Most importantly, 3 tests will allow our team to isolate the variables described above.

All in all our results make sense. I believe with 3 trials of each we can even improve upon our work to date.

Predicted Failure Engineering Calculations for Green Rectangular Prism Beam with 10% Infill
The yield stress (fy) for all members of a specific PLA color and infill should be the same. All values will be averaged and extreme values will be eliminated such that our team will develop a working yield stress (fy) for future designs. As of now, the average yield stress for all PLA material with 10% infill is fy = 3,457 psi. Utilizing this average yield stress value (fy) when will be able to predict the Engineering Calculations for the Green Rectangular Prism Beam with 10% Infill.

Given:

Span = 5.5 in

b = .5 in

h= .5 in

c = h/2 = .25 i

Ixx = 1/12*b*h^3

Ixx = 1/12*.5*.5^2

Ixx = 0.005208 in^4

Mmax = (Ixx/yc)* fy

fy = 3,457 psi (average of all test)

Mmax = (0.005208/4)*3,457 psi

Mmax = 72.0 in-lbs

Mdesign = Pl/4 (simply supported beam with single load at midpoint)

Set Mdesign = Max and solve for P

72.0 = Pl/4

P = 72.0*(4)/(5.5)

P = 52.3 lbs

Using the average data base sample fy = 3,457 psi predicts that the green PLA rectangular prism beam (10% infill) with a base of 0.5 inch and height of .5 inch will fail at approximately 52.3 lbs.

The actual failure was 42.5 lbs.

Predicted Failure Engineering Calculations for Yellow Rectangular Prism Beam with 10% Infill
The yield stress (fy) for all members of a specific PLA color and infill should be the same. All values will be averaged and extreme values will be eliminated such that our team will develop a working yield stress (fy) for future designs. As of now, the average yield stress for all PLA material with 10% infill is fy = 3,940 psi. Utilizing this average yield stress value (fy) when will be able to predict the Engineering Calculations for the Green Rectangular Prism Beam with 10% Infill.

Given:

Span = 5.5 in

b = .5 in

h= .5 in

c = h/2 = .25 i

Ixx = 1/12*b*h^3

Ixx = 1/12*.5*.5^2

Ixx = 0.005208 in^4

Mmax = (Ixx/yc)* fy

fy = 2,357 psi (average of yellow test)

Mmax = (0.005208/4)*2,357 psi

Mmax = 49.1 in-lbs

Mdesign = Pl/4 (simply supported beam with single load at midpoint)

Set Mdesign = Max and solve for P

49.1 = Pl/4

P = 49.1*(4)/(5.5)

P = 35.7 lbs

Using the yellow average data base sample fy = 2,357 psi predicts that the green PLA rectangular prism beam (10% infill) with a base of 0.5 inch and height of .5 inch will fail at approximately 52.3 lbs.

The actual failures was 17.5 lbs for test number 1 and 15.0 lbs for test number 2.

Predicted Failure Engineering Calculations for Yellow Triangular Prism Beam with 10% Infill
The yield stress (fy) for all members of a specific PLA color and infill should be the same. All values will be averaged and extreme values will be eliminated such that our team will develop a working yield stress (fy) for future designs. As of now, the average yield stress for average PLA material with 10% infill is fy = 3,457 psi. Utilizing this average yield stress value (fy) when will be able to predict the Engineering Calculations for the Yellow Triagnualr Prism Beam with 10% Infill.

Given:

Span = 5.5 in

b = .5 in

h= .43 in

c = h/3 = .1433 in

Ixx = 1/36*b*h^3

Ixx = 1/36*.433*.5^2

Ixx = 0.001104 in^4

Mmax = (Ixx/yc)* fy

fy = 3,457 psi (average of all test)

Mmax = (0.005208/4)*3,457 psi

Mmax = 26.6 in-lbs

Mdesign = Pl/4 (simply supported beam with single load at midpoint)

Set Mdesign = Max and solve for P

26.6 = Pl/4

P = 26.6*(4)/(5.5)

P = 19.4 lbs

Using the average data base sample fy = 3,457 psi predicts that the green PLA rectangular prism beam (10% infill) with a base of 0.5 inch and height of .43 inch will fail at approximately 19.4 lbs.

The actual failure was 20 lbs.

Deflection Engineering Calculations Green Rectangular - Test 3 - Prism Beam 10% Infill
Givens:

Span = 5.5 in

height (h) = 0.5 in

base (b) = 0.5 in

Ixx = (1/12)*b*h^3

Ixx = (1/12)*(0.5)*(0.5)^3

Ixx = 0.005208 in^4

E = (Pl^3)/ (deflection tested * 48 * Ixx)

E = (22.5 lbs)*(5.5 in)^3 / [(4mm/(25.4mm/in))*48*(0.005208 in^4)]

E = 95,083 psi

The elasticity for each of the data points are calculated and shown in the table below. Moreover, the load vs deflection is plotted as seen below.



Deflection Engineering Calculations Yellow Rectangular - Test 1 - Prism Beam 10% Infill
Givens:

Span = 5.5 in

height (h) = 0.5 in

base (b) = 0.5 in

Ixx = (1/12)*b*h^3

Ixx = (1/12)*(0.5)*(0.5)^3

Ixx = 0.005208 in^4

E = (Pl^3)/ (deflection tested * 48 * Ixx)

E = (10.0 lbs)*(5.5 in)^3 / [(4mm/(25.4mm/in))*48*(0.005208 in^4)]

E = 42,262 psi

The elasticity for each of the data points are calculated and shown in the table below. Moreover, the load vs deflection is plotted as seen below.



Deflection Engineering Calculations Yellow Rectangular - Test 2 - Prism Beam 10% Infill
Givens:

Span = 5.5 in

height (h) = 0.5 in

base (b) = 0.5 in

Ixx = (1/12)*b*h^3

Ixx = (1/12)*(0.5)*(0.5)^3

Ixx = 0.005208 in^4

E = (Pl^3)/ (deflection tested * 48 * Ixx)

E = (10.0 lbs)*(5.5 in)^3 / [(5mm/(25.4mm/in))*48*(0.005208 in^4)]

E = 33,810 psi

The elasticity for each of the data points are calculated and shown in the table below. Moreover, the load vs deflection is plotted as seen below.



Deflection Engineering Calculations Yellow Triangular Prism Beam 10% Infill
Givens:

Span = 5.5 in

height (h) = 0.43 in

base (b) = 0.5 in

Ixx = (1/36)*b*h^3

Ixx = (1/36)*(0.5)*(0.43)^3

Ixx = 0.001104 in^4

E = (Pl^3)/ (deflection tested * 48 * Ixx)

E = (12.5 lbs)*(5.5 in)^3 / [(9mm/(25.4mm/in))*48*(0.001104 in^4)]

E = 110,759 psi

The elasticity for each of the data points are calculated and shown in the table below. Moreover, the load vs deflection is plotted as seen below.



Bending Engineering Calculations Green Rectangular - Test 3 - Prism Beam 10% Infill
Givens:

Span = 5.5 in

P = 42.5 lbs

b = .5 in

h= .5 in

c = h/2 = .25 in

MDesign = Pl/4

MDesign = (42.5 lbs * 5.5 in)/4

MDesign = 58.4 in lbs

fy = (Mmax * c )/ Ixx

Ixx = 1/12*b*h^3

Ixx = 1/12*.5*.5^2

Ixx = 0.005208 in^4

fy = (Mmax * c )/ Ixx

fy = (58.4 in*lbs * 0.25 in)/ 0.005208 in^4

fy = 2,805 psi = 19.3 Mpa

Bending Engineering Calculations Yellow Rectangular - Test 1 - Prism Beam 10% Infill
Givens:

Span = 5.5 in

P = 17.5 lbs

b = .5 in

h= .5 in

c = h/2 = .25 in

MDesign = Pl/4

MDesign = (17.5 lbs * 5.5 in)/4

MDesign = 24.1 in lbs

fy = (Mmax * c )/ Ixx

Ixx = 1/12*b*h^3

Ixx = 1/12*.5*.5^2

Ixx = 0.005208 in^4

fy = (Mmax * c )/ Ixx

fy = (24.1 in*lbs * 0.25 in)/ 0.005208 in^4

fy = 1,155 psi = 8.0 Mpa

Bending Engineering Calculations Yellow Rectangular - Test 2 - Prism Beam 10% Infill
Givens:

Span = 5.5 in

P = 15.0 lbs

b = .5 in

h= .5 in

c = h/2 = .25 in

MDesign = Pl/4

MDesign = (15 lbs * 5.5 in)/4

MDesign = 20.6 in lbs

fy = (Mmax * c )/ Ixx

Ixx = 1/12*b*h^3

Ixx = 1/12*.5*.5^2

Ixx = 0.005208 in^4

fy = (Mmax * c )/ Ixx

fy = (20.6 in*lbs * 0.25 in)/ 0.005208 in^4

fy = 990 psi = 6.8 Mpa

Bending Engineering Calculations Yellow Triangular - Prism Beam 10% Infill
Givens:

Span = 5.5 in

P = 20.0 lbs

b = .5 in

h= .43 in

c = h/3 = .143 in

MDesign = Pl/4

MDesign = (20 lbs * 5.5 in)/4

MDesign = 27.5 in lbs

fy = (Mmax * c )/ Ixx

Ixx = 1/36*b*h^3

Ixx = 1/36*.5*.43^3

Ixx = 0.001104 in^4

fy = (Mmax * c )/ Ixx

fy = (27.5 in*lbs * 0.25 in)/ 0.001104 in^4

fy = 3,570 psi = 24.6 Mpa

Comparison of Common Material Yield Stresses
The flowing table compares our PLA material yield stress to common materials.



The PLA material does very well when comparing its yield strength to other materials. Even with only a 10% infill the PLA material test showed very respectable numbers when comparing it to other construction materials such as wood, aluminum and steel. Even with only 10% infill its fy values are very close to wood and aluminum. Moreover, the PLA material with only 10% infill has strength values which are roughly half of the 100% solid PLA material.

Comparison of Common Material Modulus of Elasticity's
The flowing table compares our PLA material Elasticity to common materials.



Clearly, the weakness of this PLA material is it's Modulus Of Elasticity (E) when comparing it to other popular construction materials. When comparing t to other materials such as wood, aluminum and steel, the E value for PLA material is virtually non-existent. However, when comparing our tested PLA material Elasticity to the published elasticity for 100% solid PAL material it does pretty well with about 15% of the elasticity values.

Overall, the PLA material with 10% infill does very well when comparing its strength to other building materials. Buts weakness is clearly its low E numbers. Simply put, this product will not have the stiffness necessary to be competitive to the common building materials currently used today.

Week 12 Narrative
Engineering Calculations were performed to find the yield stress (fy) and the elasticity (E) of the PLA material from the tests performed to date. Elasticity (E) and yield stress (fy) were calculated and compared graphically and analytically to other popular structural materials. Data tables, graphs and calculations were updated for all data compiled to date. Load vs deflection curves were also constructed for all recorded tests containing defection data. Moreover, utilizing our data base of results to date, predictions were made for Engineering Calculations of the failure load (P) of the all test performed. This gives a real life Engineering application for the materials we are developing mechanical properties for. So far the predictions have been pretty good, well within the error range of our experiment.

Test were performed, data collected and Engineering Calculations were performed for the following prism beams:


 * Yellow PLA Triangular Prism Beam with 10% infill
 * Green PLA Pentagonal Prism Beam with 10% infill

Summary of Results to Date
The following data table summarizes our testing and calculations to date (12-2-14).



 Overall Results 

Overall, the results to date make a lot of sense when compared to each other, published values of PLA material and other popular building materials. The table above summarizes and tabulates the 17 tests performed to date. Moreover, the results gives us working Mechanical Properties of the PLA material in the form of yield stress (fy) and elasticity (E) which allows us to predict the failure load of test before we preform them. This brings the project full circle, allowing us to perform real life Engineering similar to the engineering practiced everyday by structural and mechanical engineers.

When comparing the results to each other, the Red PLA material is the strongest with an average yield stress (fy) of 4,417 psi, followed by the green at 3,934 psi and the yellow at 2,410 psi. When comparing the elasticity (E), the green PLA material is first with an average 102,219 psi closely followed by red with an average value of 94,597 psi and yellow at a distant third with an average value of 73,942 psi. There are factors and variables that skew these results and they will be addressed as well below.

The published yield stress for PLA solid material is 7,300 psi. Our average value tested value for PLA material was 3,510 psi which is a very reasonable number considering we only have 10% infill compared to a solid specimen. The published elasticity value for PLA solid material is 510,000 psi. Our average value tested value for PLA material is 89,012 psi which is a very reasonable number considering we only have 10% infill compared to a solid specimen. All tested specimens to date have been with 10% infill which is significantly lower in strength (fy) and elasticity (E) than solid PLA prism beams. The results validated this and showed that our prism beams with 10% infill make sense. The source for the PLA published data can be found at http://plastics.ulprospector.com/generics/34/c/t/polylactic-acid-pla-properties-processing.

PLA material does very well when comparing its yield strength (fy) to other materials. Even with only a 10% infill the PLA material tests showed very respectable numbers when comparing it to other construction materials such as wood, aluminum and steel. Even with only 10% infill its fy values are very close to wood and aluminum. This is examined in full detail below as the values are plotted against popular building materials. Overall, the PLA material with 10% infill does very well when comparing its strength to other building materials. But its weakness is clearly its low E values. Simply put, this product will not have the stiffness necessary to be competitive to the common building materials currently used today. This is examined in full detail below as the elasticity (E) values are plotted against popular building materials. The published density value for PLA solid material is 78 lb/ft^3. Our average value tested value for PLA material is 27.7 lb/ft^3 which is a very reasonable number considering we only have 10% infill compared to a solid specimen.

 Variability/Error 

There are several sources of variability in the project to date. The first is PLA color which could affect its mechanical properties and that has been discussed above.

Shape:

Theoretically, the mechanical properties should be the same for each color regardless of shape. This would probably be true if our prism beams were 100% solid PLA material but they are only 10% infill. The 10% infill has a different affect on each shape as the Makerbot manufacturing process results in drastically different densities for the respective shapes. As a result this skews our results and creates some explainable inconsistency's between shapes. As seen from our data, the triangular shapes have the highest density's pushing 40 lb/ft^3. In contrast, the rectangular shapes have the lowest density in the low 20's lb/ft^3. This makes sense as the uniform nature of the rectangular prism is much easier to manufacture with the honey comb infill. Moreover, the percent of infill versus the surface area of the different shapes varies adding to the variably in the comparative densities. The bottom line is that 10% infill is not the same with each shape which is a major source of our variability.

Printer:

Through testing, it is evident that there is a major difference between the densities of the parts produced by the 5th generation printer and the second. So much so that a column on the data table has been added to quickly distinguish which printer produced which part. The only part which was produced by both printers to date was the Green Rectangular Prism with 10% infill. The density of the 5th generation printer is 26.4 lb/ft^3 compared to only 22.6 lb/ft^3 for the 2nd generation 3D printer. This trend between the 2 printers is consistent throughout our data. Moreover, the 2nd generation printer is struggling to produce consistent parts particularly with the yellow PLA material. Unfortunately, with all of the problems the lab had with the printers, our team had to take what we could get. The following pictures show the deficiency of the yellow parts produced by the 2nd generation printer.



Rope Thickness:

Our compiled test data shows that there is also variation between test with the thickness of rope used to support the weight during the testing procedure. The rope thickness has also been added to the data table. I am fearful that the thinner rope is causing another failure mode other than bending on the specimens resulting in lower failure loads (P). In establishing mechanical properties, it is imperative that we induce a bending failure. I recommend that for future tests we only use the bigger rope. Failure modes will be closely monitored and documented so that a true bending failure is the testing goal for all tests.

Repeatably:

I suggest that we complete 2 more trials for prism beam for a total of 3 each and average the values. This will give our team much more accurate results and allow us to isolate odd-ball tests. This will not be possible for any of the red prism beams as the lab is out of red PLA material. Three total trials can be completed for the green PLA material and other colors that are available to produce. The results seem to be reasonable but still I believe there is some experimental error and three trials of each color we be very beneficial. Most importantly, 3 tests will allow our team to isolate the variables described above.

All in all our results make sense. I believe with 3 trials of each we can even improve upon our work to date.

Predicted Failure Engineering Calculations for Green Pentagonal Prism Beam #2 with 10% Infill
The yield stress (fy) for all members of a specific PLA color and infill should be the same. All values will be averaged and extreme values will be eliminated such that our team will develop a working yield stress (fy) for future designs. As of now, the average yield stress for all PLA material with 10% infill is fy = 3,457 psi. Utilizing this average yield stress value (fy) when will be able to predict the Engineering Calculations for the Green Pentagonal Prism Beam with 10% Infill.

Given:

Length = 6.75 in

bearing = .625 in

span (l) = 5.5 in

diameter (d) = 0.5 in

radius (r) = 0.25 in

yc = 0.25 in

Ixx = (1/4)*pi*r^4

Ixx = (1/4)*pi*(0.25)^4

Ixx = 0.00252 in^4

Mmax = (Ixx/yc)* fy

fy = 3,457 psi (average of all test)

Mmax = (0.00252/4)*3,457

Mmax = 36.6 in-lbs

Mdesign = Pl/4 (simply supported beam with single load at midpoint)

Set Mdesign = Max and solve for P

36.6 = Pl/4

P = 36.6 *(4)/(5.5)

P = 26.6 lbs

Using the average data base sample fy = 3,457 psi predicts that the green PLA pentagonal prism beam (10% infill) with a diameter of 0.5 inch will fail at approximately 26.6 lbs.

The actual failure was 39.5 lbs.

The reason the Predicted load is so far from the load found in the test is because the bending stress is my calculation. The following sources of variability and error are changing the bending stress because of the following:


 * Shape
 * Color
 * Printer

These sources of variability and error are described in greater detail in the summary of results above.

Predicted Failure Engineering Calculations for Yellow Triangular Prism Beam #2 with 10% Infill
The yield stress (fy) for all members of a specific PLA color and infill should be the same. All values will be averaged and extreme values will be eliminated such that our team will develop a working yield stress (fy) for future designs. As of now, the average yield stress for average PLA material with 10% infill is fy = 3,457 psi. Utilizing this average yield stress value (fy) when will be able to predict the Engineering Calculations for the Yellow Triagnualr Prism Beam with 10% Infill.

Given:

Span = 5.5 in

b = .5 in

h= .43 in

c = h/3 = .1433 in

Ixx = 1/36*b*h^3

Ixx = 1/36*.433*.5^2

Ixx = 0.001104 in^4

Mmax = (Ixx/yc)* fy

fy = 3,457 psi (average of all test)

Mmax = (0.005208/4)*3,457 psi

Mmax = 26.6 in-lbs

Mdesign = Pl/4 (simply supported beam with single load at midpoint)

Set Mdesign = Max and solve for P

26.6 = Pl/4

P = 26.6*(4)/(5.5)

P = 19.4 lbs

Using the average data base sample fy = 3,457 psi predicts that the green PLA rectangular prism beam (10% infill) with a base of 0.5 inch and height of .43 inch will fail at approximately 19.4 lbs.

The actual failure was 15 lbs.

Deflection Engineering Calculations Green Pentagonal Prism Beam #2 10% Infill
Givens:

Span = 5.5 in

diameter (d) = 0.476 in

radius (r) = 0.238 in

yc = 0.238 in

Ixx = (1/4)*pi*r^4

Ixx = (1/4)*pi*(0.25)^4

Ixx = 0.00252 in^4

E = (Pl^3)/ (deflection tested * 48 * Ixx)

E = (20.0 lbs)*(5.5 in)^3 / [(5.5mm/(25.4mm/in))*48*(0.00252 in^4)]

E = 127,043 psi

The elasticity for each of the data points are calculated and shown in the table below. Moreover, the load vs deflection is plotted as seen below.



Deflection Engineering Calculations Yellow Triangular Prism Beam #2 10% Infill
Givens:

Span = 5.5 in

height (h) = 0.43 in

base (b) = 0.5 in

Ixx = (1/36)*b*h^3

Ixx = (1/36)*(0.5)*(0.43)^3

Ixx = 0.001104 in^4

E = (Pl^3)/ (deflection tested * 48 * Ixx)

E = (12.5 lbs)*(5.5 in)^3 / [(10mm/(25.4mm/in))*48*(0.001104 in^4)]

E = 99,683 psi

The elasticity for each of the data points are calculated and shown in the table below. Moreover, the load vs deflection is plotted as seen below.



Bending Engineering Calculations Green Pentagonal Prism Beam #2 10% Infill
Givens:

Span = 5.5 in

P = 39.5 lbs

diameter (d) = 0.476 in

radius (r) = 0.238 in

yc = 0.238 in

Ixx = (1/4)*pi*r^4

Ixx = (1/4)*pi*(0.25)^4

Ixx = 0.00252 in^4

MDesign = Pl/4

MDesign = (39.5 lbs * 5.5 in)/4        (The failure load)

MDesign = 54.3 in lbs

fy = (Mmax * c )/ Ixx

fy = (54.3 in*lbs * 0.238 in)/ 0.00252 in^4

fy = 5,130 psi = 35.37 Mpa

Bending Engineering Calculations Yellow Triangular Prism Beam #2 10% Infill
Givens:

Span = 5.5 in

P = 20.0 lbs

b = .5 in

h= .43 in

c = h/3 = .143 in

MDesign = Pl/4

MDesign = (15 lbs * 5.5 in)/4           (The Failure

MDesign = 20.625 in lbs

fy = (Mmax * c )/ Ixx

Ixx = 1/36*b*h^3

Ixx = 1/36*.5*.43^3

Ixx = 0.001104 in^4

fy = (Mmax * c )/ Ixx

fy = (20.625 in*lbs * 0.25 in)/ 0.001104 in^4

fy = 2677 psi = 18.5 Mpa

Comparison of Common Material Yield Stresses
The flowing table compares our PLA material yield stress to common materials.



The PLA material does very well when comparing its yield strength to other materials. Even with only a 10% infill the PLA material test showed very respectable numbers when comparing it to other construction materials such as wood, aluminum and steel. Even with only 10% infill its fy values are very close to wood and aluminum. Moreover, the PLA material with only 10% infill has strength values which are roughly half of the 100% solid PLA material.

Comparison of Common Material Modulus of Elasticity's
The flowing table compares our PLA material Elasticity to common materials.



Clearly, the weakness of this PLA material is it's Modulus Of Elasticity (E) when comparing it to other popular construction materials. When comparing to other materials such as wood, aluminum and steel, the E value for PLA material is virtually non-existent. However, when comparing our tested PLA material Elasticity to the published elasticity for 100% solid PAL material it does pretty well with about 15% of the elasticity values.

Overall, the PLA material with 10% infill does very well when comparing its strength to other building materials. Buts weakness is clearly its low E numbers. Simply put, this product will not have the stiffness necessary to be competitive to the common building materials currently used today.

Comparison of stress/strain to load/deflection curves
The following pictures show some samples of stress vs strain and load vs deflection curves:

This is a good summary showing the stress vs. strain curve for various infills of PLA material. It is important to note that they all take on the same shape as do the curves posted in our wiki pages for our test results. We are looking for a nice linear curve during the elastic region followed by a curve during the plastic, yield and breaking point. Stress is simply force/area. Strain is simply deflection/length. Therefore, the curves for load vs deflection and stress vs strain should be of similar shape for a good test.

This is a great example which shows that Load vs Deflection and stress vs strain are proportional. Once again, it is good practice to plot load vs deflection during a bending test. The major reason is to make sure it takes on the same shape. If there are major discrepancies with the shape of a bending test compared to these curves more than likely something is going wrong in the experiment. All of our load vs deflections test models these curve properly.