Small Scale Bridge Design Final Report

April 7, 2008

Jacob Hammer CIVE IV

100656672

Advisor: Prof. Juan Salinas

CARLETON UNIVERSITY

CIVE 4907 ENGINEERING PROJECT Jacob Hammer Page 2 of 43 06/04/2018

FINAL REPORT Jacob Hammer Page 3 of 43 06/04/2018

Table of Contents 1.0 INTRODUCTION...... 4 2.0 GOALS...... 4 3.0 BACKGROUND...... 5

3.1 COMPETITION GUIDELINES...... 5 3.2 PROPERTIES OF WOOD...... 5 3.2 ASSUMPTIONS...... 7 3.3 MATERIAL PROPERTIES...... 9 4.0 MATERIAL TESTS...... 11

4.1 BASE TENSION TESTS...... 11 4.2 COMPRESSION TESTS...... 14 4.3 SINGLE INTERFACE GLUE TESTS...... 14 4.4 DOUBLE INTERFACE GLUE TESTS...... 17 4.5 MODULUS OF ELASTICITY...... 19 4.6 DENTAL FLOSS TESTS...... 20 4.7 TENSION MEMBER CONNECTION JOINT TESTS...... 22 4.8 MEMBER TO MEMBER JOINT TESTS...... 24 5.0 BRIDGE DESIGN...... 25

5.1 OVERALL DESIGN...... 25 5.2 LAYER DESIGN...... 25 5.3 STRUCTURAL ANALYSIS...... 26 5.4 COMPRESSION MEMBER DESIGN...... 27 5.5 TENSION MEMBER DESIGN...... 28 5.6 DECK DESIGN...... 29 5.7 STRUT DESIGN...... 29 5.8 PIER DESIGN...... 29 5.9 DESIGN DIFFERENCES IN FINAL MODEL...... 30 6.0 COMPETITION RESULTS...... 31

6.1 ANTICIPATED METHOD OF FAILURE...... 31 6.2 METHOD OF FAILURE...... 31 6.3 EXPLANATION FOR FAILURE...... 32 6.4 IMPROVEMENTS / NEXT STEPS...... 32 7.0 CONCLUSION...... 33

7.1 PROJECT RESULTS...... 33 7.2 FINAL THOUGHTS...... 34 Jacob Hammer Page 4 of 43 06/04/2018

APPENDIX...... 35

APPENDIX 1 – RAW DATA FOR TEST 1...... 36 APPENDIX 2 – RAW DATA FOR TEST 2...... 37 APPENDIX 3 – RAW DATA FOR TEST 3...... 38 APPENDIX 4 – RAW DATA FOR TEST 4...... 39 APPENDIX 5 – RAW DATA FOR TEST 5...... 40 APPENDIX 6 – RAW DATA FOR TEST 6...... 41 APPENDIX 7 – RAW DATA FOR TEST 7...... 42 APPENDIX 8 – RAW DATA FOR TEST 8...... 43 APPENDIX 9 – RAW DATA FOR TEST 9...... 44 APPENDIX 10 – RAW DATA FOR TEST 10...... 45 APPENDIX 11 – RAW DATA FOR TEST 11...... 46 APPENDIX 12 – RAW DATA FOR TEST 12...... 47 APPENDIX 13 – RAW DATA FOR TEST 13...... 48 APPENDIX 14 – READOUTS FROM SAP2000 MODEL...... 49 APPENDIX 14 – READOUTS FROM SAP2000 MODEL (CONTINUED)...... 50 APPENDIX 15 – IMAGES FROM SAP2000 MODEL...... 51 APPENDIX 16 – DESIGN GUIDE...... 52

Table of Figures 3.0 BACKGROUND

3.1 ACCEPTED MATERIAL PROPERTIES OF BIRCH...... 9 4.0 MATERIAL TESTS

4.1 SINGLE STICK TENSION TEST SETUP...... 11 4.2 TRIPLE STICK DRY INTERFACE TENSION TEST SETUP...... 12 4.3 TRIPLE STICK GLUED INTERFACE TENSION TEST SETUP...... 13 4.4 COMPRESSION TEST SETUP...... 14 4.5 SINGLE INTERFACE GLUE TEST SETUP...... 15 4.6 DOUBLE INTERFACE GLUE TEST SETUP...... 17 4.7 DENTAL FLOSS TEST SETUP FIRST CONFIGURATION...... 21 4.8 DENTAL FLOSS TEST SETUP SECOND CONFIGURATION...... 21 4.9 SCARF JOINT TEST SETUP...... 22 4.10 HALF LAP SPLICE JOINT SETUP...... 23 4.11 DOWEL PIN CONNECTION SETUP...... 24 5.0 BRIDGE DESIGN

5.1 OVERALL LAYOUT OF BRIDGE DESIGN...... 25 5.2 VENEER DESIGN CONFIGURATION...... 25 5.3 ANGLE REFERENCE CHART...... 26 5.4 CORNER JOINT ECCENTRICITY...... 26 5.5 COMPRESSION MEMBER CROSS SECTION...... 27 5.6 VENEER REQUIREMENT REFERENCE CHART...... 28 5.7 TENSION MEMBER TOP VIEW CROSS-SECTION...... 28 5.8 DECK DESIGN CROSS-SECTION...... 29 5.9 STRUT DESIGN CROSS-SECTION...... 29 5.10 FINAL MODEL DESIGN...... 30 6.0 COMPETITION RESULTS

6.1 JOINT SEPARATION FAILURE...... 32 Jacob Hammer Page 5 of 43 06/04/2018

1.0 INTRODUCTION

This report is intended to outline to the department the findings of my fourth year project. This includes the research which has been performed, the resultant findings, and the analysis thereof.

2.0 GOALS

This project had three goals:

First, the main goal is to research the materials permitted for construction of a bridge, and design a bridge to be entered in the Concordia Bridge Building Competition. The project aimed to provide an analytical approach to the design and construction of the bridge and document the research that went into it.

Second, the supporting goal was to build a model bridge built out of designated building materials (see section 3.1) that is capable of supporting 3 kN. After initial research, this was increased to 5 kN, or just over 1100 pounds force. In this context, the bridge’s capacity is the maximum point loading being applied to the bridge at its centre at the point of collapse, as indicated by the testing machine. This value was picked as I believe it represents a quantitative threshold for acceptable bridge performance in the context of a fourth year engineering project. As well, this value seems to be a threshold for the top 10 positions in previous years at the Concordia Bridge Building Competition. I decided to aim for an ultimate capacity goal instead of an efficiency goal because not only is the capacity worth more in the competition scoring, but realistically, a hefty yet inefficient bridge is infinitely more functional than a highly efficient bridge with a low capacity.

Lastly, as the engineering profession is encouraged to give back to the community, this project aims to create a supporting document to be donated to the Carleton CSCE chapter summarizing the findings of the research performed to facilitate future generations. It aims to create an abridged version of this final report, detailing all the critical information somebody with no background in wood engineering would require to understand the fundamentals of how to design a bridge for this competition. Jacob Hammer Page 6 of 43 06/04/2018

3.0 BACKGROUND

3.1 Competition Guidelines

While a complete set of rules may be obtained from the CSCE Concordia website, below is an abridged set of guidelines that directly dictate restrictions on the bridge:

 The largest pre-fabricated component of the bridge must be able to fit within a 500mm by 400mm by 350mm box.  The minimum unsupported span must allow a 1000mm long by 150mm high box to pass freely underneath the bridge.  The maximum unsupported span length cannot exceed 1200mm. The maximum length of the entire bridge must not exceed 1350mm.  The minimum operating width of the bridge deck must be 150mm. It must run the entire length of the bridge. The continuous deck must be constructed entirely of wood (i.e. no solid glue decks).  The maximum width of the bridge at any point must be no more than 350mm, so it can fit into the testing apparatus.  The maximum height of the bridge (from the ground to the tallest point) must not exceed 600mm.  The maximum height of the span (the deck or platform) must less than 450 mm from the ground.  The maximum deflection of the road deck is 50mm. If the bridge has not failed once this deflection is reached, the carried load at that point will become its ultimate load.  A smooth continuous bridge deck “for vehicular traffic” must be provided along the entire span of the bridge.  The slope of this deck must not exceed 6% (slope being rise of deck over half deck length run).  The load will be applied on the deck of the bridge. An opening of 100mm by 100mm must be left above the centre of the bridge deck so that loading may be applied at the centre point distributed over this area.  Permitted materials are untreated popsicle sticks, dental floss, white glue (LePage or equivalent) and untreated tooth picks.  The maximum bridge weight is limited to 6.0 kg and the minimum weight is 1.0 kg.

3.2 Properties of Wood

These are descriptions of the basic properties of wood. They are stated here to give a baseline for all further remarks and assertions. Jacob Hammer Page 7 of 43 06/04/2018

3.1.1 Compression perpendicular to grain

Wood has no natural strength ultimate limit when compressed perpendicular to the grain. After the proportional limit, it will continue to deform and warp beyond recovery, severely affecting the wood’s properties in all other orientations. The conclusion drawn from this is that wood should not be loaded under perpendicular compression unless necessary.

3.1.2 Compression parallel to grain

Parallel to the grain, wood has a fairly reasonable strength. The design values for wood are typically 75% of the maximum crushing strength for hardwoods and 80% for softwoods. Beyond these design values, the stress-strain curve exceeds its proportional limit and the wood will begin deforming beyond recovery. Because the goal of the project is to test the absolute capacity of a bridge, no scale factor will be used and the maximum crushing strength will be accepted as the parallel compressive strength for design and analysis. At failure, the fibers will buckle and snap much like slender columns. The failure will most likely occur at the member’s joints. In the few compression tests I attempted in the Instron machine, the samples broke right at the tips of the grips.

3.1.3 Tension parallel to grain

In lieu of published values for tensile strength of wood parallel to the flow of grain, the modulus of rupture can be substituted. While this value is not a true reflection of the wood’s tensile capacity, it will serve as a conservative estimate viable for design. At failure, two basic models can occur. One is that the fibers in the wood will elongate and snap (called a “tear out”). Alternatively, the grain orientation will permit the member to fail in parallel shear as detailed below.

3.1.4 Tension perpendicular to grain

Perpendicular tensile failures are similar to a parallel shear mode detailed below. This means that the perpendicular tensile capacity of a wood is a measurement of the cohesive strength of the lignin. As observed in the published strength values, it’s similar to the value of compressive perpendicular loading and as such, it should be avoided in favour of a more accommodating loading orientation.

3.1.5 Shear parallel to grain

This is the basis for the failure mode of tensile members to “shear out”. This means that if the grain is not completely parallel to the cut of the member, the lignin will give away and rather than have the fibers themselves yield and snap, the surface between the fibers will separate creating a cleavage surface. In parallel grain tensile members, this surface will shear apart. Jacob Hammer Page 8 of 43 06/04/2018

3.1.6 Modulus of elasticity

As in all materials, the modulus of elasticity is taken as the slope of the stress- strain curve prior to the proportional limit. It’s a measurement of the tendency of a material to behave elastically before it behaves plastically.

3.1.7 Modulus of Rupture

The modulus of rupture is calculated by linearly extrapolating the stresses experienced at the proportional limit to the ultimate capacity. As it is an extrapolation, it’s not a true stress measurement of rupture, but rather a projection of the ultimate capacity.

3.2 Assumptions

3.2.1 Shrinkage

Wood will naturally shrink as its moisture content decreases. For this project, the shrinkage properties of wood will be neglected. This is for two reasons: Primarily because the sticks have already been dried prior to packaging (although the box does not indicate to what extend), but also because the shrinkage effect is proportional to the dimensions of lumber. An educated guess of the sticks’ dried moisture content can be made based of its EMC, however this would not affect shrinkage. The dimensions of the sticks are so small relative to construction lumber that shrinkage and growth effects are negligible when weighed against any inconsistencies as a result of the construction process.

It is also assumed that during the testing, construction, and transportation (to the competition) process of any test samples or bridge components, there will be no amount of precipitation or condensation present in enough quantities to be noteworthy. While contact with glue will be a major part of the construction process, it is assumed that any local expansion caused by the introduction of moisture will merely help the joint fit together better, if it has any effect at all.

3.2.2 Warping

While no warping will occur because of post-production shrinkage, the drying process prior to packaging has left sticks in varying degrees of warpage, primarily bowing and twisting. During stick selection for the test samples, sticks were selected for their ability to perform primarily in the axial direction, and less so in flexure, so sticks with a slight bow or twist were used. During stick selection for the final model, members will be exposed to small amounts of flexure due to the design chosen (detailed below), so sticks will undergo a more discriminating selection. Only sticks that show no signs of cupping and almost no signs of twisting will be used. Sticks with bowing may be used if the bending isn’t detrimental to its context in the structure. Jacob Hammer Page 9 of 43 06/04/2018

3.2.3 Loading Condition Factors

All loading factors are as per the wood code CSA-086-01.

3.2.3.1 Load Duration Factor (KD)

In testing the bridge, it is loaded with a constant point load over the span of a few minutes until failure. While this would result in a short term loading condition, the structure is being loaded to failure and as such, it not being designed to accommodate an extended life. Because of this, the KD factor for this bridge is 1.0.

3.2.3.2 Service Condition Factor (KS)

It is assumed that the bridge is designed and will operate under dry service conditions. Because of this, the KS factor for this bridge is 1.0.

3.2.3.3 Treatment Factor (KT)

As advertised on the company’s website1, the wood used for these sticks has no treatment of any kind. Because of this, the KT factor for this bridge is 1.0.

3.2.3.4 System Factor (KH)

From table 5.4.42, the system factor for tension and compression parallel to grain in a built up beam is 1.00, therefore the KH factor for this bridge is 1.0.

3.2.3.5 Lateral Stability Factor (KL)

While the frame has no bearing point lateral stability, the piers provide a wide stance. This concept was tested in previous years’ bridges and the result was found to be that it had a significant impact on lateral stability of the bridge, such that there was a negligible chance of the bridge failing to either side. Because of this, the KL factor for this bridge is 1.0.

1 http://www.loew-cornell.com/education/tipsandtechniques/flashpaper/40/index.html, January 6th, 2008 2 CSA-086-01, 2005 edition, page 30 Jacob Hammer Page 10 of 43 06/04/2018

3.3 Material Properties

3.3.1 Accepted Material Properties

ForsterTM, the company that produces the sticks I am using, has claimed on their website that all craft sticks they produce are made from 100% birch wood which has not been treated in the production process. While it is used for furniture and small fabrications, birch is not a standard construction wood, and as such stock values for it were not readily available. Research online provided the values below from the American Hardwood Information Centre3, which are detailed below in figure 3.1

(all units converted from Psi) Moisture Content Green 12% Modulus of Rupture (MPa) 44.1 116.5 Modulus of Elasticity (MPa) 8066.9 14961.6 Compression Parallel to Grain (MPa) 16.3 58.9 Compression Perp. to Grain (MPa) 1.9 7.4 Shear Parallel to Grain (MPa) 5.8 15.4 Tension Perp. To Grain (MPa) - - - 6.6 Figure 3.1

a) Results of tests on small clear specimens in the green and air-dried conditions. Definition of properties: compression parallel to grain is also called maximum crushing strength; compression perpendicular to grain is fiber stress at proportional limit; shear is maximum shearing strength; tension is maximum tensile strength; and side hardness is hardness measured when load is perpendicular to grain. b) Modulus of elasticity measured from a simply supported, center-loaded beam, on span depth ratio of 14/1. To correct for shear deflection, modulus can be increased by 10%.

3.3.2 Material Comparison and Interpretation

After testing of the axial properties of the popsicle sticks in various configurations (detailed in section 4.0), I was able to obtain approximate strength values for the popsicle sticks. Unfortunately, there is no published record of the moisture content of the packaged sticks. I can assume, however, that the properties vary on a linear proportionality. Based on this assumption, I can use the values I have calculated to approximate where the sticks lie on the moisture curve and estimate the material properties that I was unable to derive directly through testing.

Between green and 12% conditions, the ratio of tensile strength parallel to the grain to the shear strength parallel to the grain differs by only 0.97%. From this I can gather that the wood’s resistance to tensile failure in both fiber snap and shear out modes essentially increases linearly as it dries. Knowing the tensile strength of the wood from tests, I can estimate the shear strength within a reasonable area.

3 Wood Handbook, Wood as an Engineering Material, USDA Forest Service Jacob Hammer Page 11 of 43 06/04/2018

Between green and 12% conditions, the ratio of the compressive strength parallel to the grain and perpendicular to the grain differ by about 9.5%. While this value is higher than I would like, it still indicated a reasonable tight correlation. From this I can gather that the wood’s compressive strength increases at a steady rate as it dries, but the perpendicular strength gradually gets stronger in relation to the parallel strength. To err on the safe side, I will assume the same ratio in green conditions all the way through resulting in a slightly lower (but not drastically so) design value at lower moisture contents.

Between green and 12% conditions, the ratio of the compressive strength parallel to the grain and tensile strength parallel to the grain differ by about 27%. This is a very high number and can partially be accounted for due to the ratio’s being relatively small (2.7 and 2.0 respectively). This indicates that as the wood dries, the strength gain in compression slows relative to the strength gain in tension. I also know that as the wood goes from green to 12% conditions, the ratio of the parallel compressive strength to parallel shear strength differs by 35.7% (increasing from 2.8 to 3.8). Using these two relationship curves, and the tight correlation between tension and shear, I can approximate compressive strength by assuming that (a) the ratio change is linear through the drying process and (b) the average of the two estimates reflects the most accurate compressive strength.

At the 12% moisture level, I can see that the perpendicular tensile capacity is the weakest loading configuration and has a practically non-existent capacity in the green condition. From this I can assume that it is never a good idea to place birch wood in such an orientation and that I should ensure no sticks are exposed to perpendicular tensile loading as they would guarantee to be the failure point in the member. This also means that sticks should be examined to ensure that the cut of the stick aligns with the orientation of the grain. Some sticks are cut across the grain since they are marketed as craft sticks and not design to be exposed to such loading. These sticks must be discarded. In the final design, all sticks used will be inspected and any sticks with the grain orientation exceeding 10 degrees deviation will be discarded. Sticks with grain orientation almost parallel with be used for sections under tensile loading and the rest will be used for sections under compressive loading.

All that said, the tests indicated that the tensile capacity was well below the published strength values for green conditions, having a mean tensile stress of 25.7 MPa at failure averaged between the three raw tension tests. This indicates that the sticks were on average the same strength, and that the testing machine was accurate in its readings. The difference in the 5% strengths was due to the way each sample type carried the loading. The single sticks, being only a single stick with no glue or load sharing, reflect the true strength of the sticks. The built up members experienced load sharing (the full length glue contributing slightly more) and thus had higher 5% strength values. While the built up members are a better representation of the conditions in the bridge members, taking the tensile capacity from Test 1 gives the most conservative result. Jacob Hammer Page 12 of 43 06/04/2018

While it was impossible to test the compressive capacity of the sticks, the closest calculation would be to estimate using the ratios discussed above. If I take the ratio between tensile and compressive parallel capacity as 3.0, a conservatively scaled value of its green condition value, then I can estimate the compressive strength of the sticks as being roughly 4.085 MPa.

3.3.3 Accepted Working Values

While lower than the published values, accepted strength values for the sticks were found from material tests to be 12.3 MPa tensile and 4.1 MPa compressive. The modulus of elasticity was found to be 1700 MPa.

4.0 MATERIAL TESTS

Below is a discussion of all testing done so far, and still to be done. It includes diagrams, observed results (if completed), failure mode discussion, and observations on how the samples behaved differently from expected. For each subsection, the test number shown in parenthesis indicates the corresponding test results in the appendices.

For all tests, results are found in the appendix with the corresponding test number.

4.1 Base Tension Tests

This run had three different sets of samples: A single stick which had its centre narrowed, a set of three sticks with the tips glued, but the centres dry, and a set of three sticks with their entire lengths glued. The three sets were all run with the intention of finding the tensile capacity of the popsicle sticks. Figure 4.1 4.1.1 Single Stick Test [Test 1]

This test was a simple method of determining the tensile capacity by having a single member with known dimensions and applying an axial load. The centre of the member was carved out using a drum sander to create a cross section that was typically half the area of the rest of the stick. This allowed me to control the failure area of the sticks, observe the failure method, and easily calculate the corresponding stress capacity by using a calliper to calculate the cross section.

My initial theory was that these samples would fail by tear out at or very close to the vertex of the necking. Because each side of the necking was done separately, they didn’t completely line up and the two vertices were usually off by about 1 mm, although I didn’t expect this to have much effect. Jacob Hammer Page 13 of 43 06/04/2018

The most common failure method was a tear-out. The shear line would start at the vertex of the necking and would follow the grain to the edge or grips, whichever came first, and separate. When it reached the grips first, the remainder of the distance from the shear line to the edge would tear out along the grip in the direction of shortest distance to the edge. This shear out is due to the alignment of the wood grain relative to the cut of the sticks. In sticks with perfectly aligned grain (about 15%), the sample would snap at the vertex of the neck.

Figure 4.1 shows the sample setup and loading configuration. Capacity was calculated as P / A where A was the cross-sectional area at the narrowest point.

The results of this test can be observed in Appendix 1.

4.1.2 Triple Stick Dry Test [Test 2] Figure 4.2 This test was meant to calculate the tensile capacity of three sticks under axial loading to see if the individual stick capacity could be taken as a simple multiple when evaluating the capacity of a built up section. Three sticks were glued at the tips side by side and dried such that the ends were glued together but the middle section was dry. This would permit the sticks to break in the dry region measuring the capacity of the sticks alone.

After seeing how the single sticks behaved differently from my theory, my initial assumption for this test was that the samples would fail in a similar method (mostly by shear out), but because the axial was distributed over three sticks, the samples would fail at three times the capacity. Because I had gotten used to the minimum threshold required to hold the samples in place without over compressing the samples, I did not expect the crushing effects of the jaws to have an impact. As well, the relative cross- section reduction would be minimal.

In the end, this batch of test samples behaved almost exactly like I anticipated. Under the loading, the samples had a notably higher 5% strength, but the mean capacity was very close to Test 1’s. The observed failure mode was typically having all three sticks experience stress until one or two of them gave and snapped. The remainder would usually hold up the stress for a second or two longer before snapping. This shows that for a built up section, when one component broke, its share of the load would be carried over to the remaining sticks, but it would break soon-after. Therefore, for any bridge members, this test demonstrates that I can estimate with fair certainty that there is a linear relationship between area and capacity. My hypothesis about the effects of the jaw crushing the sample were also proven, as most of the samples fractured in the centre without having the failure lines approach or enter the jaws. Jacob Hammer Page 14 of 43 06/04/2018

Figure 4.2 shows the sample setup and loading configuration. Capacity was calculated as P / A where A was the cross-sectional area of three sticks. This was divided by three to get the approximate capacity per stick.

The results of this test can be observed in Appendix 2.

4.1.3 Triple Stick Glued Test [Test 3] Figure 4.3 This test was meant to calculate the tensile capacity of three sticks under axial loading to see if the individual stick capacity could be taken as a simple multiple when evaluating the capacity of a built up section. Three sticks were glued along their entire length to create a built up glued member. This test would see if, even when glued, the built up member could still be simplified as the sum of its parts.

After seeing how the first two tests ended, I assumed that this test would proceed in a similar fashion. The member would have a capacity of roughly three times test 1 and break in a shear out mode.

In the end, this test behaved almost identically to test 2, with one key difference. Because the sticks were glued together, compressed, and “cured”, they behaved as a single member, and shear planes would traverse all three sticks wherever possible at failure. Failure would cause all three sticks to break simultaneously. This shows that all the glue managed to do was hold the member together, and that the ultimate capacity was still dependant on the sticks, not the glue.

Figure 4.3 shows the sample setup and loading configuration. Capacity was calculated as P / A where A was measured as the average cross sectional area of the members at the centre. This was divided by three to get the approximate capacity per stick. Because the glue would increase the cross-sectional area by a marginal amount, I decided to take an average of 10 samples to see how much larger the cross sectional area was as a result of the glue. I found that the different was a negligible 4 mm2. This was likely due simply to measurement inaccuracy.

The results of this test can be observed in Appendix 3.

4.1.4 Conclusions

These tests were all designed to gauge the tensile capacity of the popsicle sticks. There were also designed to approximate how the capacities of build up sections would be estimated. The difference in 5% strength values between the tests was notable, however there is a good reason. Test 1 had a great deal of variability in Jacob Hammer Page 15 of 43 06/04/2018

sample construction (resulting in a larger range of results) while tests 2 and 3 had less (resulting in smaller ranges), so this would change the 5% ratings (which are essentially a function of test range). While the 5% ratings weren’t as close, the means, a better measure of the relationship of the tests, were very close. This lets me conclude that for any built up sections, I can approximate the equivalent tensile capacity as the sum of the sticks involved in it. Tests 2 and 3 showed that the glue interfaces really had no contribution towards tensile capacity, supporting my conclusion, and really only works to guide the failure lines between sticks. This conclusion can only hold provided that the sticks used have no knots or other critical flaws, and are all of uniform dimension.

Taking the 5% strengths of the weakest test is the safest bet for a design value. Therefore, I conclude that assuming a tensile capacity of 12.3 MPa will ensure that my design will almost certainly be stronger than anticipated.

4.2 Compression Tests

I had attempted to conduct simple compression tests on the sticks. Initially I tried a single stick, in the same configuration as a tensile test, but with the machine set to deliver a compression force. The stick did not buckle as I expected, but broke at the grip interface on both grips creating double-jointed member as depicted in figure 4.4. Observing that a single stick is too weak to test in compression, I tried a square member built up of 4 sticks glued together. The 4 stick widths, combined with the glue, roughly approximated a square column. Again, when I applied the compression force, the member broke in the same “double-jointed” manner. The upper grip of the Instron machine is attached by a universal joint, which prohibits compression testing properly on small samples like this. Ideally, the sample should buckle like any column under centred axial compression, but because the upper grip is free to sidesway, the reaction that would develop at the top of the Figure 4.4 column pushes the grip to the side effectively making the load conditions more accurately depicted as those in figure 4.4. For this reason, compression tests on stick samples cannot be conducted and as such, the compressive capacity of the sticks will have to be approximated by means of an empirical relationship.

4.3 Single Interface Glue Tests

This run had three sets of samples with glued interfaces of different lengths. The three sets were all run with the intention of finding the shear strength of the glue, as well as the threshold at where the glue becomes the limiting factor. Jacob Hammer Page 16 of 43 06/04/2018

4.3.1 6 cm Interface Test [Test 4]

These samples were constructed by taking two sticks, measuring a 6 cm length (total interface area of 570 mm2) along them and testing them to see the tensile capacity at which they broke, what caused them to break, and how they broke.

My initial theory was for samples with such a large bond area (almost half the length of the sticks), the limiting factor would be the sticks. I anticipated the glued portion, having been properly prepared and dried, to act as a single member and have the sticks break outside the ends of the interface.

For this batch, my theory was mostly confirmed. The sticks broke at the edge of the joint, leaving the interface intact. While a few of the sticks failed by interface separation, they were a clear minority. This shows that for a 6 cm interface length, the sticks are definitely the limiting factor. It also shows that for a built up member that consists of both dry and glued sections, the failure will almost certainly occur at the edge of the glue joint.

Figure 4.5 shows the sample setup and loading configuration. Because of the asymmetrical setup of these samples, stress could not be calculated as a simple formula of P / A. With respect to the bottom, which is firmly held in place, the grip attached to the upper part of the sample creates an eccentricity of roughly 2 mm (the thickness of one stick). As well, because the upper arm is free to sidesway, the loading on the upper part is also subject to a diagonal loading. However, the testing machine registers axial load in the direction of the traverse regardless of the orientation of the arm, ergo the number I received is the vertical loading the traverse was experiencing, not the load parallel to the direction of the arm. Because the eccentricity was also only 2 mm, relative to the length of the arm (over 50 cm), the loading at the tip of the sample would be inclined at an angle of less than 0.02 degrees to the normal, an angle which would yield a negligible effect in the calculation of the vertical loading applied at the upper end of the sample. On account of these observations, the eccentricity can be neglected for shear and tension calculations, however it should be noted that this generates a combined moment of (2 * 2 mm * P) at the centre of the sample, which assists in peeling apart the interface. When compared to the double interface test set, these glue capacities are likely to be slightly smaller than they should proportionately be. Figure 4.5

The results of this test can be observed in Appendix 4. Jacob Hammer Page 17 of 43 06/04/2018

4.3.2 4 cm Interface Test [Test 5]

These samples were constructed by taking two sticks, measuring a 4 cm length (total interface area of 380 mm2) along them and testing them to see the tensile capacity at which they broke, what caused them to break, and how they broke.

Following the observations from test 4, my hypothesis for this set of samples was that they would fail in a similar manner, at the joints, however as the interface length was shorter, there was a better chance of the glue joint being the limiting factor and thus the samples failing from interface failure.

This batch followed my theory with the number of interface failures rising from less than 5% to about 30%. This shows that while the majority of the samples still failed by the sticks breaking at the joint, the glue interface has reached a point where it can be the limiting factor if the construction conditions of the interface are inferior.

Test 5 has an identical configuration to test 4, and as such, section 4.3.1 describes the process by which the stress capacity for these samples was calculated.

The results of this test can be observed in Appendix 5.

4.3.3 2 cm Interface Test [Test 6]

These samples were constructed by taking two sticks, measuring a 2 cm length (total interface area of 190 mm2) along them and testing them to see the tensile capacity at which they broke, what caused them to break, and how they broke.

Following the observations from test 4 and 5, my hypothesis for this set of samples was that while some would fail at the joints, the interface size will have reached or passed the threshold and that it will now be almost exclusively the limiting factor.

For this batch, my theory was confirmed. Interface separation failures made up about 90% of the failure modes, with the sticks themselves showing little to no signs of elongation, or fracture. This clearly shows that with a 2cm glue joint interface, the glue has become the limiting factor.

Test 6 has an identical configuration to test 4, and as such, section 4.3.1 describes the process by which the stress capacity for these samples was calculated.

The results of this test can be observed in Appendix 6. Jacob Hammer Page 18 of 43 06/04/2018

4.3.4 Conclusions

These tests were meant to gauge the shear strength of the glue, as well as discover the threshold for when an edge-grain glue joint is weaker than the wood it’s connecting and will give first. I discovered that even that for a 570 mm2 joint, the glue has a slight chance of failing first. As the joint area decreased, the glue had a higher chance of failing, and under 200 mm2 the joint was essentially guaranteed to fail first. While it would be impossible for all sticks to be connected with joints larger than 6 cm in the actual bridge (as the sticks are just under 12 cm long), these tests only observed single shear plane failure. I shall make a tentative conclusion for now that with a built up member and sticks glued on both sides, the glue will not fail first. I will test this hypothesis in the next run of tests.

The glue used, made by Mastercraft, advertises a shear strength of “over 19.3 MPa” (taken from the back of the bottle). My tests showed that this glue performs well under this advertised capacity. I am unsure as to the conditions under which this value was decided upon, but since it was provided by the manufacturer, I’m sure that this value was unrealistic and only attained once under absolutely ideal lab conditions. Sample variance is a product of amount of glue used, compression applied during the drying process (which can thin the layer of glue between sticks) and accuracy of the interface dimensions (some sticks slid up to 2 mm under the compression in the drying process). Because of this, and the wide range of ultimate capacities under which the interface joints failed, I cannot conclude for certain what the shear capacity of the glue is. What I can ascertain is how large I need to make my interfaces to avoid having the glue fail. From these tests, my conclusion is that an area of over 600 mm2 (cumulative between both sides) would prevent a glue separation from controlling.

4.4 Double Interface Glue Tests Figure 4.6

Similar to the single interface tests, these tests were a backup to the original run of tests to verify my conclusion about the glue’s strength. The double interface allowed me to test conditions that were closer to the final members (glued on both sides) as well as allowed me to create larger interface areas. For these tests, no displacement data was recorded as the length of the samples forced the machine to operate outside of the displacement gauge’s operational range.

4.4.1 4 cm Interface Test [Test 7]

These samples were assembled as detailed in figure 4.6. Tensile force was applied to the central stick until failure. The interface at each end was 4 cm long on either side of the central stick for a total interface area of 760 mm2 at each end. Jacob Hammer Page 19 of 43 06/04/2018

My initial theory was that for such a large interface area, there would be no interface failures, and all samples would fail at the edge of the joints.

These samples primarily followed my hypothesis, but there were a few interface failures. These failures were few and were not clean interface failures observed in the smaller joint tests, but the wood around the interface failed along with the glue. I believe this was merely a result of weak wood in the side sticks and the joints failing as close to the joint as possible. While I assumed for these tests that two parallel 4 cm interfaces would be the same as a single 8 cm interface, the truth is that they’re still only 4 cm long, which had several interface failures in the single interface tests. An improper or unusually large axial force could cause one of the sides to give and with only half the support, the other side of the joint easily snaps as joint instantly has to take twice its intended loading.

Figure 4.6 shows the sample setup and loading configuration. The stick’s capacity was calculated as P / A where A was the cross-sectional area of a single stick.

The results of this test can be observed in Appendix 7.

4.4.2 3 cm Interface Test [Test 8]

These samples were assembled as detailed in figure 4.6. Tensile force was applied to the central stick until failure. The interface at each end was 3 cm long on either side of the central stick for a total interface area of 570 mm2 at each end.

From the single interface test observations, my theory was that these would follow the same failure pattern as the single interface tests, with test 8 having a few more interface failures than test 7, but a fraction of the number in test 9.

Test 8 followed the pattern I was expecting with the single interface run of tests.

Figure 4.6 shows the sample setup. The stick’s capacity was calculated as P / A where A was the cross-sectional area of a single stick.

The results of this test can be observed in Appendix 8.

4.4.3 2 cm Interface Test [Test 9]

These samples were assembled as detailed in figure 4.6. Tensile force was applied to the central stick until failure. The interface at each end was 2 cm long on either side of the central stick for a total interface area of 380 mm2 at each end.

Similar to test 6, I believed that these samples would have the highest rate of interface failures for all three tests in this run. At least half of these samples would fail by interface separation. Jacob Hammer Page 20 of 43 06/04/2018

These samples primarily followed my hypothesis, with a 38% interface failure rate. This seems to be consistent with my earlier findings as these samples had the same cumulative interface area as test 5, which had around a 35% interface failure rate.

Figure 4.6 shows the sample setup. The stick’s capacity was calculated as P / A where A was the cross-sectional area of a single stick.

The results of this test can be observed in Appendix 9.

4.4.4 Conclusions

These tests were meant to verify my conclusions from the single interface test run. After observing these tests, I can conclude firmly that I was correct. Test 7 had the same number of interface failures as test 4, showing that while both joints were sturdy, they could still fail. As the interface area got smaller, the number of samples that failed by interface separation increased proportionately, confirming that any interfaces smaller than those in test 4 or 7 would simply be inadequate. The absolute lowest shear strength found in a sample from Tests 4 to 9 in which the glue interface failed was 1.65 MPa (found in Test 7). This means that a single 9.5 mm wide popsicle stick glued along its entire length (assumed to be 10 cm) on both sides would require an axial force greater than 3.1 kN to separate the interface.

In construction of final bridge members, the largest bond I can form between sticks is to cut all sticks to the same length (by squaring off the ends) and have them overlap with half their length (about 45 mm) on either side. Following the trend of these tests, there shouldn’t be any interface failures. In the event the interface between any two given sticks fails, those sticks would still be attached on their other side, allowing the member to continue supporting the same axial load.

4.5 Modulus of Elasticity

This test is designed to test the modulus of elasticity of the popsicle sticks.

4.5.1 MoE Testing [Test 10]

A single stick is placed in the grips of the testing machine and loaded at a much slower speed than the rest of the tests (approximately 1.5 mm per minute). Readings are taken at short arbitrary intervals for several samples until a reasonable pattern emerges. These sticks were not narrowed at the centre because I needed them to last longer before they break, as well as because the test was more concerned with their behaviour before rupture instead of at rupture. Jacob Hammer Page 21 of 43 06/04/2018

I expected the sticks to fail much in the fashion of those in Test 1. I also expected the modulus curve, when graphed, to have a fairly straight correlation ending in abrupt failure given the brittle nature of wood, as opposed to the curve seen in metals.

As observed in the chart in appendix 10, the samples had a quickly emerging pattern. The stress-strain curve of the sticks was a straight line (albeit with some wiggle due to inaccuracies in recording) that was easily evaluated.

The modulus of elasticity was taken as the slope of the line of best fit, which is parallel to samples 3 and 4. It is evaluated as rise over run.

The results of this test can be observed in Appendix 10.

4.5.2 Conclusion

Using sample 4, which yielded nearly ideal results, the slope can be calculated using the equation [ Δ stress ] / [ (Δ deformation) / length ] = MoE

Assuming deformation along the entire length of the stick (113 mm): [110.6 - 9.5] / [(3786-243)/113)] = 3224 MPa

Assuming deformation along only the exposed length of the stick (60 mm): [110.6 - 9.5] / [(3786-243)/60)] = 1712 MPa

In this test, the jaws have interfered with the proper measurement of the modulus. While the entire length did not deform uniformly due to the effect of the jaws, it is also incorrect to assume that only exposed section deformed as well. As there is no way of knowing what percentage of the overall deformations occurred in each section, the most conservative estimate would be to assume 100% in the exposed region.

Therefore, the modulus of elasticity is estimated at 1700 MPa.

4.6 Dental Floss Tests

This test is designed to test the tensile capacity of dental floss and its feasibility as a cable tie to be used in a popsicle stick bridge.

4.6.1 5 cm 10 Braid Test [Test 11]

A braid of 10 strands will be weaved into a simple braid and will be coated in glue. Tests 2 and 3 have already demonstrated that the white glue will have almost no contribution in tensile capacity and thus will only serve as cohesion on the braid for testing. Jacob Hammer Page 22 of 43 06/04/2018

While I have no grounds upon which to base any numerical hypothesis for the capacity of the braids, I believe that the synthetic nature of dental floss will allow it to have a fairly uniform capacity. I also expect this to mean that the capacity of any braid can be estimated as the sum of its components.

To attach dental floss braids to the bridge, a hole would be drilled through the members and the braid threaded through. The two loose ends would be secured with a double reef knot, a good binding knot with a negligible chance of slipping. The knot would also help prevent it from sliding around is it would be too large to go through the holes. This configuration results in two possible failure modes: the braid snaps, or the member has a local tear-out and the braid removes the material holding it in. Considering the braid size, and the area over which it is acting, a local tear out seems the most likely as all the stress carried by the cable would be acting over very little area.

To test this, two anchors of 3 sticks glued together and dried will have a hole drilled through them and a braid looped between them. The anchors will be placed in the grips of the Instron and tested in tension. The machine’s readings will be used to determine the maximum tensile capacity at failure should the braid snap. Figure 4.7

As predicted, testing resulted in local tear-out failure. Because the anchors had grain parallel to the line of action, the braid easily tore out a path between the fibers. While further testing of the dental floss is required, this experiment has made it apparent that using dental floss as a cable when its line of action is parallel to the grain of the wood is an entirely bad idea. Figure 4.8 A second experiment was performed to accommodate for the grain orientation as illustrated in Figure 4.8. The floss rope was tied around two smaller blocks with their grain perpendicular to the floss. The trial sample of this test gave very unfavourable results, with the 5-braid strand taking 280 N with an accompanying deformation of 11.9 mm before the braid snapped. While this is an impressively large loading for such a small area, this means that using the dental floss would be overall unproductive on the bridge as it would deform too much to be of any use in small braids. A braid sufficiently large would require too large a hole drilled in the bridge compromising the integrity of the member.

This result also concludes that a hybrid member comprised of popsicle sticks and dental floss (in a manner similar to rebar in a concrete member) would have no real benefits. Because of the floss’s small cross-sectional area, the tensile strength of the floss would be overshadowed by the stick and by the time the floss had been braided Jacob Hammer Page 23 of 43 06/04/2018

enough to control tensile capacity, its size would significantly impact the geometry of the sticks. In compression, the floss could contribute nothing and the sticks already low capacity of 4 MPa needs as much cross-sectional area as it can get, with the floss only reducing it.

The results of this test can be observed in Appendix 11.

4.7 Tension Member Connection Joint Tests

Because of the member size restrictions of the bridge, the tension member must be made of two smaller sections that are jointed together prior to testing. In order to do this, the two base members must have a prefabricated interface that can be easily assembled prior to construction. These tests explore the possibilities considered for construction this joint. It should be noted for all tests below that glue yields strongest bonds when used between edge-grain surfaces (two sticks side to side), and weak bonds when used between end-grain surfaces (two sticks end to end).

4.7.1 Scarf Joint Test [Test 12] Figure 4.9 This configuration would consist of the two sub-members meeting at a straight interface that would span the entire cross- sectional area. As shown in figure 4.9, this interface would stretch length L and be inclined at angle θ, thus making the total glued interface area of the two sub-members be [w * h / sin (θ)]. I know from basic mechanics that for any such interface joint, the strength of the joint increases as the area of the interface increases, and thus as L increases. Therefore I will not test any interfaces with L less than 1 cm (perpendicular interfaces) as I know these will inherently be weaker than any larger L, as well as being primarily an end-grain interface, which is relatively weaker.

As the glue interface tests demonstrated, a glue interface failure becomes likelier as the interface size decreases. Therefore, after a certain threshold, the member’s cross-sectional area will become its limiting factor.

All samples failed by interface separation leaving the two halves fully intact, With interface areas well below my calculated requirements above. The samples had a superior strength and showed that the glue used is very strong in perpendicular separation, making this a very feasible candidate for the tension joint. My hypothesis was actually opposite of the results, with the shallower angles yielding worse results. Jacob Hammer Page 24 of 43 06/04/2018

Figure 4.9 shows the sample setup and loading configuration. The joint’s capacity was calculated as P / A where A was the cross-sectional area of the glue interface, calculated as [w * h / sin (θ)].

The results of this test can be observed in Appendix 12. Figure 4.10 4.7.2 Half Lap Splice Joint Test [Test 13]

Similar to the straight interface test this interface would use the edge-grain strength property of glue to its advantage. The tension member would be made of three Z-shaped pieces, with the inner piece being simply to extend the length and the outer two pieces having the joints for them to connect to the two compression members. This setup would require three pieces instead of two because having two members connect at a lap joint wouldn’t do much to reduce the sub-members’ lengths. Figure 4.10 shows how these pieces would be assembled.

I would assume the limiting factor here would be the cross- sectional area of one lip. I would assume that with the interface being completely parallel, the member will behave just like a solid prefabricated member, except for the areas where there’s one giant end-to-end interface. To err on the side of caution, I would assume the glue at this joint, even when snugly fit, to carry no tensile stress and for the other half of the sub-member to carry it all. This interface should, in theory, reduce the problem to a simple axial stress problem.

These samples were essentially much wider versions of the coupon samples used in tests 4 to 6, and yielded very similar results. The most significant similarity was deformation. While these samples had somewhat lower capacities, the deformation result was significantly lower, making this a prime candidate for a rigid joint.

Figure 4.10 shows the sample setup and loading configuration. The joint’s capacity was calculated as P / A where A was the cross-sectional area of the glue interface, calculated as [w * L].

The results of this test can be observed in Appendix 13. Jacob Hammer Page 25 of 43 06/04/2018

4.7.3 Conclusion

While the Scarf Joint test showed significantly better capacities, the Lap Splice had a fraction of the deformation. I can build the tension member to have much larger areas for the lap splice joint, permitting it to reach higher capacities, but the results from both tests clearly indicated that the scarf joint had a 34% increase in capacity, but cost a 406% increase in deformation, something I cannot afford to have in the tension member of my bridge. Therefore, I shall build the tension member joint out of a lap slice, using the calculate 5% capacity of 1.4 MPa.

4.8 Member to Member Joint Tests

This test is designed to find the best method for attaching the individual members to each other to construct the final bridge design.

4.8.1 Dowel Pin Connection [Test 14]

This test will observe the ability of a fabricated dowel (rounded glulam) to connect two members. This would be accomplished by making two members, drilling a hole through them and connecting them with a dowel as illustrated in figure 4.11. Because of the limitations of the testing machine, this joint can only be tested in tension, however the dowel would ultimately undergo bending deformation and so a compressive force of equivalent magnitude would yield the same deformations, only in the opposite directions. No glue would be used to hold this joint together.

I believe this connection method is weak on its own, but could be combined with other methods to make an overall stronger joint. Figure 4.11

This joint was a complete failure. While the dowel has been perfectly rounded down and the assembly fabricated as per figure 4.11, the two outer connections merely slid apart as the assembly was pulled. It ultimately failed when the length L (the distance from the tip to the hole, cut 1.5 times the pin diameter from the tip) tore out. This joint has proven to be a poor choice without proper fastening, which would be infeasible given materials provided. Furthermore the pin joint would be required to be used when connecting two members near the tip, making it infeasible and prone to tear-out failure.

4.7.3 Conclusion

A pin joint will not be used on this bridge, and instead members will be connected by an overlapping interface length in excess of 700 mm2 of glue. This appears to be the most rigid joint with a reasonably high capacity. Jacob Hammer Page 26 of 43 06/04/2018

Appendix Jacob Hammer Page 27 of 43 06/04/2018

Appendix 1 – Raw Data for Test 1

Test Strength Diameter Stress Test Strength Diameter Stress (N) (in) (MPa) (N) (in) (MPa) 606 0.163 13.07 1121 0.172 25.50 541 0.188 13.45 1114 0.180 26.52 483 0.218 13.93 1094 0.187 27.06 719 0.163 15.50 1117 0.184 27.18 810 0.155 16.61 1046 0.199 27.53 646 0.202 17.26 1063 0.199 27.98 763 0.185 18.67 1008 0.214 28.53 778 0.183 18.83 1172 0.194 30.07 772 0.185 18.89 1263 0.181 30.24 763 0.190 19.17 1168 0.196 30.28 798 0.194 20.48 1211 0.192 30.75 813 0.191 20.54 1086 0.222 31.89 851 0.185 20.82 1339 0.186 32.94 785 0.202 20.97 1222 0.207 33.46 926 0.174 21.31 1305 0.195 33.66 907 0.180 21.59 1436 0.184 34.95 809 0.203 21.72 1368 0.194 35.10 823 0.203 22.10 1281 0.217 36.77 828 0.202 22.12 1337 0.210 37.14 923 0.190 23.20 1561 0.181 37.37 913 0.201 24.27 1408 0.207 38.55 956 0.194 24.53 1543 0.191 38.98 957 0.196 24.81 1497 0.201 39.80 1158 0.162 24.81 1527 0.200 40.39 890 0.214 25.19 2285 0.203 61.35

Test Strength (N) Stress (MPa)

Mean 1055.800 26.957 Standard Error 46.088 1.264 Median 1027 25.347 Standard Deviation 325.891 8.938 Sample Variance 106205.184 79.889 Range 1802 48.288 Minimum 483 13.065 Maximum 2285 61.353 Conf. Level (95.0%) 92.62 2.54

5% Rating: 519.756 12.255 Jacob Hammer Page 28 of 43 06/04/2018

Appendix 2 – Raw Data for Test 2

Test Strength Displacement Stress Test Strength Displacement Stress (N) (mm) (MPa) (N) (mm) (MPa) 2754 5.354 45.53 4466 10.142 73.84 2912 7.497 48.15 4551 7.774 75.24 3361 3.777 55.57 4583 8.793 75.77 3422 6.389 56.58 4607 8.513 76.17 3499 8.751 57.85 4659 10.128 77.03 3521 6.974 58.21 4675 12.065 77.29 3618 9.484 59.82 4682 9.331 77.41 3620 5.977 59.85 4720 7.538 78.04 3658 8.881 60.48 4754 10.593 78.60 3699 9.11 61.16 4800 8.357 79.36 3797 9.369 62.78 4908 12.066 81.15 3895 8.821 64.40 4970 10.819 82.17 4018 8.646 66.43 4972 12.803 82.20 4092 8.932 67.65 4981 10.424 82.35 4151 10.684 68.63 4987 10.184 82.45 4201 6.382 69.46 5047 11.325 83.44 4215 11.138 69.69 5075 9.821 83.91 4231 9.76 69.95 5200 11.863 85.97 4240 9.729 70.10 5354 12.655 88.52 4280 7.467 70.76 5428 11.042 89.74 4377 8.988 72.37 5501 12.643 90.95 4402 11.162 72.78 5748 9.647 95.03 4409 11.738 72.90 6235 11.843 103.09 4423 10.526 73.13 6291 13.735 104.01

Test Strength (N) Displacement (mm) Stress (MPa)

Mean 4458.104 9.576 73.707 Standard Error 110.343 0.302 1.824 Median 4444.5 9.688 73.483 Standard Deviation 764.477 2.090 12.639 Sample Variance 584424.691 4.370 159.754 Range 3537 9.958 58.479 Minimum 2754 3.777 45.533 Maximum 6291 13.735 104.011 Conf. Level (95.0%) 221.981 0.607 3.670

5% Rating: 3200.652 13.014 52.918 Mean / stick: 1486.035 3.192 24.569 5% / stick: 1066.884 4.338 17.639 Jacob Hammer Page 29 of 43 06/04/2018

Appendix 3 – Raw Data for Test 3

Test Strength Displacement Stress Test Strength Displacement Stress (N) (mm) (MPa) (N) (mm) (MPa) 2977 6.996 52.49 4310 8.103 75.99 2994 5.909 52.79 4354 8.303 76.76 3195 10.127 56.33 4370 7.853 77.05 3368 8.366 59.38 4409 8.548 77.73 3470 7.545 61.18 4514 7.717 79.59 3597 9.364 63.42 4523 8.571 79.74 3636 8.961 64.11 4546 9.721 80.15 3777 7.934 66.59 4596 9.061 81.03 3800 7.513 67.00 4643 6.521 81.86 3876 7.96 68.34 4684 10.097 82.58 3899 7.8 68.74 4705 10.312 82.95 3943 7.346 69.52 4706 9.954 82.97 3995 10.326 70.44 4757 9.965 83.87 4022 7.656 70.91 4977 10.478 87.75 4031 8.131 71.07 5011 12.123 88.35 4062 6.779 71.62 5020 10.243 88.51 4069 8.884 71.74 5042 10.162 88.90 4098 9.201 72.25 5103 10.444 89.97 4109 9.157 72.45 5128 10.626 90.41 4203 7.726 74.10 5327 9.088 93.92 4210 8.04 74.23 5430 10.653 95.74 4224 9.262 74.47 5685 12.21 100.23 4266 8.925 75.21 5694 11.714 100.39 4301 11.689 75.83 5949 11.284 104.89

Test Strength (N) Displacement (mm) Stress (MPa)

Mean 4366.771 9.070 76.990 Standard Error 98.173 0.217 1.731 Median 4305.5 9.011 75.910 Standard Deviation 680.165 1.504 11.992 Sample Variance 462624.308 2.262 143.806 Range 2972 6.301 52.399 Minimum 2977 5.909 52.487 Maximum 5949 12.21 104.886 Conf. Level (95.0%) 197.499 0.437 3.482

5% Rating: 3247.999 11.544 57.265 Mean / stick: 1455.590 3.023 25.663 5% / stick: 1082.666 3.848 19.088 Jacob Hammer Page 30 of 43 06/04/2018

Appendix 4 – Raw Data for Test 4

(glue interface failures denoted in boldface) Test Glue Stick Test Glue Stick Strength Displacement Stress Stress Strength Displacement Stress Stress (N) (mm) (MPa) (MPa) (N) (mm) (MPa) (MPa) 343 0.678 0.60 17.01 1271 1.914 2.22 63.04 515 0.763 0.90 25.54 1290 1.854 2.26 63.98 742 0.772 1.30 36.80 1335 1.645 2.34 66.22 866 1.275 1.52 42.95 1396 2.209 2.44 69.24 930 1.081 1.63 46.13 1480 2.299 2.59 73.41 980 1.148 1.71 48.61 1505 2.179 2.63 74.65 1076 1.453 1.88 53.37 1553 1.936 2.72 77.03 1123 2.306 1.97 55.70 1671 2.546 2.92 82.88 1163 1.916 2.03 57.68 1714 2.362 3.00 85.01 1188 1.532 2.08 58.92 1729 0.915 3.03 85.76 1193 1.75 2.09 59.17 1764 2.438 3.09 87.49 1197 1.778 2.09 59.37 1782 2.167 3.12 88.39 1233 1.691 2.16 61.16 1955 3.333 3.42 96.97 1256 1.715 2.20 62.30 2008 2.45 3.51 99.60 1268 2.242 2.22 62.89 2084 3.839 3.65 103.37

Test Strength (N) Displacement (mm) Glue Stress (MPa) Stick Stress (MPa)

Mean 1320.333 1.873 2.310 65.489 Standard Error 76.086 0.131 0.133 3.774 Median 1269.5 1.884 2.221 62.967 Standard Deviation 416.739 0.716 0.729 20.670 Sample Variance 173671.540 0.513 0.532 427.261 Range 1741 3.161 3.046 86.354 Minimum 343 0.678 0.600 17.013 Maximum 2084 3.839 3.647 103.367 Confidence Level (95.0%) 155.613 0.267 0.272 7.718

5% Rating: 634.858 0.695 1.111 31.489

Lowest controlling glue stress: 3.12 MPa Jacob Hammer Page 31 of 43 06/04/2018

Appendix 5 – Raw Data for Test 5

(glue interface failures denoted in boldface) Test Glue Stick Test Glue Stick Strength Displacement Stress Stress Strength Displacement Stress Stress (N) (mm) (MPa) (MPa) (N) (mm) (MPa) (MPa) 638 1.389 1.67 31.64 1288 2.721 3.38 63.88 690 1.091 1.81 34.22 1290 1.53 3.39 63.98 810 1.034 2.13 40.18 1340 1.976 3.52 66.46 878 1.056 2.30 43.55 1346 1346 1346 1346 902 1.308 2.37 44.74 1405 2.22 3.69 69.69 952 1.455 2.50 47.22 1435 1.777 3.77 71.18 1070 1.134 2.81 53.07 1448 1.565 3.80 71.82 1113 1.576 2.92 55.20 1479 1.622 3.88 73.36 1144 1.695 3.00 56.74 1549 2.308 4.07 76.83 1227 2.131 3.22 60.86 1558 2.46 4.09 77.28 1247 2.632 3.27 61.85 1577 2.288 4.14 78.22 1268 1.688 3.33 62.89 1626 1.761 4.27 80.65 1279 1.832 3.36 63.44 1724 2.25 4.52 85.51 1285 1.874 3.37 63.74 1844 2.366 4.84 91.46 1285 1.12 3.37 63.74 1861 2.066 4.88 92.31

Test Strength (N) Displacement (mm) Glue Stress (MPa) Stick Stress (MPa)

Mean 1285.267 1.799 3.373 63.749 Standard Error 56.862 0.088 0.149 2.820 Median 1286.5 1.769 3.377 63.811 Standard Deviation 311.445 0.483 0.817 15.448 Sample Variance 96997.926 0.233 0.668 238.631 Range 1223 1.687 3.210 60.661 Minimum 638 1.034 1.675 31.645 Maximum 1861 2.721 4.885 92.306 Confidence Level (95.0%) 116.295 0.180 0.305 5.768

5% Rating: 772.985 1.005 2.029 38.340

Lowest controlling glue stress: 2.37 MPa Jacob Hammer Page 32 of 43 06/04/2018

Appendix 6 – Raw Data for Test 6

(glue interface failures denoted in boldface) Test Glue Stick Test Glue Stick Strength Displacement Stress Stress Strength Displacement Stress Stress (N) (mm) (MPa) (MPa) (N) (mm) (MPa) (MPa) 488 0.757 2.56 24.20 1004 1.33 5.27 49.80 619 1.658 3.25 30.70 1006 1.342 5.28 49.90 633 1.728 3.32 31.40 1054 1.353 5.53 52.28 671 0.977 3.52 33.28 1061 1.635 5.57 52.63 707 1.438 3.71 35.07 1124 1.519 5.90 55.75 734 0.889 3.85 36.41 1202 1.367 6.31 59.62 735 1.019 3.86 36.46 1236 2.219 6.49 61.31 740 1.159 3.88 36.70 1242 1.441 6.52 61.60 798 1.177 4.19 39.58 1248 1.393 6.55 61.90 858 1.814 4.50 42.56 1253 1.567 6.58 62.15 888 1.875 4.66 44.04 1305 1.611 6.85 64.73 931 1.311 4.89 46.18 1383 2.362 7.26 68.60 962 1.38 5.05 47.72 1416 1.588 7.43 70.23 965 1.299 5.07 47.86 1484 1.859 7.79 73.61 978 1.367 5.13 48.51 1744 1.941 9.15 86.50

Test Strength (N) Displacement (mm) Glue Stress (MPa) Stick Stress (MPa)

Mean 1015.633 1.479 5.331 50.376 Standard Error 53.841 0.066 0.283 2.670 Median 991 1.416 5.202 49.154 Standard Deviation 294.897 0.362 1.548 14.627 Sample Variance 86964.240 0.131 2.396 213.947 Range 1256 1.605 6.593 62.298 Minimum 488 0.757 2.562 24.205 Maximum 1744 2.362 9.155 86.503 Confidence Level (95.0%) 110.116 0.135 0.578 5.462

5% Rating: 530.571 0.884 2.785 26.316

Lowest controlling glue stress: 2.56 MPa Jacob Hammer Page 33 of 43 06/04/2018

Appendix 7 – Raw Data for Test 7

(glue interface failures denoted in boldface) Test Glue Stick Test Glue Stick Strength Stress Stress Strength Stress Stress (N) (MPa) (MPa) (N) (MPa) (MPa) 841 1.10 41.71 1627 2.14 80.70 896 1.18 44.44 1633 2.14 81.00 1042 1.37 51.68 1642 2.15 81.44 1045 1.37 51.83 1727 2.27 85.66 1049 1.38 52.03 1736 2.28 86.11 1063 1.40 52.72 1750 2.30 86.80 1223 1.60 60.66 1785 2.34 88.54 1252 1.64 62.10 1799 2.36 89.23 1256 1.65 62.30 1839 2.41 91.21 1353 1.78 67.11 1849 2.43 91.71 1355 1.78 67.21 1900 2.49 94.24 1483 1.95 73.56 1924 2.52 95.43 1491 1.96 73.95 1963 2.58 97.36 1501 1.97 74.45 2243 2.94 111.25 1552 2.04 76.98 2435 3.20 120.78 1593 2.09 79.01

Test Strength (N) Glue Stress (MPa) Stick Stress (MPa)

Mean 1566.867 2.056 77.717 Standard Error 67.000 0.088 3.323 Median 1610 2.113 79.856 Standard Deviation 366.975 0.482 18.202 Sample Variance 134670.395 0.232 331.312 Range 1539 2.020 76.335 Minimum 896 1.176 44.442 Maximum 2435 3.196 120.776 Confidence Level (95.0%) 137.031 0.180 6.797

5% Rating: 963.247 1.264 47.777

Lowest controlling glue stress: 1.65 MPa Jacob Hammer Page 34 of 43 06/04/2018

Appendix 8 – Raw Data for Test 8

(glue interface failures denoted in boldface) Test Glue Stick Test Glue Stick Strength Stress Stress Strength Stress Stress (N) (MPa) (MPa) (N) (MPa) (MPa) 742 1.30 36.80 1624 2.84 80.55 982 1.72 48.71 1630 2.85 80.85 1038 1.82 51.48 1675 2.93 83.08 1052 1.84 52.18 1691 2.96 83.87 1062 1.86 52.68 1709 2.99 84.77 1102 1.93 54.66 1714 3.00 85.01 1168 2.04 57.93 1776 3.11 88.09 1224 2.14 60.71 1776 3.11 88.09 1245 2.18 61.75 1789 3.13 88.73 1251 2.19 62.05 1795 3.14 89.03 1443 2.52 71.57 1841 3.22 91.31 1548 2.71 76.78 1885 3.30 93.50 1550 2.71 76.88 1898 3.32 94.14 1568 2.74 77.77 1910 3.34 94.74 1586 2.78 78.67 1987 3.48 98.56

Test Strength (N) Glue Stress (MPa) Stick Stress (MPa)

Mean 1508.7 2.640 74.832 Standard Error 61.387 0.107 3.045 Median 1605 2.808 79.608 Standard Deviation 336.229 0.588 16.677 Sample Variance 113049.941 0.346 278.122 Range 1245 2.178 61.752 Minimum 742 1.298 36.803 Maximum 1987 3.477 98.555 Confidence Level (95.0%) 125.550 0.220 6.227

5% Rating: 955.653 1.672 47.400

Lowest controlling glue stress: 2.04 MPa Jacob Hammer Page 35 of 43 06/04/2018

Appendix 9 – Raw Data for Test 9

(glue interface failures denoted in boldface) Test Glue Stick Test Glue Stick Strength Stress Stress Strength Stress Stress (N) (MPa) (MPa) (N) (MPa) (MPa) 685 1.80 33.98 1580 4.15 78.37 792 2.08 39.28 1587 4.17 78.72 824 2.16 40.87 1589 4.17 78.81 1033 2.71 51.24 1626 4.27 80.65 1069 2.81 53.02 1670 4.38 82.83 1117 2.93 55.40 1688 4.43 83.72 1152 3.02 57.14 1836 4.82 91.07 1153 3.03 57.19 1860 4.88 92.26 1154 3.03 57.24 1879 4.93 93.20 1173 3.08 58.18 1937 5.08 96.08 1197 3.14 59.37 1983 5.20 98.36 1431 3.76 70.98 2042 5.36 101.28 1484 3.90 73.61 2045 5.37 101.43 1537 4.03 76.24 2288 6.01 113.49 1555 4.08 77.13 2300 6.04 114.08 1559 4.09 77.33 2360 6.19 117.06 1575 4.13 78.12 2409 6.32 119.49 1578 4.14 78.27 2418 6.35 119.93

Test Strength (N) Glue Stress (MPa) Stick Stress (MPa)

Mean 1587.917 4.168 78.761 Standard Error 77.930 0.205 3.865 Median 1579 4.144 78.319 Standard Deviation 467.579 1.227 23.192 Sample Variance 218630.25 1.506 537.868 Range 1733 4.549 85.957 Minimum 685 1.798 33.976 Maximum 2418 6.346 119.933 Confidence Level (95.0%) 158.206 0.415 7.847

5% Rating: 818.817 2.149 40.613

Lowest controlling glue stress: 2.81 MPa Jacob Hammer Page 36 of 43 06/04/2018

Appendix 10 – Raw Data for Test 10

Sample 1 Sample 2 Sample 3 Sample 4 Stress Displacement Stress Displacement Stress Displacement Stress Displacement (MPa) (μm) (MPa) (μm) (MPa) (μm) (MPa) (μm) 10.2 510 9.0 643 9.4 545 9.5 243 19.6 845 26.7 945 18.0 941 18.6 753 26.9 1034 34.5 1250 21.4 1121 22.5 892 33.3 1329 41.0 1333 32.1 1484 31.5 1267 41.6 1606 47.9 1517 41.3 1727 40.9 1431 48.3 1877 53.4 1725 52.5 2120 47.6 1630 57.9 2120 57.8 2239 53.3 1852 64.1 2484 59.4 1991 69.4 2735 65.4 2275 77.7 2973 71.5 2454 87.8 3362 78.8 2757 89.5 3562 88.7 3045 94.6 3211 104.1 3575 110.6 3786

Modulus of Elasticity

4000

3500

) 3000 m μ (

t 2500 Sample 1 n e Sample 2 m 2000 e

c Sample 3 a l

p 1500 Sample 4 s i D 1000

500

0 0.0 20.0 40.0 60.0 80.0 100.0 120.0 Stress (MPa) Jacob Hammer Page 37 of 43 06/04/2018

Appendix 11 – Raw Data for Test 11

Sample # Test Strength (N) Displacement (mm) 1 280.0 11.882 Jacob Hammer Page 38 of 43 06/04/2018

Appendix 12 – Raw Data for Test 12

Sample # Test Strength (N) Displacement (mm) l H W L θ (deg) Stress (MPa) 3 1286 11.877 54.14 6.51 8.29 53.75 21.70 2.865 5 2452 11.600 55.21 6.51 8.75 54.82 21.27 5.076 8 2314 10.022 49.81 6.51 8.47 49.38 23.59 5.485 1 2309 10.970 51.23 6.51 8.17 50.81 22.94 5.517 9 2077 8.080 44.41 6.51 8.24 43.93 26.48 5.676 2 2151 11.902 44.05 6.51 8.32 43.57 26.70 5.869 10 1809 5.458 36.21 6.51 8.27 35.62 32.54 6.041 7 2202 9.649 42.25 6.51 8.5 41.75 27.85 6.132 4 2537 9.025 41.95 6.51 8.57 41.44 28.05 7.057 6 2651 9.713 34.64 6.51 8.42 34.02 34.03 9.089

Test Strength (N) Displacement (mm) l W L θ (deg) Stress (MPa)

Mean 2178.8 9.830 45.390 8.400 44.910 26.514 5.881 Standard Error 125.0185586 0.631 2.238 0.056 2.263 1.370 0.493 Median 2255.5 9.868 44.230 8.370 43.748 26.590 5.772 Std. Deviation 395.343395 1.995 7.078 0.177 7.156 4.333 1.558 Sample Variance 156296.4 3.980 50.102 0.031 51.213 18.772 2.426 Range 1365 6.444 20.570 0.580 20.802 12.756 6.224 Minimum 1286 5.458 34.640 8.170 34.023 21.274 2.865 Maximum 2651 11.902 55.210 8.750 54.825 34.030 9.089 Conf Lvl (95.0%) 282.8116273 1.427 5.064 0.126 5.119 3.099 1.114

5% Rating: 1528.518 6.548 33.747 8.110 33.139 19.387 3.318 Jacob Hammer Page 39 of 43 06/04/2018

Appendix 13 – Raw Data for Test 13

Sample # Test Strength (N) Displacement (mm) L (mm) W (mm) Stress (MPa) 3 1580 1.580 28.05 30.5 1.847 1 2004 2.810 30.31 30.5 2.168 4 2194 2.194 28.07 30.5 2.563 2 3152 3.152 30.79 30.5 3.356

Test Strength (N) Displacement (mm) L (mm) Stress (MPa)

Mean 2232.500 2.434 29.305 2.483 Standard Error 332.281 0.347 0.725 0.326 Median 2099.000 2.502 29.190 2.365 Standard Deviation 664.563 0.694 1.451 0.651 Sample Variance 441643.667 0.481 2.105 0.424 Range 1572 1.572 2.74 1.510 Minimum 1580 1.58 28.05 1.847 Maximum 3152 3.152 30.79 3.356 Confidence Level (95.0%) 1057.468 1.104 2.309 1.037

5% Rating: 1139.392 1.293 26.918 1.412 Jacob Hammer Page 40 of 43 06/04/2018

Appendix 14 – Readouts from SAP2000 Model

Frame Station P V2 V3 T M2 M3 Text mm N N N N-mm N-mm N-mm Strut Left Exterior 0 7.07 3.93 0 0 0 699.07 Strut Left Exterior 150 7.07 3.93 0 0 0 109.51 Strut Left Exterior 300 7.07 3.93 0 0 0 -480.04 Strut Left Interior 0 -11.17 -0.12 0 0 0 169.79 Strut Left Interior 150 -11.17 -0.12 0 0 0 188.06 Strut Left Interior 300 -11.17 -0.12 0 0 0 206.33 Strut Right Interior 0 -11.17 0.12 0 0 0 -169.79 Strut Right Interior 150 -11.17 0.12 0 0 0 -188.06 Strut Right Interior 300 -11.17 0.12 0 0 0 -206.33 Strut Right Exterior 0 7.07 3.93 0 0 0 480.04 Strut Right Exterior 150 7.07 3.93 0 0 0 -109.51 Strut Right Exterior 300 7.07 3.93 0 0 0 -699.07

Deck Left 0 2.274E-13 -1.776E-15 0 0 0 -5.684E-14 Deck Left 50 2.274E-13 -1.776E-15 0 0 0 3.197E-14 Deck Left 50 3.93 7.07 0 0 0 480.04 Deck Left 200 3.93 7.07 0 0 0 -580.04 Deck Left 200 4.05 -4.1 0 0 0 -749.83 Deck Left 400 4.05 -4.1 0 0 0 70.83 Deck Centre 0 -3489.9 -2500 0 0 0 -47878.95 Deck Centre 150 -3489.9 -2500 0 0 0 327121.05 Deck Centre 150 -3489.9 2500 0 0 0 327121.05 Deck Centre 300 -3489.9 2500 0 0 0 -47878.95 Deck Right 0 4.05 4.1 0 0 0 70.83 Deck Right 200 4.05 4.1 0 0 0 -749.83 Deck Right 200 3.93 -7.07 0 0 0 -580.04 Deck Right 350 3.93 -7.07 0 0 0 480.04 Deck Right 350 9.095E-13 3.553E-15 0 0 0 -1.99E-13 Deck Right 400 9.095E-13 3.553E-15 0 0 0 -3.766E-13 Jacob Hammer Page 41 of 43 06/04/2018

Appendix 14 – Readouts from SAP2000 Model (continued)

Frame Station P V2 V3 T M2 M3 Text mm N N N N-mm N-mm N-mm Pier Left 0 -2500 0 0 0 0 0 Pier Left 75 -2500 0 0 0 0 0 Pier Left 150 -2500 0 0 0 0 0 Pier Right 0 -2500 7.276E-12 0 0 0 4.657E-10 Pier Right 75 -2500 7.276E-12 0 0 0 -8.004E-11 Pier Right 150 -2500 7.276E-12 0 0 0 -6.257E-10

Comp. Left 0 -4292.7 -99.65 0 0 0 -47949.78 Comp. Left 250 -4292.7 -99.65 0 0 0 -23036.89 Comp. Left 500 -4292.7 -99.65 0 0 0 1876 Comp. Right 0 -4292.7 99.65 0 0 0 1876 Comp. Right 250 -4292.7 99.65 0 0 0 -23036.89 Comp. Right 500 -4292.7 99.65 0 0 0 -47949.78

Tension Member 0 3493.95 -4.1 0 0 0 -1876 Tension Member 50 3493.95 -4.1 0 0 0 -1670.84 Tension Member 50 3490.02 -11.17 0 0 0 -971.76 Tension Member 200 3490.02 -11.17 0 0 0 703.82 Tension Member 200 3489.9 1.59E-13 0 0 0 910.15 Tension Member 550 3489.9 1.59E-13 0 0 0 910.15 Tension Member 900 3489.9 1.59E-13 0 0 0 910.15 Tension Member 900 3490.02 11.17 0 0 0 703.82 Tension Member 1050 3490.02 11.17 0 0 0 -971.76 Tension Member 1050 3493.95 4.1 0 0 0 -1670.84 Tension Member 1100 3493.95 4.1 0 0 0 -1876 Jacob Hammer Page 42 of 43 06/04/2018

Appendix 15 – Images from SAP2000 Model

Base wireframe bridge design

Force distribution model of the bridge

Exaggerated deflection model of the bridge Jacob Hammer Page 43 of 43 06/04/2018

Appendix 16 – Design Guide