Popsicle Bridge.doc

Small Scale Bridge Design Final Report April 7, 2008 Jacob Hammer CIVE IV 100656672 Advisor: Prof. Juan Salinas

CARLETON UNIVERSITY CIVE 4907 ENGINEERING PROJECT FINAL REPORT

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Table of Contents 1.0

INTRODUCTION..............................................................................................................................4

2.0

GOALS................................................................................................................................................4

3.0

BACKGROUND.................................................................................................................................5

3.1 3.2 3.2 3.3 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 7.0 7.1 7.2

COMPETITION GUIDELINES...............................................................................................................5 PROPERTIES OF WOOD......................................................................................................................5 ASSUMPTIONS...................................................................................................................................7 MATERIAL PROPERTIES.....................................................................................................................9 MATERIAL TESTS.........................................................................................................................11 BASE TENSION TESTS......................................................................................................................11 COMPRESSION TESTS......................................................................................................................14 SINGLE INTERFACE GLUE TESTS.....................................................................................................14 DOUBLE INTERFACE GLUE TESTS...................................................................................................17 MODULUS OF ELASTICITY...............................................................................................................19 DENTAL FLOSS TESTS.....................................................................................................................20 TENSION MEMBER CONNECTION JOINT TESTS...............................................................................22 MEMBER TO MEMBER JOINT TESTS................................................................................................24 BRIDGE DESIGN............................................................................................................................25 OVERALL DESIGN...........................................................................................................................25 LAYER DESIGN................................................................................................................................25 STRUCTURAL ANALYSIS..................................................................................................................26 COMPRESSION MEMBER DESIGN....................................................................................................27 TENSION MEMBER DESIGN.............................................................................................................28 DECK DESIGN.................................................................................................................................29 STRUT DESIGN................................................................................................................................29 PIER DESIGN...................................................................................................................................29 DESIGN DIFFERENCES IN FINAL MODEL.........................................................................................30 COMPETITION RESULTS............................................................................................................31 ANTICIPATED METHOD OF FAILURE................................................................................................31 METHOD OF FAILURE......................................................................................................................31 EXPLANATION FOR FAILURE...........................................................................................................32 IMPROVEMENTS / NEXT STEPS........................................................................................................32 CONCLUSION.................................................................................................................................33 PROJECT RESULTS...........................................................................................................................33 FINAL THOUGHTS............................................................................................................................34

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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 3.1 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 6.0 6.1

BACKGROUND

ACCEPTED MATERIAL PROPERTIES OF BIRCH...................................................................................9 MATERIAL TESTS SINGLE STICK TENSION TEST SETUP..............................................................................................11 TRIPLE STICK DRY INTERFACE TENSION TEST SETUP....................................................................12 TRIPLE STICK GLUED INTERFACE TENSION TEST SETUP................................................................13 COMPRESSION TEST SETUP.............................................................................................................14 SINGLE INTERFACE GLUE TEST SETUP...........................................................................................15 DOUBLE INTERFACE GLUE TEST SETUP..........................................................................................17 DENTAL FLOSS TEST SETUP FIRST CONFIGURATION......................................................................21 DENTAL FLOSS TEST SETUP SECOND CONFIGURATION..................................................................21 SCARF JOINT TEST SETUP...............................................................................................................22 HALF LAP SPLICE JOINT SETUP......................................................................................................23 DOWEL PIN CONNECTION SETUP....................................................................................................24 BRIDGE DESIGN OVERALL LAYOUT OF BRIDGE DESIGN..........................................................................................25 VENEER DESIGN CONFIGURATION..................................................................................................25 ANGLE REFERENCE CHART.............................................................................................................26 CORNER JOINT ECCENTRICITY........................................................................................................26 COMPRESSION MEMBER CROSS SECTION.......................................................................................27 VENEER REQUIREMENT REFERENCE CHART..................................................................................28 TENSION MEMBER TOP VIEW CROSS-SECTION..............................................................................28 DECK DESIGN CROSS-SECTION.......................................................................................................29 STRUT DESIGN CROSS-SECTION......................................................................................................29 FINAL MODEL DESIGN....................................................................................................................30 COMPETITION RESULTS JOINT SEPARATION FAILURE............................................................................................................32

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1.0

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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.

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3.0 3.1

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BACKGROUND 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:             

3.2

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.

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.

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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.

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3.1.6 Modulus of elasticity As in all materials, the modulus of elasticity is taken as the slope of the stressstrain 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.

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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 K D 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 2

http://www.loew-cornell.com/education/tipsandtechniques/flashpaper/40/index.html, January 6th, 2008 CSA-086-01, 2005 edition, page 30

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3.3

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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)

Modulus of Rupture Modulus of Elasticity Compression Parallel to Grain Compression Perp. to Grain Shear Parallel to Grain Tension Perp. To Grain Figure 3.1

Moisture Content Green 12% (MPa) (MPa) (MPa) (MPa) (MPa) (MPa)

44.1 8066.9 16.3 1.9 5.8 ---

116.5 14961.6 58.9 7.4 15.4 6.6

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

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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.

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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.

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.

Figure 4.1

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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 crosssection 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.

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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

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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 Figure 4.4 to sidesway, the reaction that would develop at the top of the 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.

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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 mm 2) 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. The results of this test can be observed in Appendix 4.

Figure 4.5

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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 mm 2) 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 mm 2) 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.

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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 mm 2 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 mm 2 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 mm 2 (cumulative between both sides) would prevent a glue separation from controlling. 4.4

Double Interface Glue Tests 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.

Figure 4.6

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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.

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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.

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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.

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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

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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 crosssectional 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.

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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. 4.7.2 Half Lap Splice Joint Test [Test 13]

Figure 4.10

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 crosssectional 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.

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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.

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Appendix

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Appendix 1 – Raw Data for Test 1 Test Strength (N) 606 541 483 719 810 646 763 778 772 763 798 813 851 785 926 907 809 823 828 923 913 956 957 1158 890

Diameter (in) 0.163 0.188 0.218 0.163 0.155 0.202 0.185 0.183 0.185 0.190 0.194 0.191 0.185 0.202 0.174 0.180 0.203 0.203 0.202 0.190 0.201 0.194 0.196 0.162 0.214

Stress (MPa) 13.07 13.45 13.93 15.50 16.61 17.26 18.67 18.83 18.89 19.17 20.48 20.54 20.82 20.97 21.31 21.59 21.72 22.10 22.12 23.20 24.27 24.53 24.81 24.81 25.19

Test Strength (N) 1121 1114 1094 1117 1046 1063 1008 1172 1263 1168 1211 1086 1339 1222 1305 1436 1368 1281 1337 1561 1408 1543 1497 1527 2285

Test Strength (N) Mean Standard Error Median Standard Deviation Sample Variance Range Minimum Maximum Conf. Level (95.0%) 5% Rating:

Diameter (in) 0.172 0.180 0.187 0.184 0.199 0.199 0.214 0.194 0.181 0.196 0.192 0.222 0.186 0.207 0.195 0.184 0.194 0.217 0.210 0.181 0.207 0.191 0.201 0.200 0.203

Stress (MPa)

1055.800 46.088 1027 325.891 106205.184 1802 483 2285 92.62

26.957 1.264 25.347 8.938 79.889 48.288 13.065 61.353 2.54

519.756

12.255

Stress (MPa) 25.50 26.52 27.06 27.18 27.53 27.98 28.53 30.07 30.24 30.28 30.75 31.89 32.94 33.46 33.66 34.95 35.10 36.77 37.14 37.37 38.55 38.98 39.80 40.39 61.35

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Appendix 2 – Raw Data for Test 2 Test Strength (N) 2754 2912 3361 3422 3499 3521 3618 3620 3658 3699 3797 3895 4018 4092 4151 4201 4215 4231 4240 4280 4377 4402 4409 4423

Displacement (mm) 5.354 7.497 3.777 6.389 8.751 6.974 9.484 5.977 8.881 9.11 9.369 8.821 8.646 8.932 10.684 6.382 11.138 9.76 9.729 7.467 8.988 11.162 11.738 10.526

Stress (MPa) 45.53 48.15 55.57 56.58 57.85 58.21 59.82 59.85 60.48 61.16 62.78 64.40 66.43 67.65 68.63 69.46 69.69 69.95 70.10 70.76 72.37 72.78 72.90 73.13

Test Strength (N) Mean Standard Error Median Standard Deviation Sample Variance Range Minimum Maximum Conf. Level (95.0%) 5% Rating: Mean / stick: 5% / stick:

Test Strength (N) 4466 4551 4583 4607 4659 4675 4682 4720 4754 4800 4908 4970 4972 4981 4987 5047 5075 5200 5354 5428 5501 5748 6235 6291

Displacement (mm) 10.142 7.774 8.793 8.513 10.128 12.065 9.331 7.538 10.593 8.357 12.066 10.819 12.803 10.424 10.184 11.325 9.821 11.863 12.655 11.042 12.643 9.647 11.843 13.735

Displacement (mm)

Stress (MPa) 73.84 75.24 75.77 76.17 77.03 77.29 77.41 78.04 78.60 79.36 81.15 82.17 82.20 82.35 82.45 83.44 83.91 85.97 88.52 89.74 90.95 95.03 103.09 104.01

Stress (MPa)

4458.104 110.343 4444.5 764.477 584424.691 3537 2754 6291 221.981

9.576 0.302 9.688 2.090 4.370 9.958 3.777 13.735 0.607

73.707 1.824 73.483 12.639 159.754 58.479 45.533 104.011 3.670

3200.652 1486.035 1066.884

13.014 3.192 4.338

52.918 24.569 17.639

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Appendix 3 – Raw Data for Test 3 Test Strength (N) 2977 2994 3195 3368 3470 3597 3636 3777 3800 3876 3899 3943 3995 4022 4031 4062 4069 4098 4109 4203 4210 4224 4266 4301

Displacement (mm) 6.996 5.909 10.127 8.366 7.545 9.364 8.961 7.934 7.513 7.96 7.8 7.346 10.326 7.656 8.131 6.779 8.884 9.201 9.157 7.726 8.04 9.262 8.925 11.689

Stress (MPa) 52.49 52.79 56.33 59.38 61.18 63.42 64.11 66.59 67.00 68.34 68.74 69.52 70.44 70.91 71.07 71.62 71.74 72.25 72.45 74.10 74.23 74.47 75.21 75.83

Test Strength (N) Mean Standard Error Median Standard Deviation Sample Variance Range Minimum Maximum Conf. Level (95.0%) 5% Rating: Mean / stick: 5% / stick:

Test Strength (N) 4310 4354 4370 4409 4514 4523 4546 4596 4643 4684 4705 4706 4757 4977 5011 5020 5042 5103 5128 5327 5430 5685 5694 5949

Displacement (mm) 8.103 8.303 7.853 8.548 7.717 8.571 9.721 9.061 6.521 10.097 10.312 9.954 9.965 10.478 12.123 10.243 10.162 10.444 10.626 9.088 10.653 12.21 11.714 11.284

Displacement (mm)

Stress (MPa) 75.99 76.76 77.05 77.73 79.59 79.74 80.15 81.03 81.86 82.58 82.95 82.97 83.87 87.75 88.35 88.51 88.90 89.97 90.41 93.92 95.74 100.23 100.39 104.89

Stress (MPa)

4366.771 98.173 4305.5 680.165 462624.308 2972 2977 5949 197.499

9.070 0.217 9.011 1.504 2.262 6.301 5.909 12.21 0.437

76.990 1.731 75.910 11.992 143.806 52.399 52.487 104.886 3.482

3247.999 1455.590 1082.666

11.544 3.023 3.848

57.265 25.663 19.088

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Appendix 4 – Raw Data for Test 4 Test Strength (N) 343 515 742 866 930 980 1076 1123 1163 1188 1193 1197 1233 1256 1268

Displacement (mm) 0.678 0.763 0.772 1.275 1.081 1.148 1.453 2.306 1.916 1.532 1.75 1.778 1.691 1.715 2.242

(glue interface failures denoted in boldface) Glue Stick Test Stress Stress Strength Displacement (MPa) (MPa) (N) (mm) 0.60 17.01 1271 1.914 0.90 25.54 1290 1.854 1.30 36.80 1335 1.645 1.52 42.95 1396 2.209 1.63 46.13 1480 2.299 1.71 48.61 1505 2.179 1.88 53.37 1553 1.936 1.97 55.70 1671 2.546 2.03 57.68 1714 2.362 2.08 58.92 1729 0.915 2.09 59.17 1764 2.438 2.09 59.37 1782 2.167 2.16 61.16 1955 3.333 2.20 62.30 2008 2.45 2.22 62.89 2084 3.839

Glue Stress (MPa) 2.22 2.26 2.34 2.44 2.59 2.63 2.72 2.92 3.00 3.03 3.09 3.12 3.42 3.51 3.65

Stick Stress (MPa) 63.04 63.98 66.22 69.24 73.41 74.65 77.03 82.88 85.01 85.76 87.49 88.39 96.97 99.60 103.37

Test Strength (N) Displacement (mm) Glue Stress (MPa) Stick Stress (MPa) Mean Standard Error Median Standard Deviation Sample Variance Range Minimum Maximum Confidence Level (95.0%) 5% Rating:

1320.333 76.086 1269.5 416.739 173671.540 1741 343 2084 155.613

1.873 0.131 1.884 0.716 0.513 3.161 0.678 3.839 0.267

2.310 0.133 2.221 0.729 0.532 3.046 0.600 3.647 0.272

65.489 3.774 62.967 20.670 427.261 86.354 17.013 103.367 7.718

634.858

0.695

1.111

31.489

Lowest controlling glue stress: 3.12 MPa

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Appendix 5 – Raw Data for Test 5 Test Strength (N) 638 690 810 878 902 952 1070 1113 1144 1227 1247 1268 1279 1285 1285

Displacement (mm) 1.389 1.091 1.034 1.056 1.308 1.455 1.134 1.576 1.695 2.131 2.632 1.688 1.832 1.874 1.12

(glue interface failures denoted in boldface) Glue Stick Test Stress Stress Strength Displacement (MPa) (MPa) (N) (mm) 1.67 31.64 1288 2.721 1.81 34.22 1290 1.53 2.13 40.18 1340 1.976 2.30 43.55 1346 1346 2.37 44.74 1405 2.22 2.50 47.22 1435 1.777 2.81 53.07 1448 1.565 2.92 55.20 1479 1.622 3.00 56.74 1549 2.308 3.22 60.86 1558 2.46 3.27 61.85 1577 2.288 3.33 62.89 1626 1.761 3.36 63.44 1724 2.25 3.37 63.74 1844 2.366 3.37 63.74 1861 2.066

Glue Stress (MPa) 3.38 3.39 3.52 1346 3.69 3.77 3.80 3.88 4.07 4.09 4.14 4.27 4.52 4.84 4.88

Stick Stress (MPa) 63.88 63.98 66.46 1346 69.69 71.18 71.82 73.36 76.83 77.28 78.22 80.65 85.51 91.46 92.31

Test Strength (N) Displacement (mm) Glue Stress (MPa) Stick Stress (MPa) Mean Standard Error Median Standard Deviation Sample Variance Range Minimum Maximum Confidence Level (95.0%) 5% Rating:

1285.267 56.862 1286.5 311.445 96997.926 1223 638 1861 116.295

1.799 0.088 1.769 0.483 0.233 1.687 1.034 2.721 0.180

3.373 0.149 3.377 0.817 0.668 3.210 1.675 4.885 0.305

63.749 2.820 63.811 15.448 238.631 60.661 31.645 92.306 5.768

772.985

1.005

2.029

38.340

Lowest controlling glue stress: 2.37 MPa

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Appendix 6 – Raw Data for Test 6 Test Strength (N) 488 619 633 671 707 734 735 740 798 858 888 931 962 965 978

Displacement (mm) 0.757 1.658 1.728 0.977 1.438 0.889 1.019 1.159 1.177 1.814 1.875 1.311 1.38 1.299 1.367

(glue interface failures denoted in boldface) Glue Stick Test Stress Stress Strength Displacement (MPa) (MPa) (N) (mm) 2.56 24.20 1004 1.33 3.25 30.70 1006 1.342 3.32 31.40 1054 1.353 3.52 33.28 1061 1.635 3.71 35.07 1124 1.519 3.85 36.41 1202 1.367 3.86 36.46 1236 2.219 3.88 36.70 1242 1.441 4.19 39.58 1248 1.393 4.50 42.56 1253 1.567 4.66 44.04 1305 1.611 4.89 46.18 1383 2.362 5.05 47.72 1416 1.588 5.07 47.86 1484 1.859 5.13 48.51 1744 1.941

Glue Stress (MPa) 5.27 5.28 5.53 5.57 5.90 6.31 6.49 6.52 6.55 6.58 6.85 7.26 7.43 7.79 9.15

Stick Stress (MPa) 49.80 49.90 52.28 52.63 55.75 59.62 61.31 61.60 61.90 62.15 64.73 68.60 70.23 73.61 86.50

Test Strength (N) Displacement (mm) Glue Stress (MPa) Stick Stress (MPa) Mean Standard Error Median Standard Deviation Sample Variance Range Minimum Maximum Confidence Level (95.0%) 5% Rating:

1015.633 53.841 991 294.897 86964.240 1256 488 1744 110.116

1.479 0.066 1.416 0.362 0.131 1.605 0.757 2.362 0.135

5.331 0.283 5.202 1.548 2.396 6.593 2.562 9.155 0.578

50.376 2.670 49.154 14.627 213.947 62.298 24.205 86.503 5.462

530.571

0.884

2.785

26.316

Lowest controlling glue stress: 2.56 MPa

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Appendix 7 – Raw Data for Test 7 Test Strength (N) 841 896 1042 1045 1049 1063 1223 1252 1256 1353 1355 1483 1491 1501 1552 1593

(glue interface failures denoted in boldface) Glue Stick Test Glue Stress Stress Strength Stress (MPa) (MPa) (N) (MPa) 1.10 41.71 1627 2.14 1.18 44.44 1633 2.14 1.37 51.68 1642 2.15 1.37 51.83 1727 2.27 1.38 52.03 1736 2.28 1.40 52.72 1750 2.30 1.60 60.66 1785 2.34 1.64 62.10 1799 2.36 1.65 62.30 1839 2.41 1.78 67.11 1849 2.43 1.78 67.21 1900 2.49 1.95 73.56 1924 2.52 1.96 73.95 1963 2.58 1.97 74.45 2243 2.94 2.04 76.98 2435 3.20 2.09 79.01 Test Strength (N)

Mean Standard Error Median Standard Deviation Sample Variance Range Minimum Maximum Confidence Level (95.0%) 5% Rating:

Stick Stress (MPa) 80.70 81.00 81.44 85.66 86.11 86.80 88.54 89.23 91.21 91.71 94.24 95.43 97.36 111.25 120.78

Glue Stress (MPa)

Stick Stress (MPa)

1566.867 67.000 1610 366.975 134670.395 1539 896 2435 137.031

2.056 0.088 2.113 0.482 0.232 2.020 1.176 3.196 0.180

77.717 3.323 79.856 18.202 331.312 76.335 44.442 120.776 6.797

963.247

1.264

47.777

Lowest controlling glue stress: 1.65 MPa

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Appendix 8 – Raw Data for Test 8 Test Strength (N) 742 982 1038 1052 1062 1102 1168 1224 1245 1251 1443 1548 1550 1568 1586

Mean Standard Error Median Standard Deviation Sample Variance Range Minimum Maximum Confidence Level (95.0%) 5% Rating:

(glue interface failures denoted in boldface) Glue Stick Test Glue Stress Stress Strength Stress (MPa) (MPa) (N) (MPa) 1.30 36.80 1624 2.84 1.72 48.71 1630 2.85 1.82 51.48 1675 2.93 1.84 52.18 1691 2.96 1.86 52.68 1709 2.99 1.93 54.66 1714 3.00 2.04 57.93 1776 3.11 2.14 60.71 1776 3.11 2.18 61.75 1789 3.13 2.19 62.05 1795 3.14 2.52 71.57 1841 3.22 2.71 76.78 1885 3.30 2.71 76.88 1898 3.32 2.74 77.77 1910 3.34 2.78 78.67 1987 3.48

Stick Stress (MPa) 80.55 80.85 83.08 83.87 84.77 85.01 88.09 88.09 88.73 89.03 91.31 93.50 94.14 94.74 98.56

Test Strength (N)

Stick Stress (MPa)

Glue Stress (MPa)

1508.7 61.387 1605 336.229 113049.941 1245 742 1987 125.550

2.640 0.107 2.808 0.588 0.346 2.178 1.298 3.477 0.220

74.832 3.045 79.608 16.677 278.122 61.752 36.803 98.555 6.227

955.653

1.672

47.400

Lowest controlling glue stress: 2.04 MPa

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Appendix 9 – Raw Data for Test 9 Test Strength (N) 685 792 824 1033 1069 1117 1152 1153 1154 1173 1197 1431 1484 1537 1555 1559 1575 1578

(glue interface failures denoted in boldface) Glue Stick Test Glue Stress Stress Strength Stress (MPa) (MPa) (N) (MPa) 1.80 33.98 1580 4.15 2.08 39.28 1587 4.17 2.16 40.87 1589 4.17 2.71 51.24 1626 4.27 2.81 53.02 1670 4.38 2.93 55.40 1688 4.43 3.02 57.14 1836 4.82 3.03 57.19 1860 4.88 3.03 57.24 1879 4.93 3.08 58.18 1937 5.08 3.14 59.37 1983 5.20 3.76 70.98 2042 5.36 3.90 73.61 2045 5.37 4.03 76.24 2288 6.01 4.08 77.13 2300 6.04 4.09 77.33 2360 6.19 4.13 78.12 2409 6.32 4.14 78.27 2418 6.35 Test Strength (N)

Mean Standard Error Median Standard Deviation Sample Variance Range Minimum Maximum Confidence Level (95.0%) 5% Rating:

Stick Stress (MPa) 78.37 78.72 78.81 80.65 82.83 83.72 91.07 92.26 93.20 96.08 98.36 101.28 101.43 113.49 114.08 117.06 119.49 119.93

Glue Stress (MPa)

Stick Stress (MPa)

1587.917 77.930 1579 467.579 218630.25 1733 685 2418 158.206

4.168 0.205 4.144 1.227 1.506 4.549 1.798 6.346 0.415

78.761 3.865 78.319 23.192 537.868 85.957 33.976 119.933 7.847

818.817

2.149

40.613

Lowest controlling glue stress: 2.81 MPa

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Appendix 10 – Raw Data for Test 10 Stress (MPa) 10.2 19.6 26.9 33.3 41.6 48.3

Sample 1 Displacement (μm) 510 845 1034 1329 1606 1877

Stress (MPa) 9.0 26.7 34.5 41.0 47.9 53.4 57.9

Sample 2 Displacement (μm) 643 945 1250 1333 1517 1725 2120

Stress (MPa) 9.4 18.0 21.4 32.1 41.3 52.5 57.8 64.1 69.4 77.7 87.8 89.5

Sample 3 Displacement (μm) 545 941 1121 1484 1727 2120 2239 2484 2735 2973 3362 3562

Stress (MPa) 9.5 18.6 22.5 31.5 40.9 47.6 53.3 59.4 65.4 71.5 78.8 88.7 94.6 104.1 110.6

Sample 4 Displacement (μm) 243 753 892 1267 1431 1630 1852 1991 2275 2454 2757 3045 3211 3575 3786

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Appendix 11 – Raw Data for Test 11 Sample # 1

Test Strength (N) 280.0

Displacement (mm) 11.882

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Appendix 12 – Raw Data for Test 12 Sample # 3 5 8 1 9 2 10 7 4 6

Mean Standard Error Median Std. Deviation Sample Variance Range Minimum Maximum Conf Lvl (95.0%) 5% Rating:

W 8.29 8.75 8.47 8.17 8.24 8.32 8.27 8.5 8.57 8.42

L 53.75 54.82 49.38 50.81 43.93 43.57 35.62 41.75 41.44 34.02

θ (deg) 21.70 21.27 23.59 22.94 26.48 26.70 32.54 27.85 28.05 34.03

Stress (MPa) 2.865 5.076 5.485 5.517 5.676 5.869 6.041 6.132 7.057 9.089

l

W

L

θ (deg)

Stress (MPa)

9.830 0.631 9.868 1.995 3.980 6.444 5.458 11.902 1.427

45.390 2.238 44.230 7.078 50.102 20.570 34.640 55.210 5.064

8.400 0.056 8.370 0.177 0.031 0.580 8.170 8.750 0.126

44.910 2.263 43.748 7.156 51.213 20.802 34.023 54.825 5.119

26.514 1.370 26.590 4.333 18.772 12.756 21.274 34.030 3.099

5.881 0.493 5.772 1.558 2.426 6.224 2.865 9.089 1.114

6.548

33.747

8.110

33.139

19.387

3.318

Test Strength (N) 1286 2452 2314 2309 2077 2151 1809 2202 2537 2651

Displacement (mm) 11.877 11.600 10.022 10.970 8.080 11.902 5.458 9.649 9.025 9.713

l 54.14 55.21 49.81 51.23 44.41 44.05 36.21 42.25 41.95 34.64

Test Strength (N)

Displacement (mm)

2178.8 125.0185586 2255.5 395.343395 156296.4 1365 1286 2651 282.8116273 1528.518

H 6.51 6.51 6.51 6.51 6.51 6.51 6.51 6.51 6.51 6.51

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Appendix 13 – Raw Data for Test 13 Sample # 3 1 4 2

Mean Standard Error Median Standard Deviation Sample Variance Range Minimum Maximum Confidence Level (95.0%) 5% Rating:

Test Strength (N) 1580 2004 2194 3152

Displacement (mm) 1.580 2.810 2.194 3.152

L (mm) 28.05 30.31 28.07 30.79

W (mm) 30.5 30.5 30.5 30.5

Stress (MPa) 1.847 2.168 2.563 3.356

Test Strength (N)

Displacement (mm)

L (mm)

Stress (MPa)

2232.500 332.281 2099.000 664.563 441643.667 1572 1580 3152 1057.468

2.434 0.347 2.502 0.694 0.481 1.572 1.58 3.152 1.104

29.305 0.725 29.190 1.451 2.105 2.74 28.05 30.79 2.309

2.483 0.326 2.365 0.651 0.424 1.510 1.847 3.356 1.037

1139.392

1.293

26.918

1.412

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Appendix 14 – Readouts from SAP2000 Model Frame Text Strut Left Exterior Strut Left Exterior Strut Left Exterior Strut Left Interior Strut Left Interior Strut Left Interior Strut Right Interior Strut Right Interior Strut Right Interior Strut Right Exterior Strut Right Exterior Strut Right Exterior Deck Left Deck Left Deck Left Deck Left Deck Left Deck Left Deck Centre Deck Centre Deck Centre Deck Centre Deck Right Deck Right Deck Right Deck Right Deck Right Deck Right

Station mm 0 150 300 0 150 300 0 150 300 0 150 300 0 50 50 200 200 400 0 150 150 300 0 200 200 350 350 400

P N

V2 N

7.07 7.07 7.07 -11.17 -11.17 -11.17 -11.17 -11.17 -11.17 7.07 7.07 7.07

3.93 3.93 3.93 -0.12 -0.12 -0.12 0.12 0.12 0.12 3.93 3.93 3.93

V3 N 0 0 0 0 0 0 0 0 0 0 0 0

2.274E-13 2.274E-13 3.93 3.93 4.05 4.05 -3489.9 -3489.9 -3489.9 -3489.9 4.05 4.05 3.93 3.93 9.095E-13 9.095E-13

-1.776E-15 -1.776E-15 7.07 7.07 -4.1 -4.1 -2500 -2500 2500 2500 4.1 4.1 -7.07 -7.07 3.553E-15 3.553E-15

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

T N-mm 0 0 0 0 0 0 0 0 0 0 0 0

M2 N-mm 0 0 0 0 0 0 0 0 0 0 0 0

M3 N-mm 699.07 109.51 -480.04 169.79 188.06 206.33 -169.79 -188.06 -206.33 480.04 -109.51 -699.07

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

-5.684E-14 3.197E-14 480.04 -580.04 -749.83 70.83 -47878.95 327121.05 327121.05 -47878.95 70.83 -749.83 -580.04 480.04 -1.99E-13 -3.766E-13

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Appendix 14 – Readouts from SAP2000 Model (continued) Frame Text Pier Left Pier Left Pier Left Pier Right Pier Right Pier Right Comp. Left Comp. Left Comp. Left Comp. Right Comp. Right Comp. Right Tension Member Tension Member Tension Member Tension Member Tension Member Tension Member Tension Member Tension Member Tension Member Tension Member Tension Member

Station mm 0 75 150 0 75 150

P N -2500 -2500 -2500 -2500 -2500 -2500

0 250 500 0 250 500 0 50 50 200 200 550 900 900 1050 1050 1100

V2 N 0 0 0 7.276E-12 7.276E-12 7.276E-12

V3 N 0 0 0 0 0 0

T N-mm 0 0 0 0 0 0

M2 N-mm 0 0 0 0 0 0

M3 N-mm 0 0 0 4.657E-10 -8.004E-11 -6.257E-10

-4292.7 -4292.7 -4292.7 -4292.7 -4292.7 -4292.7

-99.65 -99.65 -99.65 99.65 99.65 99.65

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

-47949.78 -23036.89 1876 1876 -23036.89 -47949.78

3493.95 3493.95 3490.02 3490.02 3489.9 3489.9 3489.9 3490.02 3490.02 3493.95 3493.95

-4.1 -4.1 -11.17 -11.17 1.59E-13 1.59E-13 1.59E-13 11.17 11.17 4.1 4.1

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0

-1876 -1670.84 -971.76 703.82 910.15 910.15 910.15 703.82 -971.76 -1670.84 -1876

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Appendix 15 – Images from SAP2000 Model

Base wireframe bridge design

Force distribution model of the bridge

Exaggerated deflection model of the bridge

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Appendix 16 – Design Guide

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