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
Jacob Hammer
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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 ............................................................ ERROR! BOOKMARK NOT DEFINED.
OVERALL DESIGN.....................................................................ERROR! BOOKMARK NOT DEFINED.
LAYER DESIGN .........................................................................ERROR! BOOKMARK NOT DEFINED.
STRUCTURAL ANALYSIS ...........................................................ERROR! BOOKMARK NOT DEFINED.
COMPRESSION MEMBER DESIGN ..............................................ERROR! BOOKMARK NOT DEFINED.
TENSION MEMBER DESIGN .......................................................ERROR! BOOKMARK NOT DEFINED.
DECK DESIGN ...........................................................................ERROR! BOOKMARK NOT DEFINED.
STRUT DESIGN .........................................................................ERROR! BOOKMARK NOT DEFINED.
PIER DESIGN .............................................................................ERROR! BOOKMARK NOT DEFINED.
DESIGN DIFFERENCES IN FINAL MODEL ...................................ERROR! BOOKMARK NOT DEFINED.
COMPETITION RESULTS ............................................ ERROR! BOOKMARK NOT DEFINED.
ANTICIPATED METHOD OF FAILURE .........................................ERROR! BOOKMARK NOT DEFINED.
METHOD OF FAILURE ...............................................................ERROR! BOOKMARK NOT DEFINED.
EXPLANATION FOR FAILURE ....................................................ERROR! BOOKMARK NOT DEFINED.
IMPROVEMENTS / NEXT STEPS..................................................ERROR! BOOKMARK NOT DEFINED.
CONCLUSION ................................................................. ERROR! BOOKMARK NOT DEFINED.
PROJECT RESULTS ....................................................................ERROR! BOOKMARK NOT DEFINED.
FINAL THOUGHTS .....................................................................ERROR! BOOKMARK NOT DEFINED.
Jacob Hammer
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APPENDIX ..................................................................................................................................................25
APPENDIX 1 – RAW DATA FOR TEST 1 .......................................................................................................26
APPENDIX 2 – RAW DATA FOR TEST 2 .......................................................................................................27
APPENDIX 3 – RAW DATA FOR TEST 3 .......................................................................................................28
APPENDIX 4 – RAW DATA FOR TEST 4 .......................................................................................................29
APPENDIX 5 – RAW DATA FOR TEST 5 .......................................................................................................30
APPENDIX 6 – RAW DATA FOR TEST 6 .......................................................................................................31
APPENDIX 7 – RAW DATA FOR TEST 7 .......................................................................................................32
APPENDIX 8 – RAW DATA FOR TEST 8 .......................................................................................................33
APPENDIX 9 – RAW DATA FOR TEST 9 .......................................................................................................34
APPENDIX 10 – RAW DATA FOR TEST 10....................................................................................................35
APPENDIX 11 – RAW DATA FOR TEST 11....................................................................................................36
APPENDIX 12 – RAW DATA FOR TEST 12....................................................................................................37
APPENDIX 13 – RAW DATA FOR TEST 13....................................................................................................38
APPENDIX 14 – READOUTS FROM SAP2000 MODEL ..................................................................................39
APPENDIX 14 – READOUTS FROM SAP2000 MODEL (CONTINUED) ............................................................40
APPENDIX 15 – IMAGES FROM SAP2000 MODEL .......................................................................................41
APPENDIX 16 – DESIGN GUIDE ...................................................................................................................42
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
Jacob Hammer
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.
Jacob Hammer
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3.0
BACKGROUND
3.1
Competition Guidelines
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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:
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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 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
2
http://www.loew-cornell.com/education/tipsandtechniques/flashpaper/40/index.html, January 6th, 2008
CSA-086-01, 2005 edition, page 30
Jacob Hammer
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 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.
The results of this test can be observed in Appendix 4.
Figure 4.5
Jacob Hammer
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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 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
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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 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
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
Jacob Hammer
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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.
Jacob Hammer
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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.
Jacob Hammer
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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.
Jacob Hammer
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Appendix
07/03/2016
Jacob Hammer
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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
Jacob Hammer
Page 28 of 42
07/03/2016
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
Jacob Hammer
Page 29 of 42
07/03/2016
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
1782
2.167
2.09
59.37
2.16
61.16
1955
3.333
2008
2.45
2.20
62.30
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
Jacob Hammer
Page 30 of 42
07/03/2016
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
1346
1346
2.30
43.55
2.37
44.74
1405
2.22
1435
1.777
2.50
47.22
2.81
53.07
1448
1.565
1479
1.622
2.92
55.20
1549
2.308
3.00
56.74
3.22
60.86
1558
2.46
3.27
61.85
1577
2.288
1626
1.761
3.33
62.89
1724
2.25
3.36
63.44
1844
2.366
3.37
63.74
1861
2.066
3.37
63.74
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
Jacob Hammer
Page 31 of 42
07/03/2016
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
1054
1.353
3.32
31.40
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
Jacob Hammer
Page 32 of 42
07/03/2016
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
1727
2.27
1.37
51.83
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
Jacob Hammer
Page 33 of 42
07/03/2016
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
1630
2.85
1.72
48.71
1.82
51.48
1675
2.93
1691
2.96
1.84
52.18
1709
2.99
1.86
52.68
1.93
54.66
1714
3.00
2.04
57.93
1776
3.11
1776
3.11
2.14
60.71
2.18
61.75
1789
3.13
2.19
62.05
1795
3.14
1841
3.22
2.52
71.57
1885
3.30
2.71
76.78
2.71
76.88
1898
3.32
2.74
77.77
1910
3.34
1987
3.48
2.78
78.67
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
Jacob Hammer
Page 34 of 42
07/03/2016
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)
1580
4.15
1.80
33.98
1587
4.17
2.08
39.28
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
1836
4.82
3.02
57.14
3.03
57.19
1860
4.88
3.03
57.24
1879
4.93
3.08
58.18
1937
5.08
1983
5.20
3.14
59.37
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
2418
6.35
4.14
78.27
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
Jacob Hammer
Page 35 of 42
07/03/2016
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
Modulus of Elasticity
4000
Displacement (μm)
3500
3000
2500
Sample 1
2000
Sample 2
Sample 3
1500
Sample 4
1000
500
0
0.0
20.0
40.0
60.0
Stress (MPa)
80.0
100.0
120.0
Jacob Hammer
Page 36 of 42
07/03/2016
Appendix 11 – Raw Data for Test 11
Sample #
1
Test Strength (N)
280.0
Displacement (mm)
11.882
Jacob Hammer
Page 37 of 42
07/03/2016
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
Jacob Hammer
Page 38 of 42
07/03/2016
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
Jacob Hammer
Page 39 of 42
07/03/2016
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
Jacob Hammer
Page 40 of 42
07/03/2016
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
Jacob Hammer
Page 41 of 42
Appendix 15 – Images from SAP2000 Model
Base wireframe bridge design
Force distribution model of the bridge
Exaggerated deflection model of the bridge
07/03/2016
Jacob Hammer
Page 42 of 42
Appendix 16 – Design Guide
07/03/2016