LIST OF FIGURES - University of Wisconsin–Madison Papers/2015 - Florida.pdf · hand-in-hand with...

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Transcript of LIST OF FIGURES - University of Wisconsin–Madison Papers/2015 - Florida.pdf · hand-in-hand with...

Executive Summary................................................................................................................................................................ii Project Management................................................................................................................................................................1

Organization Chart…………...................................................................................................................................................2

Hull Design and Structural Analysis.......................................................................................................................................3

Development and Testing........................................................................................................................................................5

Construction………….............................................................................................................................................................8

Project Schedule………….....................................................................................................................................................10

Design Drawing…………......................................................................................................................................................11

LIST OF FIGURES

Figure 1: ForeverGlades Person-Hours...................................................................................................................................1

Figure 2: Transom Stern Flow Separation………...................................................................................................................3

Figure 3: Free Body Diagram for Men’s Sprint……...............................................................................................................4

Figure 4: Free Body Diagram for Lateral Analysis..................................................................................................................4

Figure 5: Iterative Process of Concrete Mix Design................................................................................................................5

Figure 6: Third-Point Flexure Test on Composite Panel……………………………………………………………..….......5

Figure 7: Neoprene Caps for Compression Test……..………………………………………………………………………7

Figure 8: Cross Sections Supported and Bolted to Beam...........................................................................………………….8

Figure 9: Structural Rib Form………………………............................................................................................................8

Figure 10: Initial Curing with Heated Soaker Hose………………………………………………………………………….9

Figure 11: Aesthetic Alligator in Practice Canoe…………………………………………………………….………………9

LIST OF TABLES

Table 1: ForeverGlades Concrete Properties...........................................................................................................................ii

Table 2: ForeverGlades Concrete Properties Compared to AcceleGator................................................................................7

LIST OF APPENDICES

Appendix A: References…………. ....................................................................................................................................A-1

Appendix B: Mixture Proportions…………........................................................................................................................B-1

Appendix C: Bill of Materials………..................................................................................................................................C-1

Appendix D: Example Structural Calculation…………………………………………………………………………….D-1

Encompassing the nation’s largest subtropical

wetland, Everglades National Park provides

sanctuary for thirty-six protected animal species

across nearly 1.5 million grassy acres in south

Florida. The natural, pulsing surface water flow of

the larger Everglades basin has been increasingly

disrupted due to land development since the late

1800s. While it was human intervention that

originally altered the flow balance, today, a more

holistic engineering mentality is employed to

remedy past oversights. The Comprehensive

Everglades Restoration Plan (CERP) leads the effort

to protect and preserve the water resources of the

Everglades. Located several hundred miles to the

north in Gainesville, the University of Florida (UF)

has created research and extension programs to

address these pressing issues. These programs aim

to enhance the quality of the ecosystem and

improve the abundance and diversity of native

species, while also accommodating urban and

agricultural water demands.

As one of the most comprehensive and

academically diverse public universities in the

nation, UF serves more than 50,000 students

annually with 16 colleges and more than 150

research centers and institutes (University of Florida

(a) 2014). The UF Concrete Canoe Team,

competing in one of the largest ASCE conferences,

has placed 1st in the Southeast Region the last three

years and finished 12th

(AcceleGator, 2014), 3rd

(ConquistaGator, 2013), and 5th

(VindiGator, 2012)

at the national level.

The UF Team began its season by moving

production from a satellite facility to an on-campus

research laboratory. The space proved to be

effective for recruitment purposes, drawing in a

larger, younger team than in previous years. With

youth came inexperience, prompting captains, with

the help of team veterans, to formally draft best

management practices to guide future teams.

Proximity to numerous active research projects

allowed the team to better utilize university

resources. With the move, many construction and

mix design techniques were improved in order to

meet space constraints and ensure safety of the team

members.

Outside of the lab, the paddling team was

committed to kneeling in all five races in an effort

to maximize its competitive advantage. Accordingly,

the hull design was developed to enhance paddler

stability without impeding maneuverability. The

concrete mix design focused on improving tensile

strengths while incorporating new materials to

create a low density mix. In an effort to improve

upon previous teams’ final product scores, a

schedule was created which dedicated more time to

construction planning and visual display fabrication.

Emphasis was placed on uniform gunwale thickness

when designing the canoe form. To enhance

aesthetic quality, the team integrated a three-

dimensional cast concrete alligator, both an

Everglades native and the UF mascot, into the

canoe’s interior surface.

To pay tribute to this marvel of nature and bring

awareness to the effort to preserve the diverse

ecosystem of the Everglades, UF proudly captures

the beauty of this “river of grass” with its 2015

canoe: ForeverGlades.

Maximum

Length 22.0 ft.

Maximum

Width 26.0 in.

Maximum

Height 13.5 in.

Average

Thickness 0.375 in.

Weight 178 lb

Colors Blue, Green, Tan, Yellow

Reinforcement Carbon Fiber Mesh with

Kevlar® Weave

Inner

Lay

er Wet Unit Weight 50.5 pcf

Oven Dried Unit Weight 40.6 pcf

Compressive Strength 1,512 psi

Tensile Strength 196 psi

Mid

dle

Lay

er Wet Unit Weight 54.2 pcf

Oven Dried Unit Weight 50.3 pcf

Compressive Strength 2,148 psi

Tensile Strength 282 psi

Ou

ter

Lay

er Wet Unit Weight 49.5 pcf

Oven Dried Unit Weight 40.7 pcf

Compressive Strength 1,350 psi

Tensile Strength 129 psi

Composite Flexural Strength 1,272 psi

Str

uct

ura

l

Rib

s

Wet Unit Weight 55.2 pcf

Oven Dried Unit Weight 52.7 pcf

Compressive Strength 1,666 psi

Tensile Strength 271 psi

Aes

thet

ic

Pas

te

Wet Unit Weight 120.0 pcf

Oven Dried Unit Weight 105.8 pcf

Compressive Strength N/A

Tensile Strength N/A

Table 3 Table 1 Table 2

Table 1: ForeverGlades Concrete Properties

A single head captain, acting as the project

manager, took on the tasks of recruitment,

budgeting, scheduling, and delegating for the

ForeverGlades team. To complete the team, five

captains were selected as project engineers to lead

concrete mix design, hull design/structural analysis,

visual design, construction, and paddling.

Similar to that used by CERP, an adaptive

management approach allowed the team to monitor

progress and make the appropriate changes required

to meet prescribed goals. Risk management was

ensured by pairing veterans with inexperienced

team members for construction processes, and

quality control was supplemented by using external

resources to help critique the design paper. Quality

assurance was provided throughout the project by

requiring the captains to submit progress reports

and schedules at the beginning of each week to

ensure that tasks followed the master schedule

created by the project manager

Using this master schedule, captains adhered to a

critical path rooted in team historical data and

planned improvements. This critical path included

hull design selection, mold completion, practice

canoe completion, and competition canoe

completion. Major milestones not included on the

critical path consisted of mix design finalization,

selection of the paddling team, and completion of

the design paper. These milestones were determined

based on past experience and accomplished through

clear and constant communication as well as

timeline awareness among all captains.

The ForeverGlades team understood the benefits

that fabricating both a practice and a competition

canoe would provide for quality assurance and

educating a young team. In order to ensure there

was sufficient time to design, place, and cure two

concrete canoes, the schedule for structural analysis,

hull design, mold construction, and mix design was

rigorous and closely followed. With the donation of

nearly all concrete materials and admixtures,

creating a second canoe added a minimal cost of

$600 to the ForeverGlades budget. The practice

canoe allowed 18 newly-recruited members to

become familiar with the precision required during

the placement process. Additionally, the team had

the opportunity to test new construction and mix

design techniques to mitigate errors before the

competition canoe placement one month later.

Efficiency in time management and the donation of

a second shotcrete gun allowed for a reduction of 75

person-hours from the placement of the practice

canoe to the competition canoe. Overall, the team

put in over 2,800 person-hours designing, testing,

and constructing ForeverGlades (Figure 1).

Before using the lab, each team member was

required to attend an informative, concrete canoe-

specific safety training session, as well as complete

12 hours of online safety courses through the

University. After the initial session, the team was

instructed on each tool used in the lab to ensure

competence and safety at all times. Those working

with concrete materials were required to read

material safety data sheets for the materials and

personal protective equipment was required and

supplied in all areas of the lab. The team worked

hand-in-hand with the laboratory staff to guarantee

appropriate handling of tools and materials.

The operational budget for all necessary material

procurement and construction processes of the

canoe was set at $4,800. Since no financial

assistance is received from the University itself, the

team sought to fundraise through engineering firms

and UF Concrete Canoe alumni directly. Since the

team was fortunate enough to receive several

material donations for the concrete mix design as

well as colored sealer, construction and visual

display components were left to bear the brunt of

the canoe completion cost. Over $9000 was raised

during the year to cover project expenses, travel

costs, and registration fees which allowed for a

substantial sum to be allocated to the future team.

Finally, a strict paddling regimen was overseen,

incorporating two gym sessions and two mandatory

lake practices per week beginning in the fall. The

team benefitted immensely from the opportunity to

practice in the chosen hull design (the practice

canoe) in the months leading up to the competition.

Figure 1: ForeverGlades Person-Hours

The ForeverGlades hull design team drew upon

well documented and successful hull forms from

past years to maintain a tradition of excellence in

design. Obtaining feedback from last year’s

paddlers and using AcceleGator as a baseline, the

team focused on refining the hull for improved race

performance. Design goals were geared toward

balancing straight-line speed and maneuverability,

while improving stability in order to accommodate

the kneeling paddling style.

The design team sought to increase straight line

speed by reducing the hull’s wave-making

resistance. This can be achieved by maximizing

waterline length; however, with the canoe length

constrained at 22 ft. (ASCE/NCCC 2015), other

parameters had to be altered. The bow rocker was

decreased from 5.5 in. to 4 in. This decrease in

curvature reduced maneuverability which, in turn,

increased tracking. To compensate, the rocker

curvature was maintained along the hull bottom,

providing less lateral resistance and promoting

boundary layer cohesion. This combination

maintained sufficient maneuverability while

minimizing wave-making resistance (Winters 2006).

The continued use of a transom stern this year

also helped to maximize waterline length. This

truncation allows flow to continue as if the canoe

actually extended out to a point as shown in Figure

2. The increased effective waterline length results in

a decrease in

form resistance.

Proper separation

was achieved

through correct

sizing of the

truncation by

maintaining the

Froude numbers

of at least 2.0

(Maki et al. 2005).

The ForeverGlades hull profile was flattened

slightly, which enhanced the initial stability of the

canoe (Gullion 1994). The need for improved

stability was expressed by paddlers in order to more

comfortably and effectively deliver power while

kneeling. Wave-making resistance tends to increase

with a larger surface area; however, with a flatter

bottom, the sanding process can be carried out more

accurately, giving the hull a smoother finish and

reducing friction drag when compared with

AcceleGator (University of Florida (b) 2014). A 15

degree raked bow, added for aesthetic purposes,

decreased the amount of deadwood in the bow,

further reducing wetted surface area and friction

drag. From previous years’ scale model test data,

this bow angle was determined to be the most

efficient (University of Florida 2007).

Hulls were designed using FREE!ship

(Timoshenko 2013) and compared using the fluid

dynamics program, Mitchlet (Lazauskas 2013). This

was done to accurately determine the designs with

the least wave resistance. Resistance was analyzed

for hull speeds ranging from 1 to 6 knots (1.69 to

10.12 ft./s), the estimated maximum speed during

the co-ed sprint race. From these results, 4 final

designs were tested for straight-line speed and

maneuverability. Scale models at 1:6 size were

milled using a computer numerical controlled (CNC)

machine at an on-campus fabrication center. This

scale was chosen to best maintain model similitude,

matching Froude numbers while remaining in an

acceptable range of Reynolds number.

Based on design criteria and scale model test

performance which balanced speed and turning, a

final hull was selected with a shallow arch bottom,

22-ft. length, 26-in. beam, and 2-in. transom stern.

ForeverGlades improves upon last year’s straight-

line speed while maintaining comparable turning

ability and meeting all design goals.

Structural analysis was performed with the

purpose of determining the critical tensile and

compressive strengths required for the hull to

undergo various predetermined loading cases. The

loading conditions considered included the two-

male loading, four person loading, and the

demolding, transportation, and display of the canoe.

Analysis was performed longitudinally along the

length of the canoe and laterally along the beam of

the hull to obtain critical values. For each

orientation of analysis, the canoe was assumed to be

a two-dimensional beam.

Figure 2: Transom Stern Flow

Separation

Figure 4: Free Body Diagram for Lateral Analysis

For longitudinal analysis, the hull was divided

into 3-in. sections to evaluate the location of the

maximum moment. Assuming rectangular sections

for ease of calculation, the moment of inertia for

each was determined. A program in Excel

(Microsoft 2010) was developed to find the shear

forces and bending moments along the beam using

the principles of Euler-Bernoulli beam theory.

Figure 3 shows the free body diagram used to

analyze the canoe in the longitudinal direction.

For racing conditions, the canoe was modeled to

be continuously supported by the buoyant force,

which acts equal and opposite to that of the weight

of water displaced. Using displacements for specific

loading cases, the draft was determined from the

program FREE!ship (Timoshenko 2013). From the

draft, the submerged volume of each section was

calculated and multiplied by specific weight of

water to obtain the buoyant force. The weight of the

canoe, assumed from last year’s canoe as 160 lb,

was uniformly distributed over its length. Point

loads of 160 lb and 140 lb represented the male and

female paddlers, respectively. These values were

then increased by 25% to 200 lb and 170 lb. This

increase accounted for dynamic load amplification

during the races (Paradis and Gendron 2006). The

loads were placed 4 ft. and 18 ft. from the bow,

simulating paddler placement for the men’s races.

Two female loads were added at 8 ft. and 14 ft. for

the co-ed sprint. Analysis of the display scenario

resulted in the determination of the optimal

placement of two stands at 4 ft. and 17 ft. from the

bow.

The two-male loading scenario was found to

produce the critical loading case, with a maximum

negative bending moment of 9,464 in.-lb located 11

ft. from the bow. Using the location of the section’s

neutral axis and the principle of flexure, the tensile

and compressive stresses in the section were

calculated to be approximately 84 psi and 258 psi,

respectively. Based on the concrete properties from

the previous year, the minimal acceptable tensile

and compressive strengths were determined to be

100 psi and 1,300 psi. These strengths provide a

longitudinal factor of safety of 1.2, sufficient

capacity for tolerating the stresses induced from the

considered loading cases.

During bow-initiated turns, a paddler’s hips often

push against the top of the gunwales. A lateral

analysis of the hull was required to determine these

resulting stresses (Figure 4). The co-ed sprint race

was the critical loading case for lateral analysis due

to larger forces against the gunwales and the larger

buoyant force due to the weight of the four paddlers.

A force of 200 lb was assumed to act on the

gunwales from a shift in the paddlers’ weights,

causing a moment of 2,362 in.-lb located at the

chine. The canoe was assumed to be 0.375 in. thick

with a layer of carbon fiber mesh between each of

the three layers of concrete. The carbon fiber mesh

reinforcement provides a tensile strength of 512 ksi

and elastic modulus of 33.4 Msi (TorayCA 2014).

Using the transformed area method, the moment

allowed by the reinforced concrete is 294 in.-lb,

significantly lower than the required strength.

To increase the maximum allowable moment,

three 1 in. deep structural ribs were added – one

behind the bow paddler, one amidship, and one

toward the stern – providing enough room for the

aftmost paddler. The added ribs raised the

maximum allowable moment to 6,440 in.-lb, which

increased the overall lateral factor of safety to 2.73

and assuaged concerns over paddler hip impacts.

Figure 3: Free Body Diagram for Men’s Sprint

As the 2014-2015 campaign began, the mix

design team resolved to further build upon the

success achieved in the previous year. To this end,

the ForeverGlades team looked to improve the

compressive, tensile, and flexural strengths of the

canoe, while simultaneously recapturing the low

unit weights and smooth outer finishes of years past.

In doing so, the team was able to create mixes

which surpassed calculated structural requirements

by a large degree.

The mix design used in the inner layer of the

previous year’s canoe, AcceleGator, was recreated

as a baseline for the mix design process as it

achieved high strength and aesthetic appeal. With

14-day compressive and composite flexural

strengths of 1,638 and 1,194 psi, respectively, the

control mix performed satisfactorily with a wet unit

weight of 47.7 pcf and a water-to-cementitious

materials ratio (w/cm) of 0.40 (University of

Florida (b) 2014). Nonetheless, ForeverGlades’ mix

design team set out to make substantial

improvements, designing, testing, and analyzing

over four dozen mixes through the process shown in

Figure 5. After initially curing at room temperature

for three days, the specimens were placed in a

105ºF limewater bath for an additional 11 days.

This 14-day period was chosen to maintain the

timeframe desired for the number of tests to be

completed during the development stage.

After curing, 2 in. by 4 in. cylindrical specimens

were tested in compression in general accordance

with ASTM C39. Tensile briquette specimens were

created and tested in accordance with ASTM C307,

and composite panels were tested in third-point

flexure using a modified version of ASTM C78

(Figure 6). This modified technique was employed

since the panels were too thin to conform to the

exact requirement of the standard.

In order to maintain workability while improving

upon AcceleGator’s strength-to-weight ratio, the

ForeverGlades team focused primarily upon

cementitious materials and proportions. Given the

lack of limitations on the proportion of portland

cement in this year’s competition, complete

replacement of this material was considered.

Portland cement content was lowered in steady

increments until it constituted zero percent of the

cementitious material. However, once the

proportion of portland

cement fell below 25% of the

mix’s total cementitious

material, relative strength and

bond properties were

drastically reduced.

Decreasing the amount of

portland cement required the

mix to utilize ground blast

furnace slag. Ground blast

furnace slag’s propensity for

strength gains under elevated

curing temperatures

contributed to strength

increases observed during

testing (Ferraro 2009).

The team introduced two new cementitious

materials, VCAS™ 160 and white portland cement

to the mix design regimen for consideration. Often

considered very similar to gray portland cement,

white portland cement was a novel addition for

ForeverGlades’ mix team due to its light color and

its high potential for reactivity with pozzolans,

which stems from its low ferrite content (Lubeck et

al. 2011). VCAS™ 160, a recycled glass powder,

was tested for its ability to lower water demand

which allows for the pozzolanic material to be used

in concrete with low w/cm (Hossain et al. 2008).

Ultimately, VCAS™ 160 was selected over two

alternatives, Class F fly ash and metakaolin. The

three alternatives were extensively tested in several

variations and the highest compressive strength

resulted from a complete replacement of metakaolin

and fly ash with VCAS™ 160. Furthermore, its

white color made it an attractive candidate for the

ForeverGlades team, as neither the off-white

metakaolin nor the gray fly ash could foster lighter-Figure 5: Iterative Process for Concrete Mix Design

Figure 6: Third-

Point Flexure Test

on Composite Panel

tinted mixes; which was part of the team’s aesthetic

strategy of creating a lighter-colored canoe for

sealing purposes.

Of significant concern noticed by the

AcceleGator team was the continued propagation of

cracks on the hull, an issue which arose late in the

2014 season. In order to increase tensile strength,

the ForeverGlades team employed basalt fibers.

Basalt fibers are lightweight fibers made from

molten rock with a tenacity higher than that of steel.

They improve flexural strength, do not absorb water,

and have the same coefficient of thermal expansion

as concrete (Cheng Concrete 2014). Although basalt

fibers have a lower clumping risk when mixed, they

still leave the shotcrete gun vulnerable to clogging.

To offset this risk and remain in accordance with

ASTM C1116, the well-staffed ForeverGlades team

dedicated hundreds of hours to the separation of

fibers from one another. Several methods, including

the use of compressed air, were tested to increase

the efficiency of separating fibers, but hand

separation proved most effective. As a result of

separation, the individual fibers assimilated

themselves more fluidly into the mix, and issues

with clumping and workability were largely

overcome. Furthermore, the fibers lent significant

tensile strength to the specimens tested, providing

increases of up to 137% over control mixes.

SikaLatex® R was used in previous years as a

polymer modifier. Styrene-butadiene rubber (SBR)

latex, a newly-donated material, was tested as a

potential replacement for SikaLatex® R due to its

popularity with other successful teams. A direct

replacement of SBR latex for SikaLatex® R in a

control mix led to higher workability and a lower

water demand, both of which were desirable

properties. However, SikaLatex® R was still used

for the middle layer of ForeverGlades for its air-

entraining ability; further air entrainment was

achieved through the use of Darex® AEA. This

middle layer mix provided desirable strengths and

unit weights for this year’s team. Unfortunately,

SikaLatex® R introduced voids and an undesirable

finish. For this reason, it was replaced with SBR

latex in the visible layers and structural ribs.

To achieve the level of workability necessary for

shotcreting, ADVA® Cast 600, a superplasticizer,

was used in conjunction with WRDA® 60, a mid-

range water reducer. Varying levels of these

plasticizers were employed in each layer,

accounting for differences in placement method,

aggregate gradation, and fiber content. Efforts to

prevent drying of mixes prior to placement were

aided by the use of V-MAR® 3, a rheology-

modifying admixture.

AcceleGator’s aggregate blend, developed from

rigorous testing, was adopted by the ForeverGlades

team in order to focus its efforts on changes in

cementitious materials, fibers, and admixtures. The

five aggregates, – three sizes of Poraver®, S38 and

K15 glass microspheres – allowed for superior

gradation and strength-to-weight ratios. For the two

surface layers, increased quantities of S38 and K15

were utilized in lieu of the largest-sized Poraver®,

creating a smooth, lightweight mix.

Aiming to control quality and consistency of test

results, the mix team decided to forgo the traditional

compaction method of hand tamping specimens,

employing a vibrating table during casting. Control

mixes, which were produced by both manual and

mechanical compaction, showed a stark contrast

between the methods. Specimens created using the

vibrating table, including both cylinders and

briquettes, saw significant decreases in void

quantity and size, leading to increased tensile and

compressive strengths. Most importantly, the use of

the vibration table also standardized the samples

made by eliminating human error introduced by

tamping previously observed. This produced better

comparisons between mixes and a more accurate

representation of the final concrete product used in

the canoe.

After setting, demolding, and curing for 14 days,

the bearing surfaces of the cylindrical specimens

were lightly sanded using a belt sander to remove

large deformations. New for this year, unbonded

neoprene caps per the specifications of ASTM 1232

were used during the compressive strength testing

(Figure 7). These caps allowed for consistent

comparisons between specimens by creating a

smooth, parallel bearing surface perpendicular to

the applied axial load during compressive strength

testing (NRMCA 2014).

Figure 5: Iterative Process for Concrete Mix Design

A new procedure for mixing fresh concrete was

undertaken this year to increase slump and prevent

mixes from drying out too quickly on long

placement days. As suggested by UF faculty, all wet

materials were added to the mixing bowl after dry

mixing for 45 seconds, as

opposed to adding water

reducers after an initial

wet mixing period. Fresh

mixes were noticeably

more workable, showing

an increase in slump.

Actual unit weights also

proved more consistent

with predicted unit

weights, suggesting that

Darex® AEA was most

efficacious when added

alongside the other wet

materials.

The ForeverGlades team was determined to

incorporate sustainability into every aspect of the

project. In the past, cleaning of mixing equipment

was done with a hose in a constantly draining basin

using at least 5,000 gallons of water per placement

day. As part of this year’s effort, shop towels were

replaced with cloth towels, and water usage was

closely monitored and limited on both placement

days. A basin containing 45 gallons of water was

used for cleaning large equipment while a five

gallon bucket was used to clean syringes, small

buckets, and other small batching tools. It was

determined that merely 140 gallons of water were

used for cleaning on each placement day.

The glass particles constituting all sizes of

Poraver® aggregate are recycled, providing a level

of environmental sustainability mirrored by the

recycled glass powder of VCAS™ 160. Ground

blast furnace slag represents another sustainable

material, as its use in concrete precludes its

environmentally-harmful disposal as an industrial

by-product. Substantial donations were secured for

many of the materials, including white portland

cement, slag, S38, K15, and all admixtures, save

SikaLatex® R. Economic sustainability was thereby

maximized for the mix design phase of the project.

Like many of its predecessors, ForeverGlades

includes three layers of concrete. In previous years,

the larger-sized aggregates would become dislodged

during troweling, producing a rough surface. This

year, a mix excluding larger-sized aggregates was

used for both the inner and outer layers, rather than

just the outermost layer of the canoe, as was the

case in AcceleGator. This omission allowed for an

increase in surface area and decrease in void

quantity, ultimately creating a more aesthetically-

pleasing canoe with decreased drag. The mix design

including all sizes of Poraver® proved to be

strongest in tension and compression; it was

therefore used in the middle layer and structural ribs

to provide flexural support throughout the canoe.

Finally, the inner two layers and the ribs contain

basalt fibers to aid in tension and flexure. Kevlar®-

impregnated carbon fiber mesh was used as

structural reinforcement and was embedded

between each layer of the canoe. Strips of the mesh

were also placed in between two lifts of concrete

when hand-placing the structural ribs. The final

mixes employed in ForeverGlades (shown in Table

2) developed strengths that exceeded the

requirements set by the structural anaylsis while

meeting goals set for hue and unit weight.

Figure 7: Neoprene Caps

for Compression Test

*Strengths Taken at

14 Days

Inner

Layer

Middle

Layer

Outer

Layer

Structural

Ribs

Aesthetic

Paste

AcceleGator

Inner Layers

AcceleGator

Outer Layer

Wet Unit Weight 50.5 pcf 54.2 pcf 49.5 pcf 55.2 pcf 120.0 pcf 47.7 pcf 49.3 pcf

Dry Unit Weight 40.6 pcf 50.3 pcf 40.7 pcf 52.7 pcf 105.8 pcf 36.1 pcf 35.2 pcfw/cm 0.66 0.34 0.66 0.30 0.23 0.4 0.7

Compressive Strength* 1,512 psi 2,148 psi 1,350 psi 1,666 psi N/A 1,638 psi 1,339 psi

Tensile Strength* 196 psi 282 psi 129 psi 271 psi N/A 121 psi 101 psi

Basalt Chopped Fibers Yes Yes No Yes No No NoLatex SBR SikaLatex®R SBR SBR No SikaLatex®R SikaLatex®R

Flexural Strength* N/A N/A1,272 psi 1,194 psi

Concrete Properties

Table 2: ForeverGlades Concrete Properties Compared to AcceleGator

With the move to an on-campus facility, the

ForeverGlades team had to make several

adjustments in order to better operate in the new

space. The major change involved making the canoe

form mobile in order to reduce spatial and logistical

problems within the lab. This meant eliminating the

table on which the form had been built in the past

and constructing the form directly on a steel beam.

Heavy-duty casters were attached to the beam,

allowing it to be easily maneuvered. Eliminating the

table surface also cut this year’s plywood use in half.

The form’s mobility allowed sanding to be done

outside of the lab, reducing respiratory concerns

within the team’s confined area. Additionally, this

enabled the team to accommodate the ever-

changing research projects within the shared lab

space.

Based on the team’s experience level and the

ability to better regulate layer thickness while

shotcreting, a male form was chosen for

ForeverGlades. Rather than having it CNC milled,

the form was crafted by hand. This method allowed

the team to stay within its budget and familiarize

newer team members with the level of precision that

would later be required during placement. Instead of

foam, the team chose to use wood as the primary

material for constructing the form. This choice was

motivated by the sustainable harvesting of the

available lumber and the ability to reuse pieces of

the previous year’s form.

Cross sections at 1 ft. increments were obtained

from the design software, then printed and cut from

¾ in. plywood. The cross sections were cut with an

added rectangular piece at their bases, allowing

them to fit directly into the beam and included a lip

at the gunwales. This lip

was designed at the

desired thickness of the

canoe to ensure

uniformity when

troweling on placement

day. The steel beam

contains holes every 4 in.

on-center, enabling

better accuracy in

placing the sections at 1

ft. increments. The

rigidity of the beam also

aided in keeping the

cross sections aligned. Plywood spacers and

wooden triangles braced each side of the sections

and were bolted to the beam (Figure 8). Once every

section was in place, a transit level was used to

align each one along the hull’s centerline.

The construction team nailed ½ in. wide plywood

strips to the edges of the cross sections, connecting

them and forming the canoe’s curved shape. A 5/16

in. thickness was chosen for these strips because it

provided enough flexibility to follow the hull’s

contours but enough rigidity to resist deflection

during sanding. Once completed, the team used a

belt sander to make an initial pass over the entire

form before applying Bondo® to fill in gaps and

depressions. Repeated sanding and Bondo®

applications resulted in a smooth, even form

surface. The entire form was then coated in a

laminating resin to waterproof the wood. When the

resin was completely cured, precut adhesive foam

designs were applied to the form in order to create

an inlaid effect on the concrete.

Insulation foam was used instead of wood to

create the finer details of the hull’s shape. The bow

and stern sections of the hull were sculpted from

layered foam using a variable speed orbital sander

to achieve the shape prescribed by the FREE!ship

(Timoshenko 2013) file. The three structural rib

sections were carefully hand-

sanded to achieve roughly

the desired profile. A

meticulous application of

Bondo® provided the

freedom to create the

preferred trapezoidal shape

(Figure 9). The chamfered

design was implemented to

ease demolding and mitigate

stress concentrations by

reducing sharp inside

corners.

The ForeverGlades team made it a priority to

optimize the lengthy placement day process where

possible. The practice placement day was

scrutinized by team captains, and changes were

implemented for competition placement day.

Competition placement day proved to be more

efficient as a second shotcrete gun was donated and

twice as many trowelers were trained to smooth the

Figure 8: Cross Sections

Supported and Bolted to

Beam

Figure 9: Structural Rib

Form

fresh concrete. This allowed the team to work on

larger sections of the canoe more efficiently and

finish troweling before the concrete became

unworkable.

The team began placement day by thoroughly

applying vegetable oil to the form as a natural

release agent. Next, two layers of concrete were

hand-placed in each rib, with a strip of carbon fiber

mesh reinforcement embedded between them.

Immediately thereafter, the first layer was

shotcreted and troweled to a ruled thickness of 1/8

in.; marked pins were used by trowelers to ensure a

consistent thickness throughout each layer. Once

complete, carbon fiber mesh was placed over the

entire canoe and embedded into the first layer by

hand. The next layer was also applied at 1/8 in.,

after which a second sheet of carbon fiber was

embedded into the canoe. Layer thickness was

carefully monitored at the gunwale lip.

A thicker, final layer was applied at 3/16 in. to

allow the team to more effectively sand away

exterior imperfections while maintaining the final

thickness of 3/8 in. On this layer, the gunwale lip

allowed team members to trowel straight up from its

edge, ensuring regularity along the length of the

canoe. Extra care was taken in finishing the outer

layer to minimize the amount of time needed later

for sanding. The canoe was then covered in plastic

for the next three days to retain moisture as the

concrete set.

A new, modular curing tank was constructed to

maximize the efficiency of the team’s limited lab

space. Since the tank could be easily disassembled,

the side panel was removed

and the entire form was

rolled into the tank, while

still attached to the beam. A

water heater and soaker

hose were used over the

entire canoe to recirculate

water infused with calcium

hydroxide to aid in the

curing process (Figure 10).

A double layer of burlap

ensured that the canoe’s

surface remained moist.

With the tank acting as a

catch basin, there was minimal water loss during

this phase of curing. At the end of the initial 14-day

curing, the form was removed from the tank, and

the canoe was demolded. This time frame simulates

the strength and age at which specimens were tested

during the design phase. Compressed air was

employed for the first time this year to separate the

concrete from the form, several team members were

able to lift the canoe off of the wooden form. The

foam sections used to shape the bow and stern were

left in the canoe as flotation. The curing tank was

then reassembled, filled with limewater, and the

canoe was submerged for an additional two weeks

at 135 ºF to complete curing. This system was able

to achieve a higher temperature than first

anticipated, allowing greater opportunity for

strength gain than test specimens (NRMCA 2006).

At the conclusion of the curing process, the canoe

was removed from the tank, and concrete was hand-

placed to cover the flotation at the bow and stern.

Minor air voids in the hull’s interior were also filled

in at this time. The interior and exterior of the canoe

were carefully hand sanded

to remove imperfections

and create the optimum

surface for applying sealer.

Long, wooden sanding

blocks were used to

mitigate “waviness” along

the outside walls of the

canoe. Incrementally

moving from 100 to 300

grit sandpaper helped the

team achieve the finest

finish for sealer.

To better integrate this year’s theme into the

construction of ForeverGlades, the team decided to

incorporate a three-dimensional alligator on the

interior of the hull (Figure 11). The three portions of

the alligator’s body were sculpted from clay, and a

corn starch and silicone mixture was used to create

flexible molds. To maintain continuity with the

canoe, the fine, inner layer mix was used to cast the

alligator. A special mix was created to bond it to the

hull. The alligator was then strategically placed in

the canoe based upon aesthetics and paddler safety.

ForeverGlades was then thoroughly cleaned before

carefully applying colored sealer.

Figure 10: Initial Curing

with Heated Soaker Hose

Figure 11: Aesthetic

Alligator in Practice

Canoe

ID Task Name Baseline Start Baseline Finish Actual Start Actual Finish

1 Project Management Mon 8/25/14 Fri 3/20/15 Sat 8/16/14 Sun 3/22/152 Rules & Regulations Released Mon 9/1/14 Mon 9/1/14 Wed 9/10/14 Wed 9/10/143 Create Budget Mon 8/18/14 Mon 8/25/14 Sat 8/16/14 Mon 8/25/144 Project Scheduling Mon 8/25/14 Thu 8/28/14 Thu 8/21/14 Fri 8/29/145 Fundraising Mon 8/25/14 Sat 3/21/15 Wed 10/1/14 Sun 3/22/156 Theme Development Thu 9/18/14 Fri 10/17/14 Wed 9/17/14 Fri 11/14/147 Canoe Development Fri 8/29/14 Wed 3/18/15 Mon 8/25/14 Wed 3/18/158 Mix Design Fri 8/29/14 Tue 11/18/14 Mon 8/25/14 Wed 11/26/149 Procure Materials Fri 8/29/14 Thu 10/16/14 Mon 8/25/14 Fri 10/10/14

10 Test Cementitious Materials Tue 9/16/14 Sat 10/11/14 Fri 10/10/14 Fri 10/24/1411 Test Fibers Fri 10/10/14 Fri 10/24/14 Mon 10/27/14 Fri 10/31/1412 Adjust w/cm Mon 10/27/14Mon 11/3/14 Sat 11/1/14 Fri 11/7/1413 Test Final Mix Choices Mon 11/17/14Fri 11/21/14 Fri 11/21/14 Fri 11/21/1414 Select Final Mix Design Mon 11/24/14Mon 11/24/14Wed 11/26/14 Wed 11/26/1415 Structural Analysis Mon 9/1/14 Sun 10/12/14 Wed 10/1/14 Fri 11/14/1416 Research 2-D Methods Wed 10/1/14 Sat 10/25/14 Wed 10/1/14 Sat 10/25/1417 Develop Analysis Method Wed 10/1/14 Sat 10/25/14 Wed 10/1/14 Sat 10/25/1418 Complete Analysis Sat 10/25/14 Sun 11/23/14 Sat 10/25/14 Fri 11/14/1419 Hull Design Mon 8/18/14 Sun 10/12/14 Mon 8/25/14 Mon 10/6/1420 Research Hull Design Mon 8/18/14 Thu 9/25/14 Mon 8/25/14 Thu 9/4/1421 Software Modeling Mon 8/18/14 Tue 9/30/14 Thu 9/11/14 Tue 9/23/1422 CNC Scale Models Tue 9/30/14 Wed 10/1/14 Wed 9/24/14 Thu 9/25/1423 Test Scale Models Fri 10/3/14 Sun 10/5/14 Fri 9/26/14 Sat 9/27/1424 Hull Selection Mon 10/6/14 Mon 10/6/14 Sat 10/4/14 Mon 10/6/1425 Hull Form Construction Mon 8/25/14 Sat 12/6/14 Mon 9/1/14 Sun 1/11/1526 Determine Construction Methods Mon 9/1/14 Fri 10/17/14 Mon 9/1/14 Tue 10/14/1427 Procure Materials Mon 8/25/14 Thu 1/8/15 Mon 9/1/14 Sun 1/11/1528 Cut and Install Cross-Sections Tue 10/21/14 Sat 10/25/14 Tue 10/28/14 Tue 11/4/1429 Install Wood Strips Tue 10/28/14 Sat 11/1/14 Wed 11/5/14 Wed 11/12/1430 Construct Bow and Stern Sections Tue 10/14/14 Sat 10/25/14 Tue 11/11/14 Mon 12/1/1431 Apply Automotive Body Filler Tue 11/4/14 Sat 11/15/14 Wed 11/12/14 Mon 12/1/1432 Apply Fiberglass Resin Mon 12/8/14 Mon 12/8/14 Mon 12/8/14 Mon 12/8/1433 Form Complete Wed 12/10/14Wed 12/10/14Wed 12/10/14 Wed 12/10/1434 Practice Canoe Pour Mon 11/17/14Thu 12/11/14 Mon 12/1/14 Fri 1/30/1535 Batch Dry Mix Materials Mon 11/17/14Fri 12/5/14 Mon 12/1/14 Wed 12/10/1436 Pre-Pour Day Meeting Sun 12/7/14 Sun 12/7/14 Sun 12/7/14 Sun 12/7/1437 Pour Practice Canoe Thu 12/11/14 Thu 12/11/14 Thu 12/11/14 Thu 12/11/1438 Soaker Hose Curing Sun 12/14/14 Sat 12/27/14 Sun 12/14/14 Sun 12/28/1439 Remove From Form Sat 12/27/14 Sat 12/27/14 Sun 12/28/14 Sun 12/28/1440 Cure Practice Canoe Sun 12/14/14 Sat 1/11/14 Sun 12/14/14 Wed 1/21/1541 Sand Practice Canoe Mon 1/12/15 Fri 1/16/15 Thu 1/22/15 Tue 1/27/1542 Seal and Stain Concrete Mon 1/19/15 Fri 1/23/15 Tue 1/27/15 Wed 1/28/1543 Practice Canoe Complete Sun 1/11/15 Sun 1/11/15 Thu 1/29/15 Thu 1/29/1544 Transport Practice Canoe to Lake Sun 1/25/15 Sun 1/25/15 Fri 1/30/15 Fri 1/30/1545 Competition Canoe Pour Tue 1/6/15 Sat 1/17/15 Tue 1/6/15 Sat 1/17/1546 Refurbish Mold Mon 1/5/15 Thu 1/15/15 Tue 1/6/15 Fri 1/16/1547 Apply Inlays Thu 1/15/15 Thu 1/15/15 Fri 1/16/15 Fri 1/16/1548 Batch Dry Mix Materials Tue 1/6/15 Fri 1/16/15 Tue 1/6/15 Fri 1/16/1549 Apply Mold Release Sat 1/17/15 Sat 1/17/15 Sat 1/17/15 Sat 1/17/1550 Cut Carbon Fiber Sat 1/17/15 Sat 1/17/15 Sat 1/17/15 Sat 1/17/1551 Pour Competition Canoe Sat 1/17/15 Sat 1/17/15 Sat 1/17/15 Sat 1/17/1552 Pour Samples for Testing and SubmittalSat 1/17/15 Sat 1/17/15 Sat 1/17/15 Sat 1/17/1553 Finish Competition Canoe Sat 1/10/15 Wed 3/18/15 Tue 1/20/15 Wed 3/18/1554 Soaker Hose/Wet Burlap Curing Tue 1/20/15 Sat 1/31/15 Tue 1/20/15 Sat 1/31/1555 Remove From Form Sun 2/1/15 Sun 2/1/15 Sun 2/1/15 Tue 2/3/1556 Heated Water Tank Curing Sun 2/1/15 Sun 2/15/15 Wed 2/4/15 Wed 2/18/1557 Hull Exterior Sanding Mon 2/16/15 Mon 2/23/15 Thu 2/19/15 Fri 2/27/1558 Stain and Seal Concrete Tue 2/24/15 Sat 3/14/15 Tue 3/3/15 Sun 3/15/1559 Competition Canoe Complete Sat 3/14/15 Sat 3/14/15 Wed 3/18/15 Wed 3/18/1560 Display Fri 10/17/14 Mon 2/9/15 Mon 11/17/14 Sat 3/14/1561 Design Display Fri 10/17/14 Fri 1/30/15 Mon 11/17/14 Mon 3/2/1562 Build Canoe Stands Fri 10/17/14 Sun 2/1/15 Mon 12/1/14 Fri 3/13/1563 Build Table Display Fri 10/17/14 Fri 1/30/15 Mon 1/12/15 Wed 2/25/1564 Build Cutaway Section Mon 1/26/15 Sat 3/14/15 Fri 2/20/15 Sat 3/14/1565 Academics Sun 12/14/14 Wed 3/18/15 Sat 12/20/14 Wed 3/18/1566 Design Paper Fri 12/19/14 Fri 2/13/15 Sat 12/20/14 Thu 2/26/1567 Write Rough Draft Sun 12/14/14 Sat 1/17/15 Sat 12/20/14 Mon 1/5/1568 Edit Rough Draft Sat 1/17/15 Tue 2/10/15 Tue 1/6/15 Wed 2/25/1569 Print Paper Thu 2/12/15 Thu 2/12/15 Wed 2/25/15 Wed 2/25/1570 Submit Paper Mon 2/23/15 Mon 2/23/15 Thu 2/26/15 Thu 2/26/1571 Oral Presentation Sat 2/14/15 Thu 3/19/15 Sun 1/18/15 Wed 3/18/1572 Write Script Sat 2/14/15 Sat 2/28/15 Sun 1/18/15 Fri 3/6/1573 Know Script and Study Questions Mon 3/2/15 Thu 3/19/15 Wed 3/4/15 Wed 3/18/1574 Create Presentation Sun 1/18/15 Fri 2/27/15 Sun 1/25/15 Fri 3/6/1575 Rehearsal Sat 2/28/15 Thu 3/19/15 Sat 3/7/15 Wed 3/18/1576 Athletics Sun 9/7/14 Sun 3/23/14 Sun 9/7/14 Sun 3/15/1577 Paddling Practice Sun 9/7/14 Sun 11/9/14 Sun 9/7/14 Sun 11/9/1478 Select Paddling Team Sun 11/9/14 Sun 11/9/14 Mon 11/10/14 Mon 11/10/1479 Team Practice Mon 11/3/14 Sun 3/15/15 Sat 11/15/14 Sun 3/15/1580 Southeast Regional Conference Thu 3/19/15 Sat 3/21/15 Thu 3/19/15 Sat 3/21/1581 Preparation for NCCC Mon 3/23/15 Thu 6/18/15 Sat 4/4/15 Thu 6/18/1582 Revise Design Paper Mon 3/30/15 Fri 5/15/15 Mon 4/6/15 Tue 5/12/1583 Submit Design Paper Tue 5/12/15 Fri 5/15/15 Tue 5/12/15 Tue 5/12/1584 Practice Oral Presentation Mon 3/23/15 Thu 6/18/15 Thu 4/9/15 Thu 6/18/1585 Modify Display Materials Mon 3/30/15 Thu 6/18/15 Mon 4/6/15 Thu 6/18/1586 Team Paddling Practice Sat 4/4/15 Thu 6/18/15 Sat 4/4/15 Sun 6/14/1587 National Concrete Canoe Competition Sat 6/20/15 Mon 6/22/15 Sat 6/20/15 Mon 6/22/15

8/3 8/17 8/31 9/14 9/28 10/12 10/26 11/9 11/23 12/7 12/21 1/4 1/18 2/1 2/15 3/1 3/15 3/29 4/12 4/26 5/10 5/24 6/7 6/21August 1 September 1 October 1 November 1 December 1 January 1 February 1 March 1 April 1 May 1 June 1 July 1

Task Task Milestone Baseline Baseline Milestone Critical Critical Milestone

10

Project: ForeverGladesDate: 07 May 2015 Team: University of Florida

You created this PDF from an application that is not licensed to print to novaPDF printer (http://www.novapdf.com)

ForeverGlades Schedule ScheduleForeverGlades Schedule

10

1

2 FORM ELEVATION VIEW

3 FORM ISOMETRIC VIEW

5 CROSS-SECTION LAYOUT PLAN VIEW

FOREVERGLADES FORM DRAWINGS2015 UNIVERSITY OF FLORIDA CONCRETE CANOE

NOT TO SCALE D1

5-11-2015

Title:

Project:

Drawn by:

Scale: Sheet:

Date:

University of FloridaAmerican Society of Civil Engineers Concrete Canoe Team

Item Qty. Component Description12 23 Cross-Section 3

4" Plywood3 84 Gusset Recycled 2"x4" white pine4 Rib Mold Blue Extruded Polystyrene Foam5 Bow/Stern Section Blue Extruded Polystyrene Foam

71 Aesthetic Inlay Decorative Sand-Blasting Mask

Covering1

4" Plywood Strips, Automotive Body Filler,and Resin Coating

2D1

3D1

5D1

7

8

65

8

7

5

4

4

12

3

5

1

32

7

32

9

A

A

B C

B C

4 RIB DETAIL

7

4

2

3

4D1

SECTION A-ATYPICAL SECTIONFORE OF MIDSHIPS

(extent of mold)

SECTION B-BWIDEST SECTION

(extent of mold)

SECTION C-CTYPICAL SECTIONAFT OF MIDSHIPS

(extent of mold)

3 3

9

3 3

9

33

77

7

R3"R5"

R4"

4.0"

1"

2.5"

ZACHARYPRYTULA

11

10

64

32

25.33" 20.50"17.69"

2 Bow/Stern Endcap Support

1 Steel Beam 2 C-Channel Beams welded together

6

7

8

1

Cross Section Support9 19

Gunwale Lip10

12" Plywood

12" Plywood

1/8" Plywood2

1'1' 1'1' 1'1' 1'1' 1'1' 1' 1'1' 1'1' 1'1'1'

10 9

10 10

10

58

1

8 8

15°

8

9

6

5

5.5"

9" 9" 9"

3"3" 3"

FORM PLAN VIEW

PR

OD

UC

ED

B

Y A

N A

UT

OD

ES

K E

DU

CA

TIO

NA

L P

RO

DU

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PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCTP

RO

DU

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D B

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PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

1111

ASCE/NCCC. (2015). “2015 American Society of Civil Engineers National Concrete Canoe Competition.

Rules and Regulations.”

<http://www.asce.org/uploadedFiles/Membership_and_Communities/Student_Chapters/Concrete_Canoe/Conte

nt_Pieces/nccc-rules-and-regulations.pdf> (Feb. 18, 2015).

ASTM (2010). “Standard Specifications for Air-Entraining Admixtures for Concrete.” C260/C260M – 10a,

West Conshohocken, PA.

ASTM (2010). “Standard Specification for Fiber-Reinforced Concrete.” C1116/C1116M-10a. West

Conshohocken, PA.

ASTM (2010). “Standard Test Method for Flexural Strength of Concrete (Using Simple Beam with Third-Point

Loading).” C78/C78M-10el, West Conshohocken, PA.

ASTM (2012). “Standard Specifications for Coal Fly Ash and Raw or Calcined Natural Pozzolan for Use in

Concrete.” C618 – 12a, West Conshohocken, PA.

ASTM (2012). “Standard Specification for Portland Cement.” C150/C150M – 12, West Conshohocken, PA.

ASTM (2012). “Standard Test Method for Density, Relative Density (Specific Gravity), and Absorption of Fine

Aggregates.” C128 – 12, West Conshohocken, PA.

ASTM (2012). “Standard Test Method for Tensile Strength of Chemical-Resistant Mortar, Grouts, and

Monolithic Surfacings.” C307-03(2012), West Conshohocken, PA.

ASTM (2013). “Standard Specification for Chemical Admixtures for Concrete.” C494/C494M – 13, West

Conshohocken, PA.

ASTM (2013). “Standard Specification for Concrete Aggregate.” C33/ C33M - 13, West Conshohocken, PA.

ASTM (2013). “Standard Specification for Latex and Powder Polymer Modifiers for use in Hydraulic Cement

Concrete and Mortar.” C1428 – 13, West Conshohocken, PA.

ASTM (2013). “Standard Specification for Slag Cement for Use in Concrete and Mortars.” C989/C989M – 13,

West Conshohocken, PA.

ASTM (2013). “Standard Terminology Relating to Concrete and Concrete Aggregates.” C125 – 13b,West

Conshohocken, PA.

ASTM (2013). “Standard Test Method for Density (Unit Weight), Yield, and Air Content (Gravimetric) of

Concrete.” C138/C138M – 13a, West Conshohocken, PA.

ASTM (2014). “Standard Practice for Use of Unbonded Caps in Determination of Compressive Strength of

Hardened Concrete Cylinders.” C1231/C1231M-14. West Conshohocken, PA.

ASTM (2014). “Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens.”

C39/C39M-14, West Conshohocken, PA.

Cheng Concrete (2014). “Cheng Concrete Exchange: Chopped Basalt Fiber.”

<http://store.concreteexchange.com/CHENG-Concrete-Online-Store_5/Concrete-Additives-Fibers-and-

Rebar/Chopped-Basalt-Fiber> (Dec 3, 2015).

Ferraro, Christopher C. (2009). “Determination of Test Methods for the Prediction of the Behavior of Mass

Concrete.” Doctoral Dissertation, University of Florida, Gainesville, FL.

Gray Line (n.d.). “Allow Your Imagination to go Wild in the Everglades.” Digital image.

<http://www.grayline.com/tours/miami/everglades-airboat-adventure-with-transportation-biscayne-boat-tour-

5864_13/>. (Feb . 20, 2015).

Gullion, L (1994). Canoeing. Human Kinetics Publishers, Champaign, IL, 25-26.

Hossain, A.B., Shirazi, S.A., Persun, J., Neithalath, N. (2008). “Properties of Concrete Containing Vitreous

Calcium Aluminosilicate Pozzolan.” Transportation Research Record No. 2070. Washington D.C.

Laine. (2011). Everglades Open Field. The Camp Host. Digital image.

<http://thecamphost.blogspot.com/2011/02/paynes-prairie.html?m=1>. (Feb. 20, 2015).

Lazauskas, L. (2013) Michlet. [Software] <http://www.cyberiad.net/michlet.htm> (Sep. 27, 2014).

Lubeck, A., Gastaldini, A.L.G., Barin, D.S., Siqueira, H.C. (2011). “Compressive Strength and Electrical

Properties of Concrete with White Portland Cement and Blast-furnace Slag.” Federal Univeristy of Santa Maria.

Rio Grande do Sul, Brazil.

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and-blue/> (Feb 20, 2015).

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pisem.su/indexEN.html> (Aug. 3, 2014).

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(Feb. 7, 2015).

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YD

SGAmount

(lb/yd3)

Volume

(ft3)

Amount

(lb)

Volume

(ft3)

Amount

(lb/yd3)

Volume

(ft3)

CM1 3.15 150.00 0.763 0.69 0.004 142.54 0.725

CM2 2.90 330.00 1.824 1.53 0.008 313.59 1.733

CM3 2.60 120.00 0.740 0.56 0.003 114.03 0.703

600.00 3.33 2.78 0.02 570.17 3.16

F1 2.68 3.00 0.018 0.01 0.0001 2.85 0.017

3.00 0.02 0.01 0.0001 2.85 0.02

A1 Poraver® (0.25-0.50mm) Abs: 25 0.59 130.30 3.539 0.60 0.016 123.82 3.363

A2 Abs: 0 0.15 13.25 1.416 0.06 0.007 12.59 1.345

A3 Abs: 0 0.38 218.19 9.202 1.01 0.043 207.34 8.744

361.74 14.16 1.67 0.07 343.75 13.45

W1 396.00 6.346 1.83 0.029 376.31 6.031

41.50 0.19 60.30

354.50 1.64 316.01

W2 1.00 32.57 0.15 30.95

428.57 6.35 1.98 0.03 407.26 6.03

S1 1.01 30.00 0.476 0.14 0.002 28.51 0.452

30.00 0.48 0.14 0.002 28.51 0.45

Ad1 9.6 lb /gal 34.00 13.76 4.08 0.38 0.019 13.07 3.88

Ad2 9.2 lb /gal 40.00 12.15 3.14 0.34 0.015 92.34 23.84

Ad3 8.5 lb /gal 2.00 3.87 1.51 0.11 0.007 3.68 1.44

Ad4 8.5 lb /gal 5.00 0.74 0.28 0.02 0.001 0.70 0.27

Ad4 8.4 lb /gal 48.00 158.67 32.49 4.41 0.150 150.78 30.87

41.50 0.19 60.30

M

V

T

D

D

A

Y

Ry

Mixture ID: Inner LayerDesign Proportions

(Non SSD)

Actual Batched

Proportions

Yielded

ProportionsDesign Batch Size (ft3): 0.125

Total Aggregates:

Cementitious Materials

White Cement, Type I

Blast-Furnace Slag

VCAS™ 160

Total Cementitious Materials:

Fibers

Basalt Chopped Fibers KV13

Total Fibers:

Aggregates

K15 Glass Microspheres

S38 Glass Microspheres

Styrene-butadiene Rubber Latex

Water

Water for CM Hydration (W1a + W1b)

1.00W1a. Water from Admixtures

W1b. Additional Water

Water for Aggregates, SSD

Total Water (W1 + W2) :

Solids Content of Latex Admixtures and Dyes

V-MAR® 3

Viscosity Modifying Agent

Total Solids of Admixtures:

Admixtures (including Pigments in Liquid

Form)%

Solids

Dosage

(fl oz/cw t)

Water in

Admixture

(lb)

Dosage

(fl oz/cw t)

Water in

Admixture

(lb/yd3)

WRDA® 60

Water Reducer

ADVA® CAST 600

Superplasticizer

Water in

Admixture

(lb/yd3)

Amount

(f l oz)

Darex® AEA

Air Entrainer

Styrene-butadiene Rubber

Latex

Water from Admixtures (W1a) :

Cement-Cementitious Materials Ratio 0.25 0.25

Water-Cementitious Materials Ratio 0.66 0.66 0.66

0.25

Slump, Slump Flow, in . 11.0 11.0 11.0

Mass of Concrete. lbs 1423 6.59 1353

Absolute Volume of Concrete, ft3 24.323 0.113 23.114

Theorectical Density, lb /ft3 = (M / V) 58.52 58.52 58.52

Design Density, lb /ft3 = (M / 27) 52.72

Measured Density, lb /ft3 50.09 50.09

Relative Yield = (Y / Y D ) 1.052

Air Content, % = [(T - D) / T x 100%] 9.91 14.40 14.40

Yield, ft3

= (M / D) 27 0.132 27

YD

SGAmount

(lb/yd3)

Volume

(ft3)

Amount

(lb)

Volume

(ft3)

Amount

(lb/yd3)

Volume

(ft3)

CM1 3.15 143.75 0.731 0.67 0.003 150.22 0.764

CM2 2.90 316.25 1.748 1.46 0.008 330.48 1.826

CM3 2.60 115.00 0.709 0.53 0.003 120.18 0.741

575.00 3.19 2.66 0.01 600.88 3.33

F1 2.68 3.00 0.018 0.01 0.0001 3.14 0.019

3.00 0.02 0.01 0.0001 3.14 0.02

A1 Poraver® (1.0-2.0mm) Abs: 25 0.38 122.02 5.146 0.56 0.024 127.52 5.378

A2 Abs: 25 0.47 147.71 5.037 0.68 0.023 154.36 5.263

A3 Abs: 25 0.59 126.31 3.431 0.58 0.016 131.99 3.585

A4 Abs: 0 0.15 16.06 1.715 0.07 0.008 16.78 1.793

A5 Abs: 0 0.38 40.67 1.715 0.19 0.008 42.51 1.793

452.77 17.04 2.10 0.08 473.15 17.81

W1 195.50 3.133 0.91 0.015 204.30 3.274

104.00 0.48 126.41

91.50 0.42 77.89

W2 1.00 99.01 0.46 103.47

294.51 3.13 1.36 0.01 307.77 3.27

S1 1.04 74.59 1.149 0.35 0.005 77.95 1.201

74.59 1.15 0.35 0.005 77.95 1.20

Ad1 9.6 lb /gal 34.00 9.39 2.67 0.25 0.012 9.81 2.79

Ad2 9.2 lb /gal 40.00 9.79 2.42 0.26 0.011 81.88 20.26

Ad3 8.5 lb /gal 2.00 2.01 0.75 0.05 0.003 2.10 0.79

Ad4 8.5 lb /gal 5.00 0.74 0.27 0.02 0.001 0.77 0.28

Ad4 8.7 lb /gal 37.00 397.58 97.89 10.58 0.453 415.47 102.30

104.00 0.48 126.41

M

V

T

D

D

A

Y

Ry Relative Yield = (Y / Y D ) 0.957

Air Content, % = [(T - D) / T x 100%] 9.14 5.05 5.05

Yield, ft3

= (M / D) 27 0.120 27

Design Density, lb /ft3 = (M / 27) 51.85

Measured Density, lb /ft3 54.18 54.18

Absolute Volume of Concrete, ft3 24.532 0.114 25.636

Theorectical Density, lb /ft3 = (M / V) 57.06 57.06 57.06

Slump, Slump Flow, in . 11.00 11.00 11.00

Mass of Concrete. lbs 1400 6.48 1463

0.25

Water-Cementitious Materials Ratio 0.34 0.34 0.34

Water from Admixtures (W1a) :

Cement-Cementitious Materials Ratio 0.25 0.25

WRDA® 60

Water Reducer

ADVA® CAST 600

Superplasticizer

V-MAR® 3

Viscosity Modifying Agent

Darex® AEA

Air Entrainer

SikaLatex® R

Water in

Admixture

(lb/yd3)

Amount

(f l oz)

Water in

Admixture

(lb)

Dosage

(fl oz/cw t)

Water in

Admixture

(lb/yd3)

SikaLatex® R

Total Solids of Admixtures:

Admixtures (including Pigments in Liquid

Form)%

Solids

Dosage

(fl oz/cw t)

W1b. Additional Water

Water for Aggregates, SSD

Total Water (W1 + W2) :

Solids Content of Latex Admixtures and Dyes

Water for CM Hydration (W1a + W1b)

1.00W1a. Water from Admixtures

Poraver® (0.25-0.50mm)

K15 Glass Microspheres

S38 Glass Microspheres

Total Aggregates:

Water

Fibers

Basalt Chopped Fibers KV13

Total Fibers:

Aggregates

Poraver® (0.5-1.0mm)

Cementitious Materials

White Cement, Type I

Blast-Furnace Slag

VCAS™ 160

Total Cementitious Materials:

Mixture ID: Middle LayerDesign Proportions

(Non SSD)

Actual Batched

Proportions

Yielded

ProportionsDesign Batch Size (ft3): 0.125

YD

SGAmount

(lb/yd3)

Volume

(ft3)

Amount

(lb)

Volume

(ft3)

Amount

(lb/yd3)

Volume

(ft3)

CM1 3.15 150.00 0.763 0.69 0.004 141.19 0.718

CM2 2.90 330.00 1.824 1.53 0.008 310.61 1.716

CM3 2.60 120.00 0.740 0.56 0.003 112.95 0.696

600.00 3.33 2.78 0.02 564.75 3.13

F1 N/A

A1 Poraver® (0.25-0.50mm) Abs: 25 0.59 130.30 3.539 0.60 0.016 122.64 3.331

A2 Abs: 0 0.15 13.25 1.416 0.06 0.007 12.47 1.332

A3 Abs: 0 0.38 218.19 9.202 1.01 0.043 205.37 8.661

361.74 14.16 1.67 0.07 340.49 13.32

W1 396.00 6.346 1.83 0.029 372.73 5.973

40.00 0.19 53.62

356.00 1.65 319.12

W2 1.00 32.57 0.15 30.66

428.57 6.35 1.98 0.03 403.39 5.97

S1 1.01 30.00 0.476 0.14 0.002 28.24 0.448

30.00 0.48 0.14 0.002 28.24 0.45

Ad1 9.6 lb /gal 34.00 11.11 3.30 0.31 0.015 10.46 3.10

Ad2 9.2 lb /gal 40.00 9.39 2.42 0.26 0.011 70.68 18.25

Ad3 8.5 lb /gal 2.00 3.87 1.51 0.11 0.007 3.64 1.42

Ad4 8.5 lb /gal 5.00 0.74 0.28 0.02 0.001 0.70 0.26

Ad4 8.4 lb /gal 48.00 158.67 32.49 4.41 0.150 149.35 30.58

40.00 0.19 53.62

M

V

T

D

D

A

Y

Ry

1.00

Water in

Admixture

(lb/yd3)

Darex® AEA

Air Entrainer

S38 Glass Microspheres

K15 Glass Microspheres

Styrene-butadiene Rubber Latex

W1b. Additional Water

Dosage

(fl oz/cw t)

Total Solids of Admixtures:

Water

Water for CM Hydration (W1a + W1b)

Admixtures (including Pigments in Liquid

Form)

W1a. Water from Admixtures

Total Aggregates:

Yield, ft3

= (M / D)

Measured Density, lb /ft3

Air Content, % = [(T - D) / T x 100%]

Relative Yield = (Y / Y D )

Actual Batched

ProportionsDesign Batch Size (ft

3):

Cementitious Materials

White Cement, Type I

Blast-Furnace Slag

Fiber 1

Mixture ID: Outer Layer

0.125

VCAS™ 160

Design Proportions

(Non SSD)

0.25

0.66

Yielded

Proportions

Total Fibers:

Aggregates

Total Cementitious Materials:

Fibers

270.133

15.28 15.28

49.51

9.98

27

49.51

1.062

11.00

Dosage

(fl oz/cw t)

Water in

Admixture

(lb/yd3)

%

Solids

V-MAR® 3

Viscosity Modifying Agent

Water from Admixtures (W1a) :

WRDA® 60

Water Reducer

Styrene-butadiene Rubber

Latex

0.66

ADVA® CAST 600

Superplasticizer

Amount

(f l oz)

0.66

Cement-Cementitious Materials Ratio 0.25

Water-Cementitious Materials Ratio

Total Water (W1 + W2) :

Water for Aggregates, SSD

52.60Design Density, lb /ft3 = (M / 27)

58.44

1420

Solids Content of Latex Admixtures and Dyes

0.25

Water in

Admixture

(lb)

0.113

58.44

1337

22.877

58.44

6.58

11.00

Theorectical Density, lb /ft3 = (M / V)

Absolute Volume of Concrete, ft3

Slump, Slump Flow, in . 11.00

24.305

Mass of Concrete. lbs

YD

SGAmount

(lb/yd3)

Volume

(ft3)

Amount

(lb)

Volume

(ft3)

Amount

(lb/yd3)

Volume

(ft3)

CM1 3.15 143.75 0.731 0.67 0.003 156.42 0.796

CM2 2.90 316.25 1.748 1.46 0.008 344.13 1.902

CM3 2.60 115.00 0.709 0.53 0.003 125.14 0.771

575.00 3.19 2.66 0.01 625.69 3.47

F1 2.68 3.00 0.018 0.01 0.0001 3.26 0.020

3.00 0.02 0.01 0.0001 3.26 0.02

A1 Poraver® (1.0-2.0mm) Abs: 25 0.38 124.10 5.234 0.57 0.024 135.04 5.695

A2 Abs: 25 0.46 150.23 5.234 0.70 0.024 163.47 5.695

A3 Abs: 25 0.59 128.45 3.489 0.59 0.016 139.78 3.797

A4 Abs: 0 0.15 16.33 1.745 0.08 0.008 17.77 1.898

A5 Abs: 0 0.38 41.37 1.745 0.19 0.008 45.01 1.898

460.47 17.45 2.13 0.08 501.07 18.98

W1 172.50 2.764 0.80 0.013 187.71 3.008

69.09 0.32 93.65

103.41 0.48 94.06

W2 1.00 100.69 0.47 109.57

273.19 2.76 1.26 0.01 297.28 3.01

S1 1.01 57.50 0.912 0.27 0.004 62.57 0.993

57.50 0.91 0.27 0.004 62.57 0.99

Ad1 9.6 lb /gal 34.00 11.59 3.30 0.31 0.015 12.62 3.59

Ad2 9.2 lb /gal 40.00 9.79 2.42 0.26 0.011 85.26 21.10

Ad3 8.5 lb /gal 2.00 2.16 0.81 0.06 0.004 2.35 0.88

Ad4 8.5 lb /gal 5.00 0.74 0.27 0.02 0.001 0.80 0.29

Ad4 8.4 lb /gal 48.00 317.51 62.30 8.45 0.288 345.50 67.79

69.09 0.32 93.65

M

V

T

D

D

A

Y

Ry

27

Relative Yield = (Y / Y D ) 0.919

Air Content, % = [(T - D) / T x 100%] 9.90 1.95 1.95

Yield, ft3

= (M / D) 27 0.115

Design Density, lb /ft3 = (M / 27) 50.71

Measured Density, lb /ft3 55.18 55.18

Absolute Volume of Concrete, ft3 24.328 0.113 26.473

Theorectical Density, lb /ft3 = (M / V) 56.28 56.28 56.28

Slump, Slump Flow, in . 9.00 9.00 9.00

Mass of Concrete. lbs 1369 6.34 1490

0.25 0.25

Water-Cementitious Materials Ratio 0.30 0.30 0.30

Cement-Cementitious Materials Ratio 0.25

V-MAR® 3

Viscosity Modifying Agent

Darex® AEA

Air Entrainer

Styrene-butadiene Rubber

Latex

Water from Admixtures (W1a) :

Amount

(f l oz)

Water in

Admixture

(lb)

Dosage

(fl oz/cw t)

Water in

Admixture

(lb/yd3)

WRDA® 60

Water Reducer

Dosage

(fl oz/cw t)

Water in

Admixture

(lb/yd3)

ADVA® CAST 600

Superplasticizer

Styrene-butadiene Rubber Latex

Total Solids of Admixtures:

Admixtures (including Pigments in Liquid

Form)%

Solids

Poraver® (0.5-1.0mm)

Poraver® (0.25-0.50mm)

Solids Content of Latex Admixtures and Dyes

S38 Glass Microspheres

Total Aggregates:

Water

Water for CM Hydration (W1a + W1b)

1.00W1a. Water from Admixtures

K15 Glass Microspheres

W1b. Additional Water

Water for Aggregates, SSD

Total Water (W1 + W2) :

Fibers

Basalt Chopped Fibers KV13

Total Fibers:

Aggregates

Mixture ID: Structural Ribs

Cementitious Materials

White Cement, Type I

Blast-Furnace Slag

VCAS™ 160

Total Cementitious Materials:

Design Proportions

(Non SSD)

Actual Batched

Proportions

Yielded

ProportionsDesign Batch Size (ft3): 0.125

YD

SGAmount

(lb/yd3)

Volume

(ft3)

Amount

(lb)

Volume

(ft3)

Amount

(lb/yd3)

Volume

(ft3)

CM1 3.15 1500.00 7.631 5.00 0.025 1312.29 6.676

1500.00 7.63 5.00 0.03 1312.29 6.68

F1 N/A

A1 All-Purpose Sand Abs: 4 2.65 1786.08 10.801 5.95 0.036 1562.57 9.450

1786.08 10.80 5.95 0.04 1562.57 9.45

W1 345.00 5.529 1.15 0.018 301.83 4.837

84.35 0.28 73.80

260.65 0.87 228.03

W2 1.00 71.44 0.24 62.50

416.44 5.53 1.39 0.02 364.33 4.84

S1 N/A

S2 N/A

S3 N/A

P1 N/A

Ad1 9.2 lb /gal 67.80 243.51 84.35 12.18 0.281 213.04 73.80

84.35 0.28 73.80

M

V

T

D

D

A

Y

Ry Relative Yield = (Y / Y D ) 1.143

Air Content, % = [(T - D) / T x 100%] 11.25 22.36 22.36

Yield, ft3

= (M / D) 27 0.103 27

Design Density, lb /ft3 = (M / 27) 137.13

Measured Density, lb /ft3 119.97 119.97

Absolute Volume of Concrete, ft3 23.961 0.080 20.963

Theorectical Density, lb /ft3 = (M / V) 154.52 154.52 154.52

Slump, Slump Flow, in . 11.00 11.00 11.00

Mass of Concrete. lbs 3703 12.34 3239

Cement-Cementitious Materials Ratio 1.00 1.00 1.00

Water-Cementitious Materials Ratio 0.23 0.23 0.23

Water in

Admixture

(lb)

Dosage

(fl oz/cw t)

Water in

Admixture

(lb/yd3)

Daraweld® C

Water from Admixtures (W1a) :

Water in

Admixture

(lb/yd3)

Amount

(f l oz)

Total Solids of Admixtures:

Admixtures (including Pigments in Liquid

Form)%

Solids

Dosage

(fl oz/cw t)

Pigment 1 (Powder Form)

1.00W1a. Water from Admixtures

Total Water (W1 + W2) :

Solids Content of Latex Admixtures and Dyes

Latex (if used)

Liquid Dye (if used)

Other Latex or Liquid Dye (if used)

W1b. Additional Water

Water for Aggregates, SSD

Water for CM Hydration (W1a + W1b)

Aggregates

Total Aggregates:

Water

Total Fibers:

Mixture ID: Aesthetic Paste Design Proportions

(Non SSD)

Actual Batched

Proportions

Yielded

ProportionsDesign Batch Size (ft3): 0.09

Cementitious Materials

White Cement, Type I

Total Cementitious Materials:

Fibers

Fiber 1

Material Quantity Unit Cost Total Price

White Cement, Type I 25.74 lb $0.76/lb $19.57

Slag (Grade 100) 56.64 lb $0.02/lb $1.13

VCAS™ 160 20.60 lb $0.76/lb $15.65

Quikrete® All-Purpose Sand 5.92 lb $0.10/lb $0.59

Poraver® 0.25 - 0.5 mm 22.47 lb $0.70/lb $15.73

Poraver® 0.5 - 1.0 mm 9.35 lb $0.70/lb $6.54

Poraver® 1.0 - 2.0 mm 7.72 lb $0.70/lb $5.40

S38® Glass Bubbles 24.75 lb $11.98/lb $296.46

K15® Glass Bubbles 1.67 lb $12.50/lb $20.88

High-Range Water-Reducer

(ADVA® Cast 600) 10.98 fl. oz. $0.12/lb. $1.32

Water Reducer (WRDA® 60) 10.98 fl. oz. $0.04/fl. oz. $0.44

Rheology-Modifying Admixture

(V-MAR® 3)2.94 fl. oz. $0.15/fl. oz. $0.44

Air-Entraining Admixture

(DAREX®AEA)0.67 fl. oz. $0.04/fl. oz. $0.03

Bonding Agent (Daraweld® C) 12.18 fl. oz. $0.06/fl. oz. $0.73

Latex (SikaLatex® R) 0.90 gal. $11.87/gal. $10.69

Latex (Styrene-Butadiene Rubber) 0.82 gal. $25.60/gal. $20.96

Carbon Fiber Reinforcement

(TORAYCA® T300)180 sq. ft. $2.40/sq. ft. $432.00

Fibers (Basalt KV13 Chopped) 0.34 lb. $7.82/lb. $2.68

Adhesive Foam Inlays 3 sq. ft. $8.00/sq. ft. $24.00

Foam Flotation 1 sheet $12.98/sheet $12.98

Sealer/Stain 1 gal. $45.00/gal. $45.00

Canoe Mold Lump Sum $293.09 $293.09

$1,226.31Total Production Cost

Buoyant Forces

Assumptions:

Rectangular Section

Uniform distribution of force along each section

3-in. sections, D

Wetted Width, W = 25.20 in.

Wetted Height, H = draft = 5.7 in.

Unit Weight of Water, γw = 62.4 lb/ft.3

Submerged Volume, V

𝑉 = 𝐷 ∗ 𝐻 ∗ 𝑊 = 3.0 𝑖𝑛.∗ 5.7 𝑖𝑛.∗ 25.20 𝑖𝑛.

= 430.97 𝑖𝑛.3

Submerged Area, A

𝐴 = 𝑉

𝐷=

430.97 𝑖𝑛.3

3.0 𝑖𝑛.= 143.657 𝑖𝑛.2 = 0.997 𝑓𝑡.2

Distributed Buoyant Force (FB) at One 3in. Section

𝐹𝐵 = γ𝑤 ∗ 𝐴

= 62.4 𝑙𝑏. 𝑓𝑡.3∗ 0.997 𝑓𝑡.2 = ⁄ 62.25 𝑙𝑏 𝑓𝑡.⁄

Shear Diagram

Moment Diagram

Resultant Buoyant Force Magnitude, FRB

FRB = ∑ 𝐹𝐵11𝑓𝑡.0𝑓𝑡. = 290.2 lb

Resultant Buoyant Force Location, XRB

XRB = ∑ 𝐹𝐵∗𝑥

11𝑓𝑡.0𝑓𝑡.

∑ 𝐹𝐵11𝑓𝑡.0𝑓𝑡.

= 7.38 ft.

Canoe Weight, Wc

Assumptions:

Uniform distribution of weight along entire canoe

length.

Weight of canoe, Wc = 160 lb

One 200lb male paddler located at x =4ft.

Resultant Magnitude of Canoe Weight, FRW

𝐹𝑅𝑊 = 𝑊𝑐

2=

160 𝑙𝑏

2= 80 𝑙𝑏

Resultant Location of Canoe Weight, XRW

𝑋𝑅𝑊 = 𝐿

2=

11 𝑓𝑡.

2= 5.5 𝑓𝑡.

Maximum Moment, M Located at x = 11 ft.

𝑀11𝑓𝑡. = ∑ 𝑀 = −80 𝑙𝑏 (11.00 𝑓𝑡. −5.5 𝑓𝑡. ) +

−200 𝑙𝑏(11.00 𝑓𝑡. −4 𝑓𝑡. ) +

290.2 𝑙𝑏 (11.00 𝑓𝑡. −7.38 𝑓𝑡. ) = −788 𝑓𝑡. −𝑙𝑏 =

−9464 𝑖𝑛. −𝑙𝑏

Moment of Inertia, Ixx

Assumptions:

C-channel beam

Height of gunwale, b = 13.31 in.

Thickness of bottom, t = 0.375 in.

Thickness of gunwale, s = 0.375 in.

Width of bottom (outside), d = 25.33 in.

Width of bottom (inside), h = (25.33 in. – 2*0.375 in.)

= 24.45 in.

y = location of neutral axis (from top of section)

𝐼𝑥𝑥 =2𝑠𝑏3 + ℎ𝑡3

3− 𝐴(𝑏 − 𝑦)2 = 367.6 𝑖𝑛.4

where

𝐴 = 𝑏𝑑 − ℎ(𝑏 − 𝑡) = 20.82 𝑖𝑛.2

and

𝑦 = 𝑏 −2𝑏2𝑠 + ℎ𝑡2

2𝑏𝑑 − 2ℎ(𝑏 − 𝑡)= 10.04 𝑖𝑛.

Stresses on Section

𝜎 =𝑀 ∗ 𝑐

𝐼

c = distance from neutral axis to edge of section

Compressive Stress, 𝛔

𝜎 = (−9464 𝑖𝑛 − 𝑙𝑏) ∗ (10.04 𝑖𝑛. )

367.6 𝑖𝑛.4= −258.3 𝑝𝑠𝑖

Tensile Stress, 𝛔

𝜎 = (−9464 𝑖𝑛. −𝑙𝑏) ∗ (10.04𝑖𝑛. −13.31 𝑖𝑛. )

367.6 𝑖𝑛.4

= 84.2 𝑝𝑠𝑖