University of Southern California

Design Paper 2018

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Table of Contents Executive Summary ........................................................................................................................ii Project and Quality Management .....................................................................................................1 Organization Chart ..........................................................................................................................3 Hull Design and Structural Analysis ................................................................................................4 Development and Testing ................................................................................................................6 Construction ....................................................................................................................................9 Project Schedule ............................................................................................................................11 Construction Drawing ...................................................................................................................12

List of Figures Figure 1: Person-hour breakdown by month and canoe task. ....................................................... 1 Figure 2: Mix design proportions printed and placed at dry mix station. ...................................... 2 Figure 3: Comparison of hull profiles between Drella (blue) and Ascent (red). ........................... 4 Figure 4: Three dimensional view of canoe hull from NX. .......................................................... 4 Figure 5: Moment diagrams for display, two male and female, coed and transportation cases. .... 5 Figure 6: Composite slab undergoing four point bending test. ..................................................... 7 Figure 7: Concrete cylinder after compression test completion. ................................................... 8 Figure 8: Team member separating fibers during dry mixing. ..................................................... 9

List of Tables

Table 1: Overall canoe properties including dimensions and materials. ....................................... ii Table 2: Summary of mix properties and strengths. ..................................................................... ii Table 3: Aggregate information by material. ............................................................................... 6 Table 4: Volumetric proportions of cementitious materials for fly ash and silica fume. ............... 7

List of Appendices

Appendix A: References ...............................................................................................................A1 Appendix B: Mixture Proportions .................................................................................................B1 Appendix C: Example Structural Calculations ..............................................................................C1 Appendix D: Hull Thickness/Reinforcement and Percent Open Area Calculations ......................D1

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Executive Summary The University of Southern California

(USC) is nestled in the heart of downtown Los Angeles. Its urban campus is home to the Viterbi School of Engineering, composed of 8,300 students and eight departments. USC’s chapter of the American Society of Civil Engineers (ASCE) is made up of 54 students, of which, 15 regularly attended Concrete Canoe team meetings. With the help of these members and all of ASCE, the team is hoping to continue their upward trend at the Pacific Southwest Conference (PSWC) this year in Tempe, Arizona. The team finished 5th in 2015, 8th in 2016, and 7th in 2017. 2018 came with many changes for this year’s Concrete Canoe Team. The team moved work spaces, a process which delayed construction until late in the fall. This year also featured the construction of a 21 foot rolling steel cart on which the canoe was poured, cured, and sanded. This year the team focused on revisiting the basic elements of the canoe to increase strength and performance.

In the 1960s, Andy Warhol’s new approach to art elevated him to a cultural icon. Using new techniques like silk screening and a wide array of colors, regular items like a soup cans or a bottle of soda were immortalized through Warhol’s new genre of Table 1: Overall canoe properties including dimensions and materials.

pop art. The team strove to achieve the same success through revisiting the canoe’s design; it was from this process that the team chose Warhol as the inspiration for this year’s theme. Once described as a mix between Dracula and Cinderella, Warhol earned the nickname “Drella”, a name which the team has adopted for this year’s canoe. Table 2: Summary of mix properties and strengths.

Mix Structural Shell 28-Day Compressive Strength

6743 psi 3425 psi

28-Day Tensile Strength

550 psi 381 psi

28-Day Flexural Strength

1835 psi 932 psi

Unit Wet Density

93.65 pcf 78.69 pcf

Unit Dry Density

96.09 pcf 101.56 pcf

Air Content 6.7% 22.1% Drella features major redesign in the

mix composition, construction techniques, and hull design. Starting with the mix design the team employed a new ASTM C330 aggregate for enhanced finishing and compliance as well as introducing fly ash for sustainability and strength. For construction, the team switched to a male mold to reduce difficulties with slump and thickness. This year’s hull design is entirely redesigned with a symmetric profile and rocker, as well as reduced, softer chines. The aim of these modifications is a stronger, higher performing canoe. A final modification is the use of inlays for aesthetic features instead of tiles. These features culminate in a ground-up revision which the USC Concrete Canoe team is proud to present as Drella.

Name Drella Length 19 ft Maximum Width 27 in Maximum Depth 14 in Hull Thickness ½ in Weight 300 lbs (estimated) Primary Reinforcement

Carbon Fiber Mesh

Secondary Reinforcement

PVA Fibers

Colors Black, Blue, Green, Red, White, Yellow

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Project and Quality Management This year, the USC Concrete Canoe

team aspired to make multiple extremely ambitious changes to the canoe’s design and construction. Led by two captains, one junior captain, and an additional sub-team captain, the goals for the year included new mix materials, a different hull design, and inverted construction method. The team began the year with the hopes that both the schedule and budget would easily allow for these changes. Unfortunately, this was not the case. The team was pushed out of their previous workspace due to space limitations. The new workspace, as mentioned before, was not ready until late in the fall semester. As a result, the team chose to focus mainly on the structural, aesthetic, and mix design during the first semester. Due to limited space to make and test new mix designs, all mixes were made in the span of two days, preventing the team from making any changes after initial testing. Nearly all work on the mold and canoe was pushed until second semester. Despite an extremely condensed work schedule, the canoe was still scheduled to be completed before the competition in April.

In this schedule, the critical path and associated milestones were determined by what was needed to participate in competition. This included items that were necessary for the construction of the competition canoe, from the procurement of the foam to the substantial completion of the canoe, and the steps needed to write the design paper, including the rough draft and various stages of editing.

The initial schedule differed slightly from the revised schedule. The most significant change was the decision to make the design paper a part of the critical path. Initially, only construction was put on the critical path, but, knowing the significance of the design paper for the participation in competition, this was added to the critical path. Other changes to the schedule were limited to date changes to account for the unexpected delays due to the limited access to the workspace.

The changes put in place this year also had an effect on the budget. Having been given the same amount of design team funding as for the 2017 canoe, the team had to determine how to pay for canoe materials in addition to the necessary tools and storage needed for the new workspace. The team effectively lowered expenses compared to previous years by choosing to not make a practice canoe, cutting down on material costs and labor time. The budget was then carefully managed with a tracking system and purchase log.

As always, the team put a large emphasis on safety. The new workspace for the team is located in a research lab, thus, even stricter safety measures were implemented. Masks, gloves, and closed toe shoes were required for any construction work. Any member not wearing these was not allowed to work. MSDS were printed and kept nearby in case of emergency. Any dust-heavy work and work with any exposure to chemicals was done outside for better ventilation and less exposure to hazards.

Sustainability was also a major focus this year. More environmentally sustainable materials, such as fly ash and silica fume, were used in the mixes. Masks and mixing trays were re-used to limit waste. Additionally, the display stands from the past years were reused. Economic sustainability was encouraged through the use of donated

Figure 1: Person-hour breakdown by month and canoe task.

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materials and materials already in the team’s inventory.

Quality control began prior to the actual construction process with the procurement of materials. Before the materials were ordered, the new mix design for the canoe was created based on materials compliant with the rules of the competition. Inventory was taken to determine which materials needed to be ordered and which existing materials were still good to use. Once a list of needed materials was established, the captains ordered or obtained them from trusted sources. These materials were then stored in labelled, air-tight containers to allow for easy identification of each material. This was especially important since the team had to transfer the materials to the new workspace. The team purchased shelves for the workspace to further the organizational effort of the materials.

Because of the small size of the team, the captains gave individualized attention to members by observing, correcting, and approving their work, especially during the pre-construction phases. Furthermore, all members were given safety training to ensure that all work being done was safe and efficient.

The small size of the team also meant that pour day required the contributions of many members who were not a part of the Concrete Canoe team. This required training and quality control during the construction process to ensure that the canoe complied with its intended design and proportions, since many people working on the canoe did not know the canoe’s design and building techniques. Therefore, each member who arrived on pour day was assigned to a specific task and given clear directions for the duties they needed to complete. If they had questions, they asked the captains or other experienced members.

Figure 2: Mix design proportions printed and placed at dry mix station.

During the construction process, the captains separately supervised the dry mixing, wet mixing, and concrete placement stations. At each station, the captain ensured that members were completing their assigned task accurately. Quality control of the dry mixes allowed the team to discover that the scales were not tarred to account for the weight of the cups during measuring and therefore to resolve the issue. For the wet mixes, the captains inspected the consistency of each mix before it was placed on the canoe. Some mixes encountered issues, but, through this inspection the captains were able to locate and discard these mixes. Furthermore, the wet mixes were all weighed and recorded. This allowed the captains to ensure that each mix was within an acceptable weight range and contained all necessary materials. Quality control of the placing of concrete was performed through the use of thickness gauges for each layer, ensuring that the concrete was placed evenly and consistently.

A further measure of quality control was the documentation of the materials and rules. Along with the previously mentioned MSDS binder, the captains read and understood the rules of the competition in order to ensure that each step of the process was compliant.

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Organization Chart Captains: Emmy Park, Cole Pernitsky Co-Captain: Sarah Cigas

Susan-Alexis Brown Emmy Park Cole Pernitsky Sarah Cigas

Sub-Team Paddling Aesthetics Structures Mix Design Construction Captain

Cole Pernitsky Cole Pernitsky Emmy Park Emmy Park Sarah Cigas

Susan-Alexis Brown Susan-Alexis Brown

Seniors Branden Currey Susan-Alexis Brown Susan-Alexis Brown Susan-Alexis Brown Susan-Alexis Brown Marjo Jarrin

Juniors Cyril Hui Camelia Meftoul Camelia Meftoul Desiree James Emmy Park Cole Pernitsky Emmy Park Emmy Park Emmy Park Cole Pernitsky

Emmy Park Cole Pernitsky Cole Pernitsky Cole Pernitsky Linnea Engstrom

Sophomores Alex Di Sarah Cigas Sarah Cigas Sarah Cigas Sarah Cigas Sarah Cigas Rob Vigil Rob Vigil Rob Vigil

Freshmen Annie Chang Chris Demas Annie Chang Chris Demas Annie Chang Nicole Ng Annie Chang Nicole Ng Nicole Ng

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Hull Design and Structural Analysis Canoe hulls have a few characteristic

styles, each with their own performance focuses. The concrete canoe races present the unique challenge of merging speed with maneuverability for a boat that is significantly heavier than a standard canoe. Over the past three years, the team has only made minor modifications to the hull design, instead focusing on mix design and structural integrity. With this year’s modification to the construction process, the team took the opportunity to redesign the hull to increase efficiency and maneuverability by sharpening the entry line, rounding the hull profile, and designing for symmetry. For this year’s design the team used primarily NX for the hull design, before porting to AutoCAD.

Figure 4: Three dimensional view of canoe hull from NX.

While paddling last year’s canoe the team noticed a small wake developing at the front of the canoe, indicating significant drag forces. Drella features a sharp entry line that widens linearly for 36 inches before merging to a radial arc that defines the main body of the canoe’s top profile. Compared to the 2017 canoe Ascent, Drella has reduced the entry angle of the canoe by 12%, and extended the entry line by an additional foot. This reduction in width at the front of the canoe is intended to reduce drag, leading to a smoother and more efficient paddle. Drella also features modifications to the hull profile to further increase efficiency

and reduce drag. To accomplish this, the team increased the roundness of the canoe’s bottom. This year’s hull profile is defined angularly, featuring a variable shallow arch over the first 36 degrees and then sharper arch to the vertical, creating a rounder profile across the canoe. The rounder profile can be clearly seen at the center of the canoe, as shown in Figure 2. This modification creates a narrower, more streamlined profile in the water, because with approximately the same canoe weight and paddler weight, the water line will remain unchanged. Like the entry line, the hull profile designed for Drella creates a faster, more efficient canoe.

While increasing the efficiency of the canoe, the redesigned hull profile also modifies the stability characteristics of the canoe. The rounder bottom sacrifices initial stability but increases final stability by continuing the hull’s arch higher up the sides. Based upon the paddling team’s feedback it was determined that the detriment of decreased stability would be outweighed by the increase in efficiency. Additionally, Drella’s enhanced final stability will allow paddlers to lean further into their turns. Overall this modification will lead to improving the maneuverability of the canoe.

With changes in the top and cross-sectional profiles geared towards efficiency, Drella’s side profile modifications are aimed at increasing maneuverability. Past canoes

Figure 3: Comparison of hull profiles between Drella (blue) and Ascent (red).

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have featured an asymmetrical rocker, and while these canoes tracked straight, last year’s races demonstrated the limitations of this shape in initiating sharp turns. Sprint races feature 180 degree turns, in which the canoe lost the majority of its momentum. Drella features a square stem with a 6 inch radius and a 2.5 inch rise at bow and stern, creating a symmetrical and continuous rocker. This means a more aggressive stern rocker, allowing the 19 foot long canoe to paddle like one of much shorter length. Subsequently, Drella will handle with increased maneuverability, especially on sharp turns.

Overall, Drella is 19 feet long, with a maximum depth of 14 inches and maximum width of 27 inches. Designed for efficiency and maneuverability, the canoe features a rounder hull profile with a symmetrical, 2.5 inch rocker. The team is eager to paddle with the increased maneuverability and efficiency in this year’s races at PSWC.

The structural analysis team employed a simplified two-dimensional model, assuming a uniform cross section throughout the canoe. Modeling the canoe as a beam, the boundary conditions require that the bending moment at the end must be equal to zero. As a result the highest bending moments do not occur at the ends, validating the simplification of the cross section into a constant channel shape for the purpose of determining ultimate stresses. The cross section has dimensions of 27 x 14 inches and a neutral axis 5.77 inches from the base of the canoe. This would generally place the entire base in tension. However, due to the point load of the paddlers, the bending moment is not applied to the whole canoe, and some of the slab is in compression.

Five cases are modelled in Figure 3. The display case involves a uniform canoe weight and two reaction points representing the stands. The three paddler cases (two male,

two female, and coed) all involve point loads representing the paddlers, the distributed weight of the canoe, and the distributed reaction of the water. The canoe is assumed to weigh 300 lbs, males 200 lbs, and females 160 lbs. These values are higher than expected, to allow for a factor of safety. The display reactions are 5 ft from the ends of the canoe. The paddlers are 4 ft from the end in the two person case, and 3.8 ft/ 6.65 ft from the ends in the four person case. Transporting the canoe in a female mold, the canoe is uniformly supported, and is modeled below as such. After analyzing these cases in MATLAB, the maximum bending moment was found to occur in the coed paddling case, at 273.6 ft-lb. This produces a maximum tensile stress of 59.35 psi, and a maximum compression stress of 79.64 psi. To ensure proper flotation, the team employed EPS high density foam bulkheads at the bow and stern. The volume water displaced by the canoe should be 8,300 in3. From the NX model, the team determined that without bulkheads the canoe has a volume of 4,300 in3. To provide adequate flotation, the team used 34 inch bulkheads, yielding an additional 4,200 in3 of flotation.

Figure 5: Moment diagrams for display, two male and female, coed and transportation cases.

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Development and Testing The USC Concrete Canoe team has struggled to innovate in the past years. In 2016, the canoe cracked during competition, motivating the 2017 team to focus solely on designing a high strength mix. While the 2017 mix was stronger, it was not compliant with the C330 aggregate volumetric requirements. This year, the USC Concrete Canoe team put a strong emphasis on developing a new mix that was not only compliant with the rules, but also strong, economic, and environmentally sustainable.

Given that the team had many materials left over from the 2017 canoe, most of the baseline materials for this year’s mix remained the same. The main aggregates, glass cenospheres (Poravers) of various granular sizes and K1 glass bubbles, whose properties are shown in Table 3, were used for their low density and neutral color. Table 3: Aggregate information by material.

Material SG Absorption

.1 - .3 mm Poraver 0.90 25%

.25 - .5 mm Poraver 0.59 25% 1 - 2 mm Poraver 0.39 25%

Utelite 1.73 31%

K1 Glass Bubbles 0.13 0% There were two major material changes introduced this year, the first of which was to the C330 compliant aggregate. The 2017 canoe, Ascent, used Stalite, an expanded shale aggregate. The team experienced difficulty sanding through this aggregate. Additionally, it left an uneven, rocky appearance. For the 2018 canoe, the team decided to use Utelite, a fine shale aggregate. The smaller aggregate size would reduce finishing and aesthetic issues. To further reduce the particle size, the team decided to sieve the Utelite, using the aggregates retained on the No. 35 to No. 18 sieves. The Utelite could then function as a

replacement for the .5-1 mm Poravers used in previous years. In addition, Utelite’s specific gravity of 1.73 is lower than Stalite’s 1.88. This slight difference helps to combat the growing weight from increasing the amount of ASTM C330 aggregate in order to comply with the rules. Type 1 White Portland Cement and VCAS 160 (Vitrified Calcium Alumino-Silicate) were maintained as the major cementitious materials for the 2018 canoe. The team did not need any extra properties, such as phosphate resistance or high early strength, in the cement. Thus, Type 1 White Portland Cement was used for its structural properties and white color, which is best for keeping pigment colors vibrant. VCAS 160, a pozzalon, has been used in mixes for the past few years because it increases the environmental sustainability of the concrete since it is a byproduct of fiberglass production. It also maintains pigment vibrancy. The major negatives of using VCAS are its high price and shipping distance. Portland cement can be obtained for free from a local distributor, but VCAS 160 is purchased from a company in North Carolina, lowering both economic and environmental sustainability. With this in mind, the team decided to test two other cementitious materials: silica fume and fly ash. Both of these materials could be received as a donation from a local company, decreasing the environmental impact of shipping, and both are by-products of other processes. In addition to being environmentally and economically sustainable choices, silica fume and fly ash have been proven to increase compressive strength and workability. Once the team decided what materials to use, the concrete mixes were designed. This was done by first deciding the volumetric percentage of the aggregates and keeping that constant for each mix. By

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sieving the Utelite, it could be used as a replacement for the .5-1 mm Poravers. To include a factor of safety for the required amount of C330 aggregate, the team decided 30% of the aggregate blend should be Utelite. The other aggregates, 1-2 mm Poravers, .25-.5 mm Poravers, .1-.3 Poravers, and glass bubbles, were evenly distributed to have a well-graded mix (17%, 17%, 17%, and 19%, respectively). PVA fibers were also added to the mix in this step as secondary reinforcement to improve tensile strength.

Next, the team decided the proportions of cement and cementitious materials. In order to decide whether silica fume or fly ash would be used in the final mix design, four variations of cementitious material amounts were chosen, two with silica fume and two with fly ash. The variations can be seen in Table 4: Table 4: Volumetric proportions of cementitious materials for fly ash and silica fume.

Fly Ash Mix # VCAS PC Fly Ash

1 45% 40% 15% 2 45% 35% 20%

Silica Fume

Mix # VCAS PC Silica Fume

3 45% 45% 10% 4 45% 40% 15%

These amounts were based upon manufacturer guidelines. For each of these four variations, three different water-to-cement ratios were used (.33, .35, and .40), producing 12 different mixes overall. Each of these mix had varying quantities of admixtures. As in past years, the main two admixtures used were water repellent and styrene-butadiene latex. Water repellent, which reduces water penetration in hardened concrete, was added based on manufacturer guidelines. The team decided on the amount

of SR latex during mixing, as the main purpose of this admixture was to increase overall workability of the mix.

Given limited access to workspace and a tight schedule, all 12 of these mixes were made in the span of two days. Three cylinders for compressive strength testing and two composite slabs for flexural strength testing were made of each mix. The slabs were made with carbon fiber reinforcement as their primary reinforcement, which was chosen for its flexibility, thinness, and high tensile strength. The team decided to return to 2016’s symmetric layering scheme: three layers of concrete (⅛”, ¼”, ⅛”) and one layer of reinforcement between each of these concrete layers. Since tensile stress increases away from the neutral axis of the layers, the team placed the reinforcement as close as possible to the top and bottom surfaces of the canoe. High tensile stress is then distributed over the reinforcement, decreasing the likelihood of the concrete cracking from tensile loads.

Following ASTM C39 and ASTM C78 test methods in a Universal Testing Machine, 28-day testing gave compressive strengths ranging between 5415 psi and 6941.5 psi and flexural strengths between 612.2 psi and 3302.7 psi. The team based its choice of mix on the overall workability and ratio of average compressive strength to density. The chosen mix was the 45% VCAS,

Figure 6: Composite slab undergoing four point bending test.

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35% PC, 20% fly ash mix. It had an average compressive strength of 6743 psi and an average flexural strength of 1835.2 psi. According to ACI 207R, the relationship between the compressive and tensile strength is 6.7$%′', thus the tensile strength was found to be 550.18 psi. The compressive strength of the 2017’s “Bottom” mix was 2630 psi and its flexural strength 1750 psi, making this year’s mix 156% stronger in compression and 5% stronger in flexure than 2017’s mix. The maximum compressive stress was calculated to be 79.64 psi and the maximum tensile stress was calculated to be 59.35 psi, thus the designed concrete is extremely capable of handling all loading cases.

Figure 7: Concrete cylinder after compression test completion.

The original construction plan was to use this mix throughout the entire canoe to reduce confusion during mixing. Many people who were helping pour the canoe had little to no experience with mixing concrete, so only using one mix would ideally make it easier for the inexperienced mixers. This would also improve the speed of mixing since premixes could be made without concern of preparing too much per layer.

While pouring the last layer of the canoe, the limited budget and mistakes made

during mixing caused a material shortage. In order to continue pouring the canoe, the team had to devise a new mix with existing materials. The main challenge for the team was developing a new mix after running out of SB latex. The team needed to find a new way to improve workability without adding significantly more water, which would greatly decrease strength. In 2017, the team purchased a mid-range water reducer and a shrinkage reducer. The water reducer would decrease the amount of water needed in the mix, keeping the strength higher than it would be with just water. The shrinkage reducer would prevent excess drying shrinkage from the increase in water needed for workability. Following manufacturer instructions, the team added both of these to the mix and added water until minimal workability was achieved. Cylinders made of this “Shell” mix gave a compressive strength of 3425 psi and a tensile strength of 381 psi. The strength of this mix still exceeds the required strength of the concrete, so, despite the rapid design of this mix, the team remains confident in its ability to handle the expected stresses.

While back-calculating the mix design, the team realized that the bulk loose dry density was used to calculate the weight of each material instead of the required oven dry density. This meant that, while the original design was compliant with the ASTM C330 aggregate requirement, the actual execution of this was not compliant. The actual volumetric percentage of Utelite used in Drella was 16%, significantly less than the intended 30%.

Despite the challenges faced while pouring, the team is proud of the steps taken to improve the concrete mix. This year’s mix is environmentally sustainable, economic, and strong. Innovations in material choices improved the overall mix and will help the USC Concrete Canoe team develop even better mixes in the future.

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Construction

This year’s construction process required adjustments due to the relocation of the team’s workspace. The team experienced many delays since no work could be done until renovations to the workspace had been completed. Because of this and budgetary restrictions, the team was not able to make a practice canoe as was done previously, which forced extra care to be taken with regard to detail and quality management. Another obstacle associated with the new workspace was the presence of a research based water channel in the same building. To prevent particles from the canoe or its mold from entering the water and affecting research, no work was allowed inside. Therefore, after gaining access to the workspace, the team dedicated one week towards constructing a 23’ x 3’ steel cart to transport the canoe into and out of the building. This further diverted time away from preparing the foam mold, which pushed pour day back one week.

Preparations of the foam mold began in December. In an effort to remain within budget, the team elected to hot-wire cut the foam blocks instead of getting them CNC milled. However, lack of access to a hot wire cutter forced the team to build their own.

This year, the team decided to construct the canoe using a male mold instead of a female mold to reduce issues of slumping concrete and poorly formed edges. Once the male mold pieces were cut, they were then glued together and the complete mold was placed on the steel cart. The mold was sanded to smooth the surface and to fix any unevenness caused by the cutting process. After sanding, a layer of drywall was added to the outside of the mold to further smooth the surface. In an effort to reduce the time required to apply contact paper to the mold and to create a smooth finish without seams, the team elected to use Styropoxy, a foam release agent. Two layers were applied onto

the mold. With this, the mold was ready for pour day.

Pour day began with the preparation of dry mixes. Team members were given roles of measuring out materials, separating the PVA fibers, or mixing the materials together. While the dry mixes were being prepared, the design of the canoe was also being prepared on the mold. Wax inlays in the signature of Andy Warhol were placed as a stencil on the outside center of the mold. Inlays were used this year instead of the tiles used in previous years. This created a cleaner design and reduced sanding time. Foam strips were also placed on the outside of the mold to divide it into quadrants and serve as a guide for placing the four different colors of the first layer. After the first 20 dry mixes had been prepared, the wet mixing station was established.

Figure 8: Team member separating fibers during dry mixing.

At the wet mixing station, members added pre-measured quantities of water, water repellent, and latex and mixed by hand. Due to inaccurate measurements of latex during the first round of wet mixes, the

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amount of latex added to each mix did not match the intended mix design. This problem of incorrectly tared scales, however, was later discovered through quality control by the captains and corrected. Once each mix was completed and approved by a captain, the mix was weighed and recorded and then sent to the placing station where members placed the concrete on the foam mold by hand. To ensure efficiency, dry mixing, wet mixing, and placing were occurring simultaneously so the mixes were constantly being prepared and placed.

The first 1/8” thick layer of the canoe was placed directly onto the mold. The division of this layer into quadrants guided the placement of blue, green, yellow, and red pigmented mixes. Furthermore, the captains supervised the process and ensured that the concrete layer complied with the desired thickness by using toothpicks marked as depth gauges. Once the first layer was completed, a layer of carbon fiber reinforcement was placed on the canoe. In order to resist the curling tendency of the reinforcement, the team had previously cut it into sections and flattened it three days beforehand. The second layer was then placed on top of the reinforcement using the prepared mixes. This second layer contained no pigment and was ¼” thick.

As the second layer was nearing completion, the captains realized there was a diminishing supply of SB latex, and none would be left to use on the third layer. Upon determining that there would be no way to obtain more at that time, the captains decided to make the third layer with the materials on hand. A new mix was developed using an increased amount of water for workability and additions of water reducer and shrink reducer to offset the impacts of the extra water. The altered consistency of this new mix proved difficult for placing, especially on top of the second layer of reinforcement. Furthermore, some of the new mixes

developed a strange consistency that caused them to spread rapidly. These mixes were thrown out.

The team put in considerable effort into placing the final layer, which was less workable. Also, because of the team’s restriction to working outside, the final layer was placed in limited lighting. This added a considerable amount of time to the construction process, especially since three different pigmented mixes were needed to design the exterior. After the final layer was placed, the canoe was covered with wet burlap and a tarp and transported inside. This new method of curing with soaked burlap was used so that each section of the canoe would be given a consistent amount of water, which was an issue when using the steam curing method from previous years. It remained covered by the burlap for the next seven days, with the burlap being re-wetted every other day.

After 28 days of curing, the canoe was demolded and the inlay wax was melted out of the canoe. Having resupplied materials after pour day, the structural mix that was used throughout the first and second layers of the canoe was used again in the inlays and to cover the bulkheads. Following the placement of the inlays, the exterior was sanded using electric belt sanders and 60 to 2000 grit sandpaper to create a smooth finish. The interior was lightly sanded after the inlay concrete was dry. Letters were stenciled, cut out of vinyl, and attached using the self-adhesive backs. To finish, canoe was the painted with two coats of sealant.

Throughout the construction process, the team emphasized sustainable practices through the reuse of equipment as mentioned in the project management section. Masks were labelled with member names to be used throughout pre-construction, construction, and sanding. The tins used for dry-mixing were also cleaned out after each mix and used again.

ID Task Name Duration Start Finish

0 Concrete Canoe 2017 247 days Fri 8/11/17 Sat 4/14/181 Admin 243 days Fri 8/11/17 Tue 4/10/182 Budget and Funding 15 days Fri 8/11/17 Fri 8/25/173 Receive Rules 0 days Mon 9/11/17 Mon 9/11/174 Design Paper 32 days Mon 2/5/18 Thu 3/8/185 First Draft 17 days Mon 2/5/18 Wed 2/21/186 Rules Check 8 days Thu 2/22/18 Thu 3/1/188 Engineers Notebook 15 days Thu 2/22/18 Thu 3/8/187 Final Draft 7 days Fri 3/2/18 Thu 3/8/189 Presentation Content 27 days Thu 2/22/18 Tue 3/20/1810 Presentation Rehearsal 21 days Wed 3/21/18 Tue 4/10/1811 Aesthetic Design 181 days Wed 9/20/17 Mon 3/19/1812 Theme Selection 0 days Wed 9/20/17 Wed 9/20/1713 Design Canoe Graphics 40 days Mon 12/25/17 Fri 2/2/1814 Design Paper Graphics 9 days Wed 12/27/17 Thu 1/4/1815 Design Presentation Slides 26 days Thu 2/22/18 Mon 3/19/1816 Structures 45 days Thu 9/21/17 Sat 11/4/1717 Finalize Hull Design 23 days Thu 9/21/17 Fri 10/13/1718 Simple Beam Structural Analysis 22 days Sat 10/14/17 Sat 11/4/1719 Determine Max Loading Cases 0 days Sat 11/4/17 Sat 11/4/1720 Development and Testing 67 days Sun 10/1/17 Wed 12/6/1721 Order Initial Mix Materials 34 days Sun 10/1/17 Fri 11/3/1722 Obtain ASTM C330 Compliant

Aggregates12 days Mon 10/2/17 Fri 10/13/17

23 Design Structural Mixes 21 days Sat 10/14/17 Fri 11/3/1724 Create Mixes for Testing 2 days Tue 11/7/17 Wed 11/8/1725 Test Mix Curing 28 days Thu 11/9/17 Wed 12/6/1726 Testing 0 days Wed 12/6/17 Wed 12/6/1727 Verify Mix Design with Structural

Analysis0 days Wed 12/6/17 Wed 12/6/17

28 Finalize Mix Design 0 days Wed 12/6/17 Wed 12/6/1729 Paddling 189 days Sun 10/1/17 Sat 4/7/1830 Practice 189 days Sun 10/1/17 Sat 4/7/1831 Finalize Paddling Team 0 days Wed 1/10/18 Wed 1/10/1832 Final Product Display 39 days Sat 3/3/18 Tue 4/10/1833 Design Display Stands 5 days Mon 3/19/18 Fri 3/23/1834 Procure Display Materials 8 days Sat 3/24/18 Sat 3/31/1835 Prepare Cutaway Section Mold 4 days Sat 3/3/18 Tue 3/6/1836 Place, Finish and Cure Cutaway

Section28 days Wed 3/7/18 Tue 4/3/18

37 Display Table 10 days Sun 4/1/18 Tue 4/10/1838 Construction 145 days Fri 11/17/17 Tue 4/10/1839 EPS Foam Procurement 0 days Fri 11/17/17 Fri 11/17/1740 Construct Mold 77 days Fri 11/17/17 Thu 2/1/1841 Pour Day Materials 23 days Wed 1/10/18 Thu 2/1/1842 Pour Day 0 days Sat 2/3/18 Sat 2/3/1843 Cure 28 days Sat 2/3/18 Fri 3/2/1844 Removal from Mold 0 days Fri 3/2/18 Fri 3/2/1845 Inlays and Aesthetic Additions 0 days Fri 3/2/18 Fri 3/2/1846 Sand and Patch 28 days Sat 3/10/18 Fri 4/6/1847 Apply Letters and Seal 4 days Sat 4/7/18 Tue 4/10/1848 Canoe Substantial Completion 0 days Tue 4/10/18 Tue 4/10/1849 Deliverables Due 0 days Thu 3/8/18 Thu 3/8/1850 Pacific Southwest Conference 4 days Wed 4/11/18 Sat 4/14/1851 Depart for Conference 0 days Wed 4/11/18 Wed 4/11/1852 Display and Presentation 0 days Thu 4/12/18 Thu 4/12/1853 Races 0 days Fri 4/13/18 Fri 4/13/18

9/11

9/20

11/4

12/612/6

12/6

1/10

11/17

2/3

3/23/2

4/103/8

4/114/124/13

6 13 20 27 3 10 17 24 1 8 15 22 29 5 12 19 26 3 10 17 24 31 7 14 21 28 4 11 18 25 4 11 18 25 1 8 15Aug '17 Sep '17 Oct '17 Nov '17 Dec '17 Jan '18 Feb '18 Mar '18 Apr '18

Page 1

Cole Pernitsky

LB

A1

Appendix A: References “3M Glass Bubbles K1 Product Information.” 3M, 2008.

ASTM International. C39/C39M-18 Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens. West Conshohocken, PA, 2018. Web. 25 Feb 2018.

ASTM International. C78/C78M-18 Standard Test Method for Flexural Strength of Concrete (Using Simple Beam with Third-Point Loading). West Conshohocken, PA, 2018. Web. 25 Feb 2018.

AutoCAD. Computer software. Vers. 2017. Autodesk, n.d. Web.

“Class ‘F’ Fly Ash Material Technical Data Sheet.” Diversified Minerals Inc.

Cope, James L., and Robert W. Cannon. “ACI 207.2R-95 Effect of Restraint, Volume Change, and Reinforcement on Cracking of Mass Concrete.” ACI Materials Journal, vol. 87, no. 3, 1990, doi:10.14359/2228.

“Environmental Benefits of VCAS.” VitroMinerals, VitroMinerals,

MATLAB. Computer software. Vers. R2017a. The MathWorks, Inc., n.d. Web.

“MasterLife SRA 035 Material Technical Data Sheet.” BASF, 2015.

“MasterPolyheed 1025 Material Technical Data Sheet.” BASF, 2015.

“NanoPozz100 - D Silica Fume Material Technical Data Sheet.” Diversified Minerals Inc.

“Poraver Material Technical Data Sheet.” Poraver North America, 2011.

NX. Computer software. Vers. 11. Siemens., n.d. Web.

USC Concrete Canoe Team (2015), Jurassic, Concrete Canoe Competition Design Paper.

USC Concrete Canoe Team (2016), That ‘70s Canoe, Concrete Canoe Competition Design Paper.

USC Concrete Canoe Team (2017), Ascent, Concrete Canoe Competition Design Paper.

“Utelite ASTM C330 Conformance Report.” Utelite Corporation, 2017.

“VCAS 160 Material Technical Data Sheet.” Vitro Minerals. 2005.

B1

STRUCTURAL MIX

CEMENTITIOUS MATERIALS Component Specific Gravity Volume (ft3) Amount of CM (mass/volume) (lb/yd3)

Portland Type I Cement 3.15 4.32 636.9 Total Amount of cementitious materials

1627 lb/yd3

c/cm ratio 0.76

VCAS 160 2.60 3.24 700.9

Class F Fly Ash 2.45 1.89 288.9

FIBERS Component Specific Gravity Volume (ft3) Amount of Fibers (mass/volume) (lb/yd3)

PVA Fibers 1.30 0.057 4.59 Total Amount of Fibers 4.59 lb/yd3

AGGREGATES

Aggregates ASTM C330*

Abs (%) SGOD SGSSD

Base Quantity (lb/yd3) Volume (ft3)

OD SSD

Poraver 1-2 mm N 20 0.39 0.47 46.0 55.2 1.89 Utelite Structural Fines Y 31.4 1.32 1.73 288.4 378.9 3.51 Poraver .25 - .5 mm N 28 0.59 0.76 69.6 89.1 1.89 Poraver .1-.3 mm N 25 0.90 1.13 106.1 132.7 1.89 3M Glass Bubbles K1 N 1 0.13 0.13 17.5 17.7 2.16

ADMIXTURES

Admixture lb/gal Dosage (fl. oz / cwt) % Solids Amount of Water in Admixture (lb/yd3)

SB Latex 8.5 261.3 48.0 146.79 Total Water from Admixtures, ∑wadmx

149.41 lb/yd3 Water Repellent 8.5 4.4 42.9 2.62

SOLIDS (LATEX, DYES AND POWDERED ADMIXTURES ONLY) Component Specific Gravity Volume (ft3) Amount (mass/volume) (lb/yd3) SB Latex 1.01 2.15 135.49 Total Solids from

Admixtures 153.85 lb/yd3 Pigment 2.02 0.15 18.36

WATER Amount (mass/volume) (lb/yd3) Volume (ft3) Water, lb/yd3

w: 222.9 3.93 Total Free Water from All Aggregates, lb/yd3 ∑wfree: 62.9

Total Water from All Admixtures, lb/yd3 ∑wadmx: 149.4 Batch Water, lb/yd3 wbatch: 435.2

DENSITIES, AIR CONTENT, RATIOS AND SLUMP cm fibers aggregates solids water Total Mass of Concrete, M, (lb ) 1626.67 4.59 673.55 153.85 222.89 ∑M: 2681.55

Absolute Volume of Concrete, V, (ft3) 9.45 0.057 11.34 2.30 3.57 ∑V:26.72 Theoretical Density, T, (=∑M / ∑V) 100.37 lb/ft3 Air Content [= (T – D)/T x 100%] 6.7 % Measured Density, D 93.65 lb/ft3 Slump, Slump flow <1 in. water/cement ratio, w/c: .35 water/cementitious material ratio, w/cm: .14

*Color varies for this mixture

B2

CEMENTITIOUS MATERIALS Component Specific Gravity Volume (ft3) Amount of CM (mass/volume) (lb/yd3)

Portland Type I Cement 3.15 4.32 636.9 Total Amount of cementitious materials

1627 lb/yd3

c/cm ratio 0.76

VCAS 160 2.60 3.24 700.9

Class F Fly Ash 2.45 1.89 288.9

FIBERS Component Specific Gravity Volume (ft3) Amount of Fibers (mass/volume) (lb/yd3)

PVA Fibers 1.30 0.057 4.59 Total Amount of Fibers 4.59 lb/yd3

AGGREGATES

Aggregates ASTM C330*

Abs (%) SGOD SGSSD

Base Quantity (lb/yd3) Volume (ft3)

OD SSD

Poraver 1-2 mm N 20 0.39 0.47 46.0 55.2 1.89 Utelite Structural Fines Y 31.4 1.32 1.73 288.4 378.9 3.51 Poraver .25 - .5 mm N 28 0.59 0.76 69.6 89.1 1.89 Poraver .1-.3 mm N 25 0.90 1.13 106.1 132.7 1.89 3M Glass Bubbles K1 N 1 0.13 0.13 17.5 17.7 2.16

ADMIXTURES

Admixture lb/gal Dosage (fl. oz / cwt) % Solids Amount of Water in Admixture (lb/yd3)

SRA 035 8.4 11.8 55.0 5.69 Total Water from Admixtures, ∑wadmx

15.24 lb/yd3 Polyheed 1025 8.9 12.0 49.0 6.93

Water Repellent 8.5 4.3 42.9 2.62

SOLIDS (LATEX, DYES AND POWDERED ADMIXTURES ONLY) Component Specific Gravity Volume (ft3) Amount (mass/volume) (lb/yd3)

Pigment 2.02 0.15 18.36 Total Solids from

Admixtures 18.36 lb/yd3

WATER Amount (mass/volume) (lb/yd3) Volume (ft3) Water, lb/yd3

w: 305.67 4.89 Total Free Water from All Aggregates, lb/yd3 ∑wfree: 62.85

Total Water from All Admixtures, lb/yd3 ∑wadmx: 15.24 Batch Water, lb/yd3 wbatch: 383.76

DENSITIES, AIR CONTENT, RATIOS AND SLUMP cm fibers aggregates solids water Total Mass of Concrete, M, (lb ) 1626.67 4.59 673.55 18.36 305.67 ∑M:2684.84

Absolute Volume of Concrete, V, (ft3) 9.45 0.057 11.34 0.15 4.89 ∑V:25.89 Theoretical Density, T, (=∑M / ∑V) 101.56 lb/ft3 Air Content [= (T – D)/T x 100%] 22.1%

Measured Density, D 78.69 lb/ft3 Slump, Slump flow 0 in. water/cement ratio, w/c: .48 water/cementitious material ratio, w/cm: .19

SHELL MIX

*Color varies for this mixture

B3

Appendix B: Mixture ProportionsEstablished Parameters:

- Utelite is an ASTM C330 compliant aggregate

- One batch = 1yd3

- Aggregate Volume/Mix Volume = 45%

- Aggregate Volume/Mix Volume = 35%

- Water/Cement = 35%

- Cementitious Material Ratios:

- PC = 45%

- VCAS = 35%

- Fly Ash = 20%

- Aggregate Ratios

- 1-2 mm Poravers = 17%

- Utelite = 30%

- 0.25-0.5 mm Poravers = 17%

- 0.1-0.3 mm Poravers = 17%

- Glass Bubbles = 19%

Material OD SG Density (pcf)

VCAS 2.6 162.24 pcf

Portland Cement 3.15 196.56 pcf

Fly Ash 2.45 152.88 pcf

1-2 mm Poraver 0.39 24.34 pcf

Utelite 1.32 82.16 pcf

.25 -.5 mm Poraver 0.59 36.82 pcf

.1-.3 mm Poraver 0.9 56.16 pcf

Glass Bubbles 0.13 8.11 pcf

Material SSD SG Density (pcf)

1-2 mm Poraver 0.47 29.20 pcf

Utelite 1.73 107.95 pcf

.25 -.5 mm Poraver 0.76 47.12 pcf

.1-.3 mm Poraver 1.13 70.2 pcf

Glass Bubbles 0.13 8.19 pcf

Material MC (%) Absorption (%)

1-2 mm Poraver 17.5% 20%

Utelite 10% 31.4%

.25 -.5 mm Poraver 4.84% 28%

.1-.3 mm Poraver 8.29% 25%

Glass Bubbles 0% 1%

B4

Structural Mix:

Cementitious Materials Volumes:

VCAS 160:

45% ⇤ 35% ⇡ 16%

16% ⇤ 27ft3

1batch = 4.32ft3

Type I Portland Cement:

35% ⇤ 35% ⇡ 12%

12% ⇤ 27ft3

1batch = 3.24ft3

Fly Ash:

20% ⇤ 35% ⇡ 7%

7% ⇤ 27ft3

1batch = 1.89ft3

Cementitious Materials Base Quanti-

ties:

VCAS 160:

4.32ft3 ⇤ 162.24pcf =

700.88 lbsbatch

Type I Portland Cement:

3.24ft3 ⇤ 196.56pcf =

636.85 lbsbatch

Fly Ash:

1.89ft3 ⇤ 152.88pcf =

288.94 lbsbatch

Aggregate Volumetric Breakdown:

1 - 2 mm Poravers:

17% ⇤ 45% ⇡ 7%

7% ⇤ 27ft3

1batch = 1.89ft3

Utelite:

30% ⇤ 45% ⇡ 13%

13% ⇤ 27ft3

1batch = 3.51ft3

0.25 - .5 mm Poravers:

17% ⇤ 45% ⇡ 7%

7% ⇤ 27ft3

1batch = 1.89ft3

0.1 - .3 mm Poravers:

17% ⇤ 45% ⇡ 7%

7% ⇤ 27ft3

1batch = 1.89ft3

Glass Bubbles:

19% ⇤ 45% ⇡ 8%

8% ⇤ 27ft3

1batch = 2.16ft3

% of C330 Aggregate=3.5111.34

= 30% > 25%

Aggregate Base Quantities (OD):

1 - 2 mm Poravers:

1.89ft3 ⇤ 24.34pcf =

45.99 lbsbatch

Utelite:

3.51ft3 ⇤ 82.16pcf =

288.36 lbsbatch

0.25 - .5 mm Poravers:

1.89ft3 ⇤ 36.82pcf =

69.58 lbsbatch

0.1 - .3 mm Poravers:

1.89ft3 ⇤ 56.16pcf =

106.14 lbsbatch

Glass Bubbles:

2.16ft3 ⇤ 8.11pcf =

17.52 lbsbatch

Aggregate Base Quantities (SSD):

1 - 2 mm Poravers:

1.89ft3 ⇤ 29.20pcf =

55.19 lbsbatch

Utelite:

3.51ft3 ⇤ 107.95pcf =

378.91 lbsbatch

0.25 - .5 mm Poravers:

1.89ft3 ⇤ 47.12pcf =

89.07 lbsbatch

B5

0.1 - .3 mm Poravers:

1.89ft3 ⇤ 70.2pcf =

132.68 lbsbatch

Glass Bubbles:

2.16ft3 ⇤ 8.19pcf =

17.69 lbsbatch

Admixtures Dosage:

Latex:

Density = 8.5 lbgal

Weight per batch

= 282.285 lbsbatch

CWT = 16.27 cwt

Weight per cwt

= 282.28/16.27= 17.36

Dosage

=17.36 lbs

cwt

8.5 lbsgal

(128fl.oz.

1gal )

= 261.32fl.oz.cwt

Water Repellant:

Density = 8.5 lbsgal

Weight per batch

= 4.59 lbsbatch

CWT = 16.27 cwt

Weight per cwt

= 4.59/16.27= 0.28

Dosage

=.28 lbs

cwt

8.5 lbsgal

(128fl.oz.

1gal )

= 4.25fl.oz.cwt

Amount of Water in Admixture:

Latex:

Percent Solids = 48%

Amount of Water

= 261.3fl.oz.cwt (16.266cwt)

(1�.48)( 1gal128fl.oz.)(8.5

lbsgal)

= 146.79lbs/batch

Water Repellant:

Percent Solids = 42.9%Amount of Water

= 4.25fl.oz.cwt (16.266cwt)

(1�.43)( 1gal128fl.oz.)(8.5

lbsgal)

= 2.62lbs/batch

Solids:

Latex:

Specific Gravity = 1.01

Weight of Solids

= 261.32fl.oz.cwt (16.266cwt)

(.48)( 1gal128fl.oz.)(8.5

lbsgal)

= 135.5lbs/batch

Volume of Solids

=135.5lbs/batch1.01⇤62.4pcf

= 2.15ft3

Powdered Pigment:

Specific Gravity = 2.02

Weight of Solids

=.04lbs1mix

17mixesyd3 (

27ft3

1yd3 )

= 18.36lbs/batch

Volume of Solids

=18.36lbs/batch2.02⇤62.4pcf

= .15ft3

Fibers:

Specific Gravity = 1.30

Weight of Solids

=.01lbsbatch

17mixesyd3 ⇤ 27ft3

1yd3

= 4.59 lbs/batch

Volume of Solids

=4.59lbs/batch1.30⇤62.4pcf = .057ft3

B6

Water:

Weight of Added Water

= 700.88 lbsPCbatch ⇤ .35

= 222.89 lbsbatch

Volume of Added Water

= 222.89lbs/62.4pcf

= 3.57ft3

Free Water = ⌃ Base Quantity *

MC

= 55.2(17.5%)

+378.9(10%)

+89.1(4.84%)

+132.7(8.29%)

+17.7(0%)

= 62.85 lbsbatch

Batch Water = wfree+w+wadmix

= 222.89lbs+ 62.85lbs+149.41lbs

= 435.16 lbsbatch

Unit Wet Mass

= Mcm +Mfibers +Magg. +Msolids + w

= 1626.67 + 4.59 + 673.55 +153.85 + 222.89

= 2681.55lbs/yd3

Volume of Concrete

= Vcm + Vfibers + Vagg. + Vsolids + Vw

= 9.45+0.057+11.34+2.30+3.57

= 26.72ft3

Theoretical Density

=MassofConcrete

V olumeofConcrete

=2681.55lbs26.72ft3

= 100.37pcf

Measured Density = 93.65 pcf

Air Content

=100.37pcf�93.65

100.37pcf ⇤ 100%

= 6.7%

Water to c Ratio =222.89lbs636.85lbs = .35

Water to cm Ratio =222.89lbs1626.67lbs = .14

B7

In the calculation from volume to weight for the construction of the canoe, the team used

the bulk loose dry density for the 1-2 mm Poraver, 0.25 - 0.5 mm Poraver, 0.1 - 0.3 mm

Poraver aggregates instead of the oven dried density. Thus, the mix used was not compliant

with the ASTM C330 aggregate volumetric requirement. The actual volumes of aggregates

used in the canoe are as follows:

Material SG Density (pcf)

1-2 mm Poraver 0.23 14.4 pcf

Utelite 1.73 107.95 pcf

.25 -.5 mm Poraver 0.34 21.2 pcf

.1-.3 mm Poraver 0.4 24.96 pcf

Glass Bubbles 0.13 8.19 pcf

Material Used Weight of Aggregates

1-2 mm Poraver 0.39 lbs

Utelite 0.275 lbs

0.25 -0.5 mm Poraver 0.058 lbs

0.1-0.3 mm Poraver 0.115 lbs

Glass Bubbles 0.024 lbs

Volumes:

1-2 mm Poraver:0.039lbs14.4pcf = 0.0027ft3

Utelite:0.275lbs107.95pcf = 0.0025ft3

0.25 - 0.5 mm Poraver:0.058lbs21.2pcf = 0.0027ft3

0.1 - 0.3 mm Poraver:0.115lbs24.96pcf = 0.0046ft3

Glass Bubbles:0.024lbs8.19pcf = 0.0029ft3

C330 Aggregate Proportion Compliance:

% of C330 Aggregate=0.00250.0154 = 16% < 25%

C1

Appendix C: Example Structural Calculations

Assumptions:

- Self-weight is uniformly distributed

- Paddlers are treated point loads

- Cross-section is uniform throughout

- Reinforcement area/moduli ratio arenegligible

Maximum Shear and Moment Calculations:

Case 1: 0ft x 3.8ft

⌃Fy = 0 = �V � wx+ wbx

V = (37.89 plf)x

⌃M0 = 0 = M + wx2

2 � wbx2

2

M = (18.945 plf)x2

Case 2: 3.8ft x 6.65ft

⌃Fy = 0 = �V + x(wb � w)

�200lbs

V = (37.89plfx)� 200lbs

⌃M0 = 0 = M + wx2

2 � wbx2

2

+200(x� 3.8)

M = (18.945plf)x2� (200 lbs)x

+760 lbft

Case 3: 6.65ft x 12.35ft

⌃Fy = 0 = �V + x(wb � w)

�200lbs�160lbs

V = (37.89plf)x� 360lbs

⌃M0 = 0 = M + wx2

2 � wbx2

2

+200(x�3.8)+160(x�6.65)

M = (18.945plf)x2� (360 lbs)x

+1824 lbft

Case 4: 12.35ft x 15.2ft

⌃Fy = 0 = �V + x(wb � w)

�200lbs�160lbs

V = �(15.79plf)x� 520lbs

⌃M0 = 0 = M + wx2

2 � wbx2

2

+200(x�3.8)+160(x�6.65) + 160(x� 12.35)

M = (18.945plf)x2� (520 lbs)x

+3800 lbft

Length 19ftWeight of Canoe 300 lbs

Distributed Weight of Canoe 15.79 plfBuoyant Force on Canoe 53.68 plfWeight of Male Paddler 200 lbsWeight of Female Paddler 160 lbsLocation of Male Paddlers 3.8 ft & 15.2 ftLocation of Female Paddlers 6.65 ft & 12.35 ft

Co-ed Free Body Diagram

Co-ed Moment Diagram

0 2 4 6 8 10 12 14 16 18 20

X (ft)

-50

0

50

100

150

200

250

300

M (f

t.lb)

Co-ed Shear Diagram

0 2 4 6 8 10 12 14 16 18 20

X (ft)

-150

-100

-50

0

50

100

150

V (lb

)

Case 5: 15.2ft x 19ft

⌃Fy = 0 = �V + x(wb � w)

�200lbs�160lbs�160lbs�200lbs

V = �(15.79plf)x� 720lbs

⌃M0 = 0 = M + wx2

2 � wbx2

2

+200(x�3.8)+160(x�6.65)+160(x�12.35)+200(x� 15.2)

M = (18.945plf)x2� (720 lbs)x

+6840 lbft

C2

The cross section regions, minimized due to sym-metry:

1) Side walls (x2)

2) Chines (x2)

3) Bottom

1) Side Walls:

A1 = 2Lt = 2(6”)( 12”) = 6 in2

y1 = h� L2 = 14� 6

2 = 11 in

I1 = 112 tL

3 = 112 (.5)(6)

3 = 9 in4

2) Chines: Arc radius = 6.821”; Thickness = 12”

A2 =R 1.152.628

R 7.3216.821 rdrd✓ = 1.853 in2

y2 = 1A2

RydA = 1

1.853

R 1.152.628

R 7.3216.821 r2sin(✓)drd✓

= 5.433 in

y2 = 8� 5.76 = 2.567 in (from bottom)

I2 =Ry2dA =

R 1.152.628

R 7.3216.821 r3sin2(✓)drd✓

= 55.57 in4

I2 = I2 � Ad2 = 55.57 in4

�(1.853in2)(5.433in)2

= .874in4

3) Bottom: Arc radius = 26.325”; Thickness = 12”

A3 =R 1.5711.221

R 26.82526.325 rdrd✓ = 4.651in2

y3 = 1A3

Ryc↵rdr = 1

4.651

R 26.82526.325 r2sin(↵)dr

= 26.03in

y3 = 26.3294� 26.03 = .299in (from bot-tom)

I3 =Ry2dA =

R 1.5711.221

R 26.82526.325 r3sin2(✓)drd✓

= 3154.05in4

I3 = I3 � Ad2 = 3154.05in4 �(4.651in2)(26.03in)2

= 2.714in4

Neutral Axis:

⌃A⇤y = 0 = 6in2(y�11in)+1.853in2(y�2.567in)

+4.651in2(y � .299in)

y = 5.77in

Cross-Section Dimensions

Moments of Inertia: (about neutral axis)

I1 = 9in4+Ad2 = 9in4+6in2(11�5.18)2

I1 = 212.23in4

I2 = .874in4 +Ad2

= .874in4 + 1.853in2(2.567 �5.18)2

I2 = 13.53in4

I3 = 2.714in4 +Ad2

= 2.714in4 + 4.651in2(.299 �5.18)2

I3 = 113.52in4

Itotal = I1 + I2 + I3 = 339.28in4

Internal Stresses for Co-ed Case:

� = �MyI =

273.6lbft( 12in1ft )(14in�5.77in)

339.28in4

= �79.64psi = 79.64psi (compression)

⌧ = V QIt

A2upper =R 1.152.825

R 7.3216.821 rdrd✓ = 1.156in2

y2upper = 1A2upper

RydA

= 13.497

R 1.159.825

R 7.3216.821 r2sin(✓)drd✓

= 5.882 in

Q = ⌃A ⇤ y = y1(A1) + y2upper (A2upper )

= (11in� 5.18in)(6in2)

+(5.882in�5.18in)(1.156in2)

= 69.92in3

⌧ = (144lbs)(69.92in3)(339.28in4)(.5in) = 59.35 psi

C3

Loading Case Stress Comparison

Loading Case Max Shear (lbs) Max Moment (ft-lb) Tensile Stress (psi) Compressive Stress (psi)Display 77.47 197.4 31.93 57.46

Two Paddlers (M) 47.73 168.4 47.73 49.02Two Paddlers (F) 37.49 134.7 37.49 39.21Four Paddlers 59.35 273.6 59.35 79.64Transportation 0 0 0 0

Shear Diagram - All Cases

Moment Diagram - All Cases

D1

Appendix D: Hull Thickness / Reinforcement and Percent Open Area Calculations

Appendix D: Hull Thickness/Reinforcement and Percent Open Area Calculations

Hull Thickness/Reinforcement

Canoe Thicknesses:

Gunwhales: 0.5 in

Floor: 0.5 in

Average: 0.5 in

Carbon Fiber Reinforcement Thickness: 0.0062 in

Maximum Reinforcement Thickness Percentage =0.00620.5 ⇤ 100% = 1.24%

Percent Open Area

Square opening dimensions: 0.6875 in. x 0.6875 in.

Area of single opening: 0.4727in2

D1= 0.6875 + 0.1252 = 0.75in.

D2 = 0.6875 + 0.1252 = 0.75in.

Length (sample) = 15 ⇤ 0.75 = 11.25in.

Width (sample) = 15 ⇤ 0.75 = 11.25in.

Total Number of openings = 15 ⇤ 15 = 225

Total Open Area =225 ⇤ 0.4727 in.

Total Area = 11.25in. ⇤ 11.25in. = 127in2

Percent open area =106.36127 = 83.7%