University of Southern California Design Paper

University of Southern California

Design Paper 2018

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

Executive Summary The University of Southern California pop art. The team strove to achieve the same (USC) is nestled in the heart of downtown success through revisiting the canoe’s design; Los Angeles. Its urban campus is home to the it was from this process that the team chose Viterbi School of Engineering, composed of Warhol as the inspiration for this year’s 8,300 students and eight departments. USC’s theme. Once described as a mix between chapter of the American Society of Civil Dracula and Cinderella, Warhol earned the Engineers (ASCE) is made up of 54 students, nickname “Drella”, a name which the team of which, 15 regularly attended Concrete has adopted for this year’s canoe. Canoe team meetings. With the help of these Table 2: Summary of mix properties and members and all of ASCE, the team is hoping strengths. to continue their upward trend at the Pacific Southwest Conference (PSWC) this year in Mix Structural Shell Tempe, Arizona. The team finished 5th in 28-Day 6743 psi 3425 psi 2015, 8th in 2016, and 7th in 2017. 2018 Compressive came with many changes for this year’s Strength Concrete Canoe Team. The team moved 28-Day 550 psi 381 psi work spaces, a process which delayed Tensile construction until late in the fall. This year Strength also featured the construction of a 21 foot 28-Day 1835 psi 932 psi rolling steel cart on which the canoe was Flexural poured, cured, and sanded. This year the team Strength focused on revisiting the basic elements of Unit Wet 93.65 pcf 78.69 pcf the canoe to increase strength and Density performance. Unit Dry 96.09 pcf 101.56 pcf In the 1960s, Andy Warhol’s new Density approach to art elevated him to a cultural Air Content 6.7% 22.1% icon. Using new techniques like silk Drella features major redesign in the screening and a wide array of colors, regular mix composition, construction techniques, items like a soup cans or a bottle of soda were and hull design. Starting with the mix design immortalized through Warhol’s new genre of the team employed a new ASTM C330 Table 1: Overall canoe properties including aggregate for enhanced finishing and dimensions and materials. compliance as well as introducing fly ash for sustainability and strength. For construction, Name Drella the team switched to a male mold to reduce Length 19 ft difficulties with slump and thickness. This Maximum Width 27 in year’s hull design is entirely redesigned with Maximum Depth 14 in a symmetric profile and rocker, as well as Hull Thickness ½ in reduced, softer chines. The aim of these Weight 300 lbs (estimated) modifications is a stronger, higher Primary Carbon Fiber Mesh performing canoe. A final modification is the Reinforcement use of inlays for aesthetic features instead of Secondary PVA Fibers tiles. These features culminate in a ground-up Reinforcement revision which the USC Concrete Canoe Colors Black, Blue, Green, team is proud to present as Drella. Red, White, Yellow

Project and Quality Management This year, the USC Concrete Canoe The initial schedule differed slightly team aspired to make multiple extremely from the revised schedule. The most ambitious changes to the canoe’s design and significant change was the decision to make construction. Led by two captains, one junior the design paper a part of the critical path. captain, and an additional sub-team captain, Initially, only construction was put on the the goals for the year included new mix critical path, but, knowing the significance of materials, a different hull design, and inverted the design paper for the participation in construction method. The team began the year competition, this was added to the critical with the hopes that both the schedule and path. Other changes to the schedule were budget would easily allow for these changes. limited to date changes to account for the Unfortunately, this was not the case. The team unexpected delays due to the limited access was pushed out of their previous workspace to the workspace. due to space limitations. The new workspace, The changes put in place this year as mentioned before, was not ready until late also had an effect on the budget. Having been in the fall semester. As a result, the team chose given the same amount of design team to focus mainly on the structural, aesthetic, funding as for the 2017 canoe, the team had and mix design during the first semester. Due to determine how to pay for canoe materials to limited space to make and test new mix in addition to the necessary tools and storage designs, all mixes were made in the span of needed for the new workspace. The team two days, preventing the team from making effectively lowered expenses compared to any changes after initial testing. Nearly all previous years by choosing to not make a work on the mold and canoe was pushed until practice canoe, cutting down on material second semester. Despite an extremely costs and labor time. The budget was then condensed work schedule, the canoe was still carefully managed with a tracking system and scheduled to be completed before the purchase log. competition in April. As always, the team put a large In this schedule, the critical path and emphasis on safety. The new workspace for associated milestones were determined by the team is located in a research lab, thus, what was needed to participate in even stricter safety measures were competition. This included items that were implemented. Masks, gloves, and closed toe necessary for the construction of the shoes were required for any construction competition canoe, from the procurement of work. Any member not wearing these was not the foam to the substantial completion of the allowed to work. MSDS were printed and canoe, and the steps needed to write the kept nearby in case of emergency. Any dust- design paper, including the rough draft and heavy work and work with any exposure to various stages of editing. 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 Figure 1: Person-hour breakdown by month years were reused. Economic sustainability and canoe task. was encouraged through the use of donated

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 Figure 2: Mix design proportions printed and them from trusted sources. These materials placed at dry mix station. were then stored in labelled, air-tight During the construction process, the containers to allow for easy identification of captains separately supervised the dry each material. This was especially important mixing, wet mixing, and concrete placement since the team had to transfer the materials to stations. At each station, the captain ensured the new workspace. The team purchased that members were completing their assigned shelves for the workspace to further the task accurately. Quality control of the dry organizational effort of the materials. mixes allowed the team to discover that the Because of the small size of the team, scales were not tarred to account for the the captains gave individualized attention to weight of the cups during measuring and members by observing, correcting, and therefore to resolve the issue. For the wet approving their work, especially during the mixes, the captains inspected the consistency pre-construction phases. Furthermore, all of each mix before it was placed on the canoe. members were given safety training to ensure Some mixes encountered issues, but, through that all work being done was safe and this inspection the captains were able to efficient. locate and discard these mixes. Furthermore, The small size of the team also meant the wet mixes were all weighed and recorded. that pour day required the contributions of This allowed the captains to ensure that each many members who were not a part of the mix was within an acceptable weight range Concrete Canoe team. This required training and contained all necessary materials. and quality control during the construction Quality control of the placing of concrete was process to ensure that the canoe complied performed through the use of thickness with its intended design and proportions, gauges for each layer, ensuring that the since many people working on the canoe did concrete was placed evenly and consistently. not know the canoe’s design and building A further measure of quality control techniques. Therefore, each member who was the documentation of the materials and arrived on pour day was assigned to a specific rules. Along with the previously mentioned task and given clear directions for the duties MSDS binder, the captains read and they needed to complete. If they had understood the rules of the competition in questions, they asked the captains or other order to ensure that each step of the process experienced members. was compliant.

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

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 Figure 3: Comparison of hull profiles construction process, the team took the between Drella (blue) and Ascent (red). opportunity to redesign the hull to increase efficiency and maneuverability by and reduce drag. To accomplish this, the team sharpening the entry line, rounding the hull increased the roundness of the canoe’s profile, and designing for symmetry. For this bottom. This year’s hull profile is defined year’s design the team used primarily NX for angularly, featuring a variable shallow arch the hull design, before porting to AutoCAD. 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. Figure 4: Three dimensional view of canoe hull While increasing the efficiency of the from NX. canoe, the redesigned hull profile also modifies the stability characteristics of the While paddling last year’s canoe the canoe. The rounder bottom sacrifices initial team noticed a small wake developing at the stability but increases final stability by front of the canoe, indicating significant drag continuing the hull’s arch higher up the sides. forces. Drella features a sharp entry line that Based upon the paddling team’s feedback it widens linearly for 36 inches before merging was determined that the detriment of to a radial arc that defines the main body of decreased stability would be outweighed by the canoe’s top profile. Compared to the 2017 the increase in efficiency. Additionally, canoe Ascent, Drella has reduced the entry Drella’s enhanced final stability will allow angle of the canoe by 12%, and extended the paddlers to lean further into their turns. entry line by an additional foot. This Overall this modification will lead to reduction in width at the front of the canoe is improving the maneuverability of the canoe. intended to reduce drag, leading to a With changes in the top and cross- smoother and more efficient paddle. sectional profiles geared towards efficiency, Drella also features modifications to Drella’s side profile modifications are aimed the hull profile to further increase efficiency at increasing maneuverability. Past canoes

have featured an asymmetrical rocker, and two female, and coed) all involve point loads while these canoes tracked straight, last representing the paddlers, the distributed year’s races demonstrated the limitations of weight of the canoe, and the distributed this shape in initiating sharp turns. Sprint reaction of the water. The canoe is assumed races feature 180 degree turns, in which the to weigh 300 lbs, males 200 lbs, and females canoe lost the majority of its momentum. 160 lbs. These values are higher than Drella features a square stem with a 6 inch expected, to allow for a factor of safety. The radius and a 2.5 inch rise at bow and stern, display reactions are 5 ft from the ends of the creating a symmetrical and continuous canoe. The paddlers are 4 ft from the end in rocker. This means a more aggressive stern the two person case, and 3.8 ft/ 6.65 ft from rocker, allowing the 19 foot long canoe to the ends in the four person case. Transporting paddle like one of much shorter length. the canoe in a female mold, the canoe is Subsequently, Drella will handle with uniformly supported, and is modeled below increased maneuverability, especially on as such. After analyzing these cases in sharp turns. MATLAB, the maximum bending moment Overall, Drella is 19 feet long, with a was found to occur in the coed paddling case, maximum depth of 14 inches and maximum at 273.6 ft-lb. This produces a maximum width of 27 inches. Designed for efficiency tensile stress of 59.35 psi, and a maximum and maneuverability, the canoe features a compression stress of 79.64 psi. rounder hull profile with a symmetrical, 2.5 To ensure proper flotation, the team inch rocker. The team is eager to paddle with employed EPS high density foam bulkheads the increased maneuverability and efficiency at the bow and stern. The volume water in this year’s races at PSWC. displaced by the canoe should be 8,300 in3. The structural analysis team From the NX model, the team determined employed a simplified two-dimensional that without bulkheads the canoe has a model, assuming a uniform cross section volume of 4,300 in3. To provide adequate throughout the canoe. Modeling the canoe as flotation, the team used 34 inch bulkheads, a beam, the boundary conditions require that yielding an additional 4,200 in3 of flotation. 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 Figure 5: Moment diagrams for display, two weight and two reaction points representing male and female, coed and transportation cases. the stands. The three paddler cases (two male,

Development and Testing The USC Concrete Canoe team has struggled replacement for the .5-1 mm Poravers used in to innovate in the past years. In 2016, the previous years. In addition, Utelite’s specific canoe cracked during competition, gravity of 1.73 is lower than Stalite’s 1.88. motivating the 2017 team to focus solely on This slight difference helps to combat the designing a high strength mix. While the growing weight from increasing the amount 2017 mix was stronger, it was not compliant of ASTM C330 aggregate in order to comply with the C330 aggregate volumetric with the rules. requirements. This year, the USC Concrete Type 1 White Portland Cement and Canoe team put a strong emphasis on VCAS 160 (Vitrified Calcium Alumino- developing a new mix that was not only Silicate) were maintained as the major compliant with the rules, but also strong, cementitious materials for the 2018 canoe. economic, and environmentally sustainable. The team did not need any extra properties, Given that the team had many such as phosphate resistance or high early materials left over from the 2017 canoe, most strength, in the cement. Thus, Type 1 White of the baseline materials for this year’s mix Portland Cement was used for its structural remained the same. The main aggregates, properties and white color, which is best for glass cenospheres (Poravers) of various keeping pigment colors vibrant. VCAS 160, granular sizes and K1 glass bubbles, whose a pozzalon, has been used in mixes for the properties are shown in Table 3, were used past few years because it increases the for their low density and neutral color. environmental sustainability of the concrete Table 3: Aggregate information by material. since it is a byproduct of fiberglass production. It also maintains pigment Material SG Absorption vibrancy. The major negatives of using VCAS are its high price and shipping .1 - .3 mm Poraver 0.90 25% distance. Portland cement can be obtained for free from a local distributor, but VCAS 160 .25 - .5 mm Poraver 0.59 25% is purchased from a company in North 1 - 2 mm Poraver 0.39 25% Carolina, lowering both economic and Utelite 1.73 31% environmental sustainability. With this in mind, the team decided to test two other K1 Glass Bubbles 0.13 0% cementitious materials: silica fume and fly There were two major material ash. Both of these materials could be received changes introduced this year, the first of as a donation from a local company, which was to the C330 compliant aggregate. decreasing the environmental impact of The 2017 canoe, Ascent, used Stalite, an shipping, and both are by-products of other expanded shale aggregate. The team processes. In addition to being experienced difficulty sanding through this environmentally and economically aggregate. Additionally, it left an uneven, sustainable choices, silica fume and fly ash rocky appearance. For the 2018 canoe, the have been proven to increase compressive team decided to use Utelite, a fine shale strength and workability. aggregate. The smaller aggregate size would Once the team decided what materials reduce finishing and aesthetic issues. To to use, the concrete mixes were designed. further reduce the particle size, the team This was done by first deciding the decided to sieve the Utelite, using the volumetric percentage of the aggregates and aggregates retained on the No. 35 to No. 18 keeping that constant for each mix. By sieves. The Utelite could then function as a

sieving the Utelite, it could be used as a of SR latex during mixing, as the main replacement for the .5-1 mm Poravers. To purpose of this admixture was to increase include a factor of safety for the required overall workability of the mix. 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 Figure 6: Composite slab undergoing four fume or fly ash would be used in the final mix point bending test. design, four variations of cementitious material amounts were chosen, two with Given limited access to workspace silica fume and two with fly ash. The and a tight schedule, all 12 of these mixes variations can be seen in Table 4: were made in the span of two days. Three cylinders for compressive strength testing Table 4: Volumetric proportions of cementitious and two composite slabs for flexural strength materials for fly ash and silica fume. testing were made of each mix. The slabs Fly Ash were made with carbon fiber reinforcement as their primary reinforcement, which was Mix # VCAS PC Fly Ash chosen for its flexibility, thinness, and high 1 45% 40% 15% tensile strength. The team decided to return to 2 45% 35% 20% 2016’s symmetric layering scheme: three layers of concrete (⅛”, ¼”, ⅛”) and one layer Silica Fume of reinforcement between each of these Silica Mix # VCAS PC concrete layers. Since tensile stress increases Fume away from the neutral axis of the layers, the 3 45% 45% 10% team placed the reinforcement as close as 4 45% 40% 15% possible to the top and bottom surfaces of the These amounts were based upon canoe. High tensile stress is then distributed manufacturer guidelines. For each of these over the reinforcement, decreasing the four variations, three different water-to- likelihood of the concrete cracking from cement ratios were used (.33, .35, and .40), tensile loads. producing 12 different mixes overall. Each of Following ASTM C39 and ASTM these mix had varying quantities of C78 test methods in a Universal Testing admixtures. As in past years, the main two Machine, 28-day testing gave compressive admixtures used were water repellent and strengths ranging between 5415 psi and styrene-butadiene latex. Water repellent, 6941.5 psi and flexural strengths between which reduces water penetration in hardened 612.2 psi and 3302.7 psi. The team based its concrete, was added based on manufacturer choice of mix on the overall workability and guidelines. The team decided on the amount ratio of average compressive strength to density. The chosen mix was the 45% VCAS,

35% PC, 20% fly ash mix. It had an average during mixing caused a material shortage. In compressive strength of 6743 psi and an order to continue pouring the canoe, the team average flexural strength of 1835.2 psi. had to devise a new mix with existing According to ACI 207R, the relationship materials. The main challenge for the team between the compressive and tensile strength was developing a new mix after running out is 6.7$%′', thus the tensile strength was of SB latex. The team needed to find a new found to be 550.18 psi. The compressive way to improve workability without adding strength of the 2017’s “Bottom” mix was significantly more water, which would 2630 psi and its flexural strength 1750 psi, greatly decrease strength. In 2017, the team making this year’s mix 156% stronger in purchased a mid-range water reducer and a compression and 5% stronger in flexure than shrinkage reducer. The water reducer would 2017’s mix. The maximum compressive decrease the amount of water needed in the stress was calculated to be 79.64 psi and the mix, keeping the strength higher than it maximum tensile stress was calculated to be would be with just water. The shrinkage 59.35 psi, thus the designed concrete is reducer would prevent excess drying extremely capable of handling all loading shrinkage from the increase in water needed cases. 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 Figure 7: Concrete cylinder after compression test completion. original design was compliant with the ASTM C330 aggregate requirement, the The original construction plan was to actual execution of this was not compliant. use this mix throughout the entire canoe to The actual volumetric percentage of Utelite reduce confusion during mixing. Many used in Drella was 16%, significantly less people who were helping pour the canoe had than the intended 30%. little to no experience with mixing concrete, Despite the challenges faced while so only using one mix would ideally make it pouring, the team is proud of the steps taken easier for the inexperienced mixers. This to improve the concrete mix. This year’s mix would also improve the speed of mixing since is environmentally sustainable, economic, premixes could be made without concern of and strong. Innovations in material choices preparing too much per layer. improved the overall mix and will help the While pouring the last layer of the USC Concrete Canoe team develop even canoe, the limited budget and mistakes made better mixes in the future.

Construction This year’s construction process the mold. With this, the mold was ready for required adjustments due to the relocation of pour day. the team’s workspace. The team experienced Pour day began with the preparation many delays since no work could be done of dry mixes. Team members were given until renovations to the workspace had been roles of measuring out materials, separating completed. Because of this and budgetary the PVA fibers, or mixing the materials restrictions, the team was not able to make a together. While the dry mixes were being practice canoe as was done previously, which prepared, the design of the canoe was also forced extra care to be taken with regard to being prepared on the mold. Wax inlays in the detail and quality management. Another signature of Andy Warhol were placed as a obstacle associated with the new workspace stencil on the outside center of the mold. was the presence of a research based water Inlays were used this year instead of the tiles channel in the same building. To prevent used in previous years. This created a cleaner particles from the canoe or its mold from design and reduced sanding time. Foam strips entering the water and affecting research, no were also placed on the outside of the mold work was allowed inside. Therefore, after to divide it into quadrants and serve as a guide gaining access to the workspace, the team for placing the four different colors of the dedicated one week towards constructing a first layer. After the first 20 dry mixes had 23’ x 3’ steel cart to transport the canoe into been prepared, the wet mixing station was and out of the building. This further diverted established. 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. Figure 8: Team member separating fibers during After sanding, a layer of drywall was added dry mixing. to the outside of the mold to further smooth the surface. In an effort to reduce the time At the wet mixing station, members required to apply contact paper to the mold added pre-measured quantities of water, and to create a smooth finish without seams, water repellent, and latex and mixed by hand. the team elected to use Styropoxy, a foam Due to inaccurate measurements of latex release agent. Two layers were applied onto during the first round of wet mixes, the

amount of latex added to each mix did not developed a strange consistency that caused match the intended mix design. This problem them to spread rapidly. These mixes were of incorrectly tared scales, however, was later thrown out. discovered through quality control by the The team put in considerable effort captains and corrected. Once each mix was into placing the final layer, which was less completed and approved by a captain, the mix workable. Also, because of the team’s was weighed and recorded and then sent to restriction to working outside, the final layer the placing station where members placed the was placed in limited lighting. This added a concrete on the foam mold by hand. To considerable amount of time to the ensure efficiency, dry mixing, wet mixing, construction process, especially since three and placing were occurring simultaneously different pigmented mixes were needed to so the mixes were constantly being prepared design the exterior. After the final layer was and placed. placed, the canoe was covered with wet The first 1/8” thick layer of the canoe burlap and a tarp and transported inside. This was placed directly onto the mold. The new method of curing with soaked burlap division of this layer into quadrants guided was used so that each section of the canoe the placement of blue, green, yellow, and red would be given a consistent amount of water, pigmented mixes. Furthermore, the captains which was an issue when using the steam supervised the process and ensured that the curing method from previous years. It concrete layer complied with the desired remained covered by the burlap for the next thickness by using toothpicks marked as seven days, with the burlap being re-wetted depth gauges. Once the first layer was every other day. completed, a layer of carbon fiber After 28 days of curing, the canoe reinforcement was placed on the canoe. In was demolded and the inlay wax was melted order to resist the curling tendency of the out of the canoe. Having resupplied materials reinforcement, the team had previously cut it after pour day, the structural mix that was into sections and flattened it three days used throughout the first and second layers of beforehand. The second layer was then the canoe was used again in the inlays and to placed on top of the reinforcement using the cover the bulkheads. Following the prepared mixes. This second layer contained placement of the inlays, the exterior was no pigment and was ¼” thick. sanded using electric belt sanders and 60 to As the second layer was nearing 2000 grit sandpaper to create a smooth finish. completion, the captains realized there was The interior was lightly sanded after the inlay a diminishing supply of SB latex, and none concrete was dry. Letters were stenciled, cut would be left to use on the third layer. Upon out of vinyl, and attached using the self- determining that there would be no way to adhesive backs. To finish, canoe was the obtain more at that time, the captains decided painted with two coats of sealant. to make the third layer with the materials on Throughout the construction process, hand. A new mix was developed using an the team emphasized sustainable practices increased amount of water for workability through the reuse of equipment as mentioned and additions of water reducer and shrink in the project management section. Masks reducer to offset the impacts of the extra were labelled with member names to be used water. The altered consistency of this new throughout pre-construction, construction, mix proved difficult for placing, especially and sanding. The tins used for dry-mixing on top of the second layer of reinforcement. were also cleaned out after each mix and used Furthermore, some of the new mixes again.

10 ID Task Name Duration Start Finish Aug '17 Sep '17 Oct '17 Nov '17 Dec '17 Jan '18 Feb '18 Mar '18 Apr '18 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 15 0 Concrete Canoe 2017 247 days Fri 8/11/17 Sat 4/14/18 1 Admin 243 days Fri 8/11/17 Tue 4/10/18 2 Budget and Funding 15 days Fri 8/11/17 Fri 8/25/17 3 Receive Rules 0 days Mon 9/11/17 Mon 9/11/17 9/11 4 Design Paper 32 days Mon 2/5/18 Thu 3/8/18 5 First Draft 17 days Mon 2/5/18 Wed 2/21/18 6 Rules Check 8 days Thu 2/22/18 Thu 3/1/18 8 Engineers Notebook 15 days Thu 2/22/18 Thu 3/8/18 7 Final Draft 7 days Fri 3/2/18 Thu 3/8/18 9 Presentation Content 27 days Thu 2/22/18 Tue 3/20/18 10 Presentation Rehearsal 21 days Wed 3/21/18 Tue 4/10/18 11 Aesthetic Design 181 days Wed 9/20/17 Mon 3/19/18 12 Theme Selection 0 days Wed 9/20/17 Wed 9/20/17 9/20 13 Design Canoe Graphics 40 days Mon 12/25/17 Fri 2/2/18 14 Design Paper Graphics 9 days Wed 12/27/17 Thu 1/4/18 15 Design Presentation Slides 26 days Thu 2/22/18 Mon 3/19/18 16 Structures 45 days Thu 9/21/17 Sat 11/4/17 17 Finalize Hull Design 23 days Thu 9/21/17 Fri 10/13/17 18 Simple Beam Structural Analysis 22 days Sat 10/14/17 Sat 11/4/17 19 Determine Max Loading Cases 0 days Sat 11/4/17 Sat 11/4/17 11/4 20 Development and Testing 67 days Sun 10/1/17 Wed 12/6/17 21 Order Initial Mix Materials 34 days Sun 10/1/17 Fri 11/3/17 22 Obtain ASTM C330 Compliant 12 days Mon 10/2/17 Fri 10/13/17 Aggregates 23 Design Structural Mixes 21 days Sat 10/14/17 Fri 11/3/17 24 Create Mixes for Testing 2 days Tue 11/7/17 Wed 11/8/17 25 Test Mix Curing 28 days Thu 11/9/17 Wed 12/6/17 26 Testing 0 days Wed 12/6/17 Wed 12/6/17 12/6 27 Verify Mix Design with Structural 0 days Wed 12/6/17 Wed 12/6/17 12/6 Analysis 28 Finalize Mix Design 0 days Wed 12/6/17 Wed 12/6/17 12/6 29 Paddling 189 days Sun 10/1/17 Sat 4/7/18 30 Practice 189 days Sun 10/1/17 Sat 4/7/18 31 Finalize Paddling Team 0 days Wed 1/10/18 Wed 1/10/18 1/10 32 Final Product Display 39 days Sat 3/3/18 Tue 4/10/18 33 Design Display Stands 5 days Mon 3/19/18 Fri 3/23/18 34 Procure Display Materials 8 days Sat 3/24/18 Sat 3/31/18 35 Prepare Cutaway Section Mold 4 days Sat 3/3/18 Tue 3/6/18 36 Place, Finish and Cure Cutaway 28 days Wed 3/7/18 Tue 4/3/18 Section 37 Display Table 10 days Sun 4/1/18 Tue 4/10/18 38 Construction 145 days Fri 11/17/17 Tue 4/10/18 39 EPS Foam Procurement 0 days Fri 11/17/17 Fri 11/17/17 11/17 40 Construct Mold 77 days Fri 11/17/17 Thu 2/1/18 41 Pour Day Materials 23 days Wed 1/10/18 Thu 2/1/18 42 Pour Day 0 days Sat 2/3/18 Sat 2/3/18 2/3 43 Cure 28 days Sat 2/3/18 Fri 3/2/18 44 Removal from Mold 0 days Fri 3/2/18 Fri 3/2/18 3/2 45 Inlays and Aesthetic Additions 0 days Fri 3/2/18 Fri 3/2/18 3/2 46 Sand and Patch 28 days Sat 3/10/18 Fri 4/6/18 47 Apply Letters and Seal 4 days Sat 4/7/18 Tue 4/10/18 48 Canoe Substantial Completion 0 days Tue 4/10/18 Tue 4/10/18 4/10 49 Deliverables Due 0 days Thu 3/8/18 Thu 3/8/18 3/8 50 Pacific Southwest Conference 4 days Wed 4/11/18 Sat 4/14/18 51 Depart for Conference 0 days Wed 4/11/18 Wed 4/11/18 4/11 52 Display and Presentation 0 days Thu 4/12/18 Thu 4/12/18 4/12 53 Races 0 days Fri 4/13/18 Fri 4/13/18 4/13

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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.

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 VCAS 160 2.60 3.24 700.9 1627 lb/yd3 c/cm ratio Class F Fly Ash 2.45 1.89 288.9 0.76 FIBERS Component Specific Gravity Volume (ft3) Amount of Fibers (mass/volume) (lb/yd3) Total Amount of Fibers PVA Fibers 1.30 0.057 4.59 4.59 lb/yd3 AGGREGATES Base Quantity (lb/yd3) ASTM Abs 3 Aggregates SGOD SGSSD Volume (ft ) C330* (%) 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 Dosage Admixture lb/gal % Solids Amount of Water in Admixture (lb/yd3) (fl. oz / cwt) SB Latex 8.5 261.3 48.0 146.79 Total Water from Admixtures, ∑wadmx Water Repellent 8.5 4.4 42.9 2.62 149.41 lb/yd3 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 Pigment 2.02 0.15 18.36 153.85 lb/yd3 WATER Amount (mass/volume) (lb/yd3) Volume (ft3) Water, lb/yd3 w: 222.9 3.93 3 Total Free Water from All Aggregates, lb/yd ∑wfree: 62.9 3 Total Water from All Admixtures, lb/yd ∑wadmx: 149.4 3 Batch Water, lb/yd 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

SHELL 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 VCAS 160 2.60 3.24 700.9 1627 lb/yd3 c/cm ratio Class F Fly Ash 2.45 1.89 288.9 0.76 FIBERS Component Specific Gravity Volume (ft3) Amount of Fibers (mass/volume) (lb/yd3) Total Amount of Fibers PVA Fibers 1.30 0.057 4.59 4.59 lb/yd3 AGGREGATES Base Quantity (lb/yd3) ASTM Abs 3 Aggregates SGOD SGSSD Volume (ft ) C330* (%) 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 Dosage Admixture lb/gal % Solids Amount of Water in Admixture (lb/yd3) (fl. oz / cwt) SRA 035 8.4 11.8 55.0 5.69 Total Water from Polyheed 1025 8.9 12.0 49.0 6.93 Admixtures, ∑wadmx 3 Water Repellent 8.5 4.3 42.9 2.62 15.24 lb/yd SOLIDS (LATEX, DYES AND POWDERED ADMIXTURES ONLY) Component Specific Gravity Volume (ft3) Amount (mass/volume) (lb/yd3) Total Solids from Pigment 2.02 0.15 18.36 Admixtures 18.36 lb/yd3 WATER Amount (mass/volume) (lb/yd3) Volume (ft3) Water, lb/yd3 w: 305.67 4.89 3 Total Free Water from All Aggregates, lb/yd ∑wfree: 62.85 3 Total Water from All Admixtures, lb/yd ∑wadmx: 15.24 3 Batch Water, lb/yd 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 *Color varies for this mixture

Appendix B: Mixture Proportions Established Parameters: - Utelite is an ASTM C330 compliant aggregate -Onebatch=1yd3 - Aggregate Volume/Mix Volume = 45% - Aggregate Volume/Mix Volume = 35% -Water/Cement=35% -CementitiousMaterialRatios: -PC=45% - VCAS = 35% - Fly Ash = 20% - Aggregate Ratios -1-2mmPoravers=17% - Utelite = 30% -0.25-0.5mmPoravers=17% -0.1-0.3mmPoravers=17% -GlassBubbles=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%

Structural Mix: 0.1 - .3 mm Poravers: 17% 45% 7% Cementitious Materials Volumes: ⇤ 3 ⇡ 7% 27ft =1.89ft3 VCAS 160: ⇤ 1batch Glass Bubbles: 45% 35% 16% ⇤ 27ft3 ⇡ 3 19% 45% 8% 16% =4.32ft ⇤ 3 ⇡ ⇤ 1batch 8% 27ft =2.16ft3 ⇤ 1batch Type I Portland Cement: 3.51 % of C330 Aggregate= 11.34 35% 35% 12% ⇤ 3 ⇡ 12% 27ft =3.24ft3 =30%> 25% ⇤ 1batch Fly Ash: Aggregate Base Quantities (OD): 1-2mmPoravers: 20% 35% 7% 3 ⇤27ft3 ⇡ 3 1.89ft 24.34pcf = 7% 1batch =1.89ft lbs⇤ ⇤ 45.99 batch Cementitious Materials Base Quanti- ties: Utelite: 3.51ft3 82.16pcf = VCAS 160: lbs⇤ 288.36 batch 4.32ft3 162.24pcf = lbs⇤ 0.25 - .5 mm Poravers: 700.88 batch 1.89ft3 36.82pcf = Type I Portland Cement: lbs⇤ 69.58 batch 3 3.24ft 196.56pcf = 0.1 - .3 mm Poravers: 636.85 lbs⇤ batch 1.89ft3 56.16pcf = lbs⇤ Fly Ash: 106.14 batch 1.89ft3 152.88pcf = Glass Bubbles: lbs⇤ 288.94 batch 2.16ft3 8.11pcf = 17.52 lbs⇤ Aggregate Volumetric Breakdown: batch Aggregate Base Quantities (SSD): 1-2mmPoravers: 1-2mmPoravers: 17% 45% 7% ⇤ 3 ⇡ 3 7% 27ft =1.89ft3 1.89ft 29.20pcf = ⇤ 1batch lbs⇤ 55.19 batch Utelite: Utelite: 30% 45% 13% 3 ⇤ 27ft3 ⇡ 3 3.51ft 107.95pcf = 13% 1batch =3.51ft lbs⇤ ⇤ 378.91 batch 0.25 - .5 mm Poravers: 0.25 - .5 mm Poravers: 17% 45% 7% 1.89ft3 47.12pcf = ⇤ 3 ⇡ 7% 27ft =1.89ft3 89.07 lbs⇤ ⇤ 1batch batch

0.1 - .3 mm Poravers: Amount of Water fl.oz. 3 =261.3 cwt (16.266cwt) 1.89ft 70.2pcf = 1gal lbs lbs ⇤ (1 .48)( 128fl.oz.)(8.5 gal) 132.68 batch =146.79lbs/batch Glass Bubbles: Water Repellant: 2.16ft3 8.19pcf = Percent Solids = 42.9% 17.69 lbs⇤ batch Amount of Water fl.oz. Admixtures Dosage: =4.25 cwt (16.266cwt) (1 .43)( 1gal )(8.5 lbs ) 128fl.oz. gal Latex: =2.62lbs/batch lb Density = 8.5 gal Solids: Weight per batch Latex: lbs =282.285 batch Specific Gravity = 1.01 CWT = 16.27 cwt Weight of Solids fl.oz. Weight per cwt =261.32 cwt (16.266cwt) 1gal lbs =282.28/16.27 (.48)( 128fl.oz.)(8.5 gal) =17.36 =135.5lbs/batch Dosage Volume of Solids 17.36 lbs = cwt ( 128fl.oz.) 135.5lbs/batch 8.5 lbs 1gal gal = 1.01 62.4pcf ⇤ 3 fl.oz. =2.15ft =261.32 cwt Powdered Pigment: Water Repellant: Specific Gravity = 2.02 lbs Weight of Solids Density = 8.5 gal .04lbs 17mixes 27ft3 Weight per batch = 1mix yd3 ( 1yd3 ) lbs =18.36lbs/batch =4.59 batch Volume of Solids CWT = 16.27 cwt = 18.36lbs/batch Weight per cwt 2.02 62.4pcf = .15ft⇤ 3 =4.59/16.27 =0.28 Fibers: Dosage Specific Gravity = 1.30 lbs .28 cwt 128fl.oz. = lbs ( 1gal ) Weight of Solids 8.5 gal fl.oz. =4.25 3 cwt = .01lbs 17mixes 27ft batch yd3 ⇤ 1yd3 Amount of Water in Admixture: =4.59 lbs/batch Latex: Volume of Solids

4.59lbs/batch 3 Percent Solids = 48% = 1.30 62.4pcf = .057ft ⇤

Water: Unit Wet Mass = Mcm + Mfibers + Magg. + Msolids + w Weight of Added Water =1626.67 + 4.59 + 673.55 + =700.88 lbsP C .35 153.85 + 222.89 batch ⇤ lbs =2681.55lbs/yd3 =222.89 batch Volume of Concrete Volume of Added Water = Vcm + Vfibers + Vagg. + Vsolids + Vw =222.89lbs/62.4pcf =9.45+0.057+11.34+2.30+3.57 =3.57ft3 =26.72ft3 Free Water = ⌃ Base Quantity * MC Theoretical Density = MassofConcrete =55.2(17.5%) VolumeofConcrete

+378.9(10%) 2681.55lbs = 3 +89.1(4.84%) 26.72ft +132.7(8.29%) =100.37pcf +17.7(0%) Measured Density =93.65pcf lbs Air Content =62.85 batch 100.37pcf 93.65 = 100% 100.37pcf ⇤ Batch Water = wfree+w +wadmix =6.7% =222.89lbs +62.85lbs +149.41lbs 222.89lbs Water to c Ratio = 636.85lbs =.35 lbs 222.89lbs =435.16 batch Water to cm Ratio = 1626.67lbs =.14

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:

0.039lbs 3 1-2 mm Poraver: 14.4pcf =0.0027ft 0.275lbs 3 Utelite: 107.95pcf =0.0025ft 0.058lbs 3 0.25 - 0.5 mm Poraver: 21.2pcf =0.0027ft 0.115lbs 3 0.1 - 0.3 mm Poraver: 24.96pcf =0.0046ft 0.024lbs 3 Glass Bubbles: 8.19pcf =0.0029ft C330 Aggregate Proportion Compliance:

0.0025 % of C330 Aggregate= 0.0154 =16%< 25%

Appendix C: Example Structural Calculations Assumptions: Length 19ft - Self-weight is uniformly distributed Weight of Canoe 300 lbs Distributed Weight of Canoe 15.79 plf - Paddlers are treated point loads Buoyant Force on Canoe 53.68 plf Weight of Male Paddler 200 lbs - Cross-section is uniform throughout Weight of Female Paddler 160 lbs Location of Male Paddlers 3.8 ft & 15.2 ft - Reinforcement area/moduli ratio are Location of Female Paddlers 6.65 ft & 12.35 ft negligible Maximum Shear and Moment Calculations: Co-ed Free Body Diagram Case 1:0ft x 3.8ft   ⌃F =0= V wx + w x y b V = (37.89 plf)x 2 2 ⌃M =0=M + wx wbx 0 2 2 M = (18.945 plf)x2

Case 2:3.8ft x 6.65ft   Co-ed Moment Diagram

300 ⌃Fy =0= V + x(wb w) 250 200lbs 200

V = (37.89plfx) 200lbs 150 2 2 wx wbx M (ft.lb) ⌃M =0=M + 100 0 2 2 +200(x 3.8) 50 0 M = (18.945plf)x2 (200 lbs)x -50 0 2 4 6 8 10 12 14 16 18 20 +760 lbft X (ft) Co-ed Shear Diagram Case 3:6.65ft x 12.35ft   150

⌃F =0= V + x(w w) 100 y b 200lbs 160lbs 50 V = (37.89plf)x 360lbs 0 V (lb) 2 2 wx wbx ⌃M =0=M + -50 0 2 2 +200(x 3.8)+160(x -100 6.65) -150 0 2 4 6 8 10 12 14 16 18 20 X (ft) M = (18.945plf)x2 (360 lbs)x Case 5: 15.2ft x 19ft +1824 lbft   ⌃F =0= V + x(w w) Case 4: 12.35ft x 15.2ft y b   200lbs 160lbs 160lbs 200lbs ⌃F =0= V + x(w w) y b V = (15.79plf)x 720lbs 2 2 200lbs 160lbs wx wbx ⌃M0 =0=M + 2 2 V = (15.79plf)x 520lbs +200(x 3.8)+160(x 2 2 wx wbx ⌃M0 =0=M + 2 2 6.65)+160(x 12.35)+ 200(x 15.2) +200(x 3.8)+160(x 6.65) + 160(x 12.35) M = (18.945plf)x2 (720 lbs)x M = (18.945plf)x2 (520 lbs)x +6840 lbft +3800 lbft

The cross section regions, minimized due to sym- Cross-Section Dimensions metry: 1) Side walls (x2) 2) Chines (x2) 3) Bottom

1) Side Walls:

1 2 A1 =2Lt = 2(6”)( 2 ”) = 6 in y¯ = h L = 14 6 = 11 in 1 2 2 1 3 1 3 4 I1 = 12 tL = 12 (.5)(6) =9in 2) Chines: Arc radius = 6.821”; Thickness = 1 ” 2 Moments of Inertia: (about neutral axis) 1.152 7.321 2 A2 = rdrd✓ =1.853 in 4 2 4 2 2 .628 6.821 I1 =9in +Ad =9in +6in (11 5.18) 1 1 1.152 7.321 2 y¯2 = R ydAR = r sin(✓)drd✓ 4 A2 1.853 .628 6.821 I1 = 212.23in R R R 4 2 =5.433 in I2 = .874in + Ad y¯ =8 5.76 = 2.567 in (from bottom) 4 2 2 = .874in +1.853in (2.567 2 1.152 7.321 3 2 5.18)2 I2 = y dA = .628 6.821 r sin (✓)drd✓ 4 =R 55.57 inR4 R I2 = 13.53in

2 4 4 2 I2 = I2 Ad = 55.57 in I3 =2.714in + Ad (1.853in2)(5.433in)2 =2.714in4 +4.651in2(.299 = .874in4 5.18)2 1 3) Bottom: Arc radius = 26.325”; Thickness = ” 4 2 I3 = 113.52in 1.571 26.825 2 I = I + I + I = 339.28in4 A3 = 1.221 26.325 rdrd✓ =4.651in total 1 2 3 y¯ = R1 y R↵rdr = 1 26.825 r2sin(↵)dr Internal Stresses for Co-ed Case: 3 A3 c 4.651 26.325 273.6lbft( 12in )(14in 5.77in) My 1ft = 26R.03in R = I = 339.28in4

y¯3 = 26.3294 26.03 = .299in (from bot- = 79.64psi = 79.64psi (compression) tom) 2 1.571 26.825 3 2 ⌧ = VQ I3 = y dA = 1.221 26.325 r sin (✓)drd✓ It =R 3154.05inR 4 R 1.152 7.321 2 A2upper = .825 6.821 rdrd✓ =1.156in I = I Ad2 = 3154.05in4 y¯ = 1 ydA 3 3 2upper AR2 R (4.651in2)(26.03in)2 upper R = 1 1.159 7.321 r2sin(✓)drd✓ =2.714in4 3.497 .825 6.821 =5.882 in R R Neutral Axis: Q = ⌃A y¯ =¯y (A )+¯y (A ) ⇤ 1 1 2upper 2upper ⌃A y =0=6in2(y 11in)+1.853in2(y = (11in 5.18in)(6in2) 2.567⇤ in) +(5.882in 5.18in)(1.156in2) +4.651in2(y .299in) = 69.92in3 (144lbs)(69.92in3) y =5.77in ⌧ = (339.28in4)(.5in) = 59.35 psi

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 49.02 Two Paddlers (F) 37.49 134.7 37.49 39.21 Four Paddlers 59.35 273.6 59.35 79.64 Transportation 0 0 0 0 Shear Diagram - All Cases

Moment Diagram - All Cases

AppendixAppendix D: D: Hull Hull Thickness Thickness/Reinforcement / Reinforcement and Percent and Percent Open OpenArea Calculations 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 = 0.0062 100% = 1.24% 0.5 ⇤

Percent Open Area Square opening dimensions: 0.6875 in. x 0.6875 in. Area of single opening: 0.4727in2 0.125 D1= 0.6875 + 2 =0.75in. 0.125 D2 = 0.6875 + 2 =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 106⇤ .36 Percent open area = 127 = 83.7%