Concrete Arrow TABLE OF CONTENTS LIST OF FIGURES

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2 TABLE OF CONTENTS ExecutiveSummary... ii Project Management... 1 Organization Chart... 2 Hull Design and Structural Analysis... 3 Development and Testing... 5 Construction... 8 Project Schedule Design Drawin LIST OF FIGURES Figure 1: Percentage of Person Hours... 1 Figure 2: Distribution of Expenses... 1 Figure 3: Final Hull Geometry... 3 Figure 4: Free Body Diagram for two-male race load case... 4 Figure 5: Free Body Diagram for canoe display load case... 4 Figure 6: Bending Moment Diagrams... 4 Figure 7: Flexural Testing... 5 Figure 8: Ease of reinforcement placement in Figure 9: Percentage of Cementitious Materials... 6 Figure 10: Hot Water Curing Device... 7 Figure 11: Compression Testing... 7 Figure 12: Wood Stripping on Cross Sections... 8 Figure 13: Portable Ventilation System... 8 Figure 14: Fiberglass Mold on Curing Tank... 9 LIST OF TABLES Table 1: Concrete Arrow Specifications... ii Table 2: Milestones... 1 Table 3: Hull Design Comparisons... 3 Table 4: Bending Stresses... 4 Table 5: Aggregates used and their specific gravities... 5 Table 6: Admixture Dosages... 6 Table 7: Concrete Strengths... 7 LIST OF APPENDICES Appendix A References... A-1 Appendix B Mixture Proportions... B-1 Appendix C Bill of Materials... C-1 Appendix D Example Structural Calculations... D-1 University of Tennessee at CHATTANOOGA i

3 EXECUTIVE SUMMARY Once declared the dirtiest city in America, a plan to revitalize Chattanooga was hatched in the mid- 1960s, and the city has undergone a tremendous metamorphosis. While it now stands as a glowing example of how environmental protection and economic development can coexist, across the tracks her gritty industrial bones are still visible in abandoned steel mills and defunct warehouses. Chattanooga University was founded in 1886 in the heart of Chattanooga, TN. It has since merged with several other colleges and in 1969 was renamed to The University of Tennessee at Chattanooga. UTC is host to more than 11,000 undergraduate students and offers more than 140 majors. The college is best known for its nationally ranked Business, Engineering, and Nursing programs. Although UTC has a short concrete canoe tradition, we have steadily improved since our first entry in 2011 with Nautica George. The Night Rambler (2012) and The River Voyager (2013) saw a large reduction in weight as well as a better understanding of the processes involved in casting a winning canoe. With Tennessee Jones (2014), the team placed 9 th overall in the southeastern conference. The students at the University of Tennessee at Chattanooga chose a canoe name based on the comic book superhero Green Arrow whose modern catch phrase is you have failed this city. This phrase is said to the villains before Green Arrow delivers justice. The year began with a struggle in an attempt to not only find a location to build the canoe, but also a place for the UTC ASCE chapter to call home: a place where we could work freely and have a permanent workplace for future years. It was not until early November that this workspace was attained. The team spent two months outfitting our new home with proper equipment so that form fabrication could start as soon as possible. Despite numerous setbacks, the team s desire to prevail outweighed all else. As Green Arrow might say, we will not fail this canoe. Thus our canoes name was chosen to be Concrete Arrow The team used a heavily modified version of the standardized hull design in order to mimic a typical camping canoe. Along with the changes to the hull, the 2015 canoe team decided to use 100% sustainable aggregates in Concrete Arrow. The initial planning for Concrete Arrow began in early August, and was very important for the successful functioning of the team. With only eight dedicated members this year, this planning process and close teamwork ensured a well functioning team and high quality finished product. For the 2015 competition year, the team reimplemented and improved upon the negative mold and casting methods created in the previous year. This allowed for a significant improvement in the areas of quality control and aesthetics. The University of Tennessee at Chattanooga competes with around 23 Colleges in the Southeastern Conference. Although the UTC concrete canoe team has not yet earned a top spot in the Southeast conference, as the team s techniques and finished product improve we feel our eligibility improves. Table 1. Concrete Arrow Specifications Concrete Arrow Design Specifications Concrete Properties Maximum Length ft. Wet Density 64 pcf Maximum Width ft. Oven-Dried Density 59 pcf Maximum Depth 12 in. Compressive Strength 2200 psi Average Thickness 0.75 in. Air Content 8% Overall Weight 210 lbs. Composite Flexural Strength 1800 psi Colors Reinforcement Green Themed C-Grid CT275 University of Tennessee at CHATTANOOGA ii

4 Project management The Concrete Arrow team consisted of eight dedicated members. The small nature of the team required a high level of cooperation and the volunteer efforts of current and former members of the UTC ASCE student chapter. Table 2. Milestones The core team has spent nearly 800 personhours on the project, and an additional 100 personhours came from volunteers. The percentage of person hours for each task is shown in Figure 1. Both team members and volunteers followed quality standards put into place for each project component. The biggest challenge project management faced this year was starting the 2014/2015 academic year without a workspace. This caused a disruption of the initial project timetable. In August and September efforts shifted to making arrangements to secure a lab space by mid- September. This was necessary in order to ensure that the team could start working at a reasonable date. However, due to complications, a large enough workspace was not obtained until many of the team s initial project plans and deadlines could not be accomplished or met on time. After securing a new space in mid- November, the team shifted its efforts again towards preparing and equipping the new lab, while creating new project plans to rebound from the delays earlier on in the fall semester. By December, the team s management had obtained several requisite pieces of machinery and begun to put the team back on track. In order to ensure the safety of the team throughout the project, management put into place a safety program that included, regular safety meetings, increased use of personal protective equipment, safe storage of materials, quality standards put in place for each project component and an innovative portable ventilation system. One team member was designated to oversee safety standards, and maintain MSDS for all materials used over the course of the year. Additionally, the team strove to maintain a clean and organized working environment in order to reduce the risk of accidents. The 2015 team completed all work to date on Concrete Arrow without any reportable injuries. University of Tennessee at CHATTANOOGA 1

5 Co-Captain Co-Captain Concrete Arrow Organization Chart Nikita Hemnani - Senior Canoe Participant- 2yrs Registered Participant- 2yr Bailey Ennis - Junior Canoe Participant- 2yrs Registered Participant- 2yrs Barrett Ennis - Sophomore Jacob Dodd Senior Mackenzie Defriese- Sophomore Canoe Participant- 2yrs Canoe Participant- 2yrs Canoe Participant- 1yrs Registered Participant- 2yrs Registered Participant- 1yrs Registered Participant- 1yrs Natalie Burdine - Freshmen Molly Burdine Sophomore Judy Finny - Sophomore Canoe Participant- 1yrs Canoe Participant- 1yrs Canoe Participant- 1yrs Registered Participant- 1yrs Registered Participant- 0yrs Registered Participant- 1yrs University of Tennessee at CHATTANOOGA 2

6 HULL AND STRUCTURAL ANALYSIS When creating a hull design, one could create small scale models or use hull design software to come up with an optimum combination of individual attributes. The downside to this method is that a very accurate and precise small scale model is required as to not introduce large margins of error. With limited access to equipment with these capabilities, small scale models would most likely produce inaccurate results. Thus the best method would be to observe the performance of past canoes and compare their hull designs. In 2012, Night Rambler s hull was designed to be a hybrid between a tandem racing canoe and a general tandem canoe. Its 21ft overall length gave the boat excellent ability to keep track in the water. Drawbacks to Night Ramblers hull were that its overall depth was an excessive 18.5in, which made paddling inefficient. The overall beam was also too large; measuring 35in. In addition the 21ft length made her difficult to maneuver. These changes resulted in a significantly different length to beam ratio. The shortened design of Tennessee Jones is one change that allowed for greater maneuverability, and the wider middle body offers greater stability. The desire of this year s team was to obtain the combined advantages of both Night Rambler and Tennessee Jones. Hence, the hull of Concrete Arrow has similar geometry to Tennessee Jones with the exception of an increase in overall length of about two feet. While the increase in length is not large enough to greatly affect maneuverability, it will eliminate the trouble our team had keeping the canoe on track. Furthermore, decreasing the depth and overall beam of Concrete Arrow compared to Night Rambler will increase paddle efficiency and reduce friction due to drag. Table 3. Hull Design Comparison Hull Design Comparision Overall Length 21 ft ft ft. Overall Beam 35 in. 31 in in. Depth 18.5 in. 12 in. 12 in. Front Rocker 4 in. 3 in. 4 in. For the 2014 conference the philosophy behind the hull design of Tennessee Jones was to create a canoe similar in size and handling to a common recreational fiberglass canoe. In order to achieve this desired geometry, the Standard Design was heavily modified. The design was shortened by 3 feet and the widest point was moved half a foot towards the center of the canoe. Figure 3. Final Hull Geometry Additionally, to further increase the ease of turning during the slalom races, the hull was designed to have a moderate rocker of approximately four inches. The design team considered many factors before finalizing the shape of Concrete Arrow; chief among them were: fidelity to the shape and style of a common recreational canoe, manufacturability of the associated form, and required structural performance as judged by the University of Tennessee at CHATTANOOGA 3

7 Analysis team. Through the course of construction, transportation, display, and racing, Concrete Arrow will be subjected to many different load cases. Many of these cases, however, will be unpredicted, unfavorable, and ultimately unquantifiable based on the scope of this analysis. That is, the more complicated load cases cannot be practically considered using a two-dimensional analysis. For this reason, the analysis was narrowed to three load cases: 1) two-male race, 2) four-male race, 3) canoe display. The intent of the two-dimensional analysis was to determine the internal compressive and tensile stresses and compare the results to the lab measured compressive and tensile strengths of the concrete mixture. Concrete Arrow was analyzed as a beam to calculate the maximum internal bending moment for each loading case. Static analysis lead to the determination that two-male load case would generate the maximum positive moment and the canoe display load case would generate the maximum negative moment. The free body diagrams for these load cases are given in Figures 4 and 5, respectively. The canoe weight (W C ) was 210 lbs and the weight of one male (W P ) was assumed to be 150 lbs. The buoyancy force (F B ) and display reaction forces (R A, R B ) were calculated using equilibrium equations. Figure 5. Free Body Diagram for canoe display load case Shear and bending moment diagrams were constructed for each of the load cases. Figure 6 shows the bending moment diagrams for the twomale race and canoe display loading cases. Figure 6. Bending Moment Diagrams Once the maximum positive and negative bending moments were calculated, the bending stresses could be determined using principles of mechanics of materials. The canoe was assumed to be in pure, uniaxial bending. The maximum internal stresses calculated are provided in Table 4. The concrete strengths greatly exceed the calculated stresses and as such Concrete Arrow will be structurally sound in the loading cases considered (Note, concrete strengths provided in Development and Testing) Table 4. Bending Stresses Figure 4. Free Body Diagram for two-male load case Loading Case Two-Male Case Display Case Moment (ft-lbs) Compressive Stress (psi) Tensile Stress (psi) University of Tennessee at CHATTANOOGA 4

8 DEVELOPMENT AND TESTING Due to the unavailability of an outfitted lab space until December and a concrete mixer until late February, the mix design team was constrained for time in developing an innovative mix design. Thus, the team opted to use the mix developed for Tennessee Jones in The main goals of the mix design team in 2014 were to decrease the unit weight of the mix while maintaining the same structural capacity as The River Voyager, the 2013 canoe. The first step taken in this process was to remove all aggregates with a specific gravity above 1.0. It was determined that the reason The River Voyager was heavier than desired was because of the relatively heavy sands used in its mix. These heavy sands were replaced with new sustainable expanded glass aggregates ranging in sizes of 0.1 mm-2 mm. Although the crush strengths of these aggregates were not equivalent to those omitted, the gradation curve in our mix was improved and we were able to obtain similar strengths compared to The River Voyager. Table 5 shows the comparison of the specific gravities of the aggregates used in The River Voyager compared to those used first in Tennessee Jones and later Concrete Arrow. Table 5. Aggregates used and their specific gravities The River Voyager Concrete Arrow Aggregate S.G. Aggregate S.G. Stalite Sand 0.8 Poraver mm 0.95 Masonary Sand 2.65 Poraver mm 0.7 K37 Glass Bubbles 0.37 Poraver.5-1 mm 0.5 Poraver 1-2 mm 0.4 Tensile capacity was also increased by obtaining a better secondary reinforcement material. In 2013 because of budget constraints The River Voyager used buckeye fibers that were available from previous year s materials used in Night Rambler in The 2014 canoe team was able to get a local company to donate several types of synthetic fibers. Two fibers were tested, Fibermesh 300 and Fiber mesh 650. In 2014, testing showed that the Fibermesh 650 provided a 20% increase in tensile strength over the Fibermesh 300. For this reason the 2014 team selected Fibermesh 650 for their final mix design. Based on the successes of the previous year, the 2015 team chose to continue the use of these fibers. Figure 7. Flexural Testing Many different types of reinforcement were researched to be used in Concrete Arrow. The team considered pre-impregnated carbon graphite tape, Kevlar, and also the same carbon grid that was used in The River Voyager and Tennessee Jones. After considering cost, construction resources, and the positive results of flexural tests completed by the 2014 team, it was decided to use the same carbon grid that was used in previous years. Figure 7 shows a flexural test panel containing carbon grid in a test frame. The grid has a tensile modulus of 34,000 ksi and meets the open area requirements of the competition rules. In addition the selected carbon grid has the advantage of requiring very limited concrete coverage to provide the desired strength benefits. The team decided to add an extra layer of reinforcement for additional strength in Concrete University of Tennessee at CHATTANOOGA 5

9 Arrow. Past teams have found this carbon grid very easy to place as seen in Figure 8 below. Figure 9. Percentage of Cementitious Materials Figure 8. Ease of reinforcement placement in 2014 In past years metakaolin was often used as a cementitious material to make finishing the canoe easier. Concrete Arrow, unlike The River Voyager, does not utilize metakaolin in the mix because the aggregates chosen for the mix were much easier to finish. This choice was supported by the experience of the 2014 team. We chose to use ground granulated blast furnace slag because it contributed to the light color of our concrete as well has a higher compressive strength. Fly ash and silica fume were also used as cementitious materials in Concrete Arrow because they gave us the workability and early strength, respectively. These properties were essential in 2015 in order to complete the project on time due to the truncated production schedule. Figure 9 shows the percentage of cementitious materials used in Concrete Arrow compared to those used in The River Voyager. As previously discussed, the same mix design, including admixtures, developed for Tennessee Jones was used in the casting of Concrete Arrow. The admixtures used in Concrete Arrow were ADVA Cast 575 and Daraweld C. ADVA Cast 575 is a high range water reducer that gave the mix a very good workability, without incurring a significant loss in strength by decreasing the required water cement ratio. Daraweld C is a latex bonding agent that allows for better bonding between layers of concrete during casting, as well as a smoother finish to the concrete. Daraweld C also helps prevent delamination of the concrete and reinforcement layers during placement. The admixture dosages used in 2015 are given in Table 6. The 2015 team was able to use leftovers from the supply used in previous years. Table 6. Admixture Dosages Admixture Recommended Dosage Actual Dosage ADVA Cast fl oz/cwt 4.5 fl oz/cwt Daraweld C 284 fl oz/cwt 116 fl oz/cwt 10 variations of mix designs were mixed and tested by the 2014 Mix Design team before they decided on a final design. Last year for Tennessee Jones various curing methods were employed to find their effect on the concrete. A new product called Spray Lock was tested on the lightweight concrete as well. It is sprayed on the concrete and penetrates into the capillaries to University of Tennessee at CHATTANOOGA 6

10 waterproof and protect the pore structure. Along with the spray lock curing, 28 day cold water and 4 day hot water curing were implemented on the samples. Unfortunately, the treat proof curing results were much lower than the water cured samples, and were thrown out of analysis. The hot water curing tank can be seen in Figure 10. These samples were cured for three days at 170 degrees Fahrenheit. Based on the knowledge gain last year, the 2015 team has decided to employ a four day hot water cure process. The mix design team last year was successful in creating the lightest and most innovative mix in our history. This mix was very economical for us because the cementitious materials from past years were readily available for use, and many materials had already been donated. In addition, it was also the most sustainable mix, including only sustainable aggregates in its construction. The structural design met and exceeded the strengths obtained through the structural analysis. Improved development and testing employed for Tennessee Jones in 2014 will hopefully alleviate the constrained timetable that the Concrete Arrow team is facing this year. Figure 10. Hot Water Curing Device For each mix design, five 3 x 5 inch cylinders, six 2 x 2 inch cubes, and five one-half inch wide composite panels were cast for testing. These samples were cured in the various methods mentioned and tested for strengths. The average compressive and composite flexural strengths are shown in Table 7. It was also decided that a finishing mix was not necessary for Concrete Arrow. Our structural mix would light enough in color and workable enough to yield a smooth, sandable surface. Figure 11. Compression Testing Table 7. Concrete Strengths Concrete Strengths Concrete Compressive Strength Conposite Flexural Strength 2200 psi 1800 psi University of Tennessee at CHATTANOOGA 7

11 CONSTRUCTION Concrete Arrow will be cast using a negative form build from recycled fiberboard and fiberglass. Using Excel and SolidWORKS, patterns were printed for twenty cross sections. The cross section were cut from medium density fiberboard and attached to appropriately spaced bases. High density fiberboards were cut down into strips approximately 3/4 wide and 1/8 thick. The strips were then attached to the fiberboard cross sections using staples and wood glue. Once all the strips were placed, the interior of the form was sanded until smooth in preparation for the fiber-glassing process. Chopped glass mat is then cut to size and laid in the form. Polyester resin is then applied to the matting to form the composite surface of the finished form. Two to three layers of fiberglass mat and resin are applied to the form and special care is given to fill any imperfections of the underlying wood surface. Sanding between layers will ensure a proper working surface that prevents delamination between the layers of the composite. The surface of the form will then be finished by applying a gel coat of resin which will be sanded smooth in preparation for the polyurethane topcoat. Figure 12. Fiberboard Stripping on Cross Sections In order to prepare for casting the canoe, the surface of the form is then buffed with six coats of mold wax. Air lines will be installed at various points across the form; these are used to inject air between the form surface and the canoe during removal. Finally a foam lip is installed at the top of the form to ensure a clean top edge on the finished canoe. Figure 13. Portable Ventilation System Carbon fiber grid is cut into sections matching the base, side, and front of the canoe. Sufficient pieces will be measured and precut for two layers of reinforcement. Each piece of reinforcement is tagged with a location and layer number in order to ensure appropriate placement. Blocks matching the shape of the bow and stern of the canoe are shaped out of foam to be placed in the bulkheads of the canoe. Finally depth markers are constructed from wooded dowels to be used for quality control during the casting process. In order to prevent ambiguity in the quality control process, separate sets of markers will be made for each of the three layers of concrete placed. During the casting process labor is divided into three main groups: mixing, placement, and quality control. The mix team will be responsible for organizing all of the materials, mixing and delivering the concrete to the placement team. The placement team then applies the concrete to the mold and placed the carbon fiber grid between University of Tennessee at CHATTANOOGA 8

12 layers. The quality control team will work solely on ensuring the placement and thickness of the concrete layers and the carbon fiber reinforcement layers. Figure 14 Fiberglass Mold on Curing Tank (2014) The casting process consists of five steps: placing two layers of carbon fiber between three layers of concrete. The first 1/4 layer is applied carefully to ensure few as voids between the concrete and form surface as possible. After checking the quality of the first layer with depth gauges, precut tagged reinforcement will then be placed over the first layer of concrete. A second layer of concrete, 1/4 thick is then applied; the placement team will work carefully with quality control team to ensure that the first layer of reinforcement is adequately covered. The placement team must work carefully with quality control team to ensure that the first layer of reinforcement does not shift during this step. rectangular tank. The canoe will be heat cured for four days at approximately 150º F. The tank temperature is maintained using a custom built system consisting of set of immersion heaters controlled by a PID control circuit. Accelerated curing of the entire canoe was developed in 2014, and will be critical for completing construction by conference After the curing process is completed, the canoe will be removed from the hot water tank and allowed to rest for 24 hours. The team will then be ready to begin the sanding process. It is necessary to a complete series of sanding ranging from 60 grit to 220 grit to ensure a smooth surface for staining. The staining team colored the canoe one side at a time in solid colors, and then painted comics on the interior of the canoe using stencils. The decoration process was then completed by staining, on the exterior, our university name and the name of our canoe: Concrete Arrow. Sustainability was heavily implemented throughout the project this year. When fabricating the cross sections, environmental sustainability was integrated by using fiberboard that was made from 100% recycled wood fibers. Additionally, a switch was made this year from using pine furring strips to using recycled fiberboard for the 3/4" strips forming the shape of the mold. Furthermore, the team this year tested bio-based resins and intend to use it in 2016 rather than the polyester resin used this year and in A second layer of reinforcement is applied similarly to the first and the final 1/4 layer of concrete atop of it. Using depth gauges, a final thickness of 3/4 is checked for across the entire length of the canoe. The final layer of concrete was is finished using hand floats and sponges to minimize sanding of the final product. After casting, the canoe will be open cured for four days under plastic sheeting before being transferred to a heated curing tank. The curing tank for Concrete Arrow consisted of an 800 gallon University of Tennessee at CHATTANOOGA 9

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15 Appendix A - REFERENCES ASTM (2012). Standard Test Method for Compressive Strength of Hydraulic Cement Mortars (Using 2 in. or [50 mm] Cube Specimens). C109/C 109M-08, West Conshohocken, PA. ASTM (2012) Standard Test Method for Density, Relative Density (Specific Gravity) and Absorption of Coarse Aggregates. C 127, West Conshohocken, PA ASTM (2012) Standard Specification for Portland Cement. C150/C 150M-09, West Conshohocken, PA. ASTM (2012). Standard Test Method for Specific Gravity and Absorption of Fine Aggregates. C 128, West Conshohocken, PA. ASTM (2012). Standard Test Method for Density (Unit Weight), Yield, and Air Content (Gravimetric) of Concrete. C 138/C 13 8M, West Conshohocken, PA. ASTM (2012). Standard Specification for Chemical Admixtures for Concrete. C 494/C 494M, West Conshohocken, PA. ASTM (2012). Standard Specification for Ground Granulated Blast-Furnace Slag for Use in Concrete and Mortars. C 989, West Conshohocken, PA. ASTM (2012). Standard Specification for Fiber-Reinforced Concrete and Shotcrete. C 1116, West Conshohocken, PA. ASTM (2012). Standard Specification for Latex and Powder Polymer Modifiers for Hydraulic Cement Concrete and Mortar. C 1438, West Conshohocken, PA. ASTM (2012). Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens. C 39/C 39M, West Conshohocken, PA. ASTM (2009). Standard Test Method for Flexural Properties of Thin-Section Glass-Fiber- Reinforced Concrete (Using Simple Beam with Third-Point Loading). C947-03, West Conshohocken, PA. University of Tennessee at Chattanooga (2010), Nautica George, National Concrete Canoe Competition Design Paper. University of Tennessee at Chattanooga (2012), The Night Rambler, National Concrete Canoe Competition Design Paper. University of Tennessee at Chattanooga (2013), The River Voyager, National Concrete Canoe Competition Design Paper. University of Tennessee at CHATTANOOGA A-1

16 University of Tennessee at Chattanooga (2014), Tennessee Jones, National Concrete Canoe Competition Design Paper. Grace Concrete Products, ADVA CAST 575 Material Technical Data Sheet, < Grace Concrete Products, Force 10,000 D Material Technical Data Sheet, < Grace Concrete Products, Daraweld C Material Technical Data Sheet, < NCCC Rules. (2014) American Society of Civil Engineers National Concrete Canoe Competition Rules and Regulations. Kosmatka, S.H., Wilson, M.L. (2011). Design and Control of Concrete Mixtures, 15 th ed, Portland Cement Association om_new_jersey.jpg pg University of Tennessee at CHATTANOOGA A-2

17 Appendix B - MIXTURE Proportions Y D SG Amount (lb/yd 3 ) Volume (ft 3 ) Amount (lb) Volume (ft 3 ) Amount (lb/yd 3 ) Volume (ft 3 ) CM1 Portland Cement CM2 Slag Grade CM3 Fly Ash CM4 Silica Fume Fibers F1 Propex FiberMesh Aggregates Mixture ID: Main Mix Design Batch Size (ft 3 ): Cementitious Materials A1 Poraver mm Abs: A2 Poraver mm Abs: A3 Poraver mm Abs: A4 Poraver 1-2 mm Abs: Water Total Cementitious Materials: W1 Water for CM Hydration (W1a + W1b) W1b. Additional Water Total Fibers: Total Aggregates: W1a. Water from Admixtures W2 Water for Aggregates, SSD Total Water (W1 + W2) : Design Proportions (Non SSD) Actual Batched Proportions Yielded Proportions Admixtures (including Pigments in Liquid Form) Amount (fl oz) Water in Admixture (lb) Ad1 Advacast 575 HRWR 8.9 lb/gal Ad2 Daraweld Latex 9.0 lb/gal Water from Admixtures (W1a) : % Solids Dosage (fl oz/cw t) Water in Admixture (lb/yd 3 ) Dosage (fl oz/cw t) Water in Admixture (lb/yd 3 ) Cement-Cementitious Materials Ratio Water-Cementitious Materials Ratio Slump, Slump Flow, in. M V Mass of Concrete. lbs Absolute Volume of Concrete, ft 3 T Theorectical Density, lb/ft 3 = (M / V) D D Design Density, lb/ft 3 Measured Density, lb/ft 3 = (M / 27) A Air Content, % = [(T - D) / T x 100%] Y Ry Yield, ft 3 Relative Yield = (M / D) = (Y / Y D ) / % % 11% University of Tennessee at CHATTANOOGA B-1

18 Appendix C -BILL OF Materials Concrete Material Quantity Unit Cost Total Price Portland Cement 35 lb. $0.15/ lb. $5.25 Fly Ash, Class C 20 lb. $0.03/ lb. $0.60 Slag Grade lb. $0.02/ lb. $0.30 Silica Fume 5 lb. $0.30/ lb. $1.50 Poraver Expanded Glass 56 lb. $0.70/ lb. $39.20 Propex Fibermesh lb. $12.00/ lb. $5.83 Adva Cast 575 (HRWR) 2.89 fl. oz. $0.09/ fl. oz. $0.26 Daraweld lb. $1.10/ lb. $1.90 Reinforcement Material Quantity Unit Cost Total Price C-grid Carbon Fiber 12 lin. yd. $22.00./ lin. yd. $ Mold and Finishing Material Quantity Unit Cost Total Price Wooden Mold Lump Sum $2,100 $2,100 Stain 6 L. $35.00/ L. $ Sealer 2 lbs. $49.00/ qt. $90.00 Total Production Cost of Concrete Arrow $2, University of Tennessee at CHATTANOOGA C-1

19 Appendix D - Example Structural Calculations Assumptions and Variables Below is a list of assumptions and variables. As this appendix was limited to two pages and intended to demonstrate hand-calculated stresses, certain simplifications were necessary. Weight of Canoe (W C ): Using the canoe volume, the weight was calculated with the measured concrete unit weight of 59 lbs/ft 3. The canoe weight was assumed to be uniformly distributed. The weight of canoe was calculated to be 210 lbs (11.2 lbs/ft). Length of Canoe (L) The canoe length, obtained from the hull drawing, was ft. Weight and Position of Male Paddler (W P ) The weight of one male was determined by weighing the heaviest male team member. The paddler weight was 150 lbs. The paddlers were assumed to be positioned at one-quarter the length and at three-quarters the length. Buoyancy Force (F B ) In determining the buoyancy force, the team assumed the canoe to be afloat at equilibrium. The buoyancy force is equal in magnitude to the weight of the canoe plus the weight of the two male paddlers. Buoyancy force was assumed to be uniformly distributed along the length of the canoe. The buoyancy force was calculated to be 510 lbs (27.1 lbs/ft). Cross Section Geometry The cross sectional area at the maximum moment was calculated using the hull drawings. To simplify analysis, the moment of inertia and neutral axis were calculated assuming a half-annulus cross section. The theoretical half-annulus was sized so that its area and thickness were equal to those of the true cross section. The moment of inertia was calculated to be 450 in 4. The neutral axis was calculated to be 8 inches below the lip of the canoe. Free Body Diagram Free diagrams were generated and are given in Figure 1. The first has two point loads for the weight of the paddlers (W P ), the uniformly distributed canoe weight (W C /L), and the uniformly distributed buoyancy force (F B /L). In the second free body diagram, the two distributed loads were resolved into point loads for the purpose of calculating the buoyancy force. Figure 1 Free Body Diagrams University of Tennessee at CHATTANOOGA D-1

20 Moment (ft-lbs) Shear (lbs) Concrete Arrow Shear and Bending Moment Diagrams The shear and bending moment diagrams are provided in Figure 2. As seen in the figure, the maximum moments correspond with the location of the paddlers (one-quarter and three-quarters length). The maximum moment was calculated to be 177 ft-lbs Length Fraction Length Fraction Figure 2 Shear and Bending Moment Diagrams Cross Section at Maximum Moment The cross section used to calculate the internal stresses is provided in Figure 3. As stated previously, the cross section was assumed to be in the shape of a half-annulus to simplify locating the neutral axis and calculating the moment of inertia about the neutral axis (I NA). Calculation of Internal Stresses Figure 3 Cross Sectional Properties The maximum normal stresses were calculated using the Flexure Formula as follows: σ max,compression = MC 1 I NA σ max,tension = MC 2 I NA (177 ftlbs)(8 in) = = 38 psi 450 (177 ftlbs)(5 in) = = 23 psi 450 University of Tennessee at CHATTANOOGA D-2