2004 Concrete Canoe Design Paper Milwaukee School of Engineering

Transcription

1 004 Concrete Canoe Design Paper Milwaukee School of Engineering Prepared By: John Knowles, Veronica Konieczka, and Elliot Struve

2 Newscaster #1: Special News Bulletin... A shipment of MSOE s concrete canoe supplies was lost somewhere over the South Pacific. Newscaster #: Wasn t that the same area where that famous three-hour boat tour was lost in that wild hurricane seven years ago? Newscaster #1: I think so. Hopefully the tides will be in the lost shipmates favor and they can put MSOE s supplies to good use. Newscaster #: Can they reproduce MSOE s nationally competitive concrete canoe? If only the castaways had instructions, it d be so much easier. Stay tuned for more details.. Gilligan s Island Lost Episode Table of Contents Executive Summary... i Hull Design... 1 Analysis... Development & Testing... 3 Project Management & Construction... Organization Chart... 6 Project Schedule... 7 Design Drawings... 8 Appendix A... A.1 Appendix B...B.1 Rib Mix...B.1 Finish Mix...B. Color Mix...B.3 Lightweight Mix...B.4 Canoe Name: S.S. Milwaukee Weight: 193 pounds Length: 19'-0" Width: 3" (at midship) Depth: 13" Thickness: 1/", 1" Reinforcement : Fiberglass mesh, carbon fiber tape Color: White, black, red stripe and gold rope Canoe Specifications Executive Summary The Milwaukee School of Engineering (MSOE) is a small private university located in the heart of downtown Milwaukee. The school was founded by Oscar Werwath in 1903 and is now in it s 101st year of operation. The student chapter of the American Society of Civil Engineers at MSOE consists of architectural engineering and construction management students. In 003, MSOE advanced to nationals for the first time in MSOE history and placed 8th at the National Concrete Canoe Competition. i Concrete Unit Weight: Lightweight Mix: 0.8 g/cc Finish Mix: 1.08 g/cc Color Mix: 1.08 g/cc Rib Mix: 1.19g/cc Concrete Strength: Lightweight Mix: 400 psi Finish Mix: 998 psi Color Mix: 998 psi Rib Mix: 134 psi Innovative Features: Asymmetric Finite Element Analysis, Sandwich Formwork, Rapid Prototype Tips, Strategically Placed Ribs and Carbon Fiber Reinforcement

3 Introduction The hull design is a compromise of three main design criterion: maneuverability and tracking, stability, and speed. An extensive literature search was conducted studying the hull geometries and dimensions that will maximize a canoe s performance. The result is the creation of the S.S. Milwaukee. Maneuverability and Tracking Experience proves that concrete canoe races are often decided by the team that can turn the fastest. Therefore, maneuverability was the primary design consideration for this year s canoe. Last year s design was based on a fiberglass racing canoe and featured an elliptical hull, which caused difficulty turning. This year, a flat bottom canoe was utilized because it can turn quickly in any direction (Moores 000). Rockers also add maneuverability by lifting the bow and stern out of the water, creating a pivot point at the midship. Length is a large factor affecting maneuverability. Long canoes are generally faster than shorter canoes, but are harder to turn. A length of 19'- 0" was chosen in order to adequately seat four paddlers and enable quick turning. TDF (pounds) Maneuverable canoes tend to have tracking problems. This becomes less of an issue with experienced paddlers. Stability A flat bottom hull generally rides higher in the water, causing it to be unstable (Moores 000). A rounded transition between the flat bottom and the sidewall counteracts the instability while maintaining the benefits of maneuverability. A width of 3" was also selected to ensure adequate stability. Additionally, a tumblehome will increase paddler efficiency and stability by reducing a paddler s reach and excessive leaning Instructions for Hull Design The depth of the canoe was determined from a water displacement calculation. A 7" freeboard in the four-person race is needed to ensure the canoe will not sink. A 13" depth was selected to satisfy this requirement. Speed Different hull geometries and dimensions were studied for speed. A canoe s speed is dependent on the total drag force (TDF) the water exerts on the hull (Lasauskas, Tuck, and Winters 1997). TDF = viscous resistance + wave resistance. These resistances can be quantified with a flow analysis. All canoes were designed in SolidWorks and converted into ProSurf analysis software (PROSURF manual 003). The flow analysis software approximated the TDF based on the hull geometry, wave type, etc., using Kaper equations (Winters and Knowles 004). The canoe velocity vs. TDF was plotted on a graph for each hull (see Figure 1). The 0'-0"elliptical bottom hull and flat bottom hull was studied in the flow analysis software. The difference between the two designs was approximately two pounds of force at 6. ft/s. Different hull lengths were also analyzed, and it was shown that longer canoes produce less drag. Results After analyzing the canoe lengths, widths, and geometries, the final dimensions of the S.S. Milwaukee were determined. Since maneuverability was the focus of this year s design, a 19'-0" flat bottom hull was chosen, despite its increase in drag. A " rocker was added to maximize maneuverability along with a 3" wide hull and a 7/8" tumblehome to increase stability and paddler efficiency. Finally, a depth of 13" was chosen in order to have a minimum 7" freeboard Velocity (ft/sec) 19' Elliptical Hull 19' Flat Hull Figure 1: TDF vs. Velocity 1

4 Introduction The hull geometry was exported from boat design software for the structural analysis. The structural analysis examined the expected stresses on the canoe and determined the necessary hull thickness. An iterative process between analysis and material testing was done until the material properties and thickness could resist the expected stress. Canoe Loading Paddler load, canoe weight, and resultant water pressure are the forces acting on the canoe (Figure ). The forces exerted by the paddlers were determined by pressure-indicating film, which measured the contact surface pressure between the saddle seats and the surface of the canoe. The water pressure exerted on the hull varies with depth (Mott 1994) and was determined by the displacement of the canoe in the water. Displacement is also a function of weight and thickness. Three load cases were taken into consideration with males assumed to weigh 190 pounds each and females 160 pounds each. Load Case Load Type # of Paddlers 1 Symmetric Males Symmetric Males + Females 3 Asymmetric Males 4 Asymmetric Males + Females Finite Element Analysis An elastic finite element analysis (FEA) of the hull geometry using four-node shell elements was used to determine the stress in the canoe. The final modulus of elasticity used in the analysis was 333 Instructions for Structural Analysis Canoe Weight Paddler Table 1: Load Case Descriptions Water Pressure Figure : Canoe Cross- Section Loading Ribs for Asymmetric Loading Stresses ksi for the lightweight composite and 343 ksi for the rib composite, which were determined from material testing (Figure 6). External loads were modeled with distributed forces for water pressure, canoe weight, and spring supports for paddler knees. Iterative analyses were performed, varying the thickness of the canoe until the material stress capacity was greater than the stress demand. Asymmetric Loading Analysis Asymmetric loading was determined to be an important failure mode often overlooked by concrete canoe designers. As paddlers stroke on opposite sides of the canoe, they shift their weight in opposing directions causing asymmetric stresses in portions of the canoe. This loading effect is similar to torsion in a beam. Asymmetric loading was modeled by increasing and decreasing spring stiffness in opposite knee supports. This proved to be the most significant loading case. In response, 1" thick ribs were made with the stiffer material and were placed in strategic locations to counteract these stresses. Conclusion The FEA resulted in a maximum stress of 180 psi under the paddlers knees. This high concentration of stress is unrealistic. In FEA, stresses near boundary conditions can be inaccurate; therefore, a punching shear test was used to determine required strength (page 4). Different load cases produced different areas of stress. A maximum stress of 336 psi was located in the ribs, 0 psi along the gunwales, and 69 psi in the remaining areas. These stresses were compared to the material capacities (Figure 6). Figure 3 shows the FEA for load case. The analysis concluded that the creation of a 1/" thick hull and 1" thick ribs shown on page 9 will provide adequate structural performance. Stresses in Gunwales Figure 3: Two-person Asymmetric Loading Unrealistic Stresses at Paddler Knees Examined by Punching Shear

5 Instructions for Development & Testing Introduction Based on experience and an FEA, two primary failure modes of concrete canoes are flexure and punching shear. The concrete and reinforcement were tested separately and as a composite. The final composite was chosen based upon strength, density, constructability, cost, and surface finish. Concrete Materials considered in the concrete mixture were: Binders Latex admixture Flyash* Acrylic fortifier Portland cement* *Required by NCCC rules. Rather than testing all possible mix combinations, testing was broken up into three phases. All mixes were designed using a detailed Excel spreadsheet. The most desirable mixes from each phase were determined and used in subsequent design phases. Cylinders were tested in compression (ASTM 001) to determine strength, weighed and measured to determine density and observed for finishability. Test results are shown in Figure 4. Phase I: Binder-to-Aggregate Ratio. A test using K-46 glass bubbles as aggregate was performed to find a mix with the optimal binder-toaggregate ratio. The concrete became heavier, stronger, and had a better surface finish as the ratio of binder-to-aggregate was increased. Phase II: Aggregate Type. The next phase compared two different types of glass bubbles, K-46 and K-1. The K-1 bubbles were tested using four binder-toaggregate ratios selected from Phase I. Mixes with K-1 glass bubbles proved to be lighter and have the same Interior Mix Final Mixes Compressive Strength (psi) Aggregates K-1 Glass bubbles K-46 Glass bubbles Sand* Polypropylene fibers Nylon fibers strength characteristics as mixes with K-46, without affecting the surface finish. Mixes with fibers were tested in flexure (see Flexural Testing). Fibers gave the concrete an undesirable finish, but added substantial flexural strength and made the composite more ductile. Phase III: Binder Type. Three different binder combinations were tested with portland cement: acrylic and flyash, latex and flyash, and flyash alone. Mixes with flyash alone were stronger and heavier than mixes with latex and acrylic. Mixes with latex were slightly stronger and lighter than mixes with acrylic. The cost difference between latex and acrylic, however, did not justify the use of latex. An optimal balance between flyash and acrylic was used in the final design. These three phases of testing resulted in the final selection of binder, aggregate and binderto-aggregate ratio. Reinforcement Materials considered for the reinforcement were: Carbon fiber tape Fiberglass insect screen Fiberglass mesh Steel welded wire mesh Stiffness, strength, cost, and weight are important properties in choosing a reinforcement scheme. Ideal reinforcements have a high stiffness to reduce deflection and cracking. Reinforcements were tested in tension to find stiffness and strength. Carbon fiber tape proved to be the strongest and stiffest reinforcement. Due to budget restrictions, carbon fiber Rib Mix Finish Mix Unit Weight Phase I Phase II Phase III Float Line Figure 4: Concrete Mix Design Phases tape could only be used in limited high stress areas. Steel welded wire mesh was eliminated because it added too much weight and thickness to the canoe. The fiberglass 3

6 mesh and fiberglass insect screen were both lightweight and reasonably strong. The reinforcement testing results are shown in Figure. It is difficult to determine the performance of the reinforcement without testing it together with the concrete. Composite Testing After narrowing down the concrete mix and reinforcement schemes, they were tested together as a composite. The composite material properties were compared to the FEA results, and the final composites were selected. Flexural Testing. Concrete plate specimens (.7" 14" 0.0") were made and tested according to ASTM Designation C947-99: Standard Test Method for Flexural Properties of Thin Section Glass-Fiber-Reinforced Concrete (Using Simple Beam With Third-Point Loading). This test determined the strength and stiffness of the composite, which were used in the FEA. The results of the flexural test are shown in Figure 6. Punching Shear Testing. A punching shear test was conducted on a 1" 1" 1/" specimen with the same concrete mix and reinforcement schemes used in the flexural testing. A point load was placed at the center of the specimen to emulate the contact pressure between the paddler s knee and the canoe. The test results confirmed the necessary thickness of a given composite to resist paddler load. Final Selection of Composite. In order to provide required strength, stiffness, density, and finishability, two composites of concrete and reinforcement were necessary: lightweight composite and rib composite. A factor of safety for strength of 1.3 was used based on experience, accuracy of material properties, and thoroughness of FEA. Material capacities were compared with the factored ultimate stress in that region (F u ). The lightweight composite is 1/" thick, consists of a low density concrete mix, and includes six layers of fiberglass mesh reinforcement. The interior mix has fibers to increase ductility and prevent sudden failure. A very thin finishing mix without fibers was applied to the hull surface to cover the reinforcement, resist cracking, and provide an excellent surface finish. The lightweight composite has a yield stress of 3 psi and will be used in lower stress areas of the hull (maximum stress of 69 psi, F u = 30 psi). The second composite was used in the ribs and gunwales where stiffness and strength are needed. This composite is 1" thick and consists of a stronger but heavier interior mix, one layer of carbon fiber tape, and ten layers of fiberglass mesh. Again, fibers were used in the interior mix and a finish mix was applied to cover the reinforcement. This composite has a yield stress of 4 psi compared to the maximum stress in the hull of 336 psi (F u = 437 psi). Load (lbs) Deflection (in) Welded Welded Wire Wire Mesh Mesh Fiberglass Mesh Mesh Fiberglass Screen Carbon Fiber Tape Tape Load Load (lbs) (pounds) Ε=340 ksi σ y =4 psi σ y =3 psi 0 Ε=330 ksi Deflection (inches) (in) 1/"Lightweight 1/ Lightweight Concrete Composite 1" 1 Structural 1"Rib Composite Concrete Figure : Reinforcement; Load vs. Deflection Figure 6: Final Composite; Load vs. Deflection 4

7 Instructions for Construction and Project Management Construction Formwork. The canoe form (Page 8) consists of the use of a male and female sandwich. The benefits of this method are that it maintains the complex geometry of the tumblehome and ensures uniform thickness throughout the canoe. Two-dimensional sections of the canoe were generated from a three-dimensional CAD model and used to cut hardboard on a CNC mill. Polystyrene blocks were placed between the hardboard and cut using a hot wire to match the contours of the canoe. The last 1'-0" sections of the bow and stern have a complex geometry, and formwork was rapid prototyped to ensure accuracy. To ensure straightness, the foam, hardboard, and rapid prototyped tips were aligned along a steel tube. Casting. Dry ingredients were pre-measured to make the casting day more efficient. A high strength rib mix was placed by hand into the rib and gunwale grooves. After the grooves were filled, two layers of fiberglass reinforcement were placed over the male mold. The interior lightweight concrete was then laid into 1" x1" x1/4" squares to control thickness. After a square was cast, it was transferred to the form and adjoined with the neighboring squares. Gaps were filled in by hand. After one layer of concrete was cast, two layers of reinforcement were placed over the concrete. Carbon fiber tape was also placed in the rib and gunwale locations and a final 1/4" layer of concrete was cast. Lastly, two layers of reinforcement were applied over the final layer of concrete. After the canoe was cast, the female sandwich form was vibrated over the concrete on the male form. After two days of curing, the female form was removed and a thin finishing layer was applied to the exterior of the canoe to cover the reinforcement. After 8 days, the canoe was removed from the male form and the patching layers were applied to the interior. Curing/Finishing. A humidification tent was constructed to allow proper curing conditions. After the finishing layers were applied on the exterior of the canoe, the canoe was sanded using auto body finishing tools. Four layers of stain and two coats of sealer were applied with a brush according to the manufacturer s specifications. Project Management Organizational Structure. A design-build structure (Page 6) was organized to delegate responsibility and ensure that all tasks were completed on time. The architect, principal engineer, and project manager determined the necessary committees to successfully accomplish the project goals. The chairs of each committee were determined by interest and experience. Underclassmen were committee co-chairs to encourage learning, participation, and future success. A design-build structure enables each member of the chapter to play a vital role in the creation and development of The S.S. Milwaukee. Schedule. A preliminary schedule was created in September with Microsoft Project (Page 7). The budget was correlated with the schedule to ensure that funding was available when necessary. Critical Path/Milestones. The critical path of the concrete canoe project started with the distribution of tasks, continued with the canoe design and construction, and concluded with the trip to the regional competition. The anticipated start and finish dates were within one week of the actual dates, which can be attributed to excellent project leadership. Completion of the hull design, structural analysis, determination of mix and reinforcement design, completion of the formwork, and casting the canoe were all major milestones. The timely completion of these milestones was crucial in the production of a high-caliber project. Planning and Implementation. The creation of The S.S. Milwaukee began with the ingenuity of the project leaders. Weekly meetings were conducted to discuss the canoe s schedule, budget, and design. Committee leaders presented ideas to the team and major decisions were voted upon. Also, each team member was informed of deadlines and workdays through . Documentation for every task was logged to ensure that information would be saved for future reference. A total of 108 man-hours were dedicated to the canoe: 163 were dedicated to the design, 7 to testing, and 788 to the construction of the canoe. The superlative coordination of activities and outstanding efforts of the project team will make The S.S. Milwaukee victorious.

8 Organizational Chart Principal Engineer Architect John Knowles Veronica Konieczka Develop Committees Design Decisions Team Communications Structural Analysis Materials Testing Quality Assurance Committee Chairs Hull Design Jason Link Theme Andrea Kondrasuk Construction Matt Tadisch Materials Design Beth Atkinson Paddling Danielle Ives Project Manager Eric Erdmann Project Schedule Budget/Estimate Ordering Materials Responsibilities Research Flow Analysis Coordination with Paddlers 3D Modeling Work Crews Sanket Anturkar Elliot Struve Eric Erdmann Presentation Canoe Staining T-Shirts Canoe Stands Denise Ott Catie Brazzale Dustin Stephany Construction Research Quality Control Manage Work Crews Lab Safety Adam Boucher Eric Brill Matt Nysse Others (approx. 30) Research Materials Mix Design Spreadsheet Coordinate w/ Project Engineer Testing Materials Jaimie Patton Jodi Chamra Katie Oakes Others (approx. 10) Paddling Practice Organize Workouts Strength Training Set Up Practice Races Miranda Cullins Sara Hansen Andrea Kondrasuk Jason Link Avery Snyder 6

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10 Canoe Mold and Frame Exploded Assembly Scale: 3/8=1'-0" 1 # Form Top View Scale: 3/8=1'-0" 1 Form Side View Form Front View Scale: 3/8=1'-0" Scale: 3/8=1'-0" 4 Date: March 7, 004 Sheet No. C-001 Title: Scale: 3/8" = 1'-0" Produced By: Canoe Form Schematic Drawing Milwaukee School of Engineering Page 8 Project: Engineers/Designers: JOHN KNOWLES VERONICA KONIECZKA Drawn By: 3//04 S.S. Milwaukee EJS Date: Checked By: JAK 3//04 Date:

11 3 A B C L C L B 8 A B A S.S. Milwaukee MILWAUKEE SCHOOL OF ENGINEERING B A 4 A LC C L LC C B L LC 4 3 # 6 1 Canoe Section A-A: Lateral Rib Section Scale: 1"=1'-0" C L Canoe Section B-B: Longitudinal Rib Section Scale: 1"=1'-0" Detail View A: Long. Rib Cross Section Scale: 1: Detail View B: Lat. Rib Cross Section Scale: 1:1 Isometric Canoe Scale: 1/4"=1'-0" Date: March 16, 004 Sheet No. C-00 Title: Scale: 1/" = 1'-0" Canoe Hull Schematic Drawing Produced By: Milwaukee School of Engineering Engineers/Designers: Drawn By: Date: Checked By: JOHN KNOWLES Page 9 Project: VERONICA KONIECZKA Date: EJS 3/16/04 JAK 3/0/04 S.S. Milwaukee

12 Appendix A References Moores, T. 000 CanoeCraft: An Illustrated Guide to Fine Woodstrip Construction. Firefly Books Inc. Buffalo, NY. Altair Engineering. Hypermesh Basic Training. Volume 1 and. 00. Altair Engineering Inc. Belegundu, A., Chandrupatla, T. Introduction to Finite Elements in Engineering. Third Edition. Prentice Hall Inc. Upper Saddle River, NJ. Mott, R. Applied Fluid Mechanics. Fifth Edition. Prentice Hall Inc. Upper Saddle River, NJ. Prosurf Manual. (Accessed: September 13, 003) 001 ASTM Designation C947-99: Standard Test Method for Flexural Properties of Thin Section Glass-Fiber-Reinforced Concrete (Using Simple Beam With Third-Point Loading) West Conshohocken, PA. 001 ASTM C 17-01: Standard Test Method for Density, Relative Density (Specific Gravity), and Absorption of Coarse Aggregate. West Conshohocken, PA. 001 ASTM Designation C39/C 39M-01: Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens. West Conshohocken, PA Winters and Knowles. Discussion regarding KAPER calculations. Lazauskas, Tuck, and Winters kayaks/skmag/skmag.htm (Accessed: September 1, 003) A

13 Appendix B1 Mixture Proportions Mixture Designation: Rib Mix AIR AND CEMENTITIOUS MATERIALS Component Quantity (whether base or batch) Units Air content by volume of concrete AIR: 4. % Portland cement ASTM Type: II c: kg/m 3 Flyash Description: Class C m 1 : 99.0 kg/m 3 Acrylic Description: 46% Solids m : 99.0 kg/m 3 Mass of all cementitous materials cm: 660 kg/m 3 (1) Cement-to-cementitious materials ratio c/cm: 0.70 AGGREGATES Aggregate Base Quantity (SSD aggregates) ASTM C17 BSG (SSD) Agg. Volume (m 3 /m 3 ) Batch Quantity (At stock moisture kg/m3 (unitless) content) kg/m 3 Sand W SSD,1 : W stk,1 : K-1 glass bubbles W SSD, : W stk, :.8 Mighty Mono fibers W SSD,3 : W stk,3 : 1.0 Combined W SSD,agg : W stk,agg : 1 () WATER Water W: 109 w batch : 106 kg/m 3 Volume of acrylic Concrete Coloring x 1 : 1 ml/m 3 x : 0 ml/m 3 Water from acrylic w admx1 : 116 kg/m 3 Water from concrete coloring w admx : 0 kg/m 3 Total of free (surplus) water from all aggregates? w free : -114 kg/m 3 Total water w: 109 w: 109 kg/m 3 (3) Concrete density 93 kg/m 3 Water-to-cement ratio w/c: 0.4 Water-to-cementitious material w/cm: 0.17 B1

14 Appendix B Mixture Proportions Mixture Designation: Finishing Mix AIR AND CEMENTITIOUS MATERIALS Component Quantity (whether base or batch) Units Air content by volume of concrete AIR: 6. % Portland cement ASTM Type: II c: 39 kg/m 3 Flyash Description: Class C m 1 : 84.0 kg/m 3 Acrylic Description: 46% Solids m : 84.0 kg/m 3 Mass of all cementitious materials cm: 60 kg/m 3 (1) Cement-to-cementitious materials ratio c/cm: 0.70 AGGREGATES Aggregate ASTM C17 BSG (SSD) Agg. Volume (m 3 /m 3 ) Batch Quantity (At stock moisture (unitless) content) kg/m 3 Sand W SSD,1 : W stk,1 : 149 K-1 glass bubbles W SSD, : W stk, : 38.3 Mighty Mono fibers W SSD,3 : W stk,3 : 0 Combined W SSD,agg : W stk,agg : 187 () WATER Water W: 9.4 w batch : 11 kg/m 3 Volume of acrylic Concrete Coloring Water from acrylic x 1 : 183 ml/m 3 x : 0 ml/m 3 w admx1 : 98.6 kg/m 3 Water from concrete coloring w admx : 0 kg/m 3 Total of free (surplus) water from all aggregates Σ? w free : -17 kg/m 3 Total water w: 9.4 w: 9.4 kg/m 3 (3) Concrete density 839 kg/m 3 Water-to-cement ratio w/c: 0.4 Water-to-cementitious materials ratio w/cm: 0.17 B

15 Appendix B3 Mixture Proportions AIR AND CEMENTITIOUS MATERIALS Component Quantity (whether base or batch) Units Air content by volume of concrete AIR: 6.4 % Portland cement ASTM Type: II c: 388 kg/m 3 Flyash Description: Class C m 1 : 83. kg/m 3 Acrylic Description: 46% Solids m : 83. kg/m 3 Mass of all cementitious materials cm: kg/m 3 (1) Cement-to-cementitious materials ratio c/cm: 0.70 AGGREGATES Aggregate Base Quantity (SSD ASTM C17 BSG (SSD) Agg. Volume (m 3 /m 3 ) Batch Quantity (At stock moisture aggregates) (unitless) content) kg/m 3 Sand W SSD,1 : W stk,1 : 148 K-1 glass bubbles W SSD, : W stk, : 37.9 Mighty Mono fibers W SSD,3 : W stk,3 : 0 Combined W SSD,agg : W stk,agg : 18 () Water Volume of acrylic Concrete Coloring Water from acrylic Mixture Designation: Color Finishing Mix WATER W: 91.6 w batch : 10 kg/m 3 x 1 : 181 ml/m 3 x : 8.89 ml/m 3 w admx1 : 97.7 kg/m 3 Water from concrete coloring w admx : 0 kg/m 3 Total of free (surplus) water from all aggregates Σ? w free : -16 kg/m 3 Total water w: 91.6 w: 91.6 kg/m 3 (3) Concrete density 83 kg/m 3 Water-to-cement ratio w/c: 0.4 Water-to-cementitious materials ratio w/cm: 0.17 B3

16 Appendix B4 Mixture Proportions Mixture Designation: Lightweight Mix AIR AND CEMENTITIOUS MATERIALS Component Quantity (whether base or batch) Units Air content by volume of concrete AIR:.6 % Portland cement ASTM Type: II c: 0 kg/m 3 Flyash Description: Class C m 1 : 44.0 kg/m 3 Acrylic Description: 46% Solids m : 44.0 kg/m 3 Mass of all cementitious materials cm: 94 kg/m 3 (1) Cement-to-cementitious materials ratio c/cm: 0.70 AGGREGATES Aggregate Base Quantity (SSD ASTM C17 BSG (SSD) Agg. Volume (m 3 /m 3 ) Batch Quantity (At stock moisture aggregates) (unitless) content) kg/m 3 Sand W SSD,1 : W stk,1 : 34 K-1 glass bubbles W SSD, : W stk, : 8.1 Mighty Mono fibers W SSD,3 : W stk,3 : 6.03 Combined W SSD,agg : W stk,agg : 98 () WATER Water W: 48.4 w batch : 04 kg/m 3 Volume of acrylic Concrete Coloring Water from acrylic x 1 : 9.7 ml/m 3 x : 0 ml/m 3 w admx1 : 1.7 kg/m 3 Water from concrete coloring w admx : 0 kg/m 3 Total of free (surplus) water from all aggregates? Σ w free : -07 kg/m 3 Total water w: 48.4 w: 48.4 kg/m 3 (3) Concrete density 640 kg/m 3 Water-to-cement ratio w/c: 0.4 Water-to-cementitious materials ratio w/cm: 0.17 B4