The Clemson Concrete Canoe Team is ready to Cast Away National Concrete Canoe Competition June 18-20, 2004 Washington, D.C.
Table of Contents Executive Summary i Hull Design 1 Analysis 2 Development and Testing 3 Construction 5 Project Management 5 Organizational Breakdown Structure 6 Project Schedule 7 Form Design Drawings and Bill of Materials 8 Canoe Design Drawings and Bill of Materials 9 Final Mixture Proportions B-1 Patch Mixture Proportions B-2 Orange Concrete Mixture Proportions B-3 Executive Summary After nine months of resourceful and creative work, The Clemson Concrete Canoe Team (3CT) returns to the National Concrete Canoe Competition (NCCC) with Cast Away. This fast and maneuverable canoe, described in Table I, is constructed of an ultra thin lightweight concrete composite, reinforced with polypropylene mesh and pretensioned polyethylene tendons. Clemson University is located in the foothills of western South Carolina. Founded in 1889, Clemson University is a public, land grant university of approximately 14,000 undergraduate and 3,000 graduate students. The department of civil engineering is comprised of 320 undergraduate, 80 graduate students and 19 faculty members. The Clemson Concrete Canoe Team is comprised of 24 students and a faculty advisor. 3CT has claimed the Carolinas Conference title in the concrete canoe competition every year since 1993. These regional titles have led to births in the NCCC where the team has won three national titles ( 99, 00, and 02) and has seven other top ten finishes. This year s canoe is the product of innovative construction, meticulous planning, and continuous attention to detail. The hull design has been optimized for straight line speed and maneuverability while being tailored to the strengths of the paddlers. New methods of structural analysis have decreased the likelihood of cracking in the chines. A new lightweight concrete mix is a combination of lightweight aggregates and discrete fibers designed to give Cast Away flexibility and strength (Table II). This new, lighter weight concrete mix also helped the team to reduce the weight of this year s canoe by 39 lbs (17.7 kg). The development of a new encasing construction method helped reduce the amount of time sanding and patching by 15% compared to 3CT s 2003 project. The team used time lapse photography during construction to document this new method for next year s team. A new bar coding system was integrated to monitor construction hours. These new construction and project management techniques have made this year s team ready to Cast Away from the competition. Table II: Concrete Properties English SI ASTM Standard Concrete Unit Weight 50.2 lbs/ft^3 804.1 kg/m^3 C 138 28 day Concrete Compressive Strength 1289 psi 8.89 MPa C 109 28 day Concrete Flexual Strength 409 psi 2.82 MPa C 78 28 day Cast Away Table I: Canoe Dimensions Length: 21.4 ft (6.5 m) Weight: 137 lb (62.1 kg) Thickness: 0.4 in. (1.02 cm) Depth: 12 in. (30.5 cm) Beam at Gunwale: 29 in. (73.7 cm) Beam at Waterline: 26 in. (66.0 cm) Color: Dark Green i
Hull Design To develop a hull design for this year s concrete canoe, many factors were taken into account. The straight-aways require the speed of a sprint canoe; yet the slalom course and buoy turns require the maneuverability of a whitewater canoe. After examining last year s canoe, Main Course, and its results in each race, 3CT determined that there was not one optimum design for a canoe but rather many good designs tailored to the strengths of the paddlers. 3CT s first step in developing a new hull design for Cast Away was to gather input from last year s paddlers regarding which hull characteristics were most important. The team determined speed and maneuverability to be most important due to the different requirements of the races. However, these goals could not be obtained if the paddlers were not able to perform in an efficient manner. Last year s paddlers suffered in the four person race when the middle two people were not able to easily reach the water for efficient strokes. Therefore, 3CT decided the beam and freeboard needed to be reduced, while the stability needed to be increased from last year s canoe. For the team to maintain the speed of previous canoes, the drag on the canoe needed to be reduced. The paddlers also expressed concern about stability and the lack of sufficient stability in rough water could be disastrous for this year s team. To meet these goals the team used a hull design software program. The program worked by using an optimization of design to create hull designs based on user inputs of length, beam, and draught. The team analyzed 26 different sets of parameters and selected a hull design producing slightly less drag than the previous year s canoe (Figure 1). The beam of Cast Away is also less than that of Main Course allowing the paddlers a greater range of motion (Figure 2). Upon closer examination this design is very similar to the design used by 3CT in 2000. After discovering this, team leaders examined the old form from 2000 and Total Drag (lb) Depth (in) 6 5 4 3 2 1 0 decided making modifications to it would reduce the cost of the project and give 3CT more flexibility in scheduling successive events. This design also allowed 3CT to increase speed without reducing maneuverability, thus improving upon last year s canoe. The team modified the length and freeboard of the old form to create Cast Away. Maneuverability in the canoe was maintained with 2.5 in (63.5 mm) of rocker in the bow and 1.5 in (38.1 mm) of rocker in the stern. The canoe s flatter bottom maintains maneuverability and increases stability at the beginning of the races. Cast Away, based on an old but modified hull design, will carry 3CT through the National Concrete Canoe Competition. 200 180 160 140 120 100 80 60 40 20 0 Main Course Cast Away 0 5 10 15 20 25 30 35 Speed (ft/sec) Figure 1: Total Drag of Cast Away vs. Speed Cast Away Main Course 0 5 10 15 Width (in) Figure 2: Comparison of Beams Below Waterline Cast Away 1
Analysis After the completion of the hull design, the team needed to establish the structural and material design requirements required to construct a canoe that would not exhibit excessive cracking under anticipated loading conditions and travel conditions. The target values for the concrete mix and composite section were established after determining the most severe loading conditions that Cast Away will undergo and the stress caused by these loadings. A concrete canoe undergoes two types of loading conditions, a static condition and a dynamic condition. Each of these conditions causes different stresses on the canoe. Under a static condition, the canoe is sitting in the water and the paddlers are in position. 3CT used a spreadsheet structural model to determine the maximum shear and moment the canoe will undergo during this condition. The paddlers were treated as 180 lb (68.04 kg) loads and each paddler was assumed to be three feet from their respective end of the canoe for the static condition. Each paddler was assumed to be a point load. The self weight of the canoe and the buoyancy of the water along the length of the canoe were calculated at one inch intervals and used in the structural model. The structural spreadsheet allowed the team to determine the maximum moment to be 694.3 ft-lbs (941.3 N- m) and a maximum shear of 166.7 lbs (741.5 N) when only two paddlers were in the canoe. The values were used as design loads in the concrete design program CONCAD. When using the program the thickness of the canoe was considered to be 0.4 in. (10.16 mm) with each layer of concrete being 0.0625 in. (1.59 mm) thick based on constructability considerations. The team used an iterative process of increasing the minimum strength of the concrete until the maximum moment would not cause failure in the canoe. This process yielded a concrete with a minimum compressive strength of 1000 psi (6.89 MPa), prior experience compelled the team to use a minimum flexural strength of 400 psi (2.76 MPa). Next, the dynamic loading conditions the canoe will undergo were examined. The team outfitted an old concrete canoe with strain gages at nine locations and had two paddlers use the canoe for practice. The two male paddlers were seated at their normal locations and went through the endurance and sprint courses four times each. The strain gages revealed the paddlers apply almost 72% of their weight to the areas under their knees during turns. The information from the strain gages was also used to calculate the stress by testing the modulus of elasticity of the concrete in the old canoe. The maximum stress was determined to be 362 psi (2.50 MPa). 3CT multiplied this value by a factor of safety of 1.6 to yield a minimum composite first crack strength of 600 psi (4.14 MPa). Lastly, 3CT used a finite element analysis (FEA) to model the canoe and the loading conditions it will undergo in a static condition. The team modeled the canoe in SAP 2000 using 512 shell elements of 0.4 in thick concrete with a compressive strength of 1000 psi (6.89 MPa) and maximum hydrostatic forces calculated from the spreadsheet structural model. As seen in figure 3, the FEA yielded a maximum stress of approximately 307 psi (2.12 MPa). Each paddler s weight was evenly distributed to 1.5 ft^2 (0.14 m^2) on the interior of the canoe and the canoe was assumed to be on two directional roller supports at one foot increments. One pin support was placed at the stern of the canoe to stabilize the structure. The FEA results verified the canoe to be structurally sound in a static loading condition. Figure 3: Results of FEA for the Bow of Cast Away Cast Away 2
Development and Testing After determining the minimum structural requirements for the concrete and composite sections, 3CT examined the constructability of Main Course. This allowed the team to determine other characteristics of the concrete mix that needed to be addressed. In order to reduce delamination cracking in the chines, 3CT needed to develop a mix with greater usability. The team also wanted to reduce the unit weight of the concrete and increase the flexural strength while maintaining workability to allow for faster construction. Concrete Mix Design Research on the concrete mix design was divided into three phases; this allowed the team to develop the optimum mix design for Cast Away. In each phase of concrete research, the team utilized standard tests. Compressive strength was measured with 2 inch (50.8 mm) cubes in accordance to ASTM C109. Flexural strength was determined according to ASTM C 78 by applying a load at the third points of an 8 in. (203.2 mm) long, 1.25 in (31.8 mm) wide, and 2 in. (50.8 mm) deep beam. Shrinkage was evaluated based on ASTM C157 by measuring the shrinkage strains of unrestrained prisms over a period of 28 days. Workability was assessed qualitatively while usability was measured in minutes. Phase one began by determining the optimum blend of glass bubbles for a lightweight concrete mix. Although, 3CT has used glass bubbles in previous years, the team wanted a new combination that would permit a lower unit weight. Since unit weight and strength are correlated, the team had to determine a suitable tradeoff between strength and unit weight. After evaluating over 40 different blends involving 6 types of glass bubbles with varying specific gravity (SG), size, and crush strength, the team chose a combination of K25 bubbles (SG=.25) and S32 (SG=.32) bubbles. The base mix had unit weight of 59.5 lbs/ft^3 (845.1 kg/m^3) and compressive strength of 1664 psi (11.5 MPa) and a flexural strength of 311 psi (2.14 MPa). This base mix was used as the control for all of the remaining tests. Next, two types of fly ash were tested. Mixtures containing class C and class F fly ash were tested at 28 days. The team selected the class C fly ash for its light gray color since there was no substantial difference in compressive or flexural strength and workability was constant between the two types of fly ash. Phase two involved evaluating the effects of polymer based binders. Each latex was tested for its effect on compressive and flexural strength, usability, workability, and unit weight. All three latexes tested reduced the compressive strength of the base mix, but the increase in flexural strength off-set this slight reduction. While all three latexes increased workability drastically; L2 had a much shorter pot life than L1 and L3. Using the weighted scoring table below (Table 1), the team selected L1 because of its increase of 262.8% in flexural strength, and its reduction of unit weight by 17.1% over the base mix. Phase three of the concrete research included the selection of fibers and admixtures for the mix. 3CT evaluated four polypropylene fibers and chopped carbon fibers. The fibers were used to increase the flexural strength of the mix by bridging micro-cracks and redistributing internal strains in the concrete. During testing, team leaders decided to limit the amount of fibers due to constructability concerns. The fibers make the individual layers of concrete difficult to work with and limiting the amount of fibers was important in reducing construction time. The fibers were tested at various percents of binder weight. Carbon fibers were found to increase the Table 1: Comparison of Latex Properties % increase over base mix (tested at 15% Cementious Material) Latex Designation Compressive Strength Flexural Strength Unit Weight Usability Score L1-18.3 262.8-17.1 28.0 101.4 L2-25.0 219.3-18.0-17.0 75.7 L3-23.1 258.6-18.3 8.0 95.5 Factor Weight 0.2 0.4 0.25 0.15 Cast Away 3
ultimate flexural strength of the concrete while the polypropylene fibers were used to increase the post-peak performance (Figure 4). The best polypropylene fiber (PF) was integrated with the carbon fiber (CF) at the most effective ratio (1:5.4 CF to PF) in the final mix. Next, the team tested a high range water reducer, a super plasticizer, and a shrinkage reducing admixture (SRA). With the addition of latex to the mix the super plasticizer was not needed for workability. The water reducer was not used because of lower strengths in the concrete during testing. 3CT tested the effect of the SRA on unrestrained prisms using ASTM C157 for 28 days. The team determined the reduction in shrinkage during the first 14 days of curing by the SRA would help reduce the chance of shrinkage cracking. The only admixture used in the final mix was a SRA. When combined with the shrinkage reducer, latex and fibers, the final mix a unit weight of 50.2 lbs/ft^3 (804.1 MPa) compressive strength of 1289 psi (8.89 MPa) a flexural strength of 409 psi (2.82 MPa) and a shrinkage strain of 0.003 in/in (0.076 mm/mm). These characteristics helped to produce a canoe that is 39 lbs (13.2 kg) lighter than last year. Reinforcement Testing of reinforcement began with the evaluation of six types of reinforcement: three types of polypropylene (PP) meshes, carbon fiber mesh, fiberglass mesh, and hardware cloth. 3CT needed a mesh reinforcement to cover the entire canoe, as well as individual strands of reinforcement in the gunwales. First the team obtained literature from manufacturers regarding each type of reinforcement. This eliminated the carbon fiber mesh because the potential gain in strength did not off set the high cost when compared to the polypropylene mesh. Next, each mesh was tested for in plane bending using ASTM C293 on specimens 0.4 in. (10 mm) deep, 3 in. (76 mm) wide, and 12 in. (305 mm) long. This test eliminated the hardware cloth and fiberglass mesh due to significantly lower strengths. Next, the team tested eight different schemes of polypropylene meshes. Each scheme contained three layers of reinforcement and four layers of concrete to simulate the canoe Load (lbs) 200 160 120 80 40 Carbon Fiber Polyproplyene 0 0 0.1 0.2 0.3 0.4 Deflection (in) Figure 4: Load Deflection Curve for Fibers composite. These schemes were tested for inplane bending and the two strongest schemes, based on in-plane bending, were tested for out-ofplane bending (Table 2). Next, the effect of pretensioned tendons placed in the gunwales and above the neutral axis of the canoe were tested using polyethylene and carbon fiber tendons. Pretensioning was evaluated using ASTM C1018 on beams 3 in. (76 mm) deep, 1 in. (25 mm) wide, and 10 in long (254 mm) with four pretensioned strands. Although samples containing carbon fiber produced slightly higher flexural strengths, carbon fiber was not used due to constructability problems. An increase in the pretension force in each strand resulted in an increase in composite strength; however more than 40 lbs (177.9 N) caused the strands to move out of place during construction. The final reinforcement scheme contains twelve pretensioned polyethylene strands, each with 40 lb (177.9 N) of force, spaced 0.5 in (13 mm) apart in alternating layers within the inner two concrete layers. When integrated with the pretensioned tendons, the reinforcement gives the final composite a first crack flexural strength of 645 psi (4.45 MPa) and an ultimate composite flexural strength of 1289 psi (8.89 MPa), both meeting the team s criteria. Table 2: Comparison of Reinforcement Schemes Flexural Strength of Composites (psi, MPa) Scheme In-Plane Out-of-Plane Composite Scheme 1 92.5 (0.63) 258.2 (1.78) 1289 (8.89) Scheme 3 83.5 (0.57) 219.3 (1.51) 1023 (7.05) Cast Away 4
Construction As the research portion of the project neared completion in December, the team prepared for the construction phase of the project. To place this year s canoe, the team developed a new encasing method of construction. The new method allows the interior and exterior of the canoe to be formed instead of sculpted. The male form was patched in low spots and the inlayed letters were applied. The female form was constructed from sheets of acrylic, which were heated in an oven built by the team and molded to the desired shape. Small holes were drilled in the acrylic to allow the concrete in high spots to seep out. Next, the male form was covered with a 0.4 mil plastic to act as a release agent. The female form was sprayed with an oil based release agent for ease of form removal. In preparation for construction, the dry parts of the concrete mix were prepackaged to reduce construction time. During construction, quality control was maintained by the batch coordinator overseeing each batch of concrete. Alternating layers of concrete and reinforcement were placed by hand on the male form. Twelve pretensioned polyethylene strands were placed in the middle two layers of concrete along the gunwales of the canoe (Figure 5). A 40 lb (177.9 N) force in each tendon was kept constant by measuring the extension of a calibrated spring attached to the end of each tendon and a turnbuckle. Once the fourth layer of concrete was placed, the female form encased the new concrete. This caused concrete in high areas to seep out or fill low spots. This new construction method reduced sanding and patch by 15% and construction time was reduced by 1.25 hours. The next day, the acrylic form was removed and the canoe was covered with a polyethylene sheet. To help prevent shrinkage cracking due to rapid water loss, the canoe was sprayed with water twice a day for 7 days. After curing, the exterior of the canoe was sanded and patched. Once the exterior began to take shape the canoe was removed from the form and the interior was sanded and patched. Two coats of concrete sealer were applied according to manufacturer s recommendations. Lastly, vinyl decals were applied to complete 3CT s Cast Away. Project Management Completing a project with the magnitude of the concrete canoe, on time and under budget requires detailed planning, constant communication, and comprehensive documentation. At the beginning of August, two project managers were selected based on experience and knowledge. The project managers established a new organizational breakdown structure (OBS) seen in Figure 6. Team leaders were assigned to the major parts of the project and other members were assigned based on their area of interest. A new documentation division was established to develop a bar coding system, used to keep track of construction hours and time lapse photography was used to document construction techniques. All team members were active in multiple areas to ensure each person was knowledgeable of all aspects of the project. Next, the project managers worked with the team leaders to establish a work breakdown structure (WBS). The WBS represented every component of the project hierarchically in increasing detail. Individual activities in the WBS were treated as work packages and incorporated into the schedule shown in Figure 7. The team leaders were responsible for providing weekly progress reports and completing their work packages on time according to the schedule. This type of management structure ensured all tasks were completed on time and no task was left out. This structure helped team leaders to estimate the number of days and labor-hours necessary to complete each work package on time (Figure 7). After developing the schedule from the individual work packages, the critical path activities and major milestones were noted in red in Figure 7. After all the critical path activities were completed on time, this Cast Away was ready to set sail for the competition Figure 5: Encasing Construction Method Female Form Concrete Polypropylene Reinforcement Pre-tensioned - Polyethylene tendon Male Form Cast Away 5
Project Manager Kyle Farley Project Manager Ben Williams PM in Training David Hostetler Paddling Scott Horton Documentation Chrissy Sloyer Research Hayes Jones Construction Matt Goodner Trainer Scott Horton Presentation Chrissy Sloyer Strain Gages Oner Balaban Forms Ben Williams Paddlers Chrissy Sloyer Tara Pagano Regan Moseley Kelly Crawford Lindsey Koeper Kyle Farley Scott Horton Matt Goodner David Hostetler Josh Grein Seth Dean Daniel Perry Paper Kyle Farley Graphics Tara Pagano Bar-coding and Time Lapse Photography Arman Amirkhanian Finite Element Analysis Kyle Farley Concrete Mix David Hostetler Reinforcement Josh Grein Placement Seth Dean Finishing Matt Goodner Cross-Section Michael O Dell Consultant Mary-Halis Alkis Schedule October McConnell Engineer Notebook Kelly Crawford Figure 6: Organizational Breakdown Structure Consultant Brad Putman Project Managers Team Leaders Activity Coordinators Coordinated Team Leaders, managed team finances, developed schedule Responsible for Activity Coordinators Managed and responsible for completing activities on time Cast Away 6
Component Air content by volume of concrete Cement (plain), Other cementitious material 1 Air and Cementitious Materials Quantity (whether base or batch) ASTM Type: I White Description: Class C Fly Ash Other cementitious material 2 Description: Polymer Soilds in FX 338 Other cementitious material 3 Other cementitious material 4 Description: Description: Mass of all cementitious materials cm: 344.2 Cement to cementitious materials ratio Aggregates/Fibers TABLE II.B.1.-SUMMARY OF MIXTURE PROPORTIONS MIXTURE DESIGNATION: FINAL MIX c /cm : 0.70 AGGREGATES /FIBERS Base Quantity (SSD aggregates) (kg/m3) ASTM C127 BSG (SSD) (unitless) Agg. Volume Units 24.23 % 241.0 51.6 51.6 1. Ottawa Sand W SSD,1 : 175.19 2.65 0.066 W stk,1 : 175.19 2. K25 Glass Bubbles W SSD,2 : 46.45 0.25 0.186 W stk,2 : 46.45 3. S32 Glass Bubbles WSSD,3: 59.46 0.32 0.186 Wstk,3: 59.46 4. Carbon Fibers W SSD,4 : 0.52 2.9 0.0002 W stk,4 : 0.52 5. Polypropylene Fibers WSSD,4: 3.10 0.91 0.003 Wstk,4: 2.59 Combined W SSD,agg : 284.21 W stk,agg : 284.21 (m 3 ) Batch Quantity (At stock moisture content) WATER Water W: 172.1 Wbatch : 108.4 Vol of admixture #1 Shrinkage Reducer X 1 : 3.10 Vol of admixture #2 X 2 : Vol of admixture #3 X 3 : Vol of admixture #4 X 4 : Water from admixture #1 Wadmx,1: 3.10 Water from admixture #2 Water from FX 338 Wadmx,2: 60.61 Water from admixture #3 Wadmx,3 : Water from admixture #4 Wadmx,4 : Total of free (surplus) water from all Σw : free aggregates Total water W: 172.1 w: 172.1 Concrete density 800.61 Water to cement ratio w /c : 0.71 Water to cementitious material w /cm: 0.50 Cast Away B-1
Component Air content by volume of concrete Cement (plain), Other cementitious material 1 Air and Cementitious Materials Quantity (whether base or batch) ASTM Type: I White Description: Class C Fly Ash Other cementitious material 2 Description: Polymer Soilds in FX 338 Other cementitious material 3 Other cementitious material 4 Description: Description: Mass of all cementitious materials cm : 341.4 Cement to cementitious materials ratio TABLE II.B.1.-SUMMARY OF MIXTURE PROPORTIONS MIXTURE DESIGNATION: PATCH MIX c/cm: 0.70 AGGREGATES/FIBERS Units 25.45 % 239.0 51.2 51.2 Aggregates/Fibers Base Quantity ASTM Agg. Batch Quantity (SSD aggregates) C127 Volume (At stock (kg/m3) BSG (SSD) (m 3 ) moisture content) (unitless) 1. Ottawa Sand W SSD,1 : 173.77 2.65 0.066 W stk, 1 : 173.77 2. K25 Glass Bubbles W SSD,2 : 46.07 0.25 0.184 W stk, 2 : 46.07 3. S32 Glass Bubbles W SSD,3 : 59.98 0.32 0.184 W stk, 3 : 59.98 4 5 W SSD,4 : W SSD,4 : W stk, 4 : W stk, 4 : Combined W SSD,agg : 279.82 W stk, agg : 279.82 WATER Water W: 170.7 Wbatch : 110.6 Vol of admixture #1 X 1 : Vol of admixture #2 X 2 : Vol of admixture #3 X 3 : Vol of admixture #4 X 4 : Water from admixture #1 Water from FX 338 Wadmx,1 : 60.1 Water from admixture #2 Wadmx,2: Water from admixture #3 Wadmx,3 : Water from admixture #4 Wadmx,4 : Total of free (surplus) water from all aggregates Σw : free Total water W: 170.7 w: 170.7 Concrete density 791.92 Water to cement ratio w/c: 0.72 Water to cementitious material w/cm : 0.50 Cast Away B-2
Component Air content by volume of concrete Cement (plain), Other cementitious material 1 Air and Cementitious Materials Quantity (whether base or batch) ASTM Type: I White Description: Class C Fly Ash Other cementitious material 2 Description: Polymer Soilds in FX 338 Other cementitious material 3 Other cementitious material 4 Description: Description: Mass of all cementitious materials cm: 421.4 Cement to cementitious materials ratio Aggregates/Fibers TABLE II.B.1.-SUMMARY OF MIXTURE PROPORTIONS MIXTURE DESIGNATION: ORANGE CONCRETE MIX c /cm: 0.70 AGGREGATES/FIBERS Base Quantity (SSD aggregates) (kg/m3) ASTM C127 BSG (SSD) (unitless) Agg. Volume Units 22.94 % 295.0 63.2 63.2 1. Ottawa Sand W SSD,1 : 214.89 2.65 0.081 W stk,1 : 214.89 2. S32 Glass Bubbles W SSD,2 : 95.86 0.32 0.299 W stk,2 : 95.86 3 4 5 W SSD,3 : W SSD,4 : W SSD,4 : W stk,3 : W stk,4 : W stk,4 : Combined W SSD,agg : 310.75 W stk,agg : 310.75 (m 3 ) Batch Quantity (At stock moisture content) WATER Water W: 210.73 Wbatch: 136.52 Vol of admixture #1 Orange Pigment X 1 : 18.59 Vol of admixture #2 X 2 : Vol of admixture #3 X 3 : Vol of admixture #4 X 4 : Water from admixture #1 Wadmx,1: 0 Water from admixture #2 Water from FX 338 Wadmx,2: 74.21 Water from admixture #3 Wadmx,3 : Water from admixture #4 Wadmx,4 : Total of free (surplus) water from all aggregates Σw : free Total water W: 210.73 w: 210.73 Concrete density 961.47 Water to cement ratio w/c : 0.81 Water to cementitious material w /cm: 0.50 Cast Away B-3