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University of Toronto 2007 Ecto-2 Concrete Canoe Team bluenose concrete canoe team university of toronto 2008

BLUENOSE - technical report

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Page 1: BLUENOSE - technical report

University of Toronto 2007

Ecto-2

Concrete Canoe Team

bluenoseconcrete canoe team

university of toronto 2008

Page 2: BLUENOSE - technical report

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Founded in 1827, the University of Toronto, located in the heart of downtown Toronto, has grown into Canada’s leading research uni-versity. With over 4,300 undergraduate engineers enrolled in more than 9 engineering disciplines, and an overall enrollment of over 65,000 students, the University of Toronto is also the largest univer-sity in Canada. Our team mirrors this diversity by accepting mem-bers from all disciplines, as well as other faculties to comprise our dedicated membership of over 30 students.

This year will mark the 34th anniversary of the American National Concrete Canoe Competition and the 14th year of the University of Toronto Concrete Canoe Team’s participation in the Canadian re-gional contest (CNCCC). Prior to Ecto-2’s 5th place finish in Kings-ton last year, the team has placed 6th, 5th and 3rd in the past three years and better before that.

With a thorough review of our past performances and a stronger focus on innovation, surface finish and materials science, we look to revive our winning tradition with this year’s hull design optimiza-tion algorithms and ductile pseudo-strain hardening concrete com-posite. The aesthetics of the canoe was also strongly considered, with the choice to replace stain with integrally coloured concrete. A white canoe with blue accents was chosen to mirror the colours of the University of Toronto and fit the selected theme.

Excelling in innovative design and analysis using hydrostatics and FEA software along with a rigorous mix design program, unparal-leled by previous years, the University of Toronto presents Blue-nose, the 2008 University of Toronto Concrete Canoe.

execut�ve summary

Bluenose

Length 5.9 m Maximum Width 79 cm Maximum Depth 31 cm Weight 45 kg Nominal Hull Thickness 9.5 mm

Material Properties

Composite Flexural Strength 9.1 MPa Modulus of Elasticity 1.5 GPa Layers of Carbon Fiber 3 Unit Weight 760 kg/m3

Core Mix Compressive Strength 12.2 MPa Flexural Strength 4.6 MPa Modulus of Elasticity 1.5 GPa Unit Weight 610 kg/m3 Fiber Mix Compressive Strength 12.7 MPa Flexural Strength 5.5 MPa Modulus of Elasticity 2.0 GPa Unit Weight 800 kg/m3 Pigment Mix Compressive Strength 12.5 MPa Flexural Strength 4.8 MPa Modulus of Elasticity 1.7 GPa Unit Weight 790 kg/m3

table of contentsExecutive summary ..................................................................................................................................... ihull design ..................................................................................................................................................1Analysis........................................................................................................................................................2development and Testing .............................................................................................................................3Project management and Construction ........................................................................................................5Organization Chart .......................................................................................................................................7Project schedule ...........................................................................................................................................8mold model .................................................................................................................................................9Canoe model ..............................................................................................................................................10Appendices

A – references ...................................................................................................................................A1b – mixture Proportions ....................................................................................................................b1C – gradation Curves and Tables ......................................................................................................C1

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hull des�gnOverv�ew

Concrete canoe design at the University of Toronto has historically relied primarily on the experience of the designers, and trial and error. Over the past few years, efforts have been made to move towards a more rational and quantitative method of design that allows for optimization of the canoe for speed, maneuverability, and stability. One of the crowning achievements of this year’s hull design team was to create a new canoe design with the aid of new in-house automated design software.

Shape Generat�on and Model�ng

The task of producing the ideal hull design is a mul-tivariate optimization problem. As with any optimi-zation problem, the input variables and performance function needed to be defined first. It was decided that the most relevant variables were the defining geometrical parameters of the canoe: the length, width, depth, rocker, and shape parameters. In order to define a scalar performance function, the major factors that affect the performance of a canoe were identified: speed, tracking, turning, and stability. These characteristics were quantified by variables such as low-speed resistance, leak angle, depth of freeboard, and prismatic coefficient. These quanti-ties were then normalized and weighted in order to establish an optimizing function that produced an overall measure of merit using the individual fac-tors. Weightings were based on the priorities of the paddling team; for example, turning was preferred over tracking.

A computer program, created in C++, was used to test potential designs using the aforementioned in-puts and outputs. The use of bezier splines for the curves allowed the program to test a wide variety of canoe shapes, and combined with estimated weights and material properties, it could extract necessary hydrostatic information, such as draft. In order to estimate drag, speed curves were used, which al-lows for much faster analysis than using more in-tensive computational fluid dynamics calculations.. The program then used an iterative search method to analyze canoes generated over defined input

ranges such as designs between 5 and 6 metres in length. Over one million canoes were analyzed in this manner. The design with the highest value in the objective function formed the basis for the hull design of Bluenose.

F�nal Outcome

The design features of Bluenose are catered for structural strength, paddler comfort, and excellent performance in the water. Using the in-house de-sign software, the hull design team defined prefer-ences via the objective function, with corresponding changes in the design. For example, the preference for stability resulted in a wide canoe with a maxi-mum width of 79cm. Optimized for reduced drag, the new design approaches the maximum limit at a length of 5.9m. The cross section is a boxy “U” shape with a depth of 31cm, ensuring a freeboard of at least 13cm in all load cases. This should im-prove stability and paddler comfort, which was a major failing point of previous designs. According to the analysis results, moderate rocker provided an optimal tradeoff of speed and stability for maneu-verability. The design has made improvement in re-ducing surface area, and thus weight. Bluenose has its centre of mass towards the stern, allowing for a sleeker profile, while also reducing drag. While the automated software considerably assisted in the design, it is important to note that the direction of the design was ultimately in the hand of the design team, guided by experience with past designs.

Certain features were designed without the analysis software. gunwales and ribs were inserted into the design both for aesthetics as well as for structural reinforcement. The placement of the ribs was based on past experience, with consideration in balancing the paddler loads. The hull is 11mm thick, except for the gunwales and ribs which are 25mm thick. There are four ribs, each 38mm wide, distributed symmetrically about the centre of buoyancy. The design team is confident that we have created in Bluenose, a sturdy, steady, and streamlined canoe which is capable of taking the top prize in the com-petition.

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F�n�te Element Analys�s

Accurate boundary conditions were essential for a useful finite element analysis (FEA). The results of an analysis are typically presented with a high de-gree of precision, and are meaningless if the basic assumptions about restraint behavior are flawed. One popular means of analysis is to restrain the ends of the canoe and apply forces to its body. however, this assumes that the endpoint posi-tions remain fixed relative to one another, which is not necessarily the case. rather, the proper boundary conditions should contain no such restraints at all.

A floating canoe is in a state of equilibri-um; the buoyant force of the water must perfectly counteract the gravity load of the canoe and its paddlers. In reality, readjustment of this equilibrium oc-curs by the waterline rising or fall-ing as paddlers enter and exit the canoe. Thus, to mimic the actual behavior of a canoe in water, it is necessary to know the equilib-rium position of the waterline, or draft. This information was obtained using the in-house software for hydrostatic calculations for all loading cases. given a waterline, the forces applied to the hull consist of a pressure gradient below the wa-terline, gravity acting on the canoe itself, and paddler loads. These forces will be in equi-librium.

Modell�ng

The program COs-mOsWorks (solid-Works Corp. Concord, mA) was used to per-form the FEA. The ca-

noe hull was modeled using shell el-ements of two different thicknesses, representing the main body and the ribs/gunwales. The use of shell el-ements rather than solid elements greatly increased computational effi-ciency and the accuracy to which the analysis could be conducted.

Paddler loads were modeled as cir-cular distributed loads. since numeri-cal rounding errors cause the forces to be slightly out of equilibrium, inertial relief was used to stabilize the model for analysis. since the loads in question are relatively small a linear analysis was conducted. It was assumed that the reinforcement in the concrete could be taken to be smeared throughout the shell, thus treating it as a homogeneous spheri-cally isotropic linear elastic material. since accurate stiffness values for the con-crete were not available for the analysis, the results obtained are accurate only with respect to stresses incurred, not displace-

ments. Overall displacements are expected to be small, so this is not a large concern.

Results

Analysis was performed for each of the load cases: 2, 3, and 4 paddlers, and other special con-

siderations, including cases where a paddler does not kneel on the ribs (loads placed adjacent to the

ribs). The failure criterion for the concrete is ex-pected to be the maximum principle tensile stress that exceeds the cracking stress of the concrete (9.1 mPa for the composite). According to the analyses, the maximum tensile stress incurred is 3.78 mPa in the 3-person load case given kneeling off the ribs. This corresponds to a minimum factor of safety of 2.4. If four paddlers kneel on the ribs, the maximum stress is 1.55 mPa (Figure 1), for a factor of safety of 5.9. In all cases, the stresses are highly localized under the paddlers’ knees; these stresses can be mitigated by having the paddlers kneel on blocks to better distribute their weight.

analys�s

Fig-u r e

1: 4-paddler

l o a d -ing case

— Max. prin-cipal stress on

inner surface.

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development and test�ngOverv�ew

The concrete mix design began with last year’s mix as a baseline. A large proportion of our research this year was focused on improving the ductility of our concrete composite to reduce crack propagation and increase the durability and the amount of energy the composite can absorb before failure. by com-bining this year’s new research with developments and experience from previous years, we were able to develop a novel ultra-low density pseudo-strain hardening reinforced concrete composite.

New Rules

Our aggregate selection consisted of foamed glass spheres (0.25-0.5mm) and hollow glass micro-spheres (25-90μm), was based on results from pre-vious years. Changes in rules this year removing the requirement to meet the ASTM C33 fine ag-gregate gradation allowed us to remove the larger sizes of aggregates used in previous years (greater than 0.5mm). The removal of the coarser aggregate made our baseline mix almost twice as strong as last year (2.4 vs. 4.1 mPa). We were also able to cast much thinner layers (2.4mm) than in previous years. The reduced layer thickness translated into a thinner canoe and a reduced overall weight: 45kg this year compared to 72kg last year.

Test�ng

during each phase of research and development, trial mixes were cast into 5.1 x 5.1 x 30.5cm prisms or 1.2 x 6 x 40cm thin beams and cured for 28 days at 90% relative humidity. Once cured the beams were tested in flexure in a three point bend deter-mine flexural strength and estimate the flexural stiffness based on AsTm C293 [1] and C947 – 03 [2] for the prisms and thin beams, respectively. Four beams were tested for each trial mix. After the mixes for use in the canoe were selected, the com-pressive strength of the concrete was measured by testing 52mm cubes in compression as per AsTm C109 [3]. displacement rate for all tests was at a 1mm/min. Air content was measured gravimetrical-ly. The selected aggregates, binders, fibers and ad-mixtures were mixed in various proportions to de-

velop the final Bluenose mixture. Optimal flexural strength, density and ductility was obtained using a binder composed of 84 wt% type 10 white Portland cement, 15 wt% metakaolin and 1 wt% colloidal silica nanoparticles, and modified with an acrylic polymer latex admixture. Air entrainer and hrWr were added at the recommend dosage.

Polymer Mod�ficat�on

during testing this year, it was found that incorpo-rating an acrylic latex admixture at 35% by weight of cementicious materials provided a significant improvement in flexural strength (4.1 vs. 4.6 MPa), ductility and workability while also reducing den-sity (20% reduction).

Figure 2 shows a scanning electron micrograph of a fracture surface etched in 25% hydrofluoric acid for 1hr to dissolve the inorganic This procedure made it possible to visualize the microstructure of the or-ganic polymer film and determine the effect of the acrylic latex polymer modifier. Wagner suggested that the sub-micron sized polymer particles coalesce to form a continuous film over the cementicious material [4]. Isenburg and Vanderhoff have shown that this interpenetrating polymer network reduces the formation of microcracks during curing and can reduce microcrack propagation [5]. The coalesced polymer film surrounding the hydrated cement can be seen in figure 2. The increased strength measured is attributed to the reduced number of microcracks and impeded crack propagation.

Figure 2: Scanning electron micrograph of concrete frac-ture surface etched in HF showing polymer film morphol-ogy and microcrack bridging by polymer fibrils.

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based on the work of beeldens et al. a two-step cur-ing process was used too promote the formation of an interpenetrating polymer network encompassing the cementicious particles [6]. First, the concrete was moist cured for 28 days to hydrate the cement, forming the hydrated calcium silicate network with-out coalescing the polymer film. The moist cure was followed by a drying phase after the cement hydration is nearing completion where the polymer film coalesces around the cement particles forming a continuous interpenetrating network.

Secondary Re�nforcement

Last year’s mix design incorporated ultra high molecular weight polyetheylene fibers (UHM-WPE, dyneema). The research conducted last year showed that out of the eight types of high stiffness and high strength fibers tested, Dyneema provided the greatest improvement in flexural strength (20%) while also being the lowest density fiber tested (1 g/cm3). Workability of the mix containing the Dyneema fiber was also substantially better than the other fibers. Based on research from previous years, 6mm long fibers were added were added at 1 vol% to the mix. This combination was found to provide the optimal compromise between strength and workability.

The mixes which do not contain short fibers exhibit improved workability and bonding characteristics along with reduced density. Therefore, to ensure satisfactory inter-layer bonding at minimum mass, short fiber reinforcement was only used in the outer layers of the hull where the stresses are highest. To compensate for the reduced workability, caused by the inclusion of the Dyneema fibers, we decreased the volume fraction of aggregate in the mix while increasing the binder content.

Pr�mary Re�nforcement

Last year, we were able to source a carbon fiber/S2-glass hybrid mesh (22% open area). based on the results from testing last year, we determined that three layers of reinforcement and four concrete lay-ers provide the greatest flexural strength improv-ment (200% compared to short fiber reinforced mix). As a result, we structured this year’s hull in the same manner.

Pseudo-Stra�n Harden�ng Behav�our

Our experience at past Canadian Natrional Concrete Canoe Competitions (CNCCC) we have found that the majority of damage to canoes is due to repeat-ed loading causing fatigue with subcritical crack growth leading to eventual failure. For the past three years, our concrete mixtures have been designed to prevent cracking entirely. Although this design goal was realized at a relatively low canoe weight, it was necessary to incorporate a large safety factor into the design to prevent catastrophic failure of the relatively brittle concrete composite.

This year we focused research on improving the ductility of our concrete composite to prevent cata-strophic failure. by combining a high concentration of polymer modifier with UHMWPE fibers carbon fiber mesh reinforcement we were able to create a ductile composite with a flexural strain capacity ex-ceeding 2%. Most fiber reinforced concretes (FRC) display a quasi-brittle behavior with a slightly duc-tile post-peak softening [7]. Our novel lightweight FrC exhibits a non-catastrophic failure mode char-acterized by increased load carrying ability after first cracking (Figure 3). The pseudo-strain harden-ing response makes the material much more dam-age tolerant, energy absorbent, resistant to fatigue as well as prevents catastrophic failure [8, 9].

Table 1: Summary of Mix and Composite Properties

Composite Core Mix

Fiber Mix

Pigment Mix

σflex (MPa) 9.1 4.6 5.5 4.8 σcomp (MPa) - 12.2 12.7 12.5 E (GPa) 1.5 1.5 2.0 1.7 ρ (kg/m3) 760 610 800 790

Figure 3: Sample stress-strain curve of FRC composite in flexure illustrating `pseudo-strain hardening’.

0.5 1.0 1.5 2.0 2.5

strain0

2

4

6

8

10

stressmPa

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project management and construct�onProject Management

In the fall our team held an executive meeting to determine goals and a plan of action for the year. based on our performance at the competition last year we decided to spend more time on the finish-ing stage of construction. Our sponsorship goals were higher this year due to the increased distance to competition and additional funds were secured by an increased effort from the whole team.

Organ�zat�onal Structure

The team is headed by two co-project managers, two technical managers, a technical support staff and a fitness trainer. With two project managers, each aspect of the project was given more attention than it would have been with a single overseeing officer. As can be seen on the organization chart (p. 7), duties were split between the technical project manager, who looked after the operations aspects, and the logistics project manager, who looked af-ter the financial and non-technical aspects of the team. For similar reasons, it was decided to have a large executive body to ensure that all aspects of the project were covered by someone dedicated to that particular requirement. As the project developed, these managers occasionally delegated major tasks to general team members. All other team members were encouraged to participate and ask questions about any aspect of the project that they were inter-ested in. This allowed them to gain the understand-ing required to take on leadership roles in following years.

F�nance and Resource Allocat�on

due to a surplus from last year and an increase in corporate sponsorship dollars the U of T team was able to maintain the quality of our operation while at the same time send a large team to halifax. The team was able to have a great deal of materials donated at or below cost thanks to efforts by our technical managers which mitigated our costs sub-stantially. Our major expenses included CNC ma-chining of the mold and the foam. Transportation to the competition is also a major expense this year

due to the distance and difficulty in transporting the canoe itself across the country.

Schedul�ng

The major milestone that needed to be considered while scheduling was the date of the commence-ment of the competition. Once this was known, the rest of the schedule was projected backwards. An-other constraint was the day on which to cast the actual canoe. With the date for casting set, the final day for any testing was determined to be January 1st, 2008, to allow for final testing and to give time to acquire needed materials. The start date for the first session of the year was set as September 13th, 2007. This allowed for two weeks to send out no-tices to past members and the recruitment of new members. sessions were held for concrete mix and composite design and testing on the majority of saturdays during the school year up until January 1, 2008. The thorough design and optimization of the canoe hull design required a greater number of hours (Table 2) than expected. however, the result-ing canoe not only fits the new requirements and has a streamlined shape, but the overall product is stronger and lighter than our entries in prior years.

Mold Construct�on

based on the canoe design data provided by the hull design team, a male mold model was constructed using computer-modeling software. Once the mold design was completed, the CNC machine code was commissioned to our milling contact.

The mold for the canoe was sectioned into five main pieces, four rib pieces, one cross-section piece, and several thin pieces for the gunwales and the base. The pieces were cut in several sections due

Table 2: Breakdown of Task Hours

Task Hours

Hull Design 550 Concrete Design 750 Final Product Construction 1800 Business and Administration 350 Paddling 600

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to the limited size and restricted milling angles of the CNC mill available. The milled sections were manually sanded smooth in order to remove the ex-cess foam left during machining. After sanding, all pieces were tapped or coated with heat-shrink wrap in order to produce a smooth finish on the inside of the canoe to aid in demolding the canoe. A verti-cal piece of stiff tape was placed in a small groove in the top of the base piece just inside the gunwale template to separate the blue pigment mix from the white mix during casting.

The canoe mold was assembled in stages. The thin base pieces were assembled first and fastened to the casting table and then a smaller thin piece with the same shape as the base piece was fastened to the centre of the base piece using aerosol spray glue. The offset between the smaller piece and the base provided the shape of the gunwale. Atop the smaller piece, the mold of the canoe was assembled, leav-ing a gap along the perimeter as a template for the gunwales. In between each piece of the main mold a small length was left open, leaving room for a tem-plate for each of the ribs. gaps at the intersections of different pieces of the mold were eliminated us-ing drywall filler and silicone caulking.

Canoe Construct�on

The casting of the canoe began with the ribs. The outer (fibre) mix was used. While the ribs were be-

ing cast, the inner sides of the gunwales were cast using the blue pigment mix. high modulus carbon fibre roving was used to reinforce the gunwales and the ribs. The remainder of the mold was coated in an initial layer of the outer mix. A layer of carbon fibre mesh was laid over the outer mix, and an inner (non-fibre) mix was worked in between the mesh (shown in figure 4) in order facilitate bonding be-tween layers. This process was repeated for two ad-ditional layers of carbon fibre mesh, with an outer mix being applied on the final layer instead of an in-ner mix. Each layer of concrete was approximately 2.5mm thick. Extreme care was taken in order to produce homogenous layers of minimum thickness, in order to produce a smooth, uniformly thick, and lightweight final product.

A humidity tent was then constructed around the canoe and it was left to cure for 28 days. Af-ter this curing time, the mold and the canoe were unfastened from the table, and the mold was com-pletely removed. Final finishing of the canoe in-cluded numerous hours of sanding and polishing to obtain a smooth and even surface. Ultrasound was used to measure the thickness of the hull., After polishing the canoe was sealed with an acrylic sealer. The the canoe’s name and university’s name were added after sealing..

Safety and Qual�ty Control

because of the hazardous nature of the materials required for this project, extreme care was taken in ensuring that everyone was properly trained in the safety procedures for the lab and the equipment that we were using. This included the proper use of NIOSH certified N95 masks to prevent the inhala-tion of microspheres and dust. Any required safety equipment was provided to team members by the team.

Quality control was maintained by following CsA and AsTm standards wherever applicable, includ-ing, but not limited to, test sample creation, curing, and testing methods. In cases where no standards apply, the team self-controlled its quality using standardized casting methods including using a modified miniaturized slump cone to determine mix rheology based on the guidelines prepared by ram-achandran et al [10].

Figure 4: Casting of the bow of the canoe, illustrating the placement of concrete over the reinforcement.

Page 9: BLUENOSE - technical report

Lyle gordonCo-Project manager

Operations responsibilities:• Oversee and coordinate tech-

nical and operational tasks

Concrete designdesign and testing of

concrete, reinforcement, and casting techniques

Paddlingstrength and endurance

training of paddling team members

hull designstructural and

analytical design of the canoe’s shape

Chen Chendesign manager

Owen melvillemix and Composite

design manager

Lian NiCasting manager

riley monsourFitness Trainer

mike LacourtCo-Project manager

Logistics responsibilities:• Oversee and coordinate logisti-

cal and financial operations

Trip LogisticsOrganization and

analysis of trip planning and accomodations

Finance and sponsorship

Procurement of departmental and

industry sponsorship

Presentation design and composi-

tion of presentation and technical report

Publicitydesign team publications and graphics for recruit-ment and sponsorship

Jonathan hographics designer

Edward sykesWebmaster

renzo bassetTechnical and Lab

Advisor

Prof. Kim PressnailFaculty Advisor

and Liason

Peter LeestiFinancial Account

support

Nastassja PearsonLab supervisor

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organ�zat�on chart

david ruggierodesign support

david ruggieroTrip manager

Entire Team

Legend

staff student

Tim van PuttonConstruction support

Page 10: BLUENOSE - technical report

Task Name

Project Timeline

Hull Design

Initial Design

Analysis and Refinement

Mould Design

Final Design

Mix Design

Control Mix Design

Mix Analysis and Testing

Initial Reinforcement Design

Reinforcement Analysis and Testing

Final Mix Design Assessment

Final Mix Chosen

Construction

CNC Milling

Mold Assembly

Mould Finishing

Canoe Construction

Casting

Curing

Canoe Finishing

Transportation Box

Project Management

Establish Goals

Recruitment Events

Budget Formulation

Sponsorship Package Creation

Raise Funds

Tech Report

Writing

Revision

Final

Submission

Presentation

Theme Creation

Visuals

Design

Rehearsal

Paddling

Workouts

Paddling Practice

Official Team Chosen

Competition

Management Transition

Red: Critical Path

26 02 09 16 23 30 07 14 21 28 04 11 18 25 02 09 16 23 30 06 13 20 27 03 10 17 24 02 09 16 23 30 06 13 20 27 04 11 18 25Sep '07 Oct '07 Nov '07 Dec '07 Jan '08 Feb '08 Mar '08 Apr '08 May '08

Task Baseline Baseline Milestone Actual Milestone Summary Project SummaryProject: University of Toronto Concrete Canoe

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a – references

1. American society for Testing and materials (2005). “standard Test method for Flexural strength of Concrete (Using Simple Beam With Center-Point Loading).” ASTM International Standard C293-02. West Conshohocken, PA.

2. American society for Testing and materials (2005). “standard Test method for Flexural Properties of Thin-section glass-Fiber-reinforced Concrete (Using simple beam With Third-Point Loading).” ASTM International Standard C947-03. West Conshohocken, PA.

3. American society for Testing and materials (2005). “standard Test method for Compressive strength of Hydraulic Cement Mortars (Using 2-in. or [50-mm] Cube Specimens).” ASTM International Stan-dard C109/C109m-05. West Conshohocken, PA.

4. Wagner, Herman B., (1965) “Polymer-Modified Hydraulic Cements.” I&EC Product Research and development, 4(3), 191-196.

5. Isenberg, J. E. and Vanderhoff, J. W., (1974) “Hypothesis for Reinforcement of Portland Cement by Polymer Latexes.” Journal of the American Ceramic society, 57(6), 242-245.

6. beeldens A., et al., (2005) “From microstructure to macrostructure: an integrated model of structure formation in polymer-modified concrete.” Materials and Structures, 38, 601-607.

7. Li, Victor C., et al., (1995) “Matrix design for pseudo-strain-hardening fibre reinforced cementicious composites.” materials and structures, 28, 586-595.

8. Lin, Zhong and Li, Victor C., (1997) “Crack briding in fiber reinforced cementitious composites with slip-hardening interfaces.” Journal of the mechanics and Physics of solids, 45(5), 763-787.

9. ritchie, r. O., (1999) “mechanisms of fatigue-crack propagation in ductile and brittle solids.” International Journal of Fracture, 100, 55–83.

10. Ramachandran, V. S., Shihua, Z., and Beaudoin, J. J., (1988) “Application of Miniature Tests for Workability of Superplasticized Cement Systems.” Il Cemento, 85,83-88.