Design Alternatives

The primary goals of the hull design were to ensure that the canoe’s shape provided stability, good tracking, and satisfactory maneuverability in the water. Given the various parameters, the team chose a symmetrical design, which allows for more predictable movements, in addition to a shallow-arched bottom, flared sides, and a rockered body. These features provide adequate stability during rowing maneuvers, a reduction in the probability of tipping, and improved tracking. A wider canoe was also designed for the comfort of the rowers. This allowed the team to be best suited for the challenges presented during the ASCE conference races. 

For the mixture design, the lightest concrete design was selected ensuring flotation could be achieved. The mix design chosen for the canoe utilizes a mixture of aggregates that ensure both strength of the hull as well as buoyancy. The mix adheres to both the gradation requirements and the cementitious material content guidelines. PC4, a mixture of fine-grain particles and fibers, that increases air content and reduces weight was used as a sand replacement. The material’s fibrous compound not only provides a higher tensile strength but limits cracking as well.
 
Additionally, ​the environmental effects of the mixture were taken into consideration. The team considered multiple forms of work materials for the canoe. First, a wooden mold was considered but decided that it would be too intensive to build. An earth form was also considered, placing the canoe in the ground after the wanted shape was dug out, but since Flagstaff has cold winters the canoe would not cure properly. After these considerations, a styrofoam mold was selected for ease of construction.  

Decision Matrices

Below, two decision matrices can be found that were used for selecting the hull and concrete design.

Hull Design

Categories are rated on a 1-5 scale
1 : Poor performance in the category standard
3 : The design meets the category standard
5 : Design exceeds the category standard 

Criteria Weighting:
Speed, Maneuverability, Secondary Stability (20%) - Demands for a successfully racing canoe ensuring victory.  
Initial Stability & Ease of Construction (15%) - Less user strain and ease of feeling stable getting in the canoe as well as rowing it.  
Comfortability (10%) - Increases paddler productivity because they are no restricted by the width of the canoe.  

Final Selection
D1: Shallow-Arched Bottom, Flared Sides, Rockered Body - Helps with initial and secondary stability. 
D2: Shallow-Arched Bottom, Flared Sides, Rockered Body - Hard to construct. 
D3: Flat Bottom, Flared Sides, Rockered Body - Slow speed but has effective maneuverability.
D4: Shallow Vee, Straight Sides, Rockered Body - Great speed and maneuverability but lacks stability and is difficult to construct. 

Final Choice: Design 1 

Concrete Mixture Design

Categories are rated on a 1-5 scale
1 : Poor performance in the category standard
3 : The design meets the category standard
5 : Design exceeds the category standard 

Criteria Weighting:
Strength (35%) - Capacity must exceed demand, this ensures the canoewill not fail under the forces acting upon it.  
Density (35%) - Light concrete means easier floatation and better ​​maneuverability.  
Cracking (20%) - Cracking creates leaks allowing water to enter the canoe and reduce strength.
Aesthetics (10%) - Small points for the competition but the team wanted to be proud of something they could put their names on.  

Final Selection
Mix 1 : AeroAgg is a weak aggregate and hard to come by.
Mix 2 : PC4 helps with sustainability, cracking, and is a sand replacer.
Mix 3 : Poraver is a recyclable material but is hard to come by. 

Final Choice: Mix 2 

Final Design

The final construction plans for the hull, structural, and concrete mixture designs used for the 2022-23 concrete canoe team can be found below.

Hull Design

The main focus of the hull design was to create an stable and comfortable canoe that would be able to manuevuer well through the courses presented on the competition. With a heavy mix design, the maneuverability was an essential part of this design. The image below shows a profile view of the final hull design selected, as well as its length of 228 inches, depth of 15 inches and edges. 

The following table shows the various properties of the canoe with the weight being the most important value to note. 

The next photos that can be seen are useful in showing what the canoe looks like. First, the image on the left shows the cross-section of the mold used in forming the canoe. On the right, the image shows an isometric view of what the final product of the mold should be shaped like.

Structural Analysis

Structurally, D.A.S. Boat was designed based on three primary criteria: a high concrete compressive strength, the implementation of a high tensile strength reinforcement, and the use of a lightweight concrete mix. Prior to beginning the structural analysis process, the high compressive strength of the concrete in combination with the high tensile strength of the reinforcement were expected to provide enough capacity to resist the loading demands caused by paddlers and buoyancy forces on the hull. In addition, it was anticipated that the lightweight concrete would ensure that the magnitude of the buoyancy forces would be large enough to allow the canoe to float.    

Structural analysis calculations were performed for several load cases to reflect the five expected race demonstrations to ensure the safety and stability of the canoe. The analyses utilized principles from statics and reinforced concrete design to create shear force and bending moment diagrams, determine the punching shear demand, and explore maximum loadings that the canoe will be subjected to. The process began with the team establishing point load magnitudes for each load case in addition to other forces acting on the canoe. Three primary forces were considered: self-weight, buoyancy, and point loads representing paddlers. For simplified, reliable results, the canoe was modeled as a simply supported beam.

For the two-male sprint case, point load magnitudes of 180lbs were chosen based on the average weight of the males on the Competition Team. These loads were placed three feet apart from each other, equidistant from the midspan point. To represent the self-weight of the canoe, the concrete oven dry unit weight of 69 pcf was multiplied by the 5.36 cubic foot volume of concrete used for the hull to produce a resultant with a magnitude of 370 lb This value was divided by the 19-foot length of the hull to generate a 20 pound per lineal foot (plf) distributed load acting in the direction of gravity. The buoyancy force was determined by multiplying the volume of water displaced by the canoe’s 69 pcf unit weight and dividing the result by the length of the canoe. This provided a buoyancy force of 39 plf. While the paddler point loads and buoyancy force would generally be considered live loads, they were conservatively solved for as dead loads in LRFD Load Combination 1 because they will be applied to the canoe with greater certainty than how live loads are typically assigned. The design loads placed on the simply supported analytical model of the canoe are shown in the figure below. Supports were added to the beam for stability purposes when showing the shear force and moment created in the canoe; however, no physical reactions occur at the supports.

These loads and the reactions at the supports were used to create the shear force and bending moment diagrams presented in the figure below as well. The maximum shear force for the load case was found to be 150 lb and the maximum moment was found to be 600 lb-ft. Utilizing LRFD Load Combination 1 under ASCE 7-16, a load factor of 1.4 was used to obtain a shear demand of 210 lb and a moment demand of 840 lb-ft​.

To determine if the capacity of the hull is greater than the required demand for the load case, the flexure and shear capacities were calculated using Equations 3-1 and 3-2. The calculations were completed under the assumption that the canoe can accurately be modeled as a simply supported beam, where the beam’s width is equivalent to two times the thickness of the hull. The shear capacity was found to be 1590 lbs, which is larger than the demand of 210 lb. It was determined that the moment capacity was also larger than the demand, with a solved-for value of 1290 lb-ft, surpassing the demand of 840 lb-ft. Moment capacity was conservatively solved with a strength reduction factor of 0.65 in case the canoe is in compression control. Another reduction of 3 was given to the moment capacity since only one third of lap length was used for reinforcement.  

Next, the two tables below show the demand vs. capacity comparison as well as the freeboard value under the male tandem load case. The three values solved within the shear moment diagram, bending moment diagram, and punching shear calculation are all connected in a primary way, being that they are demand values. While the actual load values given by the demand and capacity for shear, moment, and punching shear are different, they share a safe ratio between demand and capacity. Demand over capacity for shear, moment, and punching shear are as follows: 13%, 66%, and 15%.  for each load type, the capacity exceeds the demand by over 30 percent, ensuring the canoe’s structural success, even under unforeseen load conditions.