Voronoi Pedestrian Bridge

My name is Lincoln Clarke and I'm going into grade 11 at Toronto French School.

The Toronto campus has a 26 acre ravine, a true oasis in downtown Toronto, but unfortunately it is very underused despite being a great way to connect with nature. In large part, this is due to a river that flows through it, limiting the parts accessible to the school. There is a path, but it only goes along a small part of the river closest to the school, and doesn't make the most of the space. Despite the space being underused, the Toronto French School has a strong focus on the environment and has recently launched multiple initiatives to integrate the ravine in to student life as well as the education. For example, there's an environment club, one of their initiatives being to document the trees and wildlife in the ravine with the goal of protecting endangered species of trees. The ravine is also integrated into science class, where students complete water, soil and air testing, and in biology, tree identification. Finally, there are plans to build outdoor classrooms. Although these programs do exist, trips to the ravine remain infrequent. All in all, one of Toronto French School's goals is to connect students with nature in attempt to give them a strong sense of responsibility vis a vis the environment. However, it struggles to do so due to the limited infrastructure in the ravine. My Voronoi pedestrian bridge connects the school to the other side of the river, greatly expanding the ravine and ultimately allowing students to immerse themselves in nature by facilitating frequent use of the ravine. It also connects the campus to a recreation center on the other side of the ravine. Instead of crossing the river next to bustling traffic, students could instead walk through nature to go play sports at the recreation center.

This is a long Instructable as the process of designing my bridge is involved. Below is a table of contents:

1. Preliminary Planning

2. Inspiration

3. Draft Concept

4. Design Measurements

5. Stress Testing to Decide on the Shape of the Bridge

6-12. Designing the Model Bridge

13. Designing the Foundation

14. Designing the Surrounding Environment

15. Rendering

16-18. 3D Printing the Physical Prototype

19. Assembling the Architectural Model

20. Physical Prototype Showcase

21. Architectural Model Design Tips

22. Conclusion

Software:

• Autodesk Fusion 360
• Cura slicer
• Lightburn

Hardware:

• Tape measure or digital measurer (iPhone works)
• 3D printer
• Filament (PVA and PLA or resin)
• Laser Cutter
• Glue
• Paint (Black)
• Yarn
• Real Vines
• Water
• Camera

Before starting the design, the needs for the specific application must be addressed. There are many factors to take into account when building a bridge, both from a purely engineering perspective (Hard factors) and social perspective (Soft factors).

Hard Factors:

1. Type of traffic on the bridge and how many people need to cross it (Flow) - Pedestrians (some with dogs), bikers, wheelchairs - 25 people per minute would more than suffice so only one lane necessary
2. Determines necessary width = 1.3 meters
3. Determines necessary height → People can be tall. 7 ft height ≈ 2.15 meters
4. Width of the river
5. Determines the length and structural integrity
6. 11.6 meters
7. Load
8. Based on the width and length we can calculate the area of the bridge: 1.3 * 11.6 = 15.08m²
9. The Ontario Building Code requires that footbridges withstand 4.8kPa, or in other words, 4800 N per square meter
10. 15.08 * 4800 N = ≈ 72.3 kN
11. Height drop
12. 150cm
13. Curvature of the bridge and structural integrity
14. Natural factors affecting the bridge
15. Storms with erosion as the river it crosses gets to high water levels
16. Humidity - It is over a river
17. Temperature - Canada has cold winters and hot summers. The material chosen has to withstand this.
18. A proper foundation is definitely necessary

For this study, I took pictures and measurements of the area where the bridge will be implemented.

The first picture shows a comprehensive perspective of where the bridge will be built in relation to the forest and river. The next two show where it will be looking from the path.

Soft Factors:

1. Strong sentiment towards protection of nature and restoration of the ravine
2. The school puts a lot of emphasis on restoring the ravine by planting trees and getting rid of invasive species
3. This means building something in the ravine may not be accepted by all
4. Construction often has a negative impact on the environment
5. It would involve clearing an area for the bridge, though not a large one
6. To get everyone onboard, certain eco-friendly features can be integrated into the project
7. Nature at the heart of the design
8. A lattice structure on which vines can grow and suck up CO2
9. Vines can also provide visual appeal with greenery and flowers
10. Sensors to collect environment related data
11. Solar panel with battery attached to a microcontroller with sensors to collect:
12. Water level
13. Water composition - road salt, fertilizer...
14. Air quality
15. Humidity, Temperature
16. Long range RF transmitter to periodically send this data to the school (Less than 1km away) where it can be received by another microcontroller, displayed, interpreted by students and used in science class
17. Pre-fabricating the bridge to reduce the pollution of construction on the natural environment
18. Made in a factory, all the scraps can be cleaned up more easily and don't contaminate a forest
19. Using recycled materials in the manufacturing process
20. Bridges can now be 3D printed using industrial scale machines
21. Recycled material could be used in the 3D printing process
22. Choosing the right location
23. A place where no trees or very few need to be cut down to install the bridge (The large tree in the photo would not need to be cut down)

I find the tubular lattice structure of these bridges to be visually appealing. Furthermore, some of them, especially the M8 Harthill bridge and Peace bridge span over long distances without supports, proving that this lattice design works from an engineering perspective. Meanwhile, I also wanted something vines could grow on, which requires the lattice to have less spacing than in these models. This was a problem, but inspired by these designs as well as some latticed 3D prints I had come across lately, I thought of a concept that could solve the spacing issue while keeping a lattice structure: the Voronoi concept bridge.

Based the factors from the initial planning phase and my inspiration, I created my bridge concept. The design is modern and aesthetically appealing and will allow for vines to grow around the bridge, integrating nature into the infrastructure. Its tubular lattice structure also makes it strong because it is entirely made of triangles.

The sketch above shows the context and measurements of the bridge's installation site. Everything is to scale except the height/diameter of the bridge. That will be calculated in the next step.

Voronoi lattices are commonly used in 3D printing thanks to their esthetically pleasing appearance and strength. They are not uniform structures which gives them more of a natural organic look. This type of pattern was named after Russian mathematician Georgy Voronoi. The type of lattice we'll use for this design is not exactly Voronoi, but it looks quite similar and latticed 3D prints are usually called Voronoi so that is what I have named my design.

Now that we know the general design for the bridge, we need to do some math to figure out the diameter of the tube. All we know is the width of the floor (1.3 m) and the height from the floor to the ceiling (2.15 m). These can be represented by a chord and its bisector inside a circle (the tube). There is only one radius that can satisfy both the width and the height and we don't want the tube to be any wider than necessary because that increases the cost and may be oversized in its installation site.

Using algebra and trigonometry, we can find the exact value for the radius of the circle and the angle between the extremities of the chord and the center. I wrote a separate Instructable about how to solve for these values because it's quite involved.

The radius of our tube will be 1009/860 m and the angle between the extremities of the chord (floor) and the center will be 2 * arcsin(559/1009). These exact values will allow us to get the perfect measurements when we replicate it in Fusion 360.

The only other measurements are the length and height drop, which we know are 11.6m and 1.5m respectively.

Before proceeding with designing the frame of the bridge, we need to decide whether it will be an arch bridge or beam bridge. If it weren't for the drop as illustrated in the previous diagram, I would definitely go with the arch bridge because it's stronger and looks nice. However, there is this drop, so I will do a stress analysis in Fusion 360 with the 2 designs to to make a calculated decision on the shape, which is incredibly important for structural integrity. Also, the bridge is being 3D printed, so there is not much of a cost difference between the arched design and the straight one, making the decision a pure question of strength.

To do this stress analysis, I created 2 tubes:

• One swept along a straight line
• One swept along a curved line

For both I kept the height drop in mind. The thickness and diameter of both tubes are identical and only their paths vary. This allows us to do a proper study as only 1 variable is changed.

Then, I created force applicators for both, which apply weight evenly throughout the bridge. To decide on how much force to apply, I referred to the Ontario Building code. For footbridges, it mandates that structures withstand 4.8 kPa. This translates into 4.8 kN per square meter. Using the width and length of the bridge, we can find the area, which is ≈15.1 squared meters. Multiplying that by 4.8kN gives us the total force applied to the bridge. This is ≈73 kN (Rounded up).

We constrain the ends of the bridges on the bottom (Where they would be attached to the ground and supported) and apply a force of 73kN downwards to do the stress test. For the physical material I used Nylon as it is a strong and durable 3D printing material also used in construction.

Above are the results of both static stress tests. The curved design earned a safety factor of 15+ while the beam design only got 7.4. Furthermore, the curved design undergoes much less displacement than the straight one. The strength may also decrease slightly once the tube is modified into a lattice. Although both designs satisfy safety ratings for bridges, we will go with the curved design: It's stronger and visually appealing. As well as having allowed us to decide on whether to go with an arch or not, this step allows us to decide on the exact curvature by testing different ones to find the one where there's the least imbalance. For example, some curves caused more displacement at one end of the bridge than the other, which isn't ideal. I created different curvatures and ran simulations to find the strongest one.

The stress test from the curved design will also serve as our final stress test because once the tube is converted to a lattice, Fusion 360 no longer computes the simulation properly due to the complex mesh. Clearly, this isn't perfectly ideal, but seeing as the safety rating is 15+, transforming the shape into a lattice should still allow it to pass safety tests. However, if a full scale model were being built, the engineering team would probably want to stress test the bridge as it would be built just to make sure, so some debugging might be necessary.

That being said, I'm pretty confident that the final version of the bridge would pass safety tests. Triangles are very strong shapes which makes them ideal for the lattice. Furthermore, this safety test is with a tube thickness of 5cm, which can easily be increased up to 10cm. In fact, the final design uses 10cm lattice thickness because it makes it stronger, but also allows us to scale the model down and 3D print it without having super thin walls. If designing this for full scale construction, the perfect thickness would probably lie somewhere in the middle, at about 6-7 cm. To decide on one, the engineers would probably run stress tests with different thicknesses and use the smallest thickness that passed safety standards in order to save on materials.

The first part of this is similar to the stress testing. First, we need to draw the sweep path of the bridge on the YZ plane. We will make a triangle to model the situation and then create a conical curve as the bridge's path. Then we will create a sketch on the XZ plane and create a circle of diameter 2 * 1009/860. We then make the floor with theta as calculated. The one thing that changes is that the floor is split into two. There is the floor, which could be made of a rubbery material and then the interface that connects it to the lattice tube. This interface will (ideally) be a volumetric lattice. Finally, we need to make the ends, which is done by extruding the tube on both sides, creating sketch on the YZ plane and then cutting these extruded tube ends in the desired shape. Finally, sweep the floor of the sketch and the floor interface along the same curve to make 2 new bodies (Last picture). These can be hidden and saved for later.

First, turn the capture design history feature off. That allows us to freely move between the workspaces. Then, go to the surface workspace and create an 0mm offset of the outer surface of the tubular tunnel. Now you can hide the actual BREP tube because we will only be working with the surface from now on. Next, go to the mesh workspace and tesselate that surface. After tessellating it, re-mesh it "uniformly" with preview on to get the desired density. The lines with be the path for the Voronoi lattice. Once you have your mesh, convert back it into a body/surface.

Hide all bodies except the mesh. Go into the form workspace and select the pipe tool. Choose edges as the selection priority and then select all the edges of the mesh. It may be a bit slow, but a pipe should appear. Choose smooth view and then the desired radius (I used 0.1m, which may be a bit thick for real construction, but is perfect for printing a model when scaled down). Then you can adjust the number of segments, which controls how smoothly they connect to each other at the star shaped points. I used a low number of segments.

At this point, you have a nice looking lattice. However, it cannot be used in the same way as regular bodies because it is a form. You need to convert it to a body so it can be worked with later and exported as a mesh. To do this, we will use the boundary fill function of the solid workspace. It can take the contents of one body and put it within a boundary to fill it. Basically, we will make a large box around the form, then put the material that the box (actual body) is composed of into the boundaries of the form. This effectively creates a body identical to the form. In the boundary fill menu, select the form and the box and then select the cell of the box and use the cut function. Then you get a BREP body identical to the form body.

Remember the interface that connects the floor to the lattice? (Step 6) It will save material, make the bridge lighter and also be more visually appealing if its converted to a volumetric lattice. Use the volumetric lattice tool (part of the product design extension package) to convert that interface. Then convert that body to a mesh. This is necessary because when a body is affected by a volumetric lattice, it is just a visual effect and the lattice is not actually modeled. Then it has to be converted back to a body so it can be cut to fit the shape of the lattice and combined. I know, it's a lot for something simple! You may need to do this in multiple pieces because it takes a lot of computing power. Just split the initial body into multiple pieces and then choose a lower refinement. (I didn't do this step because my computer isn't super powerful and it was slowing Fusion down too much with the model being full size)

As is, the floor and interface are overflowing from the lattice which both looks really bad and is not ideal from a 3D printing perspective (more overhangs). This is pretty easy to resolve by using the original surface body that we used to make the form pipe. If we delete the faces that just compose the entry/exit and not the tube, we can patch the tube into a body (Surface workspace). Then, we can use the combine tool to intersect it with the floor and interface. This will basically just cut off any parts of the floor that are outside the center of the lattice pipes.

Now you're done designing the actual model of your bridge. You can now go on to design the foundation (Optional if you're not actually building a full scale model) and create the environment.

This step is only necessary if you're actually building the bridge and not just making a model. That being said, it's an absolutely crucial part of a bridge. For this bridge the foundation can only connect to the bottom of the ends of the tube. Therefore, the best option is probably to create a reinforced cement pad between the two end edges of the bridge and then to fix them into it with long bolts. Holes for the bolts would need to be integrated into the design if it were actually being constructed, but for the purpose of this Instructables, I will just show the main idea. First, I crated a concrete pad, and then I cut out the middle of it to save on material while still keeping stability. Then, I added stabilizers in the other direction, perpendicular to the bridge lengthwise, to make it even stronger. This might be a bit overkill or not stable enough, but a more in depth study of the site for the bridge would need to be done to calculate the necessary shape and how deep and thick the foundation must be to withstand erosion as well as other factors–It is by a river. On top of something similar to this design, deep, round pillars, as many bridges have could be needed.

This step is not absolutely necessary for designing a bridge, but it does help convey your vision to the different parties involved in the construction. Showing that you have a professional architectural model helps persuade them to go ahead with the project. I designed the environment based on the topography of the land as well as my vision for the ravine. Taking into account the production of a physical model, I decided to make 1 base version of the environment with just the topography and then derive it into 2 separate designs: one for rendering which focuses more on appearance, and one for printing, which focuses on the most important points as well as printability. The model for printing also splits the environment into 4 pieces because of my printer's limited size.

I started with the base version, including the ground, path, river and fenceposts.

I then added ropes connecting the fenceposts in the design for rendering, as well as trees and bushes. This was quite time consuming because there are a TON of trees in a forest and to make it look realistic for rendering, I had to copy and paste them one at a time. Making the trees and bushes wasn't quick either: I made 4 different tree/bush types by creating multiple sketches and then lofting them together to make a tree/bush (refer to picture). Then I tessellated them, reduced them and reconverted to BREP in order to get the geometric look I was going for. I especially wanted the geometric look for physical prototype, into which I derived 2 of these 4 tree/bush models. After making their leaves, I made trunks using lofts and sweeps. I also used parameters in order to modify the bushes until I liked how they looked.

For the fenceposts, I drew their positions in a sketch using lines, spacing them 2.53 meters apart, the same way they are in my school's ravine. Then I derived them from a design with just the post and used the pattern tool to copy them along the line I drew. After, I created the ropes using the pipe tool along the same path used for the posts and copied it at the heights of the holes in the posts. Finally, I attached them to the ground using more sketches and lofting.

Finally, I assigned appearances to everything to prepare it for rendering. This took some trial and error to get the effect I wanted. This was partly because of the water appearance, which is transparent, so must be set to very dark in order to not just see the surface under it. Part of my fix for this was creating a rocky riverbed that you would see under, and giving it a slight blue tint. This turned out beautifully as you'll see in the next step.

For printing, I first had to replace the posts with simpler ones that would print properly (without holes for ropes). Then, I split the base into 4 pieces and added inserts to connect them. I also split the paths in different places so that they help hold the 4 piece model together. Next, I created indents for the bridge to sit in. Finally, I used the 2 of the same bushes/trees as in the model for rendering and then added square inserts so they would fit into the printed base. Along with this comes square holes into the base for their placement. Throughout this whole process, I had to do a lot of math (simple but a lot of it), to figure out what the dimensions in the model would be when scaled down to 2.1%, which is what I was printing at. This was especially necessary when figuring out offsets.

I have attached 2 sets of renderings of the Voronoi bridge–1 with a gravel path and 1 with a mulch path. Either would be great, but the mulch might be a bit more natural and that is what the Toronto French School seems to be going for.

There are numerous variables involved in getting a convincing rendering. Part of the process is trial and error in order to refine all the features, but a lot of it is also calculated.

One of the most important steps in rendering an architectural model is adjusting the appearances. This can also involve creating custom ones if need be. Creating your own appearances is not that difficult but does take a bit of time. I generally derive mine from Fusion 360 appearances that use pre-existing textures, and then I replace those textures with my own. For example, when making the dirt appearance, I started with sand, and then replaced the image for the texture as well as the bump pattern. One very important part is starting with a high quality (dpi and size) texture. Otherwise, you will likely end up having it look like a model from Minecraft with the appearance repeating in a block-like pattern. This is due to having a picture of only a small amount of your desired texture (such as dirt), causing it to be copied many times onto your model. That being said, whatever size you use, you will end up with some copying, and to prevent that Minecraft like look, you can change both the rotation angle of the photo and how the pattern is laid out on you model. Another way to prevent this is to have a uniform texture. For example, you don't want a picture that is lighter in the middle than on the edges because it will amplify the blockish effect where they meet together.

Another crucial part of making it look realistic is the lighting. Both it's intensity and angle should be adjusted to get the perfect results. The gif above demonstrates how the lighting angle changes the rendering.

Finally, focusing on the central component of the model is important. For instance, when rendering my bridge, I wanted it to be the focal point of the picture. However, there may be times where you want to show your construction in its larger environment, which is what my renderings from above do.

Download this model as an STL through this Google Drive link or from Fusion 360 as attached below and then print it with PVA supports. (It isn't directly downloadable from Instructables because it is larger than the maximum file size)

Here is also a link to a Google Drive folder with all the files in .3mf format which includes Cura settings.

You will need to scale it down to fit your printer. I used 2.1% scale to fit all the parts on my 300mm*300mm bed. The clearances are also designed for this size, but would probably be fine with slight variations.

Printing PVA as a support material for PLA works incredibly well, and this complex, enclosed design is the perfect use for this. The beauty of it is that once printed, the supports just dissolve in water! You will need a dual nozzle 3D printer to do so as each nozzle is dedicated to 1 material type.

A couple of my recommendations for printing PVA (Refer to the screenshots of settings above):

1. Fully dry your filament before printing. PVA is super sensitive to moisture in the air, and it basically starts to degrade–It does dissolve in water, right.
2. Make sure you have support interface turned on! This is crucial to getting good results. PVA supports don't need to be like normal supports where they're only at 10-20% density where they meet the model. Use 15% density triangles for the main support structure and than use denser triangles as the support interface, with 0mm z gap. The supports need to be touching the model. I recommend using 0.4mm interface thickness.
3. I use Magigoo as the adhesive when working with PVA. It generally works well.
4. Print PVA at slow speeds. Your first layer is incredibly important.
5. Dual extrusion: You will need a prime tower. This is easy to add in Cura.
6. Use good quality PLA filament along with your PVA. PVA is quite expensive so its worth the extra buck to make sure the print turns out.

Once the model has printed, submerge it in warm water and wait. You may be able to peel away some of the supports after an hour or so, but don't rip too hard–it could break and the water should fully dissolve it eventually.

Print 1 of each corner, 3 of the connectors and 1 of each path, which will fit into the base.

Because the corners are each so large, I strongly suggest using the lightning infill feature in Cura to reduce both the print time and the amount of filament used. This is a newer feature of Cura that essentially allows you to print infill only where it's needed. The model will be almost hollow until it gets close to a surface, where the infill will get more dense. I used 19% infill. To save filament, I also printed only 1 bottom layer and 3 top layers along with 2 perimiters.

I also strongly suggest you print with combing mode on as it greatly reduces the print time as well. Finally, I suggest using sugar water as a bed adhesive. (Fill a container half way with sugar, then to the top with water, then microwave it and mix it to dissolve all the sugar. Then apply it to the bed once it gets to 50-75 °C using a paper towel) This solution works great, even with large surfaces like these. If it is slightly hard to get the print off, make sure the bed is fully cooled and as a last resort, use cold water to redissolve the sugar.

This step is mostly up to you. You just need to print a total of 8 shrubs/trees. You can choose different angles for the bushes as well, given by the offsets of their trunks. There are 6 different shapes for the bush, which were created with lofting in Fusion 360, then meshing and then by modifying the splines used in the lofts to generate different shapes. Same goes for the 2 tree sizes.

Personally, I printed 3 regular trees 1 larger tree, 4 bushes, 4 tree trunks, and 1 bush trunk of each angle.

Follow the instructions or watch the video:

1. Paint the bottom of the bridge black as well as the space connecting the bridge to the path.
2. Connect the 4 corners of the base with the rectangular inserts.
3. Add the paths which will also stabilize the base: They're split in different places than the corners as to help join them together.
4. Use caulking or tape to waterproof the 4 corners' connections.
5. Attach yarn to the posts using superglue.
6. Assemble the trees and bushes by inserting their trunks into the holes on their bottom surfaces.
7. Insert the trunks into the base as desired.
8. Use superglue to fix the laser cut people to the path.
9. Wrap real vines around the bridge (Optional, but does help communicate the concept).
10. Fill the river with water and (food) coloring.

My vision for the physical prototype was to incorporate real bits of nature into the model just like the bridge incorporates vines. So, l designed the architectural model to include a reservoir where real water can be added to make it look ultra-realistic. This allows to create accurate reflections of the bridge, which I must say look impressive. Furthermore, I incorporated real vines into the prototype as they would grow on the bridge once installed. I took some pictures with the vines and some without to show the transformation the bridge would undergo once installed and also to decide whether vines should be added around it because it looks great in both scenarios.

I also wanted it to be large so that as many details as possible are included. The whole thing is 60cm * 60cm which equates to ~1:48 (exact=21:1000) scale. That's huge! The sheer size of it is one of the impressive parts of the model and allow the viewer to truly grasp how the bridge would look.

To take the showcase pictures of your architectural model, use a white backdrop on the opposite side of where you take the picture from to get a cleaner look. You can also play with the lighting and angles or your picture until you get the perfect shots. Remember to take lots: it's much easier to take an extra photo and go through a few more than to have to do photoshop editing.

Colors play a huge part in how convincing your model is. Most professional models use monochrome colors (White, Black and Gray) as well as a couple others. Too many colors can cause it to look disorganized and generally aren't additive. I chose to stick to three colors along with the monochrome ones: Blue for the water, yellow for the yarn and green for the trees. I chose to make the bridge white because it has a clean look and the eye is often attracted to brighter points of a picture (Focal point).

Simplicity is important for accessories to your design. This ensures that the focus is on main component (here the bridge) and not on everything else. For example, I chose to create only a few trees and bushes and making them geometric forms. This ensures they fit within the space without crowding and also that they remain a secondary element of the landscape. Their purpose is to convey vegetation in the ravine and they achieve just that without taking away from anything else.

Details matter. I suggest looking at your design as a whole and then looking at smaller points to ensure the details have the proper textures, forms, colors, and that they come together to create great balance within a space.

Use the principles of art and design. The tips I've already mentioned all incorporate them: color, value, form, texture, balance, space, emphasis. They truly do help your model look it's best.

In conclusion, the Voronoi pedestrian bridge design fulfils it's purpose of connecting people with nature as well as bridging the gap between a school and recreation facility. It also has a small environmental impact, and eventually a positive one: It can be manufactured off-site using (recycled materials and) additive manufacturing technology, reducing the impact of construction on the ravine, and then vines can grow on it, which as well as absorbing CO2 could act as a habitat for various species. All in all, the Voronoi pedestrian bridge's aesthetically pleasing design as well as it's environmental features make it a perfect choice for a school wanting to improve their students' connection with nature while expanding already existing programs.

I hope you learned a lot through this Instructable. In the process, I greatly grew my knowledge about planning, design, simulation, rendering, 3D printing as well as learning to do a real-world case study applicable to my community.