Recentlly, I've read the book "The Art of Structural Design" by Peter Billington. In it, he mentions the Schwandbach Bridge (1933), located in Hinterfultigen, designed by Robert Maillart and I thought it would be fun to make a rough model of it using SolidWorks and a 3D printer.
I think the geometry of the bridge is incredible because although it is complex, it has a simple facade. The deck follows a curved path, but the arch underneath has a different plan. The inner edge of the deck cuts through the arch so that in a plan view, the two planes follow a similar line; however, on the other side of the bridge, the arch is flat-faced. Because of this, in a plan view, you see what looks to be a rectangle jutting out of the outer edge of the deck. The plan view I worked off of to build my model is shown in the figure below.
Fig. 1: Simplified Elevation and Plan View of Schwandbach Bridge (Source: Unknown)
Fig. 2: Elevation and Plan View of Schwandbach Bridge, including arch (Source: Unknown)
Because the arch and the deck do not necessarily line up at all points throughout the bridge, the bridge was installed with trapezoidal cross-sections (shown in Figure 3). Modeling the cross-sections in SolidWorks was probably the most difficult part since all the trapezoids were different shapes. I experimented with a few different methods of cuts and extrudes including a revolved cut around the axis connecting the two inner edges of the deck, a single lofted cut from the outer edge of the deck to the flat edge of the arch, and a lofted base from multiple profiles on the arch to the bottom face of the deck. Eventually, I settled on using multiple lofted cuts, again from the outer edge of the deck to the flat edge of the arch.
My first attempt at modelling the bridge looked something like this:
Fig. 3: First Model of the Bridge
I was quickly told that the deck and the cross-sections were much too thick. Additionally, in this model, my idea was to create a lofted base from the top face of the arch to the bottom face of the deck. Since the crown of the arch was tangent to the bottom of the deck, though, SolidWorks registered the top face of the arch as two separate faces; therefore, I could not create one continuous lofted base. Instead, I decided to create a lofted base from the bottom face of the arch to the bottom face of the deck. I highly recommend not doing this. The outcome was atrocious. There was a slight bevel that was produced in the legs and because I did not set a guide curve for the loft, the side of the cross-sections that were meant to be straight and vertical were curved.
Fig. 4: Bevel Created from Lofting the Bottom Face of the Arch to the Bottom Face of the Deck
Fig. 5: Slightly Curved Cross-Section Walls
Because of those problems, I decided to make a second iteration of the models. This time, I tried designing for construction a bit, separating the model into two parts that I could put together in an assembly so that they could more easily be printed. I made note that the bridge was quite thin and accounted for that in the best way I could, working without dimensions. In this rendition, I also attempted to make some sort of anchor shape for the arches as well.
The final parts and assembly are pictured below.
Fig. 6: Normal View of Deck. Notice there are slots I tried to make so I could accurately and visually locate where the cross-sectional supports are supposed to attach to the deck.
Fig. 7: Isometric View of the Deck. Hopefully, this helps the understanding of the path of the bridge.
Fig. 8: Normal View of Arch and Supports
Fig. 9: Isometric View of Arch and Trapezoidal Cross-Sections
Fig. 10: Elevation View of the Bridge Assembly
Fig.11: Plan View of the Bridge Assembly
Fig. 12: Isometric View of the Bridge Assembly
When printing the bridge, I realized that printing the whole assembly as one piece not only was sturdier, but also looked much cleaner since there was less glue on the model. I actually used 100% infill on the prints since it was a small print approximately 5 inches in width and since it only weighed 5 grams. The end product is pictured below.
Fig. 13: Schwandbach Bridge Model, Front
Fig. 14: Schwandbach Bridge Model, Left
Fig. 15: Schwandbach Bridge, Switzerland