Will a bridge link Northerly Island?

The Chameleon pedestrian bridge would link Soldier Field to Northery Island. But, will it stand? In this blog, I will apply basic structural principles and equations to estimate the material requirements of such a bridge. To the greatest extent possible, I have tried to remain true to the original design intent, but early schematic evaluations require lots of approximation.

My first caveat is that I’m a building engineer. The layman would be surprised at the differences between the thought processes and building codes that apply to bridges and buildings. However, given the functional intent of this pedestrian bridge, it might is some senses be better treated as a building. To that end, I’ve used the Chicago Building Code (CBC) as a baseline for determining load conditions and general requirements. As we proceed, though, you may find that more elements of common vehicle bridges will find their way into the concept by way of seeking the most efficient forms.

As a building engineer, my first inclination was to evaluate the bridge concept as a beam. In the classic, simply supported beam, the greatest bulk of the structure would necessarily need to be located in the center of the span. However, the architectural intent is to minimize the mass of the structure where it most influences the efficiency of the design. That runs counter to the simple approach. Instead, I thought of the bridge as a system of two cantilevering beams. This type of layout places the greatest cross-section size over the abutments.

Cantilever bridges were once very common, owing to the ability to construct out from the piers until meeting in the middle. This reduced or eliminated the need for temporary piers or barges located in the deepest part of the body of water below. Employing such a construction method would be advantageous in this example as well, so that the marina below could remain in operation to the fullest extent possible.

Before I could run some preliminary numbers, I needed to make several estimates about the size and scope of the project. From Google maps, I estimated a free span of 600 ft. Taking all of the abutment requirements into account the real span might be a fair distance larger, but this estimate provides a baseline for exploring the concepts. Secondly, I estimated from the architectural sections, the dimensions of the superstructure. The platforms looked to be about 25 ft wide. The total height might be 45 ft. at the maximum depth. Since the exterior shape was to be comprised of many jagged surfaces, I applied a 33% reduction of the height to approximate the relative location of the main structural elements, treated as two lumps of steel - one representing the top chord of a truss, and the other the bottom chord.

I could estimate the weight of the bridge by taking the lumped mass of steel plus another 50% to account for connections, web members and cladding. Depending on the type of façade and the interior build-out, that number could be substantially larger. For the live load, due to pedestrians and amenities, I applied the 100 PSF load stipulated by the CBC for corridors, lobbies and other public space. Notably missing from my quick calculations were allowances for the effects of mother nature. Snow accumulation and lateral wind pressures would place a particularly large demand on any actual structure.

Nevertheless, I proceeded with a basic cantilever model. With the inputs described above, I was able to use pre-derived equations (taken from the AISC Steel Manual) to estimate the deflection of the beam at it’s cantilevered end and the amount of moment accumulated above the piers. As expected for such a long span, the deflections were large. Use of the spreadsheet allowed me to incrementally increase the amount of structural steel until arriving at quantity that seemed to meet the criteria. Again using my building background, I sought a deflection of no more than the length of the span divided by 360 (an arbitrary, but typically justifiable criteria). A deflection due to live loads up to 20 in. would be acceptable.

I also experimented with the length of the back-span. Intuitively, I figured that the longer the back-span, the smaller the end displacements. However, since my simple equation assumed the same stiffness throughout the length of the beam, when the back-span length increased too much, it became too flexible to provide a steady prop for the cantilever. This suggests that the architectural concept, which shows a short but deep section behind the forward pier, conceptually meets the structural demand.

After iterating through my calculations to meet deflection and strength criteria, I arrived at a design that called for about 1200 tons of structural steel. In more graphic terms, the bridge truss superstructure would consist of thirteen 14 in. wide flange beams (I-shaped) each weighing about 120 pounds per foot. Considering the other factors left out of my analysis, this seemed like an expensive brute force way to achieve the design.

I thought back to the original intent to minimize structural mass where not required by strength demands. The simple model assumed that the entire length of the bridge consisted of the same size section. However, because we chose a cantilevered design, the forces in the members would decrease as we approached the end of the cantilever. The structural shape could also taper with that demand. I used RISA 2D, a simple finite element analysis program, to compare the effect of tapered versus constant sections. In the tapered model, I reduced the weight of the section by 60% from the pier to the free end. As a baseline to see if I was still meeting the strength and stiffness minimums, I computed the deflection due to a constant live load first. The results showed an almost negligible difference. The effect on the dead load deflection, however, was a significant 50% reduction.

These results indicated that the original design had been conceived with sound structural principles in mind. Of course, many issues still remain to be addressed. One such concern is whether the multi-faceted shell will be stable. The jagged exterior form seems to call for some type of internal space frame or self-bracing mechanism to prevent the perimeter from buckling. Surely solutions exist, but a what cost to the overall project.

Without even addressing many additional design considerations, the steel quantities that I had arrived at still seemed heavy. Perhaps more efficiencies could be realized without compromising the architecture. Looking for inspiration, I would turn to other bridge examples. In the form of suspension bridges, I remembered the principles of catenary structures. To be continued in the next post…

How would you have conducted this schematic evaluation? Do you agree with the load applied? Would you have used the full section depth to estimate the building stiffness? What other important considerations were ignored in this evaluation?

Will it stand as a "W"?

The opinion below was provided by Ken Maschke, editor of willitstand.com and structural engineer. He is NOT a member of the Walter Towers design team. Concept and images by BIG | Bjarke Ingels Group.


Will the Walter Towers stand? Sure. There are lots of leaning towers, employing a wide variety of materials and structural systems. Frequently, the most influential element of their construction is the foundation. Nevertheless, leaning towers like the famous one in Pisa stand to this day. A more compelling argument against the Walter Towers can be made on the basis of economics. But even here, smart engineering decisions can be made to lessen the cost impact.

The renderings of the development seem to show four adjacent leaning towers. It’s not clear if each is independent or conjoined where they brush by each other. In either case, the two end towers provide the greatest structural challenge, because they do not appear able to lean against anything. What prevents them from falling over?


In engineering circles, we prefer to call this overturning. All tall buildings must resist this force, but typically it’s caused by the wind. Let’s assume that the total force of the wind hits the building just above half the building’s height. The force multiplied by that distance is called overturning moment. Moment has a lot of physical meaning, but just assume for now that it provides a measurement for comparing overturning to the resistance. Then, take a portion of the building’s weight and multiply it by the distance between the extremes of the building’s lateral-force-resisting-system to compute the resistance to overturning. If the resistance is greater, you’re on your way to a stable building. If otherwise, you have three options: socket your foundations into bedrock, add weight to the building or spread apart the structural system. Each option negatively impacts the economics of the project.

Leaning towers are even more greatly influenced by overturning. That’s because the building’s weight now works against you – more lean, more overturning moment.

To resist the increased overturning, the building’s lateral force resisting system must be chosen carefully. However, most beams and columns are not engaged in the system and do not help resist overturning. That effort is typically left up to structural concrete walls and braced frames (X-braces, diagonals, chevrons, etc.). Buildings with a structural outer face, like the Hancock Tower in Chicago, are very stable in part because the lateral system is maximally spread out. However, this system typically introduces large outer braces or otherwise reduces the light entering through the façade. Most designers would prefer to locate this part of the structure within the building around windowless elevator and stair shafts.

The Walter Towers renderings seem to imply a very open façade, precluding the use of exterior braces. One way to extend the reach of the lateral system is to engage the outer columns through the use of outriggers. These are similar in concept to the outer pontoons that stabilize a trimaran sailboat. Every ten floor or so, a stiff truss connects the interior core with the exterior columns. Frequently this truss is hidden in areas intended for mechanical equipment or storage, so to minimally disrupt the programming of the building. Using a composite structural system with a central core linked to exterior outrigger columns maximizes the resistance to overturning moment while minimizing the aesthetic impact.

The extreme bend in the Walter Towers introduces complications toward providing stability in other ways too. Wind hitting the building on the face perpendicular to the lean will cause a twisting of the building. This can be countered by a strong central core, but the shape of the walls are important. To resist twisting, a closed square shape is better than an open C-shape. The extent of the tower’s bend will also influence the location of the core. Instead of placing the core in the center at the base, it should be located at a point where it can rise as high in the building as possible without itself leaning.

In order to further reduce the effect of the lean, lightweight building materials should be used in the upper half of the tower. Steel beams and columns can provide the freedom to frame the gradually changing floors at minimum weight. The need for mass and stiffness in the core, however, probably makes concrete a preferable alternative for that element.

Will the Walter Towers stand in Prague one day? I hope so. Within the design there are many opportunities to illustrate the potential of structural design practices.

What’s missing from this discussion? Are there any other design technologies that could be employed to make these buildings stand? How would you do it? Vote, comment below or contribute to the willitstand wiki.