Will a catenary span 600 ft?

The Chameleon is a design concept for linking Chicago’s Northerly Island to the shore near Soldier field. In the second part of my series exploring the potential structure of this design, I applied basic load and deflection principles to estimate a steel quantity. Unsatisfied with the brute force approach, I explored other structural forms and became intrigued by the concept of the catenary.

A catenary is the theoretical shape that a hanging chain or cable will assume when acted on only by its own weight. Such a member experiences only tension forces and is very efficient for spanning a distance. The inverse would be the classical arch, a design feature that ideally only experiences compression. Both structural concepts were widely implemented until the advent of steel beams. In fact, the Catalan architect Antoni Gaudi was known to utilize catenary models in his most famous works. A series of strings was used to construct the complex arch and vault system he desired - just upside down. Gaudi realized the relationship between strings in pure tension and stones in pure compression, a law most eloquently described by Newton. “To every action there is an equal and opposite reaction.”

The arc of the catenary is defined by a fairly simple mathematical relationship. y=a*cosh(x/a) The key constant in the equation, “a,” represents a relationship between the tensile force in the member and the applied gravitational force. By tuning the axial stiffness, or resistance to elongation, and strength of the members the arc can be adjusted. Even within fairly rigid confines, such as those set by the need to allow boats to pass beneath the bridge, a satisfactory geometry can be achieved.

Recently building engineers have begun to revisit the potential of catenary action. Many of the most recent reports have dealt with the capacity for floor systems to apply catenary effects to prevent progressive collapse. If properly detailed, the floor beams on several floors can actually form a catenary that will support a column despite the removal of a column support. These recent reports still caution that the method is only effective when large deformations occur and the system has a substantial span to depth ratio. Fortunately, both of these conditions may be permitted in our long span bridge design.

Several bridge forms that utilize this structural technique. Simple rope bridges, like those creaky death traps featured on Indiana Jones, are the most elementary catenary structure. Unlike a conventional suspension bridge, these parabolic structures follow a true catenary curve, because the flexible deck follows the free hang of the cable. The longest such rope bridge, located near Vancouver, is an incredible 450 ft. long. Of course, the problem with these true catenary structures is the bounce and sway experienced by the brave souls that cross them.

Hybrid applications of the catenary shape have been applied in more static conditions. While the cable of a suspension bridge may initially follow a catenary arc, once the deck cables are attached, the form becomes a parabola carefully computed by the designers. Nor is it essential to use cables to achieve the purpose. Tower Bridge, in London, is known as a suspension bridge, but the “cables” are actually riveted steel plate sections. Therefore, we can assume that a catenary form can be applied to a solid static form.

The major implicit challenges are tuning the member sizes to achieve the final elongated position and constructing given the daily changing member orientations (as construction load is applied). Such a non-linear analysis and sequencing model is beyond the scope of this speculative blog. However, if we overlay a tension catenary (blue) and a compression arch (red) on the elevation of the bridge, we can see potential in the architectural form. Two more parabolic lines (green) appear to close the gaps, facilitating a continuous structure. Even if the intent of the exterior surface is to be undulating and unpredictable, we could envision facet lines that follow the main structural form or find ways to embed that within the structure. I believe this is a concept that brings structural harmony and simplification to a chaotic form that is more visually indicative of the sense of turbulent times.

Taking the catenary concept one step further, I would further propose that the interior pedestrian paths be supported by the means of one massive catenary bridge. Spanning 600 ft., it would be the longest “rope bridge” in the world. Far from typical, this catenary bridge would be comprised of dual layers with a depth of 16 ft. between. Ramps would connect the two layers and provide exit from the top down to dry land. The original programming called for entertainment and snack bar venues. Providing a stable surface, not wildly influenced by passing pedestrians would be challenging. Perhaps, the catenary pedestrian bridge could be connected to the exterior structure via a system of dampers, to modulate the movement and sway.

Though the initial design suggests that the pedestrian walks be suspended from the super structure, the incorporation of a pedestrian catenary bridge might provide the necessary construction platform to facilitate the building of the shell structure. At times during construction, might the shell actually be suspended from the pedestrian bridge. This might be a significant design consideration that has greater bearing in determining the size of the catenary bridge members than the actual person load.

Though this analysis has been brief, I hope it has accurately represented the thought process of an engineer presented with a design challenge. Use of catenary and arch forms is far from new technology, but they may be appropriate for this project. Even within an apparently static form, there might be potential to implement a bridge form known in the popular mindset as awkwardly unstable. From a structural dreamer’s standpoint the irony of the design is quite satisfying. Delivering a record setting structure goes even further in achieving the goal of a landmark bridge.

What other examples of catenary bridges are out there? Does the catenary concept have merit? Do you think the pedestrian platform would be steady enough to be comfortable? How might contractors cope with the gradual change in shape that will occur in the structure throughout construction? Comment below.

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 new faces deliver landmarks?

Early in 2009, Chicago’s architecture community was a buzz about the opportunity to design spaces for the 2016 Olympics. They looked to showcase the city’s rich architectural history and implement new modern forms being explored by a new generation of architects. Adina Balasu was one such enterprising designer completing her graduate degree. As part of her studies, she devised a landmark bridge to allow pedestrians access Olympic venues on Northerly Island, just across the marina from Soldier Field.

The concept, christened Chameleon, was to create a functional bridge that would be a destination in itself. Two levels of walkway would be suspended within a futuristic space frame shell. The large interior space might also be used as a multi-purpose venue for entertainment, retail and relaxation. After the Olympics left, the structure would be a necessary link to further the planned development of the little-used island park. An inspirational form and engineering feat, visitors would make a visit to the Chameleon part of their itinerary, expanding the traditional Chicago tourist district several blocks south.

I was introduced to the project at a meeting of the AIA Young Architects Forum. Following Ms. Balasu’s presentation, we had the opportunity to discuss the details of the project. I was intrigued by the structural challenge and impressed with her desire to express the structural form in the bridge’s appearance to reflect the technology of the times.

I delayed in my review for several months before picking up the concept with a fresh perspective. Unfortunately, in that time, Chicago was passed over for the Olympic bid. Despite this missed opportunity, I started wondering who deliver the trend-setting designs of the future. The current recession seems to have stalled several major projects, and missing out on the Olympics further deflated the local architecture community. When the economy turns around again, who will be at the forefront. I suspect that many of the innovative architects that I met at the YAF will lead the charge.

The Chameleon appeals to me as one of those great next-generation architectural concepts. Over the next few blogs I will outline my thought process and presents some potential strategies for making the Chameleon stand.

What do you think, when will we escape the current economic downturn? Will their be a new generation of architects leading the way at that time? Where should enterprising structural engineers look to network with these future partners? Please comment below.

Will a floating donut design stand?

In 2007, I spent six months living and working in Copenhagen. There were many cultural differences to overcome, and a lot of new construction methods to learn. Scandinavian design is renown for being modern and forward thinking. Danish architects are leaders in long span structures, sustainable design and creative use of space. I learned to approach projects more creatively in order to achieve the design goals.

One conceptual project that I was involved with was sited adjacent to Parken, the National Football Stadium. The proposed program included a multipurpose arena, a theatre stage, parking, office space, a fitness center and an extensive green roof. Locating all of these services on the constrained site was a challenge for the architectural team. Parking was located below grade, the arena at ground level and everything else above.

In that scenario, the major challenge was finding an economical way of supporting multiple floors of occupied space above the arena. To ensure unobstructed views in the arena, a 50m (160 ft) free span was required. The first scheme was

The first concept explored a conventional box design, topped with tennis courts and a crown-like perimeter wall. However, when the long span loading concerns were shared, the architects relieved weight by removing structure above the mid-span. The resulting design featured a floating square donut above the box. Developing a structure that retained the visual intent would be difficult, but more economical than the original, more conventional, approach.

Structural design proceeded in two steps: first setting the design of the arena enclosure and secondly supporting the ancillary levels above. The intent was to have both systems vertically supported by the same set of columns, thus avoiding a transfer situation in the arena roof. In one scenario, we considered supporting the entire donut on just four corner super-columns.

The truss supporting the donut would need to be three stories tall in order to span the length of the arena. However, this was aesthetically possible, because the truss would be located along the interior face of the building. The design of the truss members depended on the loads, materials, and architectural requirements.

The layout of the diagonals can be chosen so that they are in compression or tension. Eventually, all loads find their way to the top or bottom members, called chords. The design of these members is critical, since they usually see the greatest amount of load. Different design consequences apply if a member is in tension or compression. For a member in compression, the length is especially critical, since this most determines the susceptibility to buckling. Therefore, we would prefer the longest members to be in tension. However, dealing with strange load conditions and providing room for walkways through the truss can disrupt the best laid plans.

In the end, our design mixed a Warren layout (alternating diagonal directions) with a Pratt (diagonals only in tension). The combination was due selected so that the 3-story tall truss would be stable during construction. The one-story warren truss could be erected on the ground and lifted all at once. Then the other two stories would be erected above, using the first floor as an erection platform.
We later looked at several more schemes for the proposed arena. Ultimately, the project was canceled before construction commenced. Nevertheless it presented an interesting exercise in combining universal principles with local preferences.

Will it stand into space?

Earlier this week CNN ran an article on its front page about the prospects of a space elevator. The idea, first seriously proposed by author Richard C. Clarke 30 years ago, has gained some momentum because of a series of prizes offered to pioneering inventors. NASA offers a $2 million prize to anyone who can design a suitably powered lift to crawl up a 1 km high tether. Another contest challenges teams to design a tether twice as long and strong as what currently available on the market.


Why all the enthusiasm for pursuing such science fiction? In this case, geeky altruism gives way to corporate opportunism. Offering a low cost solution to lifting satellites and research modules into geosynchronous orbit could result in a major pay day. Consider sending tourists into space at $1,000 a trip or the potential for solar energy generation free from cloud cover and other environmental restrictions.

But will it stand? Experts and enthusiasts believe that the space elevator will happen within our lifetimes. But for now, two major hurdles stand in the way: 1) finding a suitable material for the tether and 2) developing an efficient propulsion system.



The experts quoted in CNN's article estimated that a chord 25 times stronger than most advanced industrially available materials would be required. On first glance, that seemed extreme, so I ran some of my own numbers. To simply things, I assumed that the cable would pretty much just hang the whole way - the real design is certain to be more complex.

First up, the length of the tether must extend into geosynchronous orbit, so that the space platform remains directly above the base. That's over 22,000 miles up. At that elevation the force of gravity from the Earth is almost 60% smaller. That helps, but a steel cable like those used in suspension bridges would still be around 950 times over capacity. Using Kevlar represents a 10-fold improvement, but we're still not in the ballpark. At least my numbers arrived within an order of magnitude of the expert. The web is a buzz with the potential for carbon nano-tube technologies. Still in their infancy, they provide the hope for a suitable tether material.

Construction a climbing vehicle is proving to be as difficult a challenge. To date, no teams have achieved the goals of NASA's competition. The latest attempts drive a small electric motor with solar power. Try finding a 22,000 mile long extension chord. Carrying fuel on board also heavy and detracts from payload capacity. Looking ahead, many experts believe that laser propulsion holds the key, at least as an energy supply for on-board motors.

The challenges seem very exciting. Science and technology geeks like myself believe that the new technology being developed along the way is worth the cost and may be more valuable than the actual working elevator. However, the viewpoints shared by non-technical contributors to the CNN comment board are very disheartening. "Solve world hunger and stop all wars first," decries one writer. Another thinks NASA is a sham and that all monies should be directed toward the recovering economy. Certainly, there needs to be a balance to funding policy, but I for one believe that such scientific exploration return much more than the initial investment.

Where do you stand on this question? Is prize money well spent on incentives to create a space elevator? How would you approach the problem? What other materials might offer a solution? Have you heard of an innovative new energy solution? Comment below or participate on at www.spaceelevator.com

Note: I had not ever considered the possibilities of a space elevator until earlier this week. It's an intriguing and compelling technical challenge to structural engineers.

ASCE Annual Conference

This year’s ASCE Annual Convention was held in Kansas City. The event provided an excellent opportunity to network with industry leaders, learn about the direction of the profession and learn new skills for improving your business acumen. My favorite part of the conference was meeting old friends from previous ASCE commitments.

The formal conference began with several inspirational speeches. Outgoing ASCE President, Wayne Klotz, declared, “modern society cannot exist without infrastructure.” He urged the incoming leadership and all in attendance to embrace the ABCs of ASCE: advocate for, believe in and commit to advancing the profession and protecting the nation’s infrastructure. The importance of advocacy was driven home by Jim Suttle, professional engineer and mayor Omaha. In short, we all lose when engineers shy away from advocacy and the public debate.

Throughout the conference many sessions were offered to promote the profession through better management practices. These included: Negotiating Better Engineering Contracts, Maximizing Your Bottom Line - Flexible Work Arrangements, The Economic Crisis - Leveraging Infrastructure Development for Recovery, Making the Most of Generational Differences, and more. Technical tracks on sustainability and Building Information Modeling were also among the conference offerings. Students and Younger members also attended symposiums specifically tailored to their interests. There was something for everyone.

Ben Stein was the final speaker at the conference. Far from the monotone sleep inducing lectures attended by the Wonder Years’ kids, his talk was very entertaining. He woke everyone up by starting, “I like you guys because your job’s not B.S.” As opposed to the entertainers with which he frequently works, he expressed thanks that engineers work “real jobs with exactitude.” The connection between his various stories and civil engineering was subtle but important. People from all walks of life are seeking answers to the complex questions of our day. Engineers are viewed as an elite team of problem solvers with the education and creativity to solve these problems. It is a lofty charge but one we can achieve if we accept this vision for the profession.

Sunday was perhaps the most fun day of the trip. Traditionally, a service day is planned following the conclusion of the conference. This year ASCE members volunteered to make improvements to the Heartland Therapeutic Riding Ranch. This facility provides equine-assisted therapy to children and adults with disabilities through human interaction with horses. The day’s events also included outreach activities that introduced engineering principles to over 50 local children.

In addition to the typical conference events, I was busy working behind the scenes on many tasks. On the Wednesday before the conference, I attended the Committee on Younger Members meeting. There, I learned about proposed changes to the organization to adapt to the needs of upcoming generations of engineers. I also met with members of ASCE’s media relations staff to discuss the blog I write for Student and Younger members, http://blogs.asce.org/bridgingthegap/. The Committee on Pre-College Outreach, which I chair, also met informally. We brainstormed some good new ideas and sought to gain support immediately by fanning out into the afternoon ice breaker reception and talking with ASCE leaders. Friday night, I had dinner with the editor of the Journal of Leadership and Management in Engineering. He asked me to contribute a column to their next edition. What a week!

Will it stand as a Cube?

Architects and engineers are often creatively constrained by the perception of economy in conventional designs. Generations of efficient refinement of building form have led toward standard boxy structures. However, creativity and function driven design can be encapsulated within a traditional cube. The Matrix Gateway Complex would be an exception to the rule of monotony in rectilinear buildings. It would provide residents a full 3-D city experience, featuring suspended platforms linking modular housing and community venues.

Designed as both an urban gateway and a self-sustaining city, this 42-story, 180m cube prototype would be one of the greenest, most aesthetically striking and technologically innovative mixed-use buildings in the world. The Matrix Gateway Complex would contain many of the amenities of a great urban center: a hotel with fitness and conference centers, retail and office spaces, cultural and religious facilities, and waterfalls surrounded by lush green terraces. Each component would take the form of a moveable module, connected to one of five central cores, all of which would be visible from the outside through a semi-transparent exterior skin.


Will it stand?

Based on conventional beam and column floor support, the structure would appear obvious. However, the initial concept dictated that the entire structure be supported only on four central concrete cores. Columns on the grid would not extend down to a foundation. There would be potential economy in this design requirement, given that the entire building is sited over water

Early expectations were that the entire structure could act as a gravity load-resisting moment frame. This concept relies on the stiffness of the columns, beams, and their connections, similar to the concept of a Vierendeel truss. However in this case, the structure would instead cantilever away from the cores. Computer analysis indicated that the 18m span of the beams was too great to satisfy the load demand.

Alternately, large hat trusses could be constructed in the top stories of the structure (intended for mechanical and energy generation equipment). The majority of the columns would then hang from these trusses. This idea has been put to practice in the Boeing building, in Chicago. A full bay is hung over the train lines that run along side the Chicago River.

In order to preserve vast interior atria while providing links between the core clusters, a combination of moment frames, hat trusses, and inter-story trusses would need to be implemented. These elements would facilitate a stable load path for floor plates of varying size and shape. The final structural hurdle involves the asymmetrical layout of the cores. To preserve the economy of the structure, it is likely that an additional steel core, or large column, would be required to support one corner of the cube from below.

The Matrix Gateway Complex was the named the Best New Global Design for 2009 by the Chicago Athenaeum Museum of Architecture and Design. The design is by Adrian Smith + Gordon Gill Architects. Thornton Tomasetti provided schematic structural consulting.

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