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A Novel Deployable Tied Arch Bridge

Adviser: Branko Glišić

George H. Lederman

Civil and Environmental Engineering

“I ended up building a large model—10 feet long—mostly because I found I loved the act of building.”


I’m writing this piece several months after graduating, and the time that has passed has only made me appreciate my thesis more. Although writing a thesis at the time seemed like a gargantuan task, the main reason I now want to return to graduate school is to recreate my thesis experience. To me, the thesis was a once-in-a-lifetime opportunity to build and explore creations of my own imagination, all with the support of my adviser and the resources of the University.

Although I found my thesis rewarding, not everyone does—so here are some of the factors I believe contributed to my success. I not only enjoyed my topic, I enjoyed the process of working on my thesis. I loved building and testing the 10-foot-long physical model of the bridge I had designed. Although the research was independent, I had great relationships with my adviser and other people like the civil and environmental engineering (CEE) lab supervisor. Cultivating these relationships proved essential for completing my work; without their technical expertise and enthusiasm, my thesis would never have been possible. Throughout my work, I kept in mind how I would write up the final thesis. Thus when the time came, I did not have to justify my experiments; instead the experiments justified my conclusions.

I wrote my thesis about a new type of deployable bridge, an idea I had while studying abroad at Oxford. I had been researching deployable structures, and I came across a photograph of the mobile, tank-based bridge that the United States military currently uses. I was stunned by the apparent structural and mechanical inefficiency of the design, so I tried applying various known deployable mechanisms to this application to see if I could produce a more efficient structure. 

Now I thought my bridge was a good idea. But that alone is not what kept me working on this project late into the night, even when the thesis deadline itself was months away. I enjoyed the process of building the bridge with my hands, testing the various components of the bridge, then measuring to see if these results matched my predictions. I ended up building a large model—10 feet long—mostly because I found I loved the act of building. I could have done a very different thesis on an equally interesting topic—like writing a code to optimize the structure of a bridge—but I do not enjoy programming nearly as much as I enjoy building with my hands, and I doubt I would have wanted to pull all-nighters working through a process I did not enjoy. 

When I decided I wanted to try to build a physical model of my bridge, I had to approach the CEE lab supervisor, Joe Vocaturo. At the time, my adviser’s lab was under construction, so I needed to beg not only for his assistance, but also for some lab space. The first time I went into his office—ready to announce my grand plans for my model—he didn’t have time to speak with me. This was one of the low points in my thesis process. I quickly realized that without his help, my thesis would never happen so I invested some time in getting to know him. Mr. Vocaturo soon proved incredibly helpful—he drove me himself to Home Depot to pick up supplies and offered advice about my project on a daily basis. Although I could analyze my model myself, Mr. Vocaturo often knew a more practical way to build and test the physical structure. I quickly learned that by deferring to him on certain issues, I could save a considerable amount of time. 

Mr. Vocaturo was not the only person besides my adviser who played a significant role in my thesis. Larry McIntyre and Barry Runner helped to machine parts in the engineering school’s machine shop, and Dean Peter Bogucki helped me to secure more funding when I needed to purchase additional sensors. Although the thesis is independent research, barely a day of work would pass when I did not receive help from someone on the engineering school’s staff.

Deciding which experiments to perform was, of course, still up to me, and by envisioning the final product, I was able to focus my work. While at Oxford, I had completed independent work (similar to a junior paper), and I had found writing up my work much more difficult than I had imagined. While doing my research, I had gone from designing one structure to another without any clear logical connection and I had not recorded enough quantitative data to firmly support my findings. These shortcomings significantly weakened my independent work overall. So while doing research for my thesis, I kept in mind how I would justify each step in the final write-up of the thesis itself. I believe there are two justifications for this approach. The first, somewhat cynical explanation is that you only get graded on the thesis write-up so it should always be on your mind. However, a second, more wholesome explanation is that your research is only as valuable as your ability to share the knowledge you have gained, so it is important to conduct your research in a transparent manner with ample data to support your conclusions. 

In my case, this meant documenting each design decision I made while building my bridge, predicting the expected stresses on my bridge using theoretical models, and then comparing these values to measured stresses from my physical model. Each of these steps proved to be fairly difficult. 

In order to illustrate one of the ways in which envisioning the final write-up of my thesis helped direct my research, I will describe the process I went through in comparing the predicted values of stress in the bridge against the observed values. I found the observed values of stress by using fiber-optic sensors provided by Professor Branko Glišić. In order for the sensors to work properly, I had to know the material properties of the wood (in particular, the elastic modulus) that I had used to build the bridge. So I took five pieces of wood, tested them in the Instron machine, and averaged my results. When I compared my observed values to the predicted values, I found the discrepancy was too big to justify with standard sources of error. I realized that there was such a large variation in the material properties of the wood that I could not average several samples and use one number. Instead I took additional samples of wood from various locations on the bridge, and used only the material properties of the wood from that area in order to determine the stress. Finally, the predicted and observed stresses fell within an acceptable range because I had thought ahead to how I would justify my results in my final write-up. 

A final thought: My thesis experience began with a low note—the department administrator e-mailed me to say I had been assigned Professor Glišić randomly because my chosen adviser had too many students. So the assignment was random but I could not have asked for a better adviser than Professor Glišić. I’m not sure whether I got lucky or whether Princeton just happens to have the best faculty in the country—but either way, don’t be disappointed if you don’t get your first choice of adviser. For example, it turned out that measuring the performance of my bridge quantitatively was one of the most important aspects of my thesis, a study that falls under the category of structural health monitoring. And it turned out that Professor Glišić had written the authoritative textbook on structural health monitoring with fiber-optic sensors. And yet his depth of knowledge in my area of interest was not even his greatest asset as an adviser. It was his continual enthusiasm and encouragement about my project that made my thesis experience.

A Novel Deployable Tied Arch Bridge

George H. Lederman

Branko Glišić

Assistant Professor of Civil and Environmental Engineering

“Advising a senior thesis is particularly gratifying because the professor can actually ‘live’ the transformation of the candidate from a student to an engineer.”

George Lederman is one of the first senior thesis advisees in my juvenile career at Princeton University. As a new faculty member at Princeton, I knew nothing about George until he sent me a short e-mail saying that he would like to make his senior thesis on a very particular topic—a deployable tied arch bridge. He even sent me a nice drawing with a conceptual idea. I liked the idea, but as someone who worked in practice for several years, I was very much concerned about the success of the thesis for several reasons. A deployable tied arch bridge has a complex, nonlinear behavior, difficult to model numerically, and, consequently, difficult to understand. In order to perform and conclude the thesis, I judged it necessary to create appropriate numerical models, but also to build a large-scale physical model, to instrument it with sensors, and to conduct testing for both assessment of the structural behavior and the ability to deploy. Testing would involve the use of fiber-optic sensors and force sensors, while the deployment should be ensured by a special mechanism. And none of these techniques was included in regular undergraduate studies! But would a senior be able to realize all these works within the given time frame? 

I was considering whether to propose to George that he work on some less demanding project, but only until he came in my office for the second time. In fact, during his first visit in my office, I explained to George what demanding work he would have to face. He simply agreed, and after we made plans and decided on the size of the physical model, he left my office. But I could see the fire in his eyes—he accepted the challenge and he liked it very much.

A few days later, George came to my office to show me something. We went down to the lab, and I could see the first pieces of the bridge ready to be assembled. At this moment I had no doubt that he would make it, and make it exceptionally well!

Advising George was for me different from teaching regular courses. Regular teaching addresses a group of students, where the knowledge is transmitted to a group and thus the lectures are oriented and adapted to a broader public. Advising a thesis focuses on one person, thus it is important to get to know well both the candidate’s strengths and weaknesses, and to “tailor” adviser involvement so it comes in the right moment and with a right dose. While teaching a regular course rather “imposes” the teacher’s knowledge to students (though leaving some place for discussion), and the teacher provides solutions to problems, advising rather provides the necessary guidance, and at the same time leaves enough space for the candidate to face the challenges and find solutions himself, thus getting his own experience out of curricula and improving his engineering skills.

Within this framework, George demonstrated the talents of a real researcher and engineer. He developed the physical model of the bridge, he applied the sensors to the bridge model and assessed its structural behavior, and finally he compared the results with numerical models he had developed. He fully understood the behavior of the bridge, and he discovered how to improve its efficiency, i.e., how to modify the static system in order to achieve better use of materials and to bridge even greater spans. He implemented improvements and testing confirmed his assumptions. At the end of the thesis, I was amazed by the comprehensiveness of his work. Just thinking about my skepticism after the first e-mail I received from George now makes me very proud of the work he performed.

For me it was very rewarding seeing all the progress and success George made while working on his senior thesis. In regular teaching, the professor usually can evaluate himself based on students’ feedback and the grades the students get at the final exam. But advising a senior thesis is particularly gratifying because the professor can actually “live” the transformation of the candidate from a student to an engineer. He can actually follow and advise the student on how to apply the knowledge he got from his regular studies, but also on how he solves his engineering problems, manages his time, and supports the stress.

George had a strong background in the major disciplines of structural engineering. He also demonstrated a high responsibility and professionalism. But besides these virtues, George had shown three other right and necessary ingredients: passion about his work, courage to dare and try, and readiness to use his hands as well as his brain. Seeing the way he actually enjoyed the discoveries, progress, and improvements he was making in his thesis was particularly rewarding for me. 

Strangely, thinking back about this complex thesis, I can’t recall any difficult part. Probably the main reason for this, in addition to George’s great personal and professional qualities, is the fact that George and I soon established a mutual confidence and openly discussed all issues.

As the final word of this text, and based on my experience with George, I would like to invite all future seniors, when choosing their topics for their theses, to think how the topics and their personal and professional qualities are related to the following notions: knowledge, passion, challenges, responsibility, hard work, and confidence.