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Structural Modeling


  • The Structural Modeling unit will last one week. It will explore the significance and basic concepts of modeling structures using bridges as a case study. We will teach the students both how and why physical structures are built and tested as computational models. Bridges are a good example of structures that must be evaluated extensively before they are physically built. We will explore a bridge-building game build virtual virtual bridges and testing its weight capacity under variable loads. Students will build and test physical versions of their computer models structure using K'nex, and compare the two types of models - computational and physical.

Background Reading for Teachers and TAs

  • http://www.in.gov/indot/files/bridge_chapter_01.pdf
    • "Bridge building for dummies." Provides an explanation of the duties of Bridge Technicians and defines a number of terms associated with bridge constructions, as well as explaining some of the more common failure points and why they're failure points. This is perhaps unnecessary if the teachers and the TAs possessed a solid knowledge of the subject, but could be extremely helpful otherwise.

Reading Assignments for Students

  • http://pghbridges.com/basics.htm
    • This overview would be appropriate for the beginning of the unit, introducing students to a number of different basic and advanced bridge types, and various tidbits of information about them. If so desired, this could be condensed into a handout.

Reference Material

Lecture Notes

Lecture 1:


  • Review key concepts from the units on static and dynamic models, remind people of the difference, and how the two types of models work in conjunction.
    • Static Models
      • Static models are computational models that do not change over time. This could be manifested in the environment of the model, such as grass and rocks.
    • Dynamic Models
      • Dynamic Models are models change over time.
      • They include rules and specify how models should interact with their static environment
      • They can interact with other dynamic model entities
  • Why do we want to model bridges and other structures before they are built?
    • Because it's important to get a sense of when the bridge will support weight before it is built.
      • When I (Dylan) took POCO / Software Engineering, I recall a story that Charlie told about why someone he knew (I think it was his father) believed that software engineers, like other professions, should be required to get a governmental license to practice software engineering, due to the fact that now software is important enough and used widely enough that the failure of such can cause a loss of life. I believe that this story is very relevant to this point in the lecture.
  • Explain the various types of bridges introduced in Bridge Basics
    • Kingpost
      • Basic bridge type, demonstrates the core mantra, triangles are strong!
    • Queenpost
      • Similar to the Kingpost in design and concept but geared towards longer-spanning bridges.
  • Explain why and how modeling structures such as bridges is different than earlier examples of fire, etc, and how certain key aspects of the procedure and underlying theory are the same
    • Bridge simulations are necessarily more complex and comprehensive then the fire model we looked at in previous weeks. Bridges have many stress points, and each stress point must modeled individually produce accurate data, ie Will the bridge support the weight of cars, will it even support its own weight?
  • Prepare the class to do the lab. Explain the directions outlined in the lab section below.

Lecture 2:

Wrap-up/Open Questions

  • Review Components of the Lab.
  • Display a table of each group's lab results, (max load) and might show an picture and give an explanation for the best (most efficient bridge)
  • Explain how best to determine the accuracy of a bridge model.
    • Whenever possible, it is most important to draw data from multiple sources.
    • Physical models can be used to validate computational models, assuming the physical model faithfully and accurately tests the model.
    • If the computational model agrees with the physical model, both models are likely valid.
  • Where can we go from here?
    • Modeling building strain
    • Introduce the 'shake table' and show the split-screen illustration of the model building quivering on the shake table next to the computer simulation. Shake table video
    • Do bridge-builders actually build physical models, or is all the planning done in silico?
      • When a bridge model is being developed in silico, the software engineers and designers must validate the model before it can replace more traditional means.
      • At some point they must build a miniture model, or devise some other way to validate the computational model, such as placing sensors on real bridges to measure stress.
    • What are the positive features of using computational models, what are the downsides?
      • Computational models offer a virtual wet lab in that models can be constructed and tested without building (and then destroying) a simulated environment. To this end, computational models are an attractive option for engineering teams, where the more testing is integrated into the development process, the more efficient the overall operation.
      • Computational tools allow for a more frequent test cycle because after the model is designed and constructed in silico, testing the model is fairly cost effective.
      • Physical models must be reconstructed from the ground up (literally) each for each new test.
    • How will an increase in processor speeds impact these pros/cons?
      • Computational models suffer from a tension between precision and time spent performing calculations. Accurately simulating the real world can consume a processor capable of trillions of calculations per second.
      • The challenge inherent in designing and using computational models lies in the balance between accuracy and precision, and as CPUs become more powerful, complex models become more feasable.
      • If the computational model can be deemed precise, then additional CPU horsepower will greatly improve the accuracy of each test run in silico.


Nice work!
Nate's virtual bridge
Nate's knex bridge
  • The lab session will require the students to build K'nex models of bridges they designed in software. This lab will be completed in groups.

Pre-Lab Assignment

Students will complete the demo portion (through level 5) in the software program Bridge Construction Set described below. The first lecture will give them a sense of which designs are most efficient and hopefully encourage them to try to build the most efficient bridge possible, ie the bridge with the fewest number of components.


  • Split in to lab groups of four students per group.
  • Distribute Knex to the groups.
  • Recreate the bridge built with the fewest number of components by a group member using the provided Knex.
    • The BCS software automatically saves the bridges created, (and allows you to save to a file) so students will be able to call them up at lab time.
    • After deliberating long and hard over whether to use the PASCO bridge set or K'Nex, we decided that K'nex would be a better option for a few reasons.
      • 1. They break. Knex break under load, and this is a positive feature. The Pasco bridge parts are not intended to break but instead are built to be highly durable. To use the PASCO kit to validate the physical model by determining the maximum load would rely on a $399 load sensor kit per group.
      • 2. Breaking things is fun. If the above rational wasn't enough, we both agreed that students will have more fun if they actually get to see the point where their models fail.
  • When the bridge is completed, test the structural integrity by handing the bridge to the instructor.
    • 'When all the bridges are completed (or a good number) the instructor will lead the class in testing each bridge. Weights will be hung off the center of the bridge to simulate the weight of a car or truck.
  • Students should be familiar with wikis by now, so instruct them to insert a picture of their bridge, (taken with the cameras on the D224 iMacs) and the max load the bridge could hold into a table in the wiki.


  • Required elements
    • Screen Shot of the Bridge Construction set model used to build the Knex model. An explanation of the structure. What structural properties allow the bridge to support weight?
    • Image of Knex construction. This must be a (fairly detailed, probably hand drawn) diagram of the bridge, annotated to indication the stress distribution observed during testing (both in silico and with Knex) They will compare the physical model with the software model. How are they different, how much weight did the bridge support? How and why did the Knex bridge break? Be Specific? Does the Knex model verify or validate the simulation? Does this experiment support or invalidate either model? Both models?
  • Groups will be instructed to compare the point of failure in both their Knex models and their Bridge Construction Set models. The students will compare how stress is distributed both within software (using the stress display function) and make empirical observations of stress as they test their Knex models. Can they make an estimation of how the stress is being distributed when the weights are applied? Can this estimation be verified?
  • Visualization opportunities
    • There's not really an opportunity for visualization, students will only be gathering qualitative information about the way weighted bridges look. Students will be able to make informed conclusions, but will not be able to produce a graph or a table of their observations.
  • Optional elements
    • Build additional bridges in Bridge Construction Set at higher levels. Does running multiple trials further support (or reject) your claims?
      • This optional element relies on purchasing the license. If cost is an issue, we could only buy 5-10 licenses and not require the higher levels but instead offer them as an optional component, only installing the software on selected machines.


Bridge Construction Set

  • A bridge-building computer game. It offers a fairly detailed 3-D OpenGL model visualization. The game is organized into stages of increasing complexity. Available for Mac OS X / Linux / Windows.
    • After completing the demo levels, it seems that we might want to actually get licenses. The game is actually really fun. Different levels use different bridge building materials, such as iron (the basic component) steel, and cable.
    • We decided to use BCS because it visualizes the bridges in 3-D, and 3-D modeling software should make the students more comfortable translating their models to physical Knex models. (described later)
  • Students will be expected to come to the Dennis 224 Lab to use the Bridge Construction Set full version ( if we choose to purchase it ) or they can download the demo on to their personal machines.

Bill of Materials

  • Bridge Construction Set is not free software. A full license costs $19.99. A fully playable demo is available free for Mac OS X/linux/windows We will need to purchase at least 5 to ten licenses to allow for further experimentation, and a bonus question on the lab.
    • The demo allows gameplay up to level 5. Completing all five levels took me about 10-15 minutes. Note they are denoted easy. From what I've seen on youTube, this game gets a lot harder. That's so cool that you looked it up on youtube!
    • When a user opens the program, the last construction for that level is loaded. The software (even the demo) makes it easy to switch between levels.
    • Assuming we could get a volume license discount, 10 license would run the CS department $150.
  • Knex
    • We tested the viability of using the stock bridge knex set. This has a few inherent problems:
      • Trying to recreate an intentionally simple bridge such as a kingpost or a queenpost using the funky elastic pieces and small components in the bridge set is confusing. We need to keep the number of different pieces small to make sure all of the lab groups are focused and on the same page. Using a limited number of knex pieces will not only simplify the initial setup and inherent confusion, but will also make students more comfortable experimenting with their designs. If the lab groups are given too many options in building the model, they won't get much out of this lab.
      • KNEX Pieces on Wikipedia gives a good overview of the standard colored pieces. Gray is the best option at 7.5 inches. If we could buy a bulk gray pack, and a bulk pack of red. Keepin' it simple.
    • Knex Bulk Pack - Knex on ebay
    • Knex Bridge Kit - $30 at Veachs in Richmond. Buying 15 of these kits would cost $450.
  • Weights
    • Ideally we'll use bricks, of the same approx. weight to test the bridges. Bricks are cheap, and most importantly heavy. Using physics weights is ideal, but the average bridge capacity will most definitely exceed our weight supply.


CRS Questions

  • How would you describe the class of structural models?
    • a)Dynamic
    • b)Static
    • c)Accurate
    • d)Precise

  • What does the shake table show about a bridge model?
    • a)Whether the model shakes
    • b)How often the model moves in a normal environment
    • c)The effects of uneven ground on a structure
    • d)The expected effect of earthquakes and other natural disasters

  • Which is not an example of a structural model?
    • a) a bridge model
    • b) an automobile model
    • c) a building model
    • d) a beach-front shanty

Quiz Questions

  • Using the framework we've described in the past few weeks of static and dynamic models, answer the following questions: First define explain what aspect of the model is static. What aspect is dynamic?
    • The static aspect of structural modeling is represented by static structure built in the edit mode of Bridge Construction Set. This includes the simulated landmass over which we build our bridge, the static bridge structure, without applying the notion of gravity or other dynamic effects. Essentially the bridge is static until we leave the edit mode and enter the testing mode. The model becomes dynamic when we apply environmental rules such as gravity and wind.
  • Compare the King Post and the Queen Post from the student reference Bridge Building Basics. What are the advantages of each? Which bridge type is better for a smaller gap?
    • The Kingpost is better for shorter distances, because it is simpler to construct. The triangle design makes it very strong. The Queenpost is better for longer distances, however some strength is lost due to parallel midsection.

Structural Modeling Metadata

This section contains information about the goals of the unit and the approaches taken to meet them.


This unit would be well suited for one week early in the semester. The basic concepts of bridge design are fairly straightforward and do not require signifigant overhead.

Concepts, Techniques and Tools

Using models, modifying models, developing models Abstraction Accuracy vs precision Validation and verification Data collection Spreadsheet Bridge Construction Set Game

General Education Alignment

Analytical Reasoning Requirement

Abstract Reasoning

From the [Catalog Description] Courses qualifying for credit in Abstract Reasoning typically share these characteristics:

  • They focus substantially on properties of classes of abstract models and operations that apply to them.
    • Complete. The unit is designed to investigate how they can be physically and computationally represented.
  • They provide experience in generalizing from specific instances to appropriate classes of abstract models.
    • Complete. This unit relates the specific instance of structural models to the general class of all computational models.
  • They provide experience in solving concrete problems by a process of abstraction and manipulation at the abstract level. Typically this experience is provided by word problems which require students to formalize real-world problems in abstract terms, to solve them with techniques that apply at that abstract level, and to convert the solutions back into concrete results.
    • Complete. Students must hold two concepts in their minds to understand this what's going on in this unit. Firstly, they must grasp the low level details of building bridges and structures. The lab component will address this. The second challenge is to be able to relate their lab efforts to a more general construction.

Quantitative Reasoning

From the [Catalog Description] General Education courses in Quantitative Reasoning foster students' abilities to generate, interpret and evaluate quantitative information. In particular, Quantitative Reasoning courses help students develop abilities in such areas as:

  • Using and interpreting formulas, graphs and tables.
    • Partial. The students use tables to organize bridge data. The focus of this section, however is not on interpreting tabluar data.
  • Representing mathematical ideas symbolically, graphically, numerically and verbally.
    • Complete. The models provide a framework for visualizing physical (mathematical) constraints.
  • Using mathematical and statistical ideas to solve problems in a variety of contexts.
    • Complete. This is one context where we're using mathematical and statistical ideas.
  • Using simple models such as linear dependence, exponential growth or decay, or normal distribution.
    • Partial.
  • Understanding basic statistical ideas such as averages, variability and probability.
    • Complete. Testing computational models is a deterministic process. Maybe we could introduce the difference between probabilistic and deterministic.
  • Making estimates and checking the reasonableness of answers.
    • Complete. Students will try to build different types of bridges and determine the 'reasonableness' of their solutions by the simulated test outcome.
  • Recognizing the limitations of mathematical and statistical methods.
    • Complete. Physical models attempt to account for a finite number of environmental variable, such as wind and gravity, however they cannot account for all variables.

Scientific Inquiry Requirement

From the [Catalog Description] Scientific inquiry:

  • Develops students' understanding of the natural world.
    • Complete. The students are modeling bridges - the structures they depend on to travel and move from place to place. If that's not understanding of the natural world I don't know what is.
  • Strengthens students' knowledge of the scientific way of knowing — the use of systematic observation and experimentation to develop theories and test hypotheses.
    • Complete. Students must compare the two models - the model in software and the physical model. To effectivily accomplish this task they must exercise systematic observation and experimentation to demonstrate how, and most importantly why the two models behave the way they do.
  • Emphasizes and provides first-hand experience with both theoretical analysis and the collection of empirical data.
    • Complete. Students will understand how physical models and computational models can be used to simulate the same structures and processes.

Scaffolded Learning

  • The scaffold pedagogy emphasizes the importance of introducing new ideas and concepts by explaining how those new concepts fit into the context of the material previously covered. Information is contextualized as pedagogical dependencies.
  • The Structural Modeling unit is scaffolded in the sense that as students learn about the structural intricacies of bridge building, they will be able to construct more effective models. The high-level view of bridge types will allow the students to implement these qualities into the bridges they build in the simulator. Once the simulation is complete, the students will build a physical model under the expectations that the K'nex will behave as expected given the test results show by the computer program.

Inquiry Based Learning

Building Bridges and Breaking Knex is a fun, non-menacing way to explore the world of computational models. Students will figure out the importance of verification in building useful models. This lab cuts students loose to explore a topic that they probably don't know much about. This factor could be a challenge for some, but will teach them important skills applicable to a wide range of disciplines.

Structural Modeling Mechanics

General Feedback

Can you play around with it yourselves and see how many you think are reasonable?

  • Where do the cameras come into this? Before and after they break would be neat...
  • Also need an estimate of how many K'Nex models we need and how much they cost. Ditto. The software we can keep, but if the K'nex is breaking every year then we should know what kind of course fee to tack on...

  • This is good material, and the bridge building effectively shows how the mining of data can be used to make models which then help the creation of new physical manifestations-- but I think this unit needs to narrow down on exactly what it wants to teach. Will this lab have "hard modes" for extra credit? A resolution of the unit's intent will make the lecture outline a lot more coherent. Ditto
    • Yes, there will be opportunities for further investigation during the lab period, including more in depth comparisons between the physical and computational models.
  • Also, the teacher/TAs will have to make sure they got this material under their belt when this lab rolls around, or, as you mentioned above, there will have to be some "reassuring," and we don't want the students to lose faith!

What size are you thinking? Is this from the prelab? How will they evaluate which is the most efficient bridge? Also, do we have any constraints? For instance, how far it's spanning? I'm thinking there should be at least a minimum span.

    • Ok...? What's the calculation? Confused. Seconded... more detail!
    • Do we have a way for them to save and bring in their demos from the Bridge Construction Sight?
    • We might be able to contact the developers at Chronic Logic to gain more insight about this. Excellent idea, maybe they even want to donate licenses for us. Mm, free stuff.

How did you decide on this particular software over the others? Just curious.

  • I think you have all of the sections, but some of them are repeated twice, which I'm very confused about... Merge the double software and bill of materials sections! EDIT: Ahh, I see, these software/materials are specific to the pre-lab assignment. Perhaps format this a little more clearly.

Excellent! Myes, I like this better as a pre-lab assignment. Good stuff.

  • Remember to relocate past comments!
  • Where will they be expected to use this software? If this is a pre-lab assignment, do they still have to come to a computer lab to use the licensed version?

My only major suggestion would be to keep all of the meaning here while trying to simplify the way you say it. In other words, if you could write it as directions to give to the students, rather than as something for the teacher (while still keeping information necessary for the teacher in bullet points below). Ditto

  • Where will they be expected to use this software? If this is a pre-lab assignment, do they still have to come to a computer lab to use the licensed version?

This is dependent on us purchasing licenses, right?

  • Make sure to answer your own questions for us. So will these be A/B questions? Can support more options (multiple choice) if you want.

These lectures are from a very high level. It would be helpful for us (reviewers, classmates, etc) to see more bullet points of what you're thinking about. For instance, why are modeling structures different than the earlier examples? This is very important. Ditto Ditto.

Consider more background about why static models like this are useful and how they are used

Lab Feedback

  • Feedback specific to the lab component. Either in-line notes or a link to a separate page.
  • Some thoughts about what to look for:
    • How long did it take?
      • I spent about an hour constructing some of the example bridges in the book then playing around with hanging weights on them. It's entirely possible that this could take more or less time, depending on whether the students wanted to construct more or less bridges and how thoroughly they wanted to test them.
      • Less than an hour; but I used the Knex instruction booklet. I started trying to come up with my own and had trouble - maybe I'm just stupid.
    • How appropriate is it to the material in the unit?
      • Very.
      • Agreed.
    • Are the instructions complete or did you have to fill-in gaps.
      • The instructions are complete in a broad sense. In a specific sense, not so much. We currently instruct the students to build "The most efficient bridge" out of all the ones built in the group. It's difficult to decide what qualifies as the most efficient bridge... uses the least parts? Most streamlined looking? Least vulnerable to breaking? Average between one or more of the previous factors? The easy way to solve this is to simply have students pick a bridge that they would like to build, and let them decide which one that is, but that brings up the possibility that the students may pick a bridge structure that is too complicated to complete with the materials available.
      • Agreed; it seemed the only factor was price in-game.
    • Is it too easy? Too hard?
      • That depends on a variety of factors. One of the problems is the media through which we're conducting the lab. K'nex is durable, and some of the structures I tested tended to bend instead of break. Additionally, more weight will be needed in order to break some of the structures I tested, I would guess on the order of 10-20 pounds, possibly more.
      • I'm worried about it being too easy if the inherent strength of the K'nex is enough to support weight in an unrealistic manner. Additionally, some of the more uh... advanced (I guess) bridges such as suspension and cable-stayed don't work like they do in real life, being supported by the inherent strength of the medium on the deck of the bridge rather than being held up by cables, etc. This would make it more difficult to construct a model of the bridge that reacted realistically to stress.
      • Another factor that makes things more difficult is the scale of the model. Just how big do we want them to make the bridges they designed?
      • It's a little difficult to tell where the bridge is being stressed in the K'nex version unless an extreme amount of stress is applied. The plastic rods don't move very much under little stress.
      • It's not immediately easy how to build one's own bridges using the knex. I'm not sure it's all that challenging.
      • The video game is pretty easy, but fun and pedagogically useful.
      • Agreed; the knex just seem too strong.
    • Is what to look for, collect, and analyze clearly delineated?
      • I would say so, yes.
      • Yes.
    • Can you easily see what the purpose of the lab is and what you learned from it?
      • Yes.
      • Yes.

Archived Feedback

  • As you address comments in your unit move them to here with a note about how you fixed it.


Bryan Purcell, purcebr@earlham.edu Dylan Parkhurst, dcpark06@earlham.edu