This is my Spaghetti Bridge Competition page from Fall 2007. Feel free to use it for your competition. I hope it helps teams build the best spaghetti bridge ever!

**Spaghetti**** Bridge**** - Rowan University - Freshman Clinic I, Section 3 - Fall 07**

Introduction

Grading - Bridges

Grading - Project Report

The Design Process

Design Assistance - Trusses

Design Assistance - Beams

Design Assistance - Constraints

Competition Rules

Each group is to build a bridge made from spaghetti and hot melt glue. The object is to construct the bridge with the highest load to bridge weight ratio while still meeting the competition rules. Bridges will be loaded until they fail.

Bridges are judged based on:

- Aesthetics - elegance and neatness, e.g., an attractive design, no gobs of messy glue, no obvious twisting...
- Loading capacity - The more the better,
- Bridge mass - must weigh no more than amount specified in competition rules,
- Performance under load - e.g., load to bridge weight ratio and no excessive deflection or twisting, and
- Conformance with any additional competition rules.

Bridge Final Reports are graded based on:

- Writing aspects - i.e., format, spelling, grammar, references, & clarity. See the student resources page for help, especially the project report section. Given that you've been asked to turn in a project report, understand that you are expected to treat the assignment with some depth. A Project Report is a significant document.
- Technical aspects - i.e., describing the design process you followed (problem identification, problem definition, search, constraints, criteria, alternative solutions, analysis, decision, specification, & communication). See below for more on the design steps.

Follow the design steps in order to identify a good design for your spaghetti bridge. Then describe the design procces as best you can in a project report. Record EVERYTHING in your lab books. This include descriptions of the spaghetti, spaghetti beams, glue & glue gun, software used, equipment used for testing (i.e., make and model), alternatives, analyses, results, etc.

*Problem identification* - Be creative! Come up with a good reason for wanting to build a spaghetti bridge.

*Problem definition* - Make sure you understand the problem before you begin. Treat this like a mission statement. It should guide you to a good design. Use the constraints and criteria to write down spedific rules.

*Search* - Find as much spaghetti bridge information as you can, especially on the web. Learn about bridge design in general.

*Constraints* - Based on the competition rules, the rest of this website, and the results of your search, list the constraints.Constraints tell you what you must do and what you cannot do, e.g., you can only use spaghetti and hot glue and the difference between the lowest and highest points on the bridge cannot be more than 50 cm. Constraints should be measurable.

*Criteria* - Based on the competition rules, the rest of this website, and the results of your search, list the criteria for the design. Criteria re things you want to maximize or minimize to make the best design, e.g., the load to bridge mass ratio. Criteria should be measurable.

*Alternative solutions* - Each student must develop at least three truss designs (the Individual Alternatives). The team should then select at least three Individual Alternatives to investigate further (the Team Alternatives). One of these designs will be selected for further investigation (the Bridge Candidate). If further investigation indicates it is a good alternative, continue; otherwise, generate more alternatives. Design is often an incremental process. Finally, select an alternative to build (the Bridge Prototype). Even at this point, you may decide to return to an earlier point in the process and generate more alternatives.

*Analysis* - Analyze the Individual Alternatives by comparing them to successful designs found during the search process. Select the three best Individual Alternatives for further analysis. Analyze your Team Alternatives at the truss level using an appropriate computer program, such as Bridge Designer. West Point Bridge Designer may also be used. Select the Team Alternative that minimizes compressive forces and/or the length of beams in compression, keeping in mind that very large tension forces are also a problem. Also consider how easy the bridge will be to build. You now have a Bridge Candidate. First, design the individual beams for the Bridge Candidate (see the Design Assistance sections, below). Then check the bridge weight (including the beams, glue, cross bracing, loading platform,...). If the bridge is just under the maximum allowable weight, you have a Bridge Prototype! If it is way under, reanalyze in Bridge Designer with a higher load and redesign your beams. If its way over, reanalyze in Bridge Designer with a lower load and redesign your beams. Repeat until you get a bridge that is just under the maximum weight. What does "just" mean? Enough under that you aren't worried that it will end up over when you build it. Design is an incremental process. Feel free to repeat an earlier point in the design process. Also, you are welcome to select your Team Alternatives by analyzing the Individual Alternatives in Bridge Designer; however, this could be time consuming.

*Decision* - For the Individual Alternatives, the suggested analysis process is comparison with recommended/winning bridge designs (both real and spaghetti) and/or bridge design rules-of-thumb. Your desicion should be based on what you learned from your search. For the Team Alternatives, the suggested analysis process is based on the results of the Bridge Designer program and consideration of buildability. Pick the bridge that best handles load and is buildable. For the Bridge Candidate, final design is based on designing the individual beams and keeping the bridge just under the maximum weight. Use Excel to design individual beams. It is critical to design beams appropriately. A poorly designed beam is either (1) underdesigned, meaning that it fails well before other beams, thus limitting the load the bridge can handle, or (2) overdesigned, meaning that it is bigger than it needs to be and adds unecessary weight to the bridge..

*Specification* - Create good drawings of your bridge (and the alternatives). For the final design include a parts list (beams, loading platform...) and a materials/equipment list (spaghetti, glue, glue gun...). Include descriptions of the types of beams you used, i.e., number and configuration of spaghetti strands! Also describe the equipment used for testing (i.e., make and model)! You may submit drawings made by hand or with a drawing program.

*Communication* - The project report! See the project report section on the student resources page.

Study bridge design in general. Look on-line for bridge designs that have been successful in other spaghetti bridge competitions. Identify at least 3 good truss design alternatives.

Calculate tension and compression loads for each truss using the Bridge Designer program (or equivalent). Select a truss design that minimizes compressive forces or the length of members in compression. But don't forget about "buildability" and weight! Alos, very high tension forces might also be a problem. I suggest building a bridge that is close to the maximum weight and hold as much weight as possible. his may require an interative design process, designing the bridge for different loadings.

Most designs will consist of two identical truss systems, side-by-side. You will also need to connect the trusses and include cross-bracing to keep the bridge from twisting. Finally, you will need to include the loading platform.

Once you've selected a Bridge Candidate, you need to design individual beams. At its simplest, this entails ensuring that the beam can handle the tension or compression force it will be subjected to under load. You may even decide to replace some individual beams in compression with trusses.

** Beams in tension** - Calculate the maximum force (F

F_{m} = UTS x A

According to the spaghetti bridge people at Johns Hopkins (JH), the UTS of spaghetti is about 2000 pounds per square inch (psi). We tested three strands of spaghetti at Rowan. Each broke at about 15 pounds and had a diameter of approximately 1.8 mm. This results in a UTS of about 3800 psi, quite a bit higher than the JH value. To be conservative, you may want to use the JH number. If you use a built-up spaghetti beam (i.e., multiple strands) the UTS stays the same, but the total mass it can handle increased because of the increase in cross-sectional area.

Bridge Designer will give you F_{m} for each beam in tension. Then determine the required cross-sectional area of a given beam from

A = F_{m} / UTS

Determine the number of strands of spaghetti needed to make a beam with sufficient area.

** Beams in compression** - We are most concerned with failure by buckling.

The simplest way to estimate a buckling force is to make a beam and load it on a balance. Hold the beam vertically and press against one end, pushing it into the balance until it just begins to deflect. The reading on the balance is an estimate of the buckling force (or mass). Build beams the same length as specific beams in your Bridge Candidate and test. Build beams with more and more strands, until you find one with a sufficient buckling force. This method will work, but may be time consuming. It might be better to save this until you are building the Bridge Prototype, using it as a final check.

You can design beams quickly using Excel and buckling theory. The buckling force (P_{c}) is a function of Young's Modulus (E), the area moment of inertia (I), and the length (L).

P_{c} = E I (pi)^{2} L^{-2}

"pi" is 3.14159. L is the length of the beam. E is the ratio between stress and strain for a given material. Stress is the force per area. Strain is the fractional change in length. E is usually measured by pulling apart a beam and measuring the resulting strain and stress. For many materials, the relationship is linear over a significant range of strains. The JH spaghetti bridge people suggest it is about 10,000,000 psi for Spaghetti. Tests conducted at Rowan University, using two different methods, suggest it is about 1,000,000 psi. You will measure E in class. Use the class value.

I is the second moment of area around a given axis. When calculating the buckling force, we calculate I based on an axis through the centroid of a beam's cross-sectional area, which for symmetrical areas is simply the center. For example, for a cylinder (such as a single strand of spaghetti), about its center:

I = pi d^{4} / 64

Combining the last two equations, one can see that, for cylindrical beams, P_{c} increases with diameter (d) to the 4th power and decreases with length (l) to the 2nd power. You can make a beam that can withstand a larger buckling force by making it wider (e.g., thicker spaghetti or building up a beam with multiple strands) or by making it shorter (e.g., shorter piece of spaghetti). A single long beam can also be replaced with a truss made of shorter beams.

You can use the P_{c} formula to predict the buckling force of any beam. I's for some typical built-up spaghetti beams are given in the Spaghetti Bridge 2nd Moment of Inertia Page. Just plug in the diameter of a single spaghetti strand into the appropriate formula to calculate I.

Solve the P_{c} equation for I and you can estimate the I needed for any beam subject to a given buckling force. Bridge Designer will give you P_{c} for any beam in your bridge in compression. You also know the Length of each beam because it's your design!. You will estimate E in class.

I = P_{c} L^{2} E^{-1 }(pi)^{-2}

Use the equations on the Sphaghetti Bridge 2nd Moment of Inertia Page to identify a beam with large enough I. Remember, d in the equations on the Sphaghetti Bridge 2nd Moment of Inertia Page is the diameter of a single strand of spaghetti.

*The Safety Factor* - Engineers often use a Safety Factor (SF) when designing. Beams are typically meant to withstand a particular tension or compression force. If you size a beam to handle twice the design load, or twice the predicted buckling force, you've used an SF of 2. Larger safety factors are used when uncertainty is greater and/or the consequences of failure are higher. Uncertainty may be the result of lack of experience, gaps in theory, or reliance on assumptions. No one will die if your spaghetti bridge fails, but your grade may suffer. You can gain experience by testing your bridge on your own and modifying it based on your results. Are there gaps in your theory of buckling force? What assumptions have been made to apply the equations given above? One assumption is that the individual spaghetti pieces in built-up beams are perfectly attached to each other (e.g., they don't slip past each other). Another assumption is that the presence of the glue doesn't effect the materials properties, e.g., E. What safety factor should you use?

Because there is no maximum load the bridge should handle (i.e., the more load the better), perhaps the safety factor is not applicable for this competition. With regards to getting a good grade, I suggest builidng the best bridge you can, with a mass close to the maximum allowable. In otherwords, just try to maximize the load your bridge can handle. That way you will, hopefully, avoid having your bridge fail at a low loading. If your bridge is well designed and constructed, it will have a high load to bridge mass ratio. The proper specification of each beam is critical to obtaining the highest ratio, as the weakest beam (relative to the tension or compression force it must handle) will cause bridge failure, while beams that are larger than needed reduce your load to bridge weight ratio.

**Design Assistance - Constraints**

The mass of your bridge is constrained by the rules of the competition. After designing your truss and selecting the various built-up spaghetti beams you intend to use, predict the as-built mass of your bridge. Make up at least one beam of each type and measure its mass and length, so you can determine its mass / unit length. If you haven't already, measure its buckling force, and compare it the theoretical! Then, using your bridge plans, estimate the total length of each beam type used in the bridge. Add any additional weight, e.g., the loading platform / U-bolt and additional glue for connections. Add in a contingency factor to be safe. Do this all in Excel. Include the resulting tables (properly documented) in your final report). If your bridge is over weight, go back to the truss or beam design stage.

1. The bridge is to be built from spaghetti (cylindrical forms of pasta) and hot melt glue. Both will be provided. **Be careful with the hot glue. If too much is used it can cook and melt the spaghetti. Always work on wax paper (supplied). Don't make a mess! Clean up after yourselves! Do not leave plugged-in glue guns unattended! If you need more supplies contact the CEE technician, Mr. Nolan. **

2. The bridge shall be free-standing and must span two level surfaces which are 1 m apart. Thus, the bridge needs to be MORE than 1 m long.

3. The support for the bridge shall be from the top of the level surfaces. The edges of the level surfaces cannot be used in any way for support. Any vertical surfaces cannot be used in any way for support.

4. The bridge must be constructed so that a (hypothetical) deck could be added to provide a suitable road surface across the full span of the bridge at approximately the height of the two level surfaces (see rule 1). A block of wood (5 cm width x 6cm high x 10 cm long) representing a vehicle must be able to move along the length of the hypothetical deck.

5. You must incorporate a "loading platform" consisting of a U-bolt secured to a piece of plywood 0.7 cm x 5 cm x 10 cm (supplied). This platform is to be attached at the center of the bridge just below the hypothetical decking. All loads will be suspended from this U-bolt, and there must be a clear space directly below it to allow loads to be attached. Loads will be attached using an S-hook, and, if necessary, a 10 mm diameter metal rod extension. If during loading, the bridge twists in such a way as to cause the bridge to touch the rod at any point other than the U-bolt, thus lending additional support, the bridge will be disqualified. Make sure the platform is attached well, as all of the weight applied to the bridge is transferred through it.

6. The maximum vertical depth of the bridge, from the highest point in its structure to the lowest cannot exceed 50 cm. This does not include the loading platform. The bridge can go above and/or below the support surfaces.

7. The maximum weight of the bridge including the loading platform must not exceed 0.75 kilograms.

Note: These rules were adopted from the Johns Hopkins Spaghetti Bridge contest, which in turn are similar to rules developed for contests at Okanagan University College. For a bridge meeting similar restrictions, load capacity to bridge mass ratios of around 90 have been designed, built and tested (according to Camosun College). That's a load mass of 65 kg. Okanagan University claims a world record of 176 kg for a 1 m bridge using epoxy, a load capacity to bridge mass ratio of 235!