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Design and Construction of a Spaghetti Bridge Michael Karweit Department of Chemical Engineering Johns Hopkins University

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Why build a spaghetti bridge? 1) To take math and science out of the textbook and into a project involving design, planning, and construction. 2) Because the process is instructive and fun, and it exemplifies the difficulties of putting theory into practice. Math and science? Now I’m worried. What kind of math and science? In principle, you can build a bridge without math and science. But if you want to build one that can carry a maximum load, then you need to understand the material properties of spaghetti, the theory of beams, and the physics of canceling forces (statics).

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Why spaghetti? Why not toothpicks or balsa wood? Spaghetti is very unforgiving. Design is much more important in a spaghetti bridge than a toothpick one. Spaghetti is also available in a nice form for construction--long cylindrical rods. And, one can’t complain about the cost... So, what’s the project goal? To build a bridge out of only spaghetti and glue that spans a meter, weighs no more than 750 gms, and supports the heaviest load suspended from the center of the span. The bridge is to be supported only by horizontal surfaces at each end.

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Some properties of spaghetti (dry) 1. Ultimate tensile strength ~2000 psi 2. Stiffness (Young’s modulus) E ~10,000,000 psi (E=stress/strain) For comparison, cast aluminum (wet or dry): 1. Ultimate tensile strength ~10,000psi 2. Stiffness E~10,000,000psi

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Glues: 1) White glue: Not good. Since it’s water based, the spaghetti is softened by the glue. Glue joints take forever to dry. Once dry, joints are not very strong. 2) Model airplane glue: So so. Dries relatively quickly but is slightly flexible when dry. Glue joints should be rigid. 3) Hot-melt plastics (glue guns): Easiest to use, but joints far too flexible. 4) Epoxy: Best solution--especially the 5 minute kind. Creates rigid joints. Is messy. Requires careful mixing.

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Using 5-minute epoxy: 1) Purchase variety in two separate tubes with nozzle tips. (Double plunger varieties are too wasteful.) 2) Mix epoxy and make glue joints on wax paper. Epoxy releases from wax paper fairly readily. 3) Mix very small batches--enough for maybe 5 glue joints. 4) Proportions are very important--50 - 50. Too far away from this ratio and epoxy will never harden. Many bridges fail because of unhardened joints.

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Using 5-minute epoxy (continued): 5) Squeeze same-size circular blobs of epoxy and hardener onto wax paper. Look to see that they’re of similar height. (You’re interested in equal volumes of epoxy and hardener). Mix together with a matchstick. Dime-size blobs yield enough epoxy for 6 or so joints. 6) Lacquer thinner (nail polisher remover) is good for cleaning up uncured epoxy from surfaces and fingers.

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Beams and loads--tension: Beam under tension Maximum load is tensile strength times cross-sectional area. For regular spaghetti (diameter = 2mm), maximum load is ~ 10 pounds. Load capacity does not depend on length. Failure occurs when ultimate tensile strength is exceeded.

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Beams and loads--compression: Beam in compression Failure occurs two ways: 1) When L/d < 10, failure is by crushing 2) When L/d > 10, failure is by buckling We are almost always concerned with failure by buckling. L d

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Beams and loads--compressive buckling: Buckling strength F =k d 4 /L 2 To determine constant of proportionality k: 1) measure length and diameter of a piece of spaghetti 2) hold spaghetti vertically on postal scale 3) press down on spaghetti until it begins to bend 4) read load F on postal scale 5) calculate k

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Some consequences of buckling properties: If a beam of length L and diameter d can support a compressive load of F, L d F then a beam of length L/2 and diameter d can support a compressive load of 4F. L/2 d 4F

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L 2d 16F and a beam of length L and diameter 2d can support a compressive load of 16F. Bigger beams can be fabricated out of smaller beams, as in a truss. The fabricated beam will have the same buckling strength as a solid beam, provided the buckling/tension strengths of the component beams are not exceeded.

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Beams and loads--bending: Very little strength. Never design a structure that relies on bending strength to support a load.

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Statics: 1) At each joint or node: 2) Joints are assumed to carry no bending loads; therefore all forces are compression or tension and lie in the directions of the beams. x y -F F/2

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Use Bridge Designer to calculate loads: http://www.jhu.edu/~virtlab/bridge/bridge.htm

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Design and construction ideas: 1) Triangles are a construction engineer’s best friend, i.e. there are no bending moments in triangular elements. Good design Bad design (truss strength depends on bending strengths of members)

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Design and construction ideas (cont.): 2) Taller is better: note loads on these two structures.

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Design and construction ideas (cont.): 3) Don’t forget about the 3rd dimension. A good design in the x-y plane, may be a terrible one in the z-direction. 4) Recall: tension members do not need to be fabricated as trusses. Their strength depends only on cross- sectional area. 5) Plan the total bridge design. Estimate the weight of each of the components, so that you will not exceed the weight limit. 6) Make a full-size pattern of your bridge. Build the bridge on this pattern. This will ensure that all components will assemble properly.

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Design and construction ideas (cont.):. 7) If a number of strands of spaghetti are to be used together as a single member, do not glue their entire lengths. “Spot” glue them at intervals of about 1”. This will provide adequate strength without adding excessive weight. 8) For economy of time, joints should be “overlaid” not “butted”. Butt joints require careful sizing. Overlaid joints do not. Excess material may be cut off after assembly. Butt jointsOverlaid joints

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Which is the better design and why (cont.)? a) b) a)b)

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Which is the better design and why? a)b) a)b)

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> 5cm. < 2mm. Bridge Decking Load 100 cm < 50 cm Loading Platform and U-bolt < 5cm Total Weight < 750gms. Bridge Schematic:

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