 How can math help me understand my world?  What factors influence bridge strength?

Project Directors use good judgment to make suggests to guide carpenters in ways to help their team understand how to strengthen their bridge.

 Bridges can be designed in different ways to withstand certain loads and potentially destructive forces.

 START EARLY, PLAN THOROUGHLY, AND WORK STEADILY. Do not put your work off to the night before it is due. Toothpick bridges need time to dry property.  * Try different constructions. Build as many versions of your prototype bridge as possible. There is a list of suggested bridges.  Keep track of time. You may have to let go of an idea so that your final design can be thoroughly tested. Final building day is next Friday, January 14 th.  The spacing between the intersections of toothpicks greatly affects the strength of your toothpick bridge. Test each toothpick BEFORE you use it. When using flat toothpicks to build your bridge, roll the toothpick between your fingers first to see if it can stand up to a little pressure without breaking. If using round toothpicks, apply a little pressure to bend it. Good glue joints make for good strength.

 Your bridge’s strength is also dependent on its vertical height. However, this is not to say “the higher the better” as there are limits.  Consider the strengths and weaknesses of a single toothpick under these three forces: COMPRESSION, TENSION, AND SHEER.  Watch out for “stress risers”. Before breaking your bridge will give and bend under the load of your test weights. Remember what happened to the Tacoma Narrows Bridge collapse of 1940? What caused it to collapse?

If you have made some parts of your toothpick bridge so strong and hard that it will not give (be flexible), your toothpick bridge will fail in another area sooner than if the whole bridge were able to adjust to the forces acting on it. To reduce drying time, do initial gluing with SMALL drops of glue (applied with an extra toothpick). You can go back later and reinforce these small drops with more glue after everything dries. GOOD LUCK AND HAVE FUN.

 Compression: Compression is a pushing (compressing) force. The shorter a piece of wood is, the more compression it can hold. The longer a piece of wood is, the less compression it can hold. When you compress a long stick of wood you will notice that it starts to bend. When a piece of wood breaks because of compression, we say it failed from buckling.  Typically the top chord of a bridge, including model bridges, will be in compression. Different truss designs spread out the force so that various internal parts will be in compression as well.

 Tension: Tension is a pulling force. Wood has the ability to resist a lot of tension. It would be hard to break a popsicle stick if you held both ends and pulled apart. Tension may be applied parallel to the grain of the wood, but should be avoided perpendicular to the grain. Wood is very strong in tension parallel to the grain, but much weaker in tension perpendicular to the grain. Also, unlike in compression, the ability of wood to resist tension does not change with its length. A shorter piece of wood should hold the same amount of tension as a longer piece. Compression:Compression is a pushing (compressing) force. The shorter a piece of wood is, the more compression it can hold. The longer a piece of wood is, the less compression it can hold. When you compress a long stick of wood you will notice that it starts to bend. When a piece of wood breaks because of compression, we say it failed from buckling. Typically the top chord of a bridge, including model bridges, will be in compression. Different truss designs spread out the force so that various internal parts will be in compression as well.CompressionTension:Tension is a pulling force. Wood has the ability to resist a lot of tension. It would be hard to break a popsicle stick if you held both ends and pulled apart. Tension may be applied parallel to the grain of the wood, but should be avoided perpendicular to the grain. Wood is very strong in tension parallel to the grain, but much weaker in tension perpendicular to the grain. Also, unlike in compression, the ability of wood to resist tension does not change with its length. A shorter piece of wood should hold the same amount of tension as a longer piece.TensionTorsion:Torsion is a twisting force. When you wring out a cloth, you are applying torsion to the cloth. If you take a stick pretzel, twist one end, and hold the other end still, it will break very easily. If you do that with a baseball bat, it will not break. However, if you take a piece of licorice and apply torsion to it, the licorice will twist around several times before it breaks. Each of these materials has a different way of responding to torsion. Bridge designers must watch for torsion and try to reduce it as much as possible.TorsionShear:Shear is a interesting force. It happens when there are two opposing forces acting on the same point. If you hold a piece of wood with both hands next to each other, and push up with one hand and down with the other, you are applying shear to that piece of wood. Shear usually occurs horizontally, and not vertically.

 Torsion: Torsion is a twisting force. When you wring out a cloth, you are applying torsion to the cloth. If you take a stick pretzel, twist one end, and hold the other end still, it will break very easily. If you do that with a baseball bat, it will not break. However, if you take a piece of licorice and apply torsion to it, the licorice will twist around several times before it breaks. Each of these materials has a different way of responding to torsion. Bridge designers must watch for torsion and try to reduce it as much as possible.

 Shear: Shear is a interesting force. It happens when there are two opposing forces acting on the same point.  If you hold a piece of wood with both hands next to each other, and push up with one hand and down with the other, you are applying shear to that piece of wood. Shear usually occurs horizontally, and not vertically.

 Weight distribution  Truss system  Bracing via support spacing  Piers or towers  TRIANGLES…TRIANGLES…TRIANGLES  Triangulation  Strength  Length of bridge  Weight of bridge  Forces of compression  Forces from tension  Bridge stability  Quadrilaterals used

 As Project Director you are responsible for producing a crew of workers that understand the dynamics of bridge construction and the forces that act on those bridges.  As part of your job you are to find a creative way to have your workers understand and be able to explain the basic concepts behind bridge design.  You are to go to the Warehouse & purchase your materials packet. Observe what will be required of your employees to learn. You may decide on any method of teaching that you feel will promote the best quality of learning of these concepts. You can be as creative as you feel is necessary.  If you need more materials or resources to achieve your goal, be specific when asking for the items you think you will need.  NOTE: There will be a team competition on the day after your last building day. It is critical that every member of your team do well. You may discuss your challenge with your construction crew and all of you can determine the method that best suits you in order to learn the material provided. Understand that this is not a memorization task. It is about understanding the underlying concepts of bridges.