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Design Your Future: Bridges

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<ul><li>Simple </li></ul><ul><ul><li>Basic geometric shape. </li></ul></ul><ul><li>Strong </li></ul><ul><ul><li>Can’t be deformed without changing a length of a side or breaking a joint. </li></ul></ul><ul><li>Cool </li></ul><ul><ul><li>Three is a magic number. Yes it is. </li></ul></ul>triangles

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truss bridges

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<ul><li>Rigid bodies </li></ul><ul><ul><li>Statics </li></ul></ul><ul><ul><li>Dynamics </li></ul></ul><ul><li>Deformable bodies </li></ul><ul><li>Fluids </li></ul>engineering mechanics

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<ul><li>Newton’s Laws of Motion </li></ul><ul><ul><li>A body persists its state of rest or of uniform motion unless acted upon by an external unbalanced force. </li></ul></ul><ul><ul><li>Force equals mass times acceleration ( F = m a ) </li></ul></ul><ul><ul><li>To every action there is an equal and opposite reaction. </li></ul></ul><ul><li>Statics is the branch of mechanics concerned with forces in equilibrium </li></ul><ul><ul><li>So Statics is F = m a and a = 0, so F =0. </li></ul></ul>statics

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<ul><li>Forces have a direction and a magnitude, aka a vector such as 5 lb f at 20 o </li></ul><ul><li>For Bridges: Loads, Reactions & Internal Forces </li></ul><ul><li>Loads – Applied Force </li></ul><ul><li>Reactions – Newton’s 1 st Law </li></ul><ul><li>Internal Forces – Developed within members </li></ul><ul><ul><li>Truss bridges are designed so that members are in Tension or Compression. </li></ul></ul>forces 5 lb f

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internal forces: compression

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internal forces: compression

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W=mg internal forces: compression N

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internal forces: tension

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internal forces: tension

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internal forces: tension W=mg T

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free body diagram

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N 1 free body diagram F L =10 lb f N 2 <ul><li>Sum the forces in Y </li></ul><ul><li>F=ma=m*0, so EF=0 </li></ul><ul><ul><li>N 1 + N 2 – F L = 0 </li></ul></ul><ul><ul><li>N 1 + N 2 = F L </li></ul></ul><ul><ul><li>Assume N 1 = N 2 </li></ul></ul><ul><ul><li>2N=F L </li></ul></ul><ul><ul><li>N = F L /2 = 10lb f / 2 </li></ul></ul><ul><ul><li>N=5lb f </li></ul></ul>y x

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Compression and Tension F L =10 lb f F 1 F 2 y x <ul><li>The top members are in T or C? </li></ul><ul><li>See that F 1 is greater than half of F? </li></ul>

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Compression and Tension F 1 F 2 y x <ul><li>How are these Fs related to the last Fs? </li></ul>N 2 N 1

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Compression and Tension F 1 y x <ul><li>Is the bottom member in T or C? </li></ul>F 3 N 1

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free body diagram

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<ul><li>Sponge experiment from PBS Building Big : </li></ul><ul><li>Simple truss bridge forces: </li></ul>bridges

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<ul><li>Background image adapted under CC-SA </li></ul><ul><li>Tire Swing Barnwood Gallery (CC-SA ala Google) </li></ul><ul><li>Turtle adapted under GNU-FDL </li></ul><ul><li>This Astoria-Megler Bridge , the longest continuous truss bridge in North America. </li></ul><ul><li>Sponges adapted from PBS Building Big </li></ul><ul><li>Bridge from West Point Bridge Builder </li></ul>Credits

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Next Steps <ul><li>Physical Bridge Curriculum </li></ul><ul><ul><li>Static misconceptions </li></ul></ul><ul><li>Digital Bridge Curriculum </li></ul><ul><li>Links </li></ul><ul><ul><li>Engineering process bridge curriculum </li></ul></ul><ul><ul><li>PBS Building Big and small exercises </li></ul></ul><ul><ul><li>Amazing manila folder curriculum </li></ul></ul><ul><ul><li>Lots of bridge links </li></ul></ul><ul><ul><li>Interesting simple analysis </li></ul></ul>