Post on 14-Jun-2015
description
transcript
Design Your Future: Bridges
• Simple– Basic geometric shape.
• Strong– Can’t be deformed without changing a length of a
side or breaking a joint.
• Cool– Three is a magic number. Yes it is.
triangles
truss bridges
• Rigid bodies– Statics– Dynamics
• Deformable bodies• Fluids
engineering mechanics
• Newton’s Laws of Motion1. A body persists its state of rest or of uniform
motion unless acted upon by an external unbalanced force.
2. Force equals mass times acceleration (F = ma)3. To every action there is an equal and opposite
reaction.
• Statics is the branch of mechanics concerned with forces in equilibrium– So Statics is F = ma and a = 0, so F=0.
statics
• Forces have a direction and a magnitude, aka a vector such as 5 lbf
at 20o
For Bridges: Loads, Reactions & Internal Forces• Loads – Applied Force• Reactions – Newton’s 1st Law• Internal Forces – Developed within members– Truss bridges are designed so that members are in
Tension or Compression.
forces
5 lb f
internal forces: compression
internal forces: compression
W=mg
internal forces: compression
N
internal forces: tension
internal forces: tension
W=mg
T
internal forces: tension
free body diagram
N1
free body diagram
FL=10 lbf
N2
Sum the forces in Y•F=ma=m*0, so EF=0•N1 + N2 – FL = 0•N1 + N2 = FL
•Assume N1 = N2
•2N=FL
•N = FL/2 = 10lbf / 2•N=5lbf
y
x
Compression and Tension
FL=10 lbf
F1 F2
y
x
•The top members are in T or C?•See that F1 is greater than half of F?
Compression and Tension
F1 F2
y
x
•How are these Fs related to the last Fs?
N2N1
Compression and Tension
F1
y
x
•Is the bottom member in T or C?
F3N1
free body diagram
• Sponge experiment from PBS Building Big:
• Simple truss bridge forces:
bridges
• Background image adapted under CC-SA• Tire Swing Barnwood Gallery (CC-SA ala Google)• Turtle adapted under GNU-FDL• This Astoria-Megler Bridge, the longest
continuous truss bridge in North America.• Sponges adapted from PBS Building Big • Bridge from West Point Bridge Builder
Credits
Next Steps• Physical Bridge Curriculum• Static misconceptions• Digital Bridge Curriculum• Links• Engineering process bridge curriculum• PBS Building Big and small exercises• Amazing manila folder curriculum• Lots of bridge links• Interesting simple analysis