Statics in Bridges

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Statics in Bridges
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What is a force?

• A force is a push or pull on an object
  (compression and tension).

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Stationary objects are static.

• No net forces
• No net moments (torques)

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Are there forces on you now?

• Gravity is pulling you down.
• The stool is pushing you up.
• Force is compression.
• Each leg supports ¼ of the weight
• Total forces are zero (statics).

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What forces are on this girl?

• Net force is zero.
• Gravity pulls the girl down (weight).
• Force in the line is tension.
• Sample calculation-

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Bending is Bad

• Bending- Beams have very little bending strength.
  
• Never design a structure that relies on bending
  strength to support a load.

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Design and construction ideas 1) Triangles are
a construction engineers 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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Truss Bridges

• Your bridge will be essentially a truss.

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In a truss bridge forces are at an angle.
Since the bridge is stationary the Net force
must be zero.
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Beams and loads--compression
d
L
Beam in compression
Failure occurs two ways 1) When L/d lt 10,
failure is by crushing 2) When L/d gt 10,
failure is by buckling We are almost always
concerned with failure by buckling.
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Compression- Buckling Strength F (k)d4/L2 If
a beam of length L and diameter d can support a
compressive load of F,
d
F
L
then a beam of length L/2 and diameter d
can support a compressive load of 4F.
d
4F
L/2
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Compression- Buckling Strength F (k)d4/L2
d
F
L
and a beam of length L and diameter 2d
can support a compressive load of 16F.
2d
16F
L
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Compression- Buckling Strength F (k)d4/L2

• In compression short and fat members are good.
• 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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Tension FkR2
Beam under tension

• Failure occurs when tensile strength is exceeded.
• Maximum load is tensile strength times
  cross-sectional area.
• Load capacity does not depend on length.

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Use Bridge Designer to calculate
loads http//www.jhu.edu/virtlab/bridge/bridge
.htm
Tension members are in RED Compression members
are in BLUE
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• Design and construction ideas
• Taller is better note loads on these two
  structures.

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Which is the better design and why (cont.)?
a)
b)
a)
b)
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Calculate Tension Compression Values for the
Balsa Bridge

• Tension FkR2
• Balsa wood k19.9 MPa
• Compression F Ep3R4
• 64L2
• Balsa wood E1130 MPa
• E youngs modulus (a measure of the rigidity of
  a material, the large E is the less the material
  will deform when under stress)

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Some properties of balsa wood (dry)
Density 150 kg/m3 .0054 lb/in2
Compressive Strength 12.1 MPa 1750 lb/in2
Tensile Strength 19.9 MPa 2890 lbs/in2
Elastic Modulus- Compression 460 MPa 66,700 lb/in2
Elastic Modulus- Tension 1280 MPa 185,300 lb/in2
For comparison, cast aluminum (wet or dry) 1.
Ultimate tensile strength 10,000psi 2.
Stiffness E10,000,000psi
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• Design and construction ideas
• Dont forget about the 3rd dimension. A good
  design in the x-y plane, may be a terrible one in
  the z-direction.
• Plan the total bridge design. Estimate the
  weight of each of the components, so that you
  will not exceed the weight limit (95 grams).
• Make a full-size pattern of your bridge. Build
  the bridge on this pattern. This will ensure
  that all components will assemble properly (use
  wax paper).
• Rough cut members then sand to the desired
  length.
• Common disqualifications
• angles must be over 30 degrees.
• Gluing cannot go beyond 3mm from a joint.
• Mass of bridge lt95 grams

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Types of Trusses
K Truss
Warren/ Neville Truss
Howe Truss
Pratt Truss
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Use Bridge Builder

• Go to http//www.jhu.edu/virtlab/virtual-laborato
  ry/

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Statics
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Cantilevered truss--Firth of Forth rail bridge
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Suspension--Golden Gate
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New River gorge--largest single arched span
(1978)