ESM 2204 Mechanics of Deformable Bodies

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ESM 2204 Mechanics of Deformable Bodies

• Instructor for this section
• Prof. John Duke

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Preliminaries

• Handout Syllabus
• Handout Survey (Quiz comment)
• Time management comment
• Expectations
• What do you, Michael Jordan, and Mia Hamm have in
  common?

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Why bother?

• This course is required for my major!
• and/or
• I want to design stuff!
• Stuff is deformable!
• I need to know about deformable bodies to design
  stuff!

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An example of stuff
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More stuff
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Highway signs

• Experience wind loads from wind
• Experience wind loads from passing trucks
• Experience dead loads due to weight, ice, flocks
  of birds
• Highway signs fall down and kill people!
• Designing stuff is serious business!

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FBD-Statics
REACTION?
See BJ problem 8.38 page 515 for a similar
problem
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Typical reactions on a cut surface
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The reactions P,Vy,Vz, T, My, Mz are caused by
stresses, forces distributed over the cut
surface we created. These are the stresses we
want to be able to determine in this course.
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• is used for normal stress ? is used for
  shear stress
• - sigma ?-
  tau

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Z, k
Surfaces are characterized by their area,
location of the centroid, and by the direction
unit vector normal perpendicular to the
surface.
X, i
Y, j
-Y, -j
Cut surfaces
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3 different states of stress
?yz
?zy
Pure shear stress
?z
?z
General Situation (multiplying the
stress components by the area over which they
act gives the force caused by that stress
component).
Normal stress In one direction, uni-axial
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Total force
Distributed force
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(No Transcript)
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If many forces act it might not be possible to
make the surface cut perpendicular to all the
forces. In those cases there may be a component
of the force perpendicular to the surface, and
a component parallel to the surface.
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x
IF the force is uniformly distributed over
the Area, A. Otherwise we would say the
average stress is P/A.
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St Venant Module fromBJ website
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Always make the cut away from where forces
are applied!
P1
P1
P2
P1
P2
P2
x
BJ 1.2
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ANSWERS 14.93 mm
BJ 1.6
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Gray areas experience no load
BJ 1.9
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20kN
2CE
2BD
2 links BD and CE