Download - Modeling of Structural System
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Modeling of Structural Systems
Idealization: some planar structural systems aresimplifications of 3D systems
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Modeling of Structural Systems
Idealization: some planar structural systems aresimplifications of 3D systems
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Modeling of Structural Systems
Idealizations:Kinematic: small strains and small rotations
tan
This assumption is very important. It simplifiesanalysis considerably (geometric linearity) butprecludes the consideration of buckling CEE 472
We will point it out every time it occurs
Write equilibrium in undeformed configuration
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Modeling of Structural Systems
Idealizations:Material: linear elastic
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What may the stress-strain curve of an inelastic
material look like?
Strain
S t r e s s
Will look at this type of material behavior (elastoplastic) inCEE 376. Will solve structural problems in CEE 674
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Modeling of Structural Systems
Idealizations: LoadsDead loadsLive loads
Moving loads (bridges)Snow loadsWind loads
Water or soil pressureTemperature changeForced fit ( construction or fabrication misfit, nonuniform foundationsettlement)
Earthquake motionBlast loadsImpact loads
In CEE 371 static loads only. Dynamic loads CEE 678
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Modeling of Structural Systems
Idealizations: Supports and connections
Corresponding SymbolicIdealization
A real fixed connection in asteel frame
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Corresponding Symbolic
Idealization
A real moment transmitting
connection in a steel frame
Idealizations of Boundary Conditions for
Mathematical Modeling
What is known? Unknown?
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Rigid connection
Zero relative movements
3 unknown internal forces
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Corresponding SymbolicIdealization
Idealizations of Boundary Conditions for
Mathematical Modeling
What is known? Unknown?
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Pinned connection
1 unknown relative rotation 2 unknown internal forces
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Truss pinned connection
Godden D6REAL
Idealized
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Spring connections
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Boundary Condition Idealization Symbols
for Mathematical Modeling: 1 of 2
1 static2 kinematic
1 static2 kinematic
1 static2 kinematic
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Boundary Condition Idealization Symbols forMathematical Modeling: 2 of 2
1 static2 kinematic
2 static1 kinematic
2 static1 kinematic
3 static0 kinematic
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Degree-of-Freedom, DOFWhat do you notice in the Number of Unknowns column?
Each support or connection condition implies both static andkinematic information, something we know or dont knowabout forces and displacements .
A prescribed displacement implies an unknown reaction force
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Degree-of-Freedom, DOF
DOF = Location and direction on model where force or
displacement information is required.
Usually:
degrees of freedom = kinematic unknowns = kinematicindeterminacy
static indeterminacy = static unknowns - # equilibriumequations