modeling of structural system

8/9/2019 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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Idealization: some planar structural systems aresimplifications of 3D systems


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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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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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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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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

modeling of structural system

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