7 - sdof - general sdof systems

Structural Analysis

(Dynamics Part)-spring 2013

(Generalized Single Degree Of Freedom

Systems)

Fawad Muzaffar M.Sc. Structures (Stanford University)

Ph.D. Structures (Stanford University)

Civil Engineering

Department

1

• Categorization of SDOF Systems:

– For formulation of equation of motion, SDOF systems can be categorized into

i. Assemblage of rigid components connected with deformable connections.

ii. Systems having distributed flexibility with continuous deformation

throughout the structure.

Generalized Single Degree Of

Freedom Systems - Categories

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• Mass Moment of Inertial of Rigid Bodies:

Generalized Single Degree Of Freedom

Systems – Mass Moment of Inertia

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• Calculation of Generalized Properties using Virtual Work

Generalized Single Degree Of Freedom

Systems –Assemblage of Rigid Systems

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• Step # 1: Identify the DOF and Consider Deformed Shape of the System:

Step # 2: Quantify and Draw Resistive Forces Acting on the System:

Work out displacements at B,C, D, E, F and G

Then

Generalized Single Degree Of Freedom

Systems–Assemblage of Rigid Systems

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Generalized Single Degree Of Freedom

Systems–Assemblage of Rigid Systems

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• Step # 3: Apply Virtual Displacement, Calculate Internal and External Work:

Internal Work:

Generalized Single Degree Of Freedom

Systems–Assemblage of Rigid Systems

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Generalized Single Degree Of Freedom

Systems–Assemblage of Rigid Systems

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Now,

Since E’E” is perpendicular to AE’

Similarly

Hence

Generalized Single Degree Of Freedom

Systems–Assemblage of Rigid Systems

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Generalized Single Degree Of Freedom

Systems–Assemblage of Rigid Systems

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Generalized Single Degree Of Freedom

Systems–Assemblage of Rigid Systems

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Generalized Single Degree Of Freedom

Systems–Assemblage of Rigid Systems

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• Distributed Flexibility – Derivation of

Generalized Properties:

– It is assumed that only a single

deformation pattern cab develop.

– The deformed shape is described by

shape function.

– Generalized properties of the system

can be evaluated using principle of

virtual work, i.e.

Generalized Single Degree Of Freedom

Systems-Distributed Flexibility

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• Evaluation of External & Internal Work:

Generalized Single Degree Of Freedom

Systems-Distributed Flexibility

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Generalized Single Degree Of Freedom

Systems-Distributed Flexibility

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Equating external and internal work

Generalized Single Degree Of Freedom

Systems-Distributed Flexibility

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Generalized Single Degree Of Freedom

Systems-Distributed Flexibility

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f

Generalized Single Degree Of Freedom

Systems-Distributed Flexibility

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