7 - sdof - general sdof systems
DESCRIPTION
Periodic Loding MechanismTRANSCRIPT
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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