dynamic analysis of framed structure_r
TRANSCRIPT
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DYNAM
ANALYSIS
FRAM
STRUCTU
PREPARED BY : KRU
GUIDED BY : DR.
SEMINAR PRESENTATION
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CONTENTS
Introduction
Dynamic Analysis
Importance of Dynamic Analysis (Videos)
Problem Formulation
Equation of Motion
Derivation of Global Stiffness & Mass Matrices
Eigen Value Problem QR Method (Manual Example)
Displacement Calculation
Computer Program & Example
Input-Output
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INTRODUCTION
Almost of loads that are applicable to any structure are Dynamic in natThey vary with time)
The distinction is made between the dynamic and the static analysis on thewhether the applied action has enough acceleration in comparisonstructure's natural frequency. If a load is applied sufficiently slowly, thforces (Newton's second law of motion) can be ignored and the analysisimplified as static analysis.
Structural dynamics, therefore, is a type of structural analysis which cobehaviour of structures subjected to dynamic (actions having high acce
loading.
Dynamic loads include people, wind, waves, traffic, earthquakes, and blasts
Dynamic analysis can be used to find dynamic displacements, time and modal analysis
http://en.wikipedia.org/wiki/Structural_analysishttp://en.wikipedia.org/wiki/Structurehttp://en.wikipedia.org/wiki/Dynamics_(physics)http://en.wikipedia.org/wiki/Earthquakehttp://en.wikipedia.org/wiki/Displacement_(vector)http://en.wikipedia.org/wiki/Modal_analysishttp://en.wikipedia.org/wiki/Modal_analysishttp://en.wikipedia.org/wiki/Modal_analysishttp://en.wikipedia.org/wiki/Modal_analysishttp://en.wikipedia.org/wiki/Displacement_(vector)http://en.wikipedia.org/wiki/Earthquakehttp://en.wikipedia.org/wiki/Dynamics_(physics)http://en.wikipedia.org/wiki/Structurehttp://en.wikipedia.org/wiki/Structural_analysishttp://en.wikipedia.org/wiki/Structural_analysishttp://en.wikipedia.org/wiki/Structural_analysis -
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PROBLEM FORMULATION
Equation of Motion
(t) + c(t) + kx(t) = F(t)Where m = Mass Matrix (Lumped / Consistent)
k = Stiffness Matrix
C = Damping Matrix
F = Force Matrix
For Free Vibration of Plane Frame withoutDamping
(t) + kx(t) = 0
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PROBLEM FORMULATION
Mass & Stiffness Matrices are derived by combining for Bar Element (Axial) & Element (Transverse disp. & Rotation).
Shape Function (N)
Bar Element : [ 1
]
Beam Element : [ 1 3
+
2
x
2
+
3
-
2
+
]
Strain Displacement Relation (B)
Bar Element : [
]
Beam Element : [6
+
2
4
+
6
6
2
2
+
6
]
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PROBLEM FORMULATION
Stiffness Matrix =
0
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PROBLEM FORMULATION
global Stiffness Matrix =
Where T = Transpose Matrix
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PROBLEM FORMULATION
Mass Matrix =
0
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PROBLEM FORMULATION
global Mass Matrix =
Where T = Transpose Matrix same as earlier
Eigen Value Problem = | k - m2 | {} = 0
Eigen Value (Natural Frequency) & Eigen Vector (Mode Shapes)
From Modal Matrix Modal Equations = {}
x F
Nodal Displacement {y} = [] x z , where is z is solution of equation of motio
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EXAMPLE
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EXAMPLE
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EXAMPLE