A Simplified Nonlinear Analysis Procedure Using Linear Analysis

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A Simplified Nonlinear Analysis Procedure Using
Linear Analysis

• Date 12/11/2009
• Alireza Asgari
• Mike Mehrain

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Simplified Approach to Nonlinear

• Linear Analysis
• Nonlinear Analysis
• Simplified Nonlinear
• Linear Analysis ? Stiffness, Period, DCR ?
  Approximate Push over Curve? Plastic Deformation
  of Different Elements? Building Performance

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Case Studies

• Case 1 One Story Parking Structure
• Case 2 15 Story Parking Structure
• Simplified Method
• Nonlinear Analysis
• Comparison-Level of Accuracy

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Building 1

• Simple One Story Structure ? Demonstrate The
  Approach
• Gravity ? Post-tensioned Light-weight Concrete
  Flat Slab
• Reinforced Concrete Columns
• Lateral ? Concrete Shear Walls Both Direction
  (N-S Analysis wo Torsion)

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• The Linear Analysis ? Base Shear 8,000 Kips
  Drift 0.31
• Wall 1 Demand 2,000 Kips , Wall 1 Capacity160
  Kips Max D/C12.5
• ? Wall 1 Yield _at_ Drift 160/2000 X 0.31
  0.025

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• At This Drift Calculate The Forces in Other Walls
• Next Event is Next Highest D/C
• Wall 2 Yields _at_ 320 Kips. Drift 320/2000 X 0.31
  0.05
• Wall 1 Shear Remains. Other Walls Can Be
  Calculated
• Repeat The Process ? Nonlinear Curve Produced
  from The D/C Values in Comparison With a
  Nonlinear Analysis.

Steps?
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• No Strength Degradation Can Be Used
• Total Shear Deformations 0.55 Push Over
  Curve Method in ASCE 41
• ? Individual Wall Plastic Deformation

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Building 2

• 15 Story Structure Gravity ? Cast-in-place One
  Way Flat Slabs Reinforced Concrete Columns
• Lateral ? Concrete Shear Walls Coupling Beams

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Simplified Method

• Linear Analysis ? Initial Stiffness First Yield
  Point (First Line of The Push Over Curve)
• Capacities ? Maximum Base Shear (Horizontal Line
  of The Push Over Curve)
• Connecting Line ? Approximated By A Simplified
  Step By Step DCR
• Calculate Various DCR Values. From Max DCR Use
  Step By Step Procedure

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• Shear Demand Moment Demand / 1488"
• Total Base Flexural Capacity Associated with
  Coupling Beam
• 2 x Coupling Beam Capacity x Number (15) x L2 /
  L1
• Flexural Demand of Coupling Beam
• 2 x ? Coupling Beam Demand x L2 / L1

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Steps?
Element W/ Maximum DCR Yields ? Shear of Element
Will Not Exceed Repeat Until All Elements Are
Yielded
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NONLINEAR MODEL

• NSP Analysis ? Perform-3d
• Properties Equal to The Linear Analysis
• Concrete Shear Walls Modeled as Beam Column
  Elements
• Refinements Not Used (Fiber Elements, Strain
  Hardening, Strength Degradation)
• Triangular Lateral Load Patterns
• Target Displacement From Coefficient Method In
  ASCE 41

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Pushover Curve
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• Plastic deformation Total roof drift - elastic
  roof drift from the step by step method
• Wall Plastic rotation plastic roof deformation
  / height of the wall
• coupling beams Plastic rotation plastic
  deformation at roof level / height of the wall,
  corrected for the presence of rigid link at the
  end of coupling beams

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• Procedure can not consider
• Other Failure Mechanism (Weak Story)
• Strong Coupling Beam Weak Pier
• Element Degradation

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Questions?