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Cyclic Elastoplastic Analysis and Stability
Evaluation of Steel Braces of Hollow Section
Iraj H.P. Mamaghani Assistant Professor
University of North Dakota SEI Structures
Congress April 24-26, 2008 Vancouver, BC,
Canada
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Outlines

• Introduction
• Parameters Concerning Seismic Design and
  Ductility Evaluation of Cold-formed Steel Braces
  of Circular Hollow Sections
• FEM Modeling and Numerical Analysis Under Cyclic
  Loads
• Effects of Structural and Material Parameters on
  Cyclic Inelastic Behavior
• Conclusions

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• Steel Braced Frames
• Structural efficiency in providing significant
  lateral
• strength and stiffness
• Avoiding the brittle fracture found in
  beam-to-column
• connections in moment resisting steel frames
  

Steel Brace Types
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Capacity Design Procedure

• Concentrically Braced Frames
• Seismic Design Steel Specifications
  CAN-CSAS16.1 1989
• 
  AISC 1997
• Requires yielding in the braces as primary
  members
• Avoiding possible catastrophic failure by
  brace rupture
• in the event of a severe seismic loading.
• The secondary members of the frame should
  remain elastic
• and hence carry forces induced by the
  yielding members

• Performance-Based Design Specifications
• requires accurate predictions of inelastic
  limit states up to
• structural collapse

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Seismic Design Philosophy? Under severe
earthquakes, braces are allowed to undergo
compression buckling or tensile yield to
dissipate the imposed energy while columns and
collector beams respond elastically.

• Understanding the behavior of the bracing
  members
• under idealized cyclic loading is an
  important step in
• the careful design of steel braced frames.

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Type of Braces
Tension-Only Braces Designed to resist tensile
force having almost no compressive
strength. Tension-Compression Braces Provide
better performance under cyclic loading

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• Cyclic behavior of steel braces
• material nonlinearity
• - residual stresses
• - yield plateau
• - strain hardening
• - Bauschinger effect
• structural nonlinearity
• - brace slenderness parameter
• - cross-section slenderness
• width-to-thickness ratio
• radius-to-thickness ratio
• - initial out of straightness of the
  brace
• boundary condition
• loading history

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Physical Phenomena

• yielding in tension
• buckling in compression
• postbuckling deterioration of compressive load
  capacity
• deterioration of axial stiffness with cycling
• low cycle fatigue fractures at plastic regions

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Characteristic Parameters of Steel Tubular
Braces
Section Slenderness
(Box Hollow Section)
(Circular Hollow Section)
Brace Slenderness Ratio Parameter
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Circular Hollow Section
Plastic Design Limits AISC(1997)
Non-Compact Sections AISC(1997)
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Brace Slenderness Limit (AISC 1997)
Special Concentrically Braced Frames
Ordinary Concentrically Braced Frames
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Finite Element Analysis (ABAQUS)
S4R Shell Element Three dimensional Double
curved Four node with six degrees of freedom
per node Bilinear interpolation Reduced
integration Geometrical Nonlinearity
Updated Lagrangian Formulation Material
Nonlinearity KH, IH, 2SM Modified
Newton-Raphson Method Coupled with
displacement control Displacement Convergence
Criterion 10-5
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Elchalakani et al. Tests (2003)
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Material Model

• AS 1163 grade C350L0 (equivalent to ASTM A500
  tubes)
• Trilinear Stress-Strain Material
• Kinematic Hardening Rule

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Finite Element Meshing and Analysis Program
I. Original Meshing Pattern 2100 shell
elements (70 elements along the brace length and
30 elements in the circumferential direction)
II. Fine Mesh total number of 3300 shell
elements doubling the mesh number at the central
segment and at the ends of the brace III. Load
Step-Increment Analysis (meshing same as Type I)

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Loading Program

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Example 1 S7A Circular Brace Non-Compact Member
Having Inelastic Behavior m18.24 gt m10 likely
to occur near source excitation
Normalized axial load versus axial displacemen
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Effects of mesh density and load steps
Normalized axial load versus axial displacemen
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Deflection Local Buckling Progress
Deflection at the top face (Node 1088) and bottom
face (Node 1104) of the cross-section at midspan.
Local buckling progress at midspan
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Deformed configuration of brace S7A at the end of
compression and tension loading
Compression

• Compression

Tension
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Example 2 S7B Circular Brace
Deflection at midspan
Axial load vs. axial displacement
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Step by step deformation S4B
Undeformed
Loop 1
Loop 3
Loop 5
Loop 7
Loop 9
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Example 3 S7C Circular Brace
Axial load vs. axial displacement
Deflection at midspan
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Step by step deformation S4C
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Step by step deformation S4C
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Deformed configuration of brace S7C at the end of
compression loading
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CONCLUSIONS

• Some important parameters considered in the
  practical seismic design and ductility evaluation
  of steel braces of tubular sections were
  presented.
• The inelastic cyclic behavior of cold-formed
  steel braces of circular hollow sections was
  examined through finite element analysis using
  ABAQUS and employing a tri-linear kinematic
  strain hardening model to account for material
  nonlinearity.

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Than You Questions?