NON LINEAR 3D STRUCTURAL ANALYSIS OF A STEEL BEAM SUBJECTED TO EQUAL AND OPPOSITE END MOMENTS DUE TO

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NON LINEAR 3D STRUCTURAL ANALYSIS OF A STEEL
BEAM SUBJECTED TO EQUAL AND OPPOSITE END MOMENTS
DUE TO EARTHQUAKE FORCES

• A PROJECT FOR MIE 605
• BY
• ANNAPURNA GORTHY
• SUBMITTED TO
• PROFESSOR IAN GROSSE
• May 11, 1999

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NORTHRIDGE EARTHQUAKE

• Prior to Northridge Earthquake, all
  beam-to-column connections in structures were
  designated as ductile moment resisting frames
  that were assumed to be capable of transferring
  the nominal plastic moment of the beams to the
  columns
• On January 17, 1994, an earthquake and of
  magnitude 6.7 on Ritcher scale struck the Los
  Angeles area, epicenter being at Northridge,
  causing over 20 billion in damage.
• The Northridge earthquake caused a number of
  beam-to-column welded structural connections to
  fail.
• This project is intended to analyse a steel
  beam model designed to withstand earthquake
  forces and determining the moment carrying
  capacity of the beam with the new design.

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EFFECT OF EARTHQUAKE FORCES ON STEEL FRAMES

• A strong earthquake would be expected to develop
  plastic hinges at the beam ends in a traditional
  fully restrained moment frame.
• POST-NORTHRIDGE BEAM-TO-COLUMN CONNECTION
  DESIGN STRATEGIES FOR NEW BUILDINGS
• Reinforcing the connection
• Having dog bone cutouts in the beam flanges in
  the regions adjacent to the beam column
  connections
• Both strategies effectively move the
  plastic hinge away from the face of the column,
  thus avoiding the problems related to the
  potential fragility of groove welds.

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ADVANTAGES OF DOGBONE/REDUCED BEAM SECTIONS

• The dogbone results in only a small reduction in
  strength and stiffness of a frame, but can
  provide a large increase in ductility, the key
  survival of a structure in a strong earthquake.
• The dogbone does not result in a change in the
  inertia of the beam where necessary ( mid span)
  for deflection requirements.

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TYPES OF DOGBONE

• CONSTANT CUT
  DOGBONE
• TAPERED CUT DOGBONE
• RADIUS CUT DOGBONE

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CONSTANT CUT DOGBONE
TAPERED CUT DOGBONE
2.625 in
R 20.375 in
10.45 in
FACE OF COLUMN
20 in
5 in
CENTERLINE OF DOGBONE
RADIUS CUT DOGBONE SHOWING THE DIMENSIONS
BEING USED
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PHYSICAL SYSTEM

• The physical system consists of a steel beam of
  length L 23 ft 276 inches, that is fixed at
  its ends to the columns and subjected to equal
  and opposite end moments.
• The steel beam is a standard W30X99 section of 50
  ksi yield strength.

15 in (TYP)
CENTERLINE OF DOGBONE
M
M
L 23 ft
M
M
BENDING MOMENT DIAGRAM
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FINITE ELEMENT MODEL

• The physical system shown can be represented by a
  finite element model as shown below.
• The finite element model essentially consists of
  a cantilever beam of span L/2 23/2 feet 138
  inches ( where L is the total length of the
  beam in the physical system) and subjected to a
  concentrated load P at the free end of the
  cantilever beam, fixed at the other end
• This arrangement essentially results in the same
  bending moment diagram for the finite element
  model as the physical system.
• The centerline of dogbone cutout is located at a
  distance of 15 inches from the face of the column.

P
138 in L/2
M
BENDING MOMENT DIAGRAM
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TO BUILD THE PHYSICAL SYSTEM INTO A FINITE
ELEMENT MODEL EASILY, THE FOLLOWING ASSUMPTIONS
HAVE BEEN MADE

• A cantilever beam of span length L/2 11.5 ft
  138 inches and subjected to a concentrated load
  at the free end is modeled, which essentially
  gives the same bending moment diagram as a
  fixed-fixed beam of length L (23 ft) and
  subjected to equal and opposite end moments.
• End of the cantilever beam has been assumed to be
  rigid/fixed.
• Elastic perfectly plastic stress strain diagram
  has been assumed for simplicity
• Load has been modeled as a concentrated load.
• Stress concentrations around fillets have been
  neglected.
• Shear effects have been neglected.

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ANSYS INPUT DATA

• TYPE OF ANALYSIS - STATIC
  STRUCTURAL NON LINEAR
• 
  ANALYSIS USING BILINEAR KINEMATIC
  
• 
  HARDENING TYPE OF PLASTICITY RULE
• 
  
• PROBLEM - 3D
• DIMENSIONALITY
• ELEMENT TYPE - SOLID 45
  3-D 8-NODE BRICK ELEMENT
• 
  
• MESHING -
  FREE MESHING WITH SMART SIZING
• BEAM SECTION - STANDARD
  W30X99 SECTION
• 
  
• 
  
  

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ANSYS INPUT DATA

• LOADING - POINT LOAD AT THE
  FREE END OF THE
• 
  CANTILEVER BEAM
• CONSTRAINTS - FIXED END CONDITION
• 
  
• NON LINEAR - LARGE DEFORMATION
  EFFECTS - ON
• ANALYSIS NEWTON RAPHSON
  OPTION - PROGRAM
• OPTIONS EQUATION
  SOLVER - FRONTAL SOLVER
• 
  LOADING WITHIN A LOAD STEP - STEPPED

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MATERIAL NON LINEARITY
E 29000
ksi Poissons ratio 0.3 Yield Stress
50 ksi Density
0.2836 lbs/ft3
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PLASTIC STRESS
ELASTIC STRESS
STANDARD W SHAPE
DISTRIBUTION
DISTRIBUTION
CROSS SECTION
ELASTIC AND PLASTIC STRESS DISTRIBUTIONS IN WIDE
FLANGE
STRUCTURAL SHAPE SUBJECTED TO FLEXURE
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FORCE
DISPLACEMENT
FORCE VS DISPLACEMENT PLOT FOR DESIGN A FINITE
ELEMENT MODEL
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CONCLUSION

• Maximum stress occurs at the dogbone cutout
  region.
• Dogbone cutout has been found to be extremely
  useful in moving the plastic hinge away from the
  face of the column, and thus enabling the
  structure to withstand earthquake forces.
• As ANSYS results are more conservative, they can
  be safely used for future work rather than
  conducting expensive experiments.

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FUTURE WORK

• ANALYSIS OF A COMPLETE STRUCTURAL FRAME SUBJECTED
  TO AXIAL AND TRANSVERSE LOADING.
• PARAMETRIC MODELING OF FRAME SO THAT RADIUS CUT
  DOGBONES OF VARIOUS DIMENSIONS CAN BE TRIED OUT.
• SUBMODELING OF THE DOGBONE CUTOUT PORTION TO GET
  MORE ACCURATE RESULTS.