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
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.
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
.
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.
TYPES OF DOGBONE
•
CONSTANT CUT DOGBONE
•
TAPERED CUT DOGBONE
•
RADIUS CUT DOGBONE
CONSTANT CUT DOGBONE
TAPERED CUT DOGBONE
RADIUS CUT DOGBONE SHOWING THE DIMENSIONS BEING USED
R = 20.375 in
20 in
FACE OF COLUMN
5 in
10.45 in
2.625 in
CENTERLINE OF DOGBONE
PHYSICAL SYSTEM
•
The physical system consists of a steel beam of length ‘L’ = 23 ft = 276
inches, that is fixed at it’s 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.
M
M
L= 23 ft
CENTERLINE OF DOGBONE
15 in (TYP)
M
M
BENDING MOMENT DIAGRAM
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
M
BENDING MOMENT DIAGRAM
138 in = L/2
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.
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
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
STRAIN
ELASTIC PERFECTLY PLASTIC
(NON LINEAR) STRESS

STRAIN
DIAGRAM FOR STEEL BEAM
MODEL WITH AN YIELD STRESS OF
50 KSI FOR DESIGN ‘A’ AS WELL AS
DESIGN ‘B’
50 KSI
STRESS
0
E = 29000 ksi
Poisson’s ratio = 0.3
Yield Stress = 50 ksi
Density = 0.2836
lbs/ft^
3
MATERIAL NON LINEARITY
STANDARD W SHAPE
ELASTIC STRESS
DISTRIBUTION
PLASTIC STRESS
DISTRIBUTION
ELASTIC AND PLASTIC STRESS DISTRIBUTIONS IN WIDE FLANGE
STRUCTURAL SHAPE SUBJECTED TO FLEXURE
CROSS SECTION
DESIGN ‘A’
FINITE ELEMENT MODEL OF DESIGN ‘A’ STEEL BEAM
BEFORE APPLYING ANY BOUNDARY CONDITIONS
MESHING SHOWN FOR DESIGN ‘A’ BEAM MODEL
ELEMENT
TYPE : SOLID 45
8 NODES – 3D SPACE
RESULTS SHOWING VON MISES STRESSES FOR FINAL
CONVERGED SOLUTION OF NON LINEAR STATIC
STRUCTURAL ANALYSIS FOR DESIGN ‘A’ FINITE ELEMENT
MODEL
FORCE
DISPLACEMENT
FORCE VS DISPLACEMENT PLOT FOR DESIGN ‘A’ FINITE ELEMENT MODEL
DESIGN B
FULL CROSS SECTION OF FINITE ELEMENT MODEL
BEFORE APPLYING SYMMETRIC BOUNDARY
CONDITIONS ALONG YZ PLANE
MESHING SHOWN FOR DESIGN ‘B’ BEAM MODEL
ELEMENT
TYPE : STRUCTURAL BRICK
SOLID 45
8 NODES – 3D SPACE
RESULTS SHOWING VON MISES STRESSES FOR FINAL
CONVERGED SOLUTION OF NON LINEAR STATIC
STRUCTURAL ANALYSIS FOR DESIGN ‘B’ FINITE ELEMENT
MODEL
ANALYSIS RESULTS
FAILURE LOAD IN KILO POUNDS
ANALYTICAL
ANSYS
EXPERIMENTAL
IMENTAL
DESIGN 'A'
83.4
61.82
89
DESIGN 'B'
101.7
68.5
109
MOMENT CARRYING CAPACITY OF DESIGN 'A' BEAM = 61.82 x (138  15) = 7604 kipin
MOMENT CARRYING CAPACITY OF DESIGN 'B' BEAM = 68.5 x ( 138  15) = 8425.5 kipin
DISCUSSION OF RESULTS:
a) Design 'B' model failed at a higher load than Design 'A' model, which should be the case
as section modulus is higher for Design 'B'
b) For both the cases, ANSYS results are lower than analytical and experimental results.
Reasons could be
1) Simplified Model
2) Assumption of ElasticPerfectly plastic stressstrain diagram
3) Element type being of lower order.
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
.
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.
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