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

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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


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 kip-in
MOMENT CARRYING CAPACITY OF DESIGN 'B' BEAM = 68.5 x ( 138 - 15) = 8425.5 kip-in
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 Elastic-Perfectly plastic stress-strain 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.