Numerical analysis of blast loaded civilian structures
by Bert Jeffrey Lutzenberger
A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Civil
Engineering
Montana State University
© Copyright by Bert Jeffrey Lutzenberger (2000)
Abstract:
Malevolent bomb attacks on high profile civilian structures have raised concerns about the
vulnerability of multistory civilian structures to terrorist attack. Given the availability of bomb-making
materials and the ease with which large explosive devices can be assembled and employed, malevolent
bomb attacks on multistory government and civilian structures continue to pose a significant threat to
this type of structure. With this in mind, there exists a need within the engineering community for
methods to analytically model and predict the response of multistory structures to blast loads.
While classical solutions may be used to analyze the initial response of a structure to a blast type load,
they cannot efficiently characterize damage accumulation and failure in areas of extreme stress and
strain. Therefore, an alternate approach was presented that used a combination of implicit and explicit
finite element methods to characterize structural response before, during and after detonation of an
explosive device near a structure of interest.
Public domain versions of the explicit and implicit finite element codes DYNA3D and NIKE3D were
used in the following manner. First, the implicit finite element formulation was used to determine the
initial stress field in a typical multistory civilian structure due to gravity loads. Then, the nodal data
resulting from the implicit code were passed to the explicit code as initial conditions prior to the
application of a blast load. Once the static stresses and strains had been transferred and initialized in the
explicit formulation, a calculated pressure front was applied to predetermined structural members in the
form of a distributed impulse load. The explicit formulation was then used to predict localized
structural damage and material failure resulting from the blast load. The resulting state of the structure
due to the blast load was then assessed based on post-blast nodal data.
Nodal responses of cantilever beam and two-bay portal test cases showed that the beam-continuum
interface used to reduce model size correlated well with similar models that consisted of either
continuum or beam elements only. It was also found that transferring nodal data between the two codes
did not introduce significant error into the analyses. Finally, the proposed methodology was tested on a
model with structural characteristics similar to those of the Alfred P. Murrah federal building. The
methodology was found to significantly reduce computational cost while adequately characterizing
failure based on the chosen failure material model and prescribed blast load. N U M E R IC A L AN ALYSIS O F B L A ST L O A D ED
C IV IL IA N STRU C TU R ES
by
Bert Jeffrey Lutzenberger
A thesis submitted in partial fulfillment
of the requirements for the degree
of
Master of Science
in
Civil Engineering
MONTANA STATE UNIVERSITY
Bozeman, Montana
December, 2000
\
A PPR O V A L
of a thesis submitted by
Bert Jeffrey Lutzenberger
This thesis has been read by each member of the thesis committee and has been
found to be satisfactory regarding content, English usage, format, citations, bibliographic
style, and consistency, and is ready for submission to the College of Graduate Studies.
Dr. Don Rabem
j/— > C -y -'v
(Signature)
Date
Approved for the Department of Civil Engineering
?7J 4-/ AQ
Dr. Don Rabem
(Signature)
Date 1
Approved for the College of Graduate Studies
Dr. Bruce McLeod
Date
Ill
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degree at Montana State University, I agree that the Library shall make it available to
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Requests for permission for extended
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TABLE OF CONTENTS
Page
1. IN T R O D U C T IO N ...................................................... :.........
Background.................................................................................
Scope of W ork............................................................................
Finite Element Codes............................................................
Components of Research......................................................
...I
...I
... 4
... 4
... 5
8
2. L ITE R A T U R E R E V IE W .....................................................
...
Introduction.................................................................................
Terrorist Threat................................ ...........................................
World Trade Center..............................................................
Alfred P. Murrah Federal Building......................................
American Embassies............................................................
Current Methods..................................................................
Blast Modeling...........................................................................
Undisturbed Blast Profile.....................................................
Military Design Aids............................................................
Petrochemical Design Aids..................................................
Blast Wave Modeling with Computational Fluid Dynamics
Structural Models...................................................................... .
Dynamic Systems.................................................................
Numerical Methods Solutions..............................................
Finite Element Applications................................................
Literature Review Conclusion...................................................
....
....9
.... 9
..10
..11
..12
..13
..16
..16
..17
..18
3. FIN IT E E L E M E N T C H A L L E N G E S ..... .........................
„25
Introduction................................................................................
Structural Response Phases........................................................
Finite Element Formulations.....................................................
Explicit Formulations........................................ .................
Implicit Formulations.........................................................
...25
...26
8
.... 8
.... 8
..20
..21
.2 3
...27
...27
...28
TABLE OF CONTENTS (continued)
Page
4. A P P R O A C H ......................................................................................
31
Material Models in NIKE3D and DYNA3D...................................................... 33
Constitutive Modeling................................................................................... 33
Elastic Material Model..........................................................................
35
Bilinear Elastic-Plastic Model....................................................................... 36
. Elastic-Plastic Model with Failure................................................. *............. 38
Concrete Plasticity and Damage Model......................................................... 40
Beam-Continuum Interface................................................................................ 42
Finite Elements in NIKE3D and DYNA3D..................................................... 42*
Beam-Continuum Interface Model....... ,....................................................... 44
Data Translation................................................................................................. 46
Compatibility of Integration Techniques....................................................... 47
Material Modeling Compatibility.................................................................. 48
Transfer Sequence.......................................................................................
49
Blast Model........................................................................................................ 52
Approach Conclusion......................................................................................... 54
5. C A N T IL E V E R B E A M A N D T W O -B A Y PO R TA L M O D E L S .......55
Cantilever Beam Model....................................................................................... 55
Physical Model...................................................................
Finite Element Analyses................................................................................ 59
Deflection Comparisons.................................................................................72
Solution Time Comparisons............... Z........................................................76
Two-Bay Portal M odel........................................................................................ 78
Physical Model............................................................................................... 78
Finite Element Analysis................................................................................. 82
55
6. T EST CASE: A L FR E D P. M U R R A H FE D E R A L B U IL D IN G .......92
Building Model.........................................................
Parameters...................................................................................................... 92
Finite Element Model of the Alfred P. Murrah Federal Building..................93
Finite Element Analysis................................................................................. 98
7. C O N C L U SIO N A N D C LO SIN G R E M A R K S ..................................... 107
Cantilever Beam Model.....................................................................
Two-Bay Portal M odel...................................................................................... HO
Alfred P. Murrah Federal Building Model........................................................ I l l
Closing Remarks...................................................................
109
112
vi
TABLE OF CONTENTS (continued)
R E FE R EN C ES C IT E D .................................................................................... 113
APPENDIX: PSEUDO-MURRAH FE MODEL INPUT FILES........ 118
V ll
J
LIST OF TABLES
Table
'
Page
I . I Analysis matrix for cantilever beam model........................................................7
1.2 Analysis matrix for two-bay portal and the multistory civilian structure......7
2.1 Blast profile parameters for various charge weights and standoff distances......16
3.1 Advantages and disadvantages of explicit and implicit finite element
formulations..........................................................................................................29
5.1 Relative error between continuum and beam-continuum models for
NIKE3D, DYNA3D and the combined formulation solution method................ 72
5.2 Vertical nodal displacements for the cantilever beam models at 18, 36,
54, and 72 inches along the length of the beams................................................ 74
5.3 MaYimnm relative errors between continuum and beam-continuum models
for NTKE3D, DYNA3D and the combined formulation solution method..........75
5.4 Maximum absolute horizontal displacements for each of the two-bay
portal models..................................................................................................
6.1 Material properties for concrete and steel used for the elastic-plastic
and elastic-plastic with failure material models...................................................97
6.2 Maximum vertical displacements for each of the building model analyses.....100
V
85
viii
LIST OF FIGURES
Figure
Page „
2.1 Typical undisturbed blast profile.........................................................................13
2.2 Hopkinson-Cranz or “cubed-root” scaling of self-similar
explosive charges differing only in size.............................................................. 15
2.3 A single degree of freedom system represented as a viscous
damped oscillator................................................................................ ............... 18
2.4 A multiple degree of freedom system represented as a
series of viscous damped oscillators...................... .............................................19
4.1 Stress-strain curves for (a) elastic material behavior and
(b) inelastic material behavior with elastic recovery.......................................... 36
4.2 Stress-strain curve showing a bilinear isotropic (P=I)
and kinematic (P=O) hardening model...................................................... ........ 37
4.3 Two-dimensional von Mises yield surface for principal stress.......................... 38
4.4 Three-dimensional von Mises cylinder with plastic strain and
hydrostatic stress failure criterion....................................................................... 40
4.5 Eight-node brick element showing three translational degrees
of freedom at a single node.................................................................................43
4.6 Finite elements for (a) a structural beam element and (b) a
structural shell element showing three translational degrees
of freedom and three rotational degrees of freedom at a each node...................43
4.7 Continuum-beam interface showing a beam element conpected ■
to a rigid shell element connected to eight-node brick elements....:...................45
4.8 Flow chart showing the sequence of data passing from
NIKE3D to DYNA3D to NIKE3D.................................................................... 49
LIST OF FIGURES (Continued)
Figure
Page
4.9 Sequence of input commands to transfer data from
NIKE3D to DYNA3D and back to NIKE3D...................................................... 51
4.10 Undisturbed blast profile for a 500-pound ANFO
bomb with a standoff distance of 20 feet......................................................... 53
5.1 Cantilever beam model for preliminary tests...................................................... 55
5.2 Cantilever beam model with beam elements...................................................... 57
5.3 Cantilever beam modeled with continuum elements.......................................... 58
5.4 Cantilever beam model with beam elements and continuum elements..............58
5.5 Load curve for implicit analyses........................................................................ 59
5.6 Load curve for explicit analyses........................................................................ 60
5.7 Load curve for combined formulation solutions............ .....................................61
5.8 Deflected shape of the beam element model for the implicit analysis
due to the 500'0-lb point load applied to the free end of the cantilever beam.....62
5.9 Deflected shape of the continuum element model for the implicit
analysis due to the 5000-lb point load applied to the free end of the
cantilever beam................................................................................................... 63
5.10 Deflected shape of the beam-continuum model for the implicit analysis
due to the 5000-lb point load applied to the free end of the cantilever beam... 64
5.11 Nodal vertical displacement predicted by the NIKE3D solution at 36 inches
along the length of the cantilever beam.......................................................... 65
5.12 Nodal vertical displacement predicted by the NIKE3D solution at 72 inches
along the length of the cantilever beam...........................................................66
5.13 Vertical nodal displacements predicted by the NIKE3D.................................. 67
LIST OF FIGURES (Continued)
Figure
Page
5.14 Vertical nodal displacements predicted by DYNA3D
at 36 inches along the length of the beam.............. ..........................................68
5.15 Vertical nodal displacements predicted by DYNA3D
at 72 inches along the length of the beam........................................................ 68
5.16 Vertical nodal displacements predicted by DYNA3D...................................... 69
5.17 Vertical nodal displacements predicted by the combined
formulation analyses at 36 inches along the length of the beam ..................... 70
5.18 Vertical nodal displacements predicted by the combined
formulation analyses at 72 inches along the length of the beam ..................... 71
5.19 Vertical nodal displacements predicted by the combined
formulation analyses......................................................................................... 71
5.20 Horizontal nodal displacement comparison for the
cantilever beam analyses................................................................................... 73
5.21 Compute time necessary to complete analyses in seconds................................ 77
5.22 Two-bay portal model showing applied loads, boundary
conditions and locations where nodal data was compared.............................. 79
5.23 Two-bay portal modeled with beam elements................................................... BO
5.24 Two-bay portal modeled with continuum elements......................................
81
5.25 Two-bay portal modeled witLcontinuum and beam elements.......................... 82
5.26 Load profiles of (I) the gravity and distributed load applied to
the spandrel beams and\2) the dynamic load applied to the center
column of the two-bay portal models............................................................... 84
5.27 Predicted deflected shape using beam and continuum elements
and the combined formulation analysis with the elastic-plastic
material model.................................................................................................. 86
LIST OF FIGURES (Continued)
Figure
Page
5.28 Predicted deflected shape using beam and continuum elements and
the combined formulation analysis with the elastic-plastic-failure material.... 87
5.29 Horizontal nodal time histories for the two-bay portal models at point a .......88
5.30 Horizontal nodal time histories for the two-bay portal models at point b .......89
5.31 Horizontal nodal time histories for the two-bay portal models at point c .......90
5.32 Horizontal nodal time histories for the two-bay portal models at point d .......91
5.33 Compute time required to solve each of the two-bay portal models................92
6.1 Floor plan (first floor) of the nine-story portion of the Alfred P. Murrah
building showing the section modeled and the location of the symmetry
plane......................................................................................................................94
6.2 Floor plan (second floor) of the nine-story portion of the Alfred P. Murrah
building showing the section modeled and the location of the symmetry
plane......................................................................................................................95
6.3 Floor plan (third floor) of the nine-story portion of the Alfred P. Murrah
building showing the section modeled and the location of the symmetry
plane......................................................................................................................95
6.4 Floor plan (fourth floor) of the nine-story portion of the Alfred P. Murrah
building showing the section modeled and the location of the symmetry
plane........ .........................................................
6.5 Visualization of the section modeled (floor slabs removed for clarity)
and the placement of the blast source. Symmetry plane applied at the
middle column in front of the point of detonation.............................................. 96
6.6 Finite element model of section modeled............................................................ 98
6.7 Load profiles for dead and live loads and the applied blast load.........................99
6.8 Deformation of the combined formulation, bilinear elastic-plastic
model after 2.0 seconds. Note the large deflection of the column
due to the blast load............................................................................................^ l
LIST OF FIGURES (Continued)
Figure
Page
6.9 Deformation in the combined formulation, bilinear elastic-plastic
model with failure after 2.0 seconds. Note that the column has failed
due to the blast load and that both transfer girders are beginning to collapse... 102
6.10 Nodal displacement time history for the pseudo-Murrah
models in the x-direction................................................................................ 103
6.11 Nodal displacement time history for the pseudo-Murrah
models in the y-direction................................................................................ 104
6.12 Nodal displacement time history for the pseudo-Murrah
models in the z-direction...............................................
105
X lll
ABSTRACT
Malevolent bomb attacks on high profile civilian structures have raised concerns
about the vulnerability of multistory civilian structures to terrorist attack. Given the
availability of bomb-making materials and the ease with which large explosive devices
can be assembled and employed, malevolent bomb attacks on multistory government and
civilian structures continue to pose a significant threat to this type of structure. With this
in mind, there exists a need within the engineering community for methods to analytically
model and predict the response of multistory structures to blast loads.
While classical solutions may be used to analyze the initial response of a structure
to a blast type load, they cannot efficiently characterize damage accumulation and failure
in areas of extreme stress and strain. Therefore, an alternate approach was presented that
used a combination of implicit and explicit finite element methods to characterize
structural response before, during and after detonation of an explosive device near a
structure of interest.
Public domain versions of the explicit and implicit finite element codes DYNA3D
and NIKE3D were used in the following manner. First, the implicit finite element
formulation was used to determine the initial stress field in a typical multistory civilian
structure due to gravity loads. Then, the nodal data resulting from the implicit code were
passed to the explicit code as initial conditions prior to the application of a blast load.
Once the static stresses and strains had been transferred and initialized in the explicit
formulation, a calculated pressure front was applied to predetermined structural members
in the form of a distributed impulse load. The explicit formulation was then used to
predict localized structural damage and material failure resulting from the blast load. The
resulting state of the structure due to the blast load was then assessed based on post-blast
nodal data.
Nodal responses of cantilever beam and two-bay portal test cases showed that the
beam-continuum interface used to reduce model size correlated well with similar models
that consisted of either continuum or beam elements only. It was also found that
transferring nodal data between the two codes did not introduce significant error into the
analyses. Finally, the proposed methodology was tested on a model with structural
characteristics similar to those of the Alfred P. Murrah federal building. The
methodology was found to significantly reduce computational cost while adequately
characterizing failure based on the chosen failure material model and prescribed blast
load.
I
CHAPTER ONE
INTRODUCTION
Background
Bomb attacks at the World Trade Center in New York City, the Alfred P. Murrah
Federal Building in Oklahoma City, and American Embassies overseas have raised
concerns about the vulnerability of multistory civilian structures to terrorist attack. Given
the availability of materials and the ease with which large explosive devices can be
assembled and employed, it is reasonable to assume that malevolent bomb attacks on
government and civilian structures will continue to pose a significant threat to this type of
structure. An increased concern for designing multistory civilian structures to withstand
bomb attacks is currently driving the need for a comprehensive method to analytically
model the response of civilian structures to blast loads.
A numerical methodology
capable of predicting the effects of blast loads on multistory, civilian structures would
allow scientists and engineers to investigate reasonable defenses in structural design to
mitigate possible loss of life resulting from terrorist bomb attacks.
Simulation tools incorporating various numerical approximation schemes have
been developed for use in the defense sector to predict the response of mechanical and
structural systems to dynamic loads such as air-blasts and projectile impacts. With the
proper methodology, public domain versions of these tools, which are readily available,
can be applied to analyze blast effects on multistory civilian structures.
2
Before these tools can be applied, the basic mechanical behavior of multistory
civilian structures under dynamic loads must be known. Due to the inherently flexible
nature of multistory civilian structures, structural response to blast loading occurs in two
distinct and equally important phases. First, within milliseconds after detonation, a blast
wave causes permanent local damage to structural members in the immediate vicinity of
the blast.
Second, after local damage has occurred, new load paths develop as
gravitational loads are redistributed to the remaining structural members. In extreme
situations, the latter of these phases can lead to buckling and progressive collapse of a
structure.
For traditional structural and mechanical response analyses, depending on the
particular application, only one of these phases is typically considered. For example, in
blast containment and high velocity impact simulations, local damage is the dominant
response mechanism, typically occurring within the first few milliseconds of loading.
Alternatively, in structural applications involving earthquake and wind loading, overall
structural stability is the dominant concern; thus, analyses focus on the overall structural
response for many seconds after initial loading. Due to the nature of these distinctly
different load cases, different numerical techniques are better suited to model the
governing response mechanism of the particular system.
Analyses of blast loaded civilian structures are unique because both phases of
response are equally important in the overall instability of the structure resulting from a
blast load. Gravity loads must first be initialized and local damage accumulation must be
accurately predicted to determine the structural consequences of the initial blast load.
Once the localized damage has been predicted, the stability of the newly damaged
structure must then be assessed. These distinctly different phases can be predicted using
3
numerical approximation techniques similar to those used to solve the above mentioned
examples.
However, numerical compatibility between the approximation techniques
corresponding to each phase of structural response must be maintained.
This research employs public domain versions of DYNA3D (Whirley, 1993a) and
NIKE3D (Maker, 1990), available through Lawrence Livermore National Laboratory, to:
1. Determine initial localized blast damage in a multistory civilian structure subjected to
a typical terrorist bomb blast.
2. Predict the resulting redistribution of dead and live loads in the newly damaged
structure.
3. Predict the overall structural integrity resulting from I and 2.
The proposed methodology combines two different finite element (FE) techniques in the
following manner. First, an implicit finite element formulation is used to determine the
initial stress field in a typical multistory civilian structure due to gravity loads. Then,
stresses, strains and the resulting nodal displacements and velocities from the implicit
code are passed to an explicit FE code. Once the static stresses and strains have been
transferred and initialized in the explicit formulation, a calculated blast load is applied to
predetermined structural members in the form of a distributed impulse load. The explicit
formulation is then used to predict localized structural damage resulting from the blast
load. Finally, after dynamic vibrations in the structure have dissipated, the new stress,
strain and resulting displacement and velocity fields are passed back to the implicit
formulation where a dynamic implicit analysis is used to determine the resulting integrity
of the structure.
The explicit and implicit modeling capabilities associated with initializing gravity
loads, predicting blast damage and tracking the resulting post-blast integrity of a structure
4
are specifically addressed. The translation between the two formulations is discussed and
a beam-continuum interface, used to reduce the size of the finite -element mesh, is
presented. Analysis results from initial tests on simple steel cantilevered beam models
using a linear elastic material model are presented. Analysis results from tests on a steel
two-bay portal model using elastic, elastic-plastic, and elastic-plastic-failure material
models are also discussed. Compute times are compared between test cases to assess the
validity of the proposed methodology.
Finally, analysis results from tests on large
multistory civilian structure with structural characteristics similar to those of the Alfred
P. Murrah Federal Building are presented.
Scope of Work
The goal of this work was to implement explicit and implicit finite element codes
in analyses of blast loaded multistory civilian structures. An explicit finite element code
was used to study the initial damage phase, while an implicit formulation was used to
initialize gravity loads in the static structure and predict the dynamic post-blast response
of the damaged structure.
An implicit formulation was chosen for gravity initialization and post-blast
analysis because it yields efficient static and low rate dynamic solutions when large time
increments can be taken. An explicit formulation was chosen for the initial damage
resulting from the blast load because the associated solution method consists of solving
multiple uncoupled equations over small increments in time. Explicit formulations are
conditionally stable based on the time increment size. This conditional stability requires
time increments to be on the order of microseconds or smaller making explicit
formulations unsuitable for low rate problems where large time increments will suffice.
5
Finite Element Codes
Several finite element code sets were considered for this research. Due to the
availability of source code, extensive material model libraries and the ability to transfer
data between the two codes, public domain versions of the explicit and implicit finite
element codes DYNA3D (Whirley, 1993a) and NIKE3D (Maker, 1990) were chosen.
These two codes were combined to analytically predict the response of a typical
multistory civilian structure to blast loading. As with previous studies, an explicit finite
element formulation (DYNA3D) was used to characterize the initial structural damage
resulting from a typical bomb blast (Crawford et ah, 1997).
However, after initial
deformation, passing the velocity and strain fields from the explicit analysis to an implicit
analysis (NIKE3D), which was used to determine the post-blast performance of the
damaged structure, further refined the analysis.
The combination of the two finite
element codes and the translation between the two formulations provide a numerical
methodology to determine the structural consequences of bomb attacks on civilian
structures.
Components of Research
Several components associated with the NIKE3D/DYNA3D FE code set were
explored. All models used in the research were preprocessed via ANSYS (Revision 5.6).
A Perl script was written to translate the ANSYS model database to NIKE3D and
DYNA3D database formats. Static solutions of the models were generated in ANSYS5.5
to validate translation of model parameters to NIKE3D and DYNA3D.
Static and
dynamic analyses of similar test models were run in NIKE3D and DYNA3D to illustrate
the computational differences between the two formulations. Computation times were
6
compared between models containing beam elements, continuum elements and hybrid
models containing both types of elements.
The beam-continuum interface method
applied to the hybrid model was also validated using these test cases.
In addition to investigating solution and element formulations, three different
material models were compared. A standard isotropic, linear-elastic material model was
used in early models to study mesh connectivity and overall model behavior. The models
were then refined by the addition of an isotropic-kinematic, elastic-plastic material
model. Finally, failure criteria were added to the material model to study the importance
of characterizing failure in a blast loaded structure.
NIKE3D and DYNA3D are capable of writing databases during analysis that can
be read by their counterparts. For this research, the pre-blast static stress state was
initialized via NIKE3D. At the end of the NIKE3D static initialization, the model data
was written to a DYNA3D initialization file. The static stress field was then initialized in
DYNA3D and a blast load in the form of a uniform distributed load was applied to the
structure. After predicting the damage resulting from the blast, the model data was
written back to a NIKE3D initialization file. This file was read into NIKE3D where the
analysis continued to track the post-blast response of the structure.
The test cases used to explore the primary components associated with the
proposed methodology are shown in Table 1.1 and Table 1.2. An elastic cantilever beam
model was used for preliminary tests of the beam-continuum interface and code
translation validation.
A two-bay portal model was introduced to further test these
components on a structure with increased geometric complexity. This model offered a
comprehensive model to expediently test the solution formulations, material models,
beam-continuum interface and data translation between NIKE3D and DYNA3D. The
7
resulting methodology was then applied to the multistory civilian structure model to
illustrate its ability to handle large models.
Table 1.1 Analysis Matrix for Cantilever Beam Models
Model
DYNA3D
NIKE3D
NIKE3D-DYNA3D-NIKE3D
Continuums
X
X
X
Beams
X
X
X
Beams and Continuums
X
X
X
Table 1.2 Analysis Matrix for 2-Bay Portal and the Multistory Civilian Structure
2-Bay Portal
(continuums)
2-Bay
Portal
(beams)
2-Bay Portal
(beams and
continuums)
X
X
X
Model
DYNA3D
Elastic-Plastic
DYNA3D
Elastic-Plastic-Failure
NIKE3D
Elastic-Plastic
NIKE3D-DYNA3D-NIKE3D
Elastic-Plastic
NIKE3D-DYNA3D-NIKE3D
Elastic-Plastic-Failure
Civilian
Structure
(beams and
continuums)
X
X
'
X
X
X
X
X
X
X
X
X
X
X
The combination of the cantilever beam models, the two bay portal models, and
the multistory structure model served to study the methodology on models with
increasingly more complex geometries. Finite element material models, a beamcontinuum interface and data exchange between the two codes exercised the effects of the
methodology on the models. The analyses in Table 1.1 and Table 1.2 were completed to
assess the validity of the proposed modeling methodology.
8
;
CHAPTER TWO
LITERATURE REVIEW
Introduction
A comprehensive literature review was conducted to assess observations from
recent terrorist bomb attacks on civilian structures and identify currently available
analysis tools and numerical methodologies capable of predicting the response of these
structures to blast loading.
Documented terrorist attacks on civilian structures
demonstrate the need for analysis tools capable of determining the vulnerability of this
type of structure to blast loads. Blast models capable of predicting peak overpressure and
impulse duration are presented to provide a method to characterize and apply blast loads
to structural models. Finally, current developments and applications of finite element
solutions to dynamically loaded structures are reviewed.
Terrorist Threat
World Trade Center
In February 1992, an 1800-lb Ammonium Nitrate-Fuel Oil (ANFO) bomb
exploded on an exit ramp inside an underground parking area at the World Trade Center
in New York City. The explosion occurred near one of the main columns supporting the
110-story structure.
The column did not fail under the direct blast load but lateral
9
restraint provided by two concrete floors was lost.
Fortunately, the steel column,
measuring 4-ft by 4-ft, did not buckle under the increased effective length. However,
several injuries and fatalities occurred due to fragmentation, blast overpressure and
smoke inhalation (Longinow, 1996). The fact that the World Trade Center remained
relatively stable under the blast load speaks well for structural redundancies in design,
Alfred P. Murrah Federal Building
In April 1995, at 9:00 a. m. a 4800-lb ANFO bomb exploded 20-ft away from the
nine-story Alfred P. Murrah Federal Building in Oklahoma City.
The explosion
collapsed a transfer girder, which supported columns from the seven floors above it.
Once the transfer girder failed, all seven floors supported by the columns progressively
collapsed. The initial blast and subsequent structural collapse destroyed one third of the
building killing 169 civilians and injuring more than 500 (Massa, 1995).
In this case, structural redundancies were clearly inadequate for the blast loading
case. Although this building did conform to the government building code at the time it
was built, blast load cases were not considered in design. Ultimately, the initial blast
damage and the resulting progressive collapse was found to be consistent with what
would be expected for an ordinary moment frame of the design available in the mid1970s subjected to a blast load.
American Embassies
Most recently, two separate bombings occurred at U.S. Embassies in Nairobi and
Dar es Salaam in Tanzania. The bombing in Nairobi killed a total 254 initiating one of
the largest FBI international-terrorism investigations in history. Although both of these
10
building were designed with consideration of blast loads, the design was based on
empirical observations, which were not specific to the particular geometry of each
structure (U. S. Department of State, 1989).
Current Methods
Unfortunately, because of the availability of commercial explosives and the ease
with which large bombs can be assembled, there is a growing concern in the United
States that terrorist attacks on civilian structures may become more common in the future.
v
To avoid further loss of life, reasonable defenses must be employed to minimize the
threat of future attacks on civilian structures. In the case of the Oklahoma City bombing,
an estimated 80% of the fatalities were caused by structural collapse (Prendergast, 1995).
One way to mitigate this type of failure would be to include redundancies in the design of
structures so that even with a key structural element removed, the structure would remain
stable under alternate load paths (Hinman, 1995). Currently standing structures can be
retrofitted with blast walls and established perimeters to increase the standoff distance
between the structure and a bomb attack (Chapman et al., 1994). The National Research
Council offers similar recommendations to mitigate blast effects on commercial buildings
(The National Research Council, 1996). Regardless of the design approach, a thorough
analysis of the structure must be performed to assess vulnerable areas within the structure
and determine the consequences of a malevolent bomb attack (Prendergast, 1995).
Until recently, the effect of blast loading on structural systems has been a concern
of almost exclusively the military. Additional research has been pursued by process
industries dealing with explosive materials and the blast mining industry. Consideration
of blast loads from terrorist bomb attacks on civilian structures has been addressed for
11
American Embassies overseas (Ettouney, 1996). However, the current design philosophy
for civilian structures in the United States does not include the same consideration.
The bombings of the World Trade Center in New York City and the Alfred P.
Murrah Federal Building in Oklahoma City clearly demonstrate a need to design multi­
story civilian structures with future terrorist threat in mind (Longinow, 1996). Present
research in this field consists mostly of deterrence and prevention of terrorist attacks in
the form of physical security with little effort being expended on analytically assessing
the response of this type of structure to blast loading. One noted exception is the work of
Crawford et al. (1997), which used the Lagrangian finite element code DYNA3D
(Whirley, 1993a) to study the effectiveness of jacketing columns on multistory reinforced
concrete structures to resist blast loads. The focus of the analysis, however, was on the
localized response of lower-story perimeter columns only.
Blast Modeling
The development and propagation of blast waves has been well characterized by
the military.
When a high explosive material is initiated it can bum, deflagrate or
detonate (DOE/TIC, 1981). Detonation, the most severe of these reactions, initiates a
blast wave. In general, a blast can be defined as a process whereby a pressure wave is
generated in air by a rapid release of energy {Major, 1994). A blast front is generated
when the air surrounding an explosion is compressed by the release of energy
immediately after detonation.
The blast wave propagates away from the point of
detonation at a sonic velocity with a peak overpressure proportional to the charge type
and weight. When the blast front encounters a solid object, it reflects back onto itself
12
which has the effect of reinforcing the pressure imposed on the object (Dharaneepathy,
1995; Ettouney, 1996; Beshara, 1994a).
In addition to a blast wave, an explosive source detonated near the ground may
also produce ground vibrations. The amount of explosive energy partitioned for the
ground vibration is a function of the characteristics of the ground and the shape of
explosive (DOE/TIC, 1981).
Structural damage resulting from blast induced ground
vibrations has been classified by the blast mining industry by means of the “peak particle
velocity” (PPV). The PPV is related to the charge weight and distance from the point of
interest by a power function. Extensive research on damage resulting from blast induced
ground motion has been conducted by the blast mining community (Singh and Thorte,
1985; Favreau et al., 1989; Dowding, 1994; Yu and Vongpaisal, 1996).
Although blast induced ground vibrations play a significant role in both military
and blast mining applications, a majority of the energy of a typical terrorist bomb blast is
partitioned to the blast wave. Therefore, the ground motion is of little consequence to the
overall behavior of a multistory civilian structure (Mlaker et al., 1998). Thus, ground
motion was neglected in this study.
Undisturbed Blast Profile
Blast wave properties are traditionally defined and measured for an undisturbed or
side-on wave as it propagates through air. Figure 2.1 shows a typical blast profile. The
peak overpressure (peak blast pressure above ambient air pressure) occurs almost
instantaneously after the blast shock wave passes a point. This is followed by a decrease
in the positive phase to a pressure below ambient air pressure; and finally, a gradual
increase back to the ambient air pressure.
13
Overpressure
Ambient air
pressure
Time
Positive
phase
Negative
phase
Figure 2.1 Typical undisturbed blast profile.
Military Design Aids
Much of the current literature available on blast characteristics originates from
military research. Research conducted by the military after World War II has, however,
focused primarily on blast loads resulting from nuclear weapons. Although magnitudes
differ dramatically, conventional blast characteristics are similar to those of nuclear
weapons. Current military design aids include generalized empirical formulations to
estimate ground motion characteristics and blast wave properties for both nuclear and
conventional weapons (TM5, 1965).
Scaling of blast wave properties from an explosive source is a common practice.
Scaling laws allow the prediction of blast wave properties for large-scale explosions to be
based on tests of a much smaller scale. The most common form of blast scaling is
Hopkinson-Cranz or “cubed-root” scaling. This law states that two self-similar explosive
14
charges, differing only in size, produce identical blast waves of different size, scaled
proportional to the difference in size between the two explosive charges. The scaling
laws are written as follows:
Equation 2.1
Equation 2.2
where Z is the scale factor, R is the distance from the center of the explosive source, E is
the total heat energy of detonation, and W is the weight of the charge (Hopkinson, 1915,
Cranz, 1926).
Furthermore, an object located at a point some distance R from the center of the
explosive charge of characteristic dimension d will be subjected to a blast wave with
amplitude P, duration td, and a characteristic time history. The Hopkinson-Cranz scaling
law states that for the same object in the same atmosphere at a point some distance ZR
from the center of the same charge with a characteristic dimension of Zd will be
subjected to a blast wave with amplitude ZP, duration Ztd, and a characteristic time
history scaled by Z. Figure 2.2 shows the implications of the Hopkinsin-Cranz scaling
law. '
15
•tv
P
>
Figure 2.2 Hopkinson-Cranz or “cubed-root” scaling of self-similar explosive
charges differing only in size.
The U. S. Department of Energy has published empirical data that correlates peak
blast pressure, blast duration and blast front arrival time to a scaled distance obtained by
the Hopkinson-Cranz scaling laws (DOE/TIC, 1981). The table below shows peak sideon pressure, peak reflected pressure, arrival time of blast front and the blast duration.
The peak side-on pressure is the maximum pressure of the undisturbed blast wave. The
reflected peak pressure accounts for the blast being reflected back onto itself after it
encounters an object. This has the effect of amplifying the pressure wave. The blast
duration is the time duration of the positive phase of the blast wave. Negative pressure
phases for conventional explosives are traditionally neglected, as the positive pressure
phase for conventional explosives is generally much larger than the negative pressure
phase. Finally, the arrival time is the time required for the blast wave to travel the
specified standoff distance. Note the significant decrease in peak pressure when the
standoff distance is doubled (Table 2.1).
16
Table 2.1 Blast Profile Parameters for Various Charge Weights at Different Standoff
Distances
Side-on Peak
Blast
Arrival
ANFO Standoff
Pressure
Duration
Time
Weight Distance
(psi)
(pounds) (feet) (milliseconds) (milliseconds)
140
111.0
3.21
20
500
200
90.0
2.52
20
1000
375
15.1
1.50
20
5000
800
13.3
1.60
20
10000
24
110.1
12.0
40
500
30
130.0
10.0
40
1000
150
150.4
5.60
40
5000
290
140.0
4.52
40
10000
Reflected Peak
Pressure
(psi)
700
1500
5500
8000
100
175
1250
2250
Petrochemical Design Aids
In the petrochemical process industry, blast loads are often considered in the
design of structures.
Classification of process industry explosives includes high
explosives, gas and vapor cloud explosions, aerosol explosions, and rapid phase transition
{Major, 1994). Design aids published for use in the petrochemical process industry
include design parameters such as fragment generation, peak overpressure prediction, and
injury and damage estimates.
Blast Wave Models with Computational Fluid Dynamics
The blast model presented above describes an undisturbed incoming wave front.
However, it is important to note that near field obstacles have a significant effect on the
shape of the blast wave and the way in which it is transmitted to a complex structure.
Structural geometry can also have a significant effect on the shape of a blast wave after it
encounters the structure. In fact, as the complexity of near field obstacles and structural
geometry increases, a computational method of characterizing the blast front becomes
17
necessary. These analyses are typically performed using computational fluid dynamic
- (CFD) methods involving finite difference techniques (Nash and Dom, 1997;
Vanderstraeten et ah, 1996; van Wingefden et ah, 1999; Bennett and Strugul, 1989;
Marconi, 1994).
Currently, computational resources capable of coupling the blast-structure
interaction with structural deformation are rarely available in the civilian sector,
particularly for large models. Characterizing of the blast wave in conjunction with
structural deformation is not the intent of this study. As such, blast loads employed in
this research are applied in the form of distributed loads over selected members in the
vicinity of the explosive charge.
Structural Models
The analysis of blast effects on structural systems is a field that has been
historically dominated by military applications. Blast effects on deliberately hardened
military structures have been well characterized by the Department of Defense. Current
military design aids include ground motion characteristics, projectile impact, and blast
wave development, with suggested structural analysis techniques ranging from singledegree-of-freedom models to numerical method techniques involving systems of
multiple-degrees-of-freedom
(TM-5,
1965;
DOE/TIC,
1981).
Additionally,
characterization of the response of structural systems to dynamic loading has been
established in the field of earthquake engineering (Biggs, 1964). The primary concern of
this field, however, has been with predicting the response of structural systems subjected
to ground motions using quasi-static loads. Several seismic building codes are currently
used throughout the United States (UBC, 1994).
18
Dynamic Systems
Theoretical models have been developed to predict the response of structural
systems to arbitrary dynamic loads (Paz, 1997; Biggs, 1964; Clough and Penzien, 1975).
The models include single-degree-of-freedom (SDOF) systems, multiple-degree-offfeedom (MDOF) systems and incremental integration techniques. SDOF models offer
an efficient method to predict the response of simple structures under dynamic loading.
In a SDOF system a structure is idealized as an equivalent mass, spring and dashpot,
mathematically represented by a second-order ordinary differential equation with
constant coefficients (Paz, 1997). Figure 2.3 shows the idealized SDOF system
Figure 2.3 A single degree of freedom system represented as a viscous
damped oscillator.
where m is the mass, c is the damping coefficient, k is the stiffness, flj) represents a
forcing function and y is the displacement coordinate (degree of freedom). The equation
of motion for this system can be written as follows:
Equation 2.3
my + cy + ky = f ( t )
19
For more complex structures, MDOF models are preferred.
MDOF models
consist of a system of masses, springs, and dashpots, which form a series of coupled,
second-order ordinary differential equations that satisfy modal orthogonality conditions
(Paz, 1997). Figure 2.4 shows an idealized MDOF system.
Figure 2.4 A multiple degree of freedom system represented as a series of viscous
damped oscillators.
The equations of motion for this system can be written as follows:
Equation 2.4
[ M] { y } + [ C] { y} + [ K] { y } = {/(f)}
where [M] represents the mass matrix, [C] is the damping matrix, [AT] is the stiffness
matrix, {/(f)} is a forcing function vector and {y} is the displacement coordinate vector
(degrees of freedom).
Generally, both of these systems relate linear damping and
stiffness characteristics to the equations of motion and therefore do not predict nonlinear
structural behaviors.
20
Numerical Methods Solutions
The most applicable and widely used method for the analysis of arbitrary
nonlinear systems is the incremental integration method.
Incremental integration
methods are well suited to model nonlinear responses occurring from inertial effects of
load impulse, material hardening effects and energy absorbed by plastic deformation. In
its simplest conceptual form, the response history is divided into successive increments of
time.
Dynamic equilibrium is satisfied at the beginning of each time increment by
modifying the constitutive properties of the system based on its current state of
deformation and stress. Then, the response of the system is approximated as a linear
system for the next time increment. Thus, the nonlinear solution is approximated as a
series of linear solutions (Clough and Penzien, 1975). Incremental integration for the z'th
step of the SDOF equation given above yields:
Equation 2.5
mAjX + CAyi + JcAyi = AFi
With the increase in computational capabilities, the incremental integration
technique has been extended as a numerical tool in the form of the finite element method.
The finite element method has consequently become a dominating analysis technique for
a wide variety of engineering applications (Mackerle, 1996).
The nonlinear analysis of structural systems using the finite element method has
been improved by including complex, rate-dependent constitutive models that
approximate damage based on calculated states of stress (Beshara, 1992). Additional
improvements have been made in time integration methods and solution formulations for
the governing nonlinear equations (Beshara, 1991).
21
Finite Element Applications
Finite element codes have been used to study the effects of impulsive loads on
military structures (Mackerle, 1996).
The analyses range from simple linear-elastic
response to nonlinear, rate dependent models. Implicit finite element codes have been
used to simulate the response of underground monolithic structures subjected to blast
loading (Yang, 1997).
Rate and history dependent constitutive models have been
developed for many different types of materials. Beshara (1992) developed a rate and
history dependent material model to predict the response of dynamically loaded
reinforced concrete (Beshara, 1991).
These analyses were in agreement with
experimental results in predicting deflection histories and flexural and shear cracks as
well as predicting the redistribution of stresses in the concrete and the stress history for
the reinforcement. Additional work done by Krauthammer and Stevens (1994) used
explicit and implicit finite element formulations to model blast loaded buried reinforced
concrete arches.
The method agreed well with test data from two unique, buried
reinforced concrete arches.
Finite element methods have also been used in the petrochemical process industry
to optimize the design of blast containment walls. Louca, Punjani and Harding (1996)
used an explicit finite element code (DYNA3D) to predict the behavior of stiffened
panels subjected to blast loading with geometries similar to those used in current offshore
structures. By using numerical methods, the analysts were able to reduce the shutdown
time for retrofit and optimize the design of the strengthened blast wall. For a similar
application, Groenenboom and van der Weijde (1996) used numerical methods to
optimize the strengthening of a blast wall between the compression and process area, and
22
the rest of the platform area on the Beryl Bravo platform. The analysis, which included
effects from plasticity, strain rate and buckling, correlated well with experimental and
theoretical SDOF models.
Additional research in this area has produced similar results. Louca, Pan and
Harding (1998) investigated the significance of including imperfections in the analysis of
stiffened and unstiffened plates subjected to blast loading using explicit finite element
techniques.
Deformation and failure of blast-loaded square plates was assessed by
Rudrapatna, Vaziri and Olson (1999) using a nodal release algorithm within the finite
element method to simulate failure. Their results confirmed the importance of including
the effects of both tensile and bending strain on the tearing and the shear failure of square
plates subjected to blast loads.
The finite element method has only recently been employed in the study of blast
effects on civilian structures. Work by Crawford et al. (1997) investigated the effects of
standoff distance and column jacketing on enhancing the resistance of reinforced
concrete structures to blast loads using explicit finite element methods. Jacketing the
columns with a steel or composite wrap prevented shear failure of the columns when
subjected to blast loads.
Explicit finite element techniques are well suited for dynamic loading
applications. However, because stress waves in the materials must be accurately resolved
in space and time, large-scale analyses tend to be computationally intensive. Research
has been conducted to employ multiple processor computers to efficiently solve largescale problems with practical compute times.
Namburu et al. (1998) used scalable
software to solve a large-scale problem on multiple processor machines. Results from the
23
numerical analysis which contained 142,369 hexahedral elements, 9,656 beam elements
and 6,486 slide surfaces, were in excellent agreement with experimental results.
Literature Review Conclusion
Bomb attacks on multistory civilian structures warrant a need to consider blast
type loads in the design of this type of structure. The bomb attack at the World Trade
Center showed the importance of including structural redundancies in structural design.
This was again shown at the Alfred P. Murrah federal building, which did not include
adequate redundancies in design and consequently failed catastrophically under a blast
load.
Current analysis techniques indicate a lack of efficient methodologies to properly
characterize the entire response history of multistory civilian structures to blast loads. As
such, most blast design analyses have been based on either quasi-static load cases or local _
damage modeling exclusively.
Blast models available through military design aids offer an effective means to
characterize blast loads similar to those of a typical terrorist bomb type. The HopkinsonCranz scaling law gives blast profile characteristics for spherical explosive charges
(Hopkinson, 1915, Cranz, 1926); and The Major Hazards Assessment Panel
Overpressure Working Party (1994) gives TNT equivalency values for many different
explosives including ANFO.
24
As a result of increasing computational power, simple dynamic systems in the
form of damped mass oscillators have been extended to incremental integration
techniques involving the finite element method.
The mathematical formulations
associated with the finite element method yield results that are in good agreement with
experimental results for dynamically loaded systems.
r
25
1
CHAPTER THREE
FINITE ELEMENT CHALLENGES
Introduction
The development of numerical models and the corresponding methodologies to
predict failure and collapse of multistory civilian structures under blast loading enables
analysts to assess the vulnerability of these structures to terrorist attack. The challenges
presented with predicting the consequences of explosive detonation near a multistory
civilian structure include characterization of the:
1. blast wave given the charge type, weight, containment, and location,
2. initial damage resulting from detonation,
3. attenuation of the blast wave and the initial response of the structure as loads
are redistributed over the damaged structure,
4. overall response of the damaged structure, and
5. progressive collapses of portions of the structure as elements fail under the
redistribution of loads.
This chapter addresses the use of implicit and explicit finite element codes in the analysis
of blast loaded multistory civilian structures.
26
Structural Response Phases
The numerical analysis of weapons effects on civilian structures is a relatively
unexplored field.
Public domain versions of Lagrangian and Eulerian based finite
element codes developed for use in the defense sector are well suited to study the effects
of blast loads on civilian structures. For civilian structures, numerical analyses using
these codes must be able to predict local damage resulting from a blast as well as the
ultimate structural integrity of the damaged structure.
Unlike typical civilian structures, blast resistant military structures are designed to
remain completely functional during and after nuclear and/or conventional weapons
attacks. These low profile structures are deliberately hardened yielding an extremely
Z
rigid structure capable of withstanding typical military blast loads. Due to their rigid
nature, the analysis of this type of structure has focused primarily on the damage
occurring during a blast with minimal concern for the effects of post-blast response.
In contrast, multistory civilian structures are typically unhardened and inherently
flexible. Consequently, the response of these structures to blast loading occurs in two
distinct and equally important phases. The first phase, occurring within milliseconds, is
associated with plastic deformation of structural elements near the blast. The second
phase involves the post-blast behavior of the entire structure due to the initial permanent
damage. Each of these phases must be accurately modeled to predict the overall stability
of a multistory civilian structure.
27
Finite Element Formulations
Explicit Formulations
In the past, analyses of structural systems subjected to blast loading have been
performed on deliberately hardened structures in the form of bunkers and blast
containment walls.
These structures are typically designed to survive blast loads;
therefore, total structural collapse is generally not an issue.
Local effects occurring
within milliseconds of the initial blast have typically been modeled for these structures
using explicit finite element codes.
Explicit codes are well suited to model the initial effect from blast loads
(Mackerle, 1996).
Inertial effects from load impulse, energy absorbed by plastic
deformation and strain hardening or softening effects can be efficiently included in the
finite element formulations. Most explicit formulations use a central difference method
to integrate the equations of motion through time. Additionally, the equations of motion
can be uncoupled by lumping the mass matrix to produce a diagonal matrix. This
■
eliminates the need to simultaneously solve the equations o f motion yielding the
following uncoupled equation of momentum:
Equation 3.1
Man+1 = f ext - f mt
where an+i is the new acceleration, f ext is an external force, f mt is the internal force and
M is the mass. The stability of the explicit central difference method is governed by
satisfying the Courant Condition on each time step At.
Conceptually, the Courant
Condition restricts the time step size to the time required for an elastic stress wave to
travel across the shortest dimension of the smallest element in the mesh. For complex
28
problems involving high rate loading, this can result in analyses that run for days on large
computers and may only model the first milliseconds of the analysis.
It is known that blast pressure diminishes proportional to the distance cubed from
a point of detonation (DOE/TIC, 1981).
Consequently, blast pressures generated by
typical terrorist bombs tend to cause damage only to structural elements within the
immediate vicinity of the detonation. Explicit finite element codes are ideally suited to
model this phase of response.
Implicit Formulation
The most common form of the finite element method utilizes implicit time
integration. . For this method, geometric equilibrium is satisfied based on nodal
displacements resulting from applied loads. The equations of equilibrium are represented
by the following linear system:
Equation 3.2
[K ]{Am}= {f }
where [K\ is the stiffness matrix, [Au) is the displacement vector and (F)is the force
vector. For nonlinear solutions, the linear system is iterated at each step until a user
defined convergence tolerance is met. However, the solution of the linear system and the
iterations at each step require a large amount of computational effort.
Implicit finite element formulations can be solved quite efficiently for low-rate
dynamic loads over long time periods using quasi-static load cases. Furthermore, the
unconditional stability of implicit integration allows time-steps and element sizes much
larger than can be used with explicit methods. Therefore, although not as well suited for
the initial blast analysis, implicit formulations can be used to model structural response
29
occurring seconds after an initial blast. This includes predicting alternate load paths that
develop as a result of initial blast damage as well as determining the overall stability of
the damaged structure. Additionally, the implicit formulation can be used to initialize
gravity loads prior to a detonation.
The choice of the integration scheme used for analysis is based on the advantages
and disadvantages of each for both phases of structural response. Table 3.1 lists some of
the advantages and disadvantages of using explicit, implicit and a combination of both
integration techniques.
Table 3.1 Advantages and disadvantages of explicit and implicit finite element
formulations
I n te g r a tio n S c h e m e
Advantage
•
•
Explicit
•
•
•
•
•
•
Implicit
•
•
•
•
•
Combination
•
•
Disadvantage
Conditionally stable
Track stress waves through the •
medium
•
Courant Condition governs time
step size
Iteration not required at each
time step
•
Static loads must be applied
slowly or dynamic relaxation
Efficiently
include
strain
technique must be used
hardening and softening effects
modes
must be
Include inertial effects from load • Hourglass
stabilized
impulse
Automatic contact, slide surfaces
and restarts
•
Convergence
and
accuracy
Unconditionally stable
governed by time step size
Large time steps can be used
Iteration required at each time
Static loads can be initially •
step especially for nonlinear
applied
effects
Account for strain hardening and
•
Dynamic
loads applied quasisoftening effects
statically
Automatic time-step size
Contact and slide surfaces
Initialize gravity loads implicitly • Code must be translated from
implicit to explicit to implicit
Predict initial damage from
•
Element formulations must be
dynamic loads explicitly
compatible
Include nonlinear effects from
dynamic loading and strain • Velocity and strain field must be
transferred
hardening and softening
Predict
overallstructural
response over long time periods
implicitly
30
Several commercial and military based Lagrangian finite element codes are faced
with the advantages and disadvantages mentioned in Table 3.1. Current advances in
Lagrangian based explicit finite element codes have been made primarily as a result of
military and defense applications in the form of nuclear weapons effects and
penetrator/armor interaction. These codes include DYNA3D (Whirley, 1993a), Pronto
(Taylor, 1987), ABAQUS Explicit (Hibbett et ah, 1995b) and EPIC (Johnson, 1987).
Additional advances in implicit and explicit finite element codes have been made which
allow analyses to be transferred between the two integration schemes. Two versions of
the explicit/implicit finite element codes (DYNA3D/NIKE3D) are currently available.
The commercial version LS-DYNA is available and the public domain versions of
DYNA3D and NIKE3D are available through Lawrence Livermore National Laboratory.
The latter has some advantages as it is free and the source codes are available, allowing
modifications to be made to the codes.
A second pair of explicit/implicit codes,
Pronto/JAC, is maintained by Sandia National Laboratory.
These codes are rarely
available to the public due to security issues. The third pair of explicit/implicit codes,
ABAQUS explicit/ABAQUS standard, is commercially available. However, neither of
the last two sets is available in source code format making the DYNA/NIKE set more
appealing for this research.
31
CHAPTER FOUR
APPROACH
The presented methodology applies an implicit finite element solution, NIKE3D,
to initially solve the stress field existing in a multistory civilian structure under typical
design live and dead loads.
A distributed load with a profile similar to that of a
conventional blast profile is then applied to predetermined structural members to simulate
a blast load with a magnitude comparable to a typical ANFO bomb. This stage in the
analysis is solved with an explicit FE code, DYNA3D. Finally,"after vibrations from the
blast load have attenuated in the structure, the explicit solution is passed back to the
implicit code to determine the resulting integrity of the structure. This procedure as
applied to the large model was first validated on small test models.
The methodology was approached using a public domain version of an explicit
and implicit finite element code set. Based on a literature review of blast dynamics and
the associated use of explicit and implicit finite element codes (Mackerle, 1996), the
DYNA3D/NIKE3D (Maker, 1990) code set was chosen for this research. A public
domain version of DYNA3D/NIKE3D was obtained from Lawrence Livermore National
Laboratory. Both the explicit and implicit codes contain comprehensive material model
libraries with advanced failure, contact and slide surface algorithms. Restart capabilities
include element and material deletion, boundary condition modification, and translation
between implicit and explicit codes.
.32
Empirical blast data published by the Department of Energy was used to
determine the blast characteristics for typical ANFO bombs with differing weights and
standoff distances (DOE/TIC, 1981). Specifically, the peak magnitude, approximate time
history and arrival time for the blast profile was generated for given charge weights,
detonation heights and standoff distances using the Hopkinson-Cranz scaling laws.
A cantilever beam model was used to initially test material models, continuumbeam interfaces and compute times for explicit and implicit formulations. This model
was also used to test the code set’s ability to translate data between the two formulations.
A two-bay portal model was then introduced to test the same capabilities on a more
complex geometry. The components investigated with these two models include:
1. Material models with the following behaviors: elastic, kinematic/isotropic
elastoplastic and isotropic hardening with failure.
2. Continuum to beam interface.
3. Data translation between NIKE3D and DYNA3D.
4. Blast profile development and its application to a structure.
As a final case study, a model with structural properties similar to those of the
Alfred P. Murrah Federal building was analyzed using the proposed methodology. A
calculated blast load of approximately the same magnitude as the ANFO bomb
responsible for collapsing the Alfred P. Murrah Federal building was applied to the
model.
The NIKE3D/DYNA3D code set was applied to the model to predict the
response history of the structure. Then, the response of the model was compared with the
response of the Alfred P. Murrah Federal building under the same blast load.
33
Material Models in NIKE3D and DYNA3D
As with most sophisticated finite element packages, NIKE3D and DYNA3D have
extensive material model libraries. Material models included in this code set range from
simple linear elastic models to strain rate-dependent viscoplastic models. Some models
are specific to continuum elements only while others work for structural elements as well
as continuum elements.
Three different material models were implemented for this research. All three
material models were implemented in both codes and work with continuum elements,
beam elements and shell elements. The material models used include:
1. Isotropic Elastic
2. Isotropic Elastic-Plastic with kinematic and isotropic hardening
3. Isotropic Elastic-Plastic with isotropic hardening and failure
Although isotropic material models were used for this research, an anisotropic
material model specifically designed to model concrete plasticity and damage
accumulation is discussed and suggested to further refine the methodology as applied to
multistory civilian structures.
Constitutive Modeling
The behavior of a material model in a finite element packages is based on the
constitutive properties of the material.
Some common material behaviors include
isotropic, transverse isotropic, and orthotropic. A material is said to be isotropic if the
material elastic constants remain invariant under any and all rotation of axes. Steel is an
example of an isotropic material. A material is said to be transversely isotropic if there
exists an axis for which the elastic constants remain invariant under rotation about that
34
axis.
Layered materials can be transversely isotropic.
An orthotropic material is a
material for which there exists three mutually orthogonal directions in which the material
properties remain invariant.
Reinforced concrete is an example of an orthotropic
material.
In general, for a homogeneous material, the anisotropic, linear elastic stress
components can be related to the strain components in the following way:
Equation 4.1
where
C iJ k i
T» = ^ykieUi
is a set of constants called the elastic constants,
Xij
is the stress tensor, and %
is the strain tensor. This equation is the generalized Hooke’s law for a homogeneous
linear elastic material.
For an orthotropic material, inversion of axes yields twelve elastic constants. In
matrix form they are:
C12
C13
0
0
0
C21 C22
C23
0
0
0
C31 C32
0
0
C33
0
0
0
0
0
0
C55
0
0
C11
Equation 4.2
C /*/
0
0
0
C44
0
0
0
0
0
C66
35
where:
c" =i
cV -J -
C“ -
t
V
C33
C21
I
~ Ez
C"
= _ % L
Ex
c -
C,
C -
"
1
c -
1
C
Next, for cubic symmetry, the properties are required to be the same in three orthogonal
directions. A rotation of 90° about the orthogonal axes further reduces the number of
coefficients to nine. Finally, for an isotropic material, the properties are required to be
invariant about any and all rotations. A rotation of dQ about any axis reduces the number
of coefficients to two.
Thus, only Young’s modulus, E, and Poisson’s ratio, v, are
required for an isotropic, linear elastic material.
Elastic Material Model
Many structural materials such as metal, wood, concrete and plastics behave in a
linear elastic manner for an initial region on the stress-strain curve.
This region is
represented on a stress-strain curve by a line beginning at the origin with a slope equal to
Young’s modulus, E. Poisson’s ratio, v, which relates the strain in principal directions, is
the only other elastic constant needed to describe a linear elastic material. The linear
relationship between stress and strain for an isotropic material can be expressed by
Hooke’s law:
Equation 4.3
a = Ee
where E is Young’s modulus, a is stress and e is strain. Most structures are designed to
perform within the linear elastic range.
36
Isotropic linear elastic material models are often used in finite element analyses to
obtain initial solutions because they are relatively trivial to solve due to their linear nature
and the simplicity of the elastic constant matrix. However, they are not well suited to
model problems involving large deflections as they assume a material will strain
infinitely under an infinite stress without experiencing any permanent deformation.
Bilinear Elastic-Plastic Model
If a linear elastic material is loaded within the elastic range it can be unloaded and
reloaded without significantly changing the material behavior, neglecting fatigue effects.
If, on the other hand, the material is loaded beyond its elastic range, the internal structure
of the material is altered and the material properties change.
When this occurs, the
material is said to plastically deform. Loading into the plastic range causes permanent
strain in the material; that is, the material does not return to its original shape. Figure 4.1
show elastic versus plastic deformation on a stress-strain curve.
Loading
Loading
Unloading
Unloading
Elastic Range
Plastic Range
Residual
Strain
Elastic
Recovery
Figure 4.1 Stress-strain curves for (a) elastic material behavior and (b) inelastic
material behavior with elastic recovery.
37
To account for plastic deformation, a bilinear, kinematic/isotropic elastic-plastic
material model was used. This model is available in both NIKE3D and DYNA3D and
translates well between each code.
The material model incorporates linear strain
hardening and includes a hardening parameter, p, that specifies a combination of
kinematic and isotropic hardening. In Figure 4.2 the elastic region on the stress-strain
curve ends at the yield stress, G0. Once the von Mises stress reaches a specified yield
stress, plastic deformation begins. The plastic region is approximated by the tangent
modulus, Er- The yield surface is determined by the hardening parameter /3. If j3 is one,
the yield surface expands in a purely isotropic fashion; if /3 is zero, the yield surface
translates kinematically (with no isotropic expansion).
F ig u r e 4 .2 S tr e s s -s tr a in c u r v e s h o w in g a b ilin e a r is o tr o p ic
h a r d e n in g m o d e l.
(P=I)
a n d k in e m a tic
( P = O)
Under monotonic loading, isotropic and kinematic elastic-plastic models behave
identically.
However, note that reverse loading for the isotropic hardening model
predicts reverse yielding when the stress reaches the negative of the maximum stress.
38
Reverse loading for the kinematic hardening model predicts reverse yielding when the
stress has relaxed by twice the yield stress. For most metals, P is typically set for a
combination of isotropic and kinematic material behavior.
This model is well suited for problems where linear elastic and plastic
deformation are expected. It should be noted that the development and application of the
bilinear elastic-plastic material model is based on homogeneous and isotropic materials,
when von Mises stress is applicable. The generalized two-dimensional von Mises yield
surfaces defined in principal stress space is represented by Figure 4.3. It should be noted
that plasticity models are also available for anisotropic materials in the NIKE3D and
DYNA3D material libraries. However, they were not implemented in this study.
Yield Envelope
Figure 4.3 Two-dimensional von Mises yield surface for principal stress.
Elastic-Plastic Model with Failure
The elastic-plastic material model behaves well for problems involving large
deformations when material failure is not expected. However, in applications involving
extreme load cases, such as blast loads, material failure must be considered. The failure
39
model used in this research removes elements when specified failure criteria have been
reached. Unfortunately, the model is only implemented in the explicit code, DYNA3D.
Removing elements in an explicit code is a relatively straightforward task, as
mesh reformulation does not involve reconstruction of a stiffness matrix. Implicit finite
element methods, on the other hand, require reformulation of the stiffness matrix to
account for the deleted elements. Failure in implicit codes does not typically involve
removing elements from the mesh; instead, the element stiffness can be reduced to a
value much lower than its original stiffness.
The failure model used for this study behaves identical to the bilinear,
kinematic/isotropic, elastic-plastic material model with (3 equal to one, except two failure
criteria are incorporated. An effective plastic strain criterion and a hydrostatic tension
based criterion are included in this model. If the effective plastic strain in an element
reaches the specified effective plastic strain at failure, then the shear capacity in the
element is set to zero and the element can only support hydrostatic stress. If the tensile
pressure in the element reaches the specified failure pressure then all stresses in the
element are set to zero for the remaining analysis. Elements can be removed based on
either or both failure criteria.
Figure 4.4 shows a von Mises yield surface in three-dimensional principal space.
In three-dimensional space, the von Mises yield surface forms an infinitely long cylinder
centered about the hydrostatic stress line. This line represents the unique state of stress in
a material where all three principal stresses are equal. Notice that without failure criteria,
the material would infinitely yield. The plastic strain at failure criterion used for this
40
study limits the length of the yield cylinder while the hydrostatic tension at failure
criterion limits the length of the hydrostatic line in the tensile direction.
CT2
Hydrostatic
CTi=CT2 =CT2
Distortion Energy Density
(Von Mises)
Figure 4.4 Three-dimensional von Mises cylinder with plastic strain and
hydrostatic stress failure criterion.
Concrete Plasticity and Damage Model
The failure model used for this research is based on isotropic materials behavior.
This type of model is well suited to model failure in isotropic materials such as steel.
However, many civilian structures are made of reinforced concrete, which has very
different material properties in tension and compression.
considered an orthotropic, composite material.
Reinforced concrete is
Accordingly, plasticity and damage
accumulation modeling in reinforced concrete is not easily characterized.
Current
material models can include cracking, crushing, and yielding for uniaxial, biaxial and
triaxial states of stress at different confinement pressures. All of which are dependent
41
upon the three-dimensional stress or strain state of the material. Current plasticity and
damage model theory can be found in Finite Element Analysis of Reinforced Concrete
(1982), Finite Element Analysis of Reinforced Concrete Structures (1986), and
Constitutive Laws for Engineering Materials (Desai, Sirwardane, 1984).
Both NIKE3D and DYNA3D material model libraries contain a model that
describes orthotropic damage of brittle materials and is designed primarily for concrete.
In compression, the material is treated as elastic, perfectly plastic using the J2 flow
theory. In tension, the model accounts for degradation of tensile strength and shear
capacity across smeared cracks. Fracture toughness, gc, which is the energy per unit area
of crack advancement, is additionally included. Finally, a viscosity term, p, accounts for
rate-dependent behavior in the form of a Perzyna regularization method. For a full
description of this model see Govindjee, Kay, Simo (1995).
Suggested tabular values for this model are given in the code documentation.
However, the values were calibrated for unconfined plain concrete without rate effects.
Reinforcing steel can be included by means of a reinforcement fraction, or by discretely
modeling the reinforcing bars with truss elements.
Either method of introducing
reinforcing bars requires the material model to be calibrated to include the confining
effect resulting from the reinforcing bars.
If calibrated properly, this model would yield a more accurate solution to the
proposed methodology. Unfortunately, calibration of the model for plain and reinforced
concrete was beyond the scope of this research. However, further study of the model for
subsequent work on the proposed methodology is strongly suggested.
42
Beam-Continuum Interface
r
One of the major obstacles involved with this research is the size of the problem.
This was solved by combining structural beam and shell elements with continuum
elements.
Structural beam and shell elements, developed for finite element codes,
mathematically approximate a complex cross-section based on its physical properties.
Though these elements perform very well under most load conditions, they do not
adequately account for transverse deformations resulting from extreme load cases. In
cases of extreme dynamic loads, continuum elements are typically chosen. Therefore,
continuum elements can be used to model the portion of the structure closest to the blast,
while structural beam and shell elements can be used for areas further from the blast.
The use of structural elements in combination with continuum elements requires
special attention at the interface boundary. Specifically, two conditions must be met at
the interface. First of all, plane sections must remain plane in bending, as this is assumed
in the formulation of the beam elements. Second, nodal rotations and translations must
be compatible.
Finite Elements in NIKE3D and DYNA3D
The basic continuum element implemented in NIKE3D and DYNA3D is an eightnode solid element. Each node in the brick has three translational degrees of freedom and
no rotational degrees of freedom. By default, the DYNA3D continuum uses one-point
integration over the volume, while the NIKE3D continuum is integrated with a 2x2x2
point Gauss quadrature rule.
These elements are valid in both codes for large
displacements and large strains. Figure 4.5 on the next page shows a typical eight-node
solid element with three degrees of freedom at each node.
43
MJ
^
X
M2
Ul
Figure 4.5 Eight-node brick element showing three translational degrees of freedom at
a single node.
Several beam and shell structural elements are implemented in both codes. Beam
and shell elements generally have rotational degrees of freedom at each node in addition
to displacement degrees of freedom. Figures 4.6a and 4.6b show a two-node beam
element and a four-node shell element, respectively.
Figure 4.6 Finite elements for (a) a structural beam element and (b) a structural shell
element showing three translational degrees of freedom and three rotational
degrees of freedom at a single node.
Two beam element formulations are implemented in DYNA3D. The Hughes-Liu
beam element is an extension of the Hughes-Liu shell element.
It uses one-point
integration over the length and either user-defined or pre-defined integration (2x2 Gauss
44
quadrature) over the cross-section.
This model is useful for modeling plasticity at
different points through the cross-section. The Belytschko-Schwer formulation relates
resultant moments and forces to curvatures and displacements. It is not integrated over
the cross section. Although this beam element is faster in computation than the HughesLiu beam element, it is less accurate for general elastoplastic analysis. Additionally, the
Belytschko-Schwer beam element is not compatible with the NIKE3D beam elements.
Beam elements in NIKE3D use one-point integration over the length and have
many options for integration over the cross-section.
The 2x2 Gauss quadrature
integration option satisfies beam element compatibility between NIKE3D and DYNA3D.
The five shell element formulations implemented in DYNA3D are the HughesLiu shell, Belytschko-Tsay shell, the reduced integration YASE shell, the full integration
YASE shell and the Bathe-Dvorkin shell. The Hughes-Liu shell also implemented in
NIKE3D, uses 2x2 Gauss integration in the plane of the shell and a variety of integration
schemes through the thickness.
Beam-Continuum Interface Model
The beam-continuum interface was established to constrain the added rotational
degrees of freedom in the beam element at the interface and ensure that the continuum
cross-section remained plane in bending. The addition of relatively stiff shell elements to
the continuum surfaces at the interface constrained the surface to remain perpendicular to
the beam element centerline under bending.
continuum interface.
Figure 4.7 illustrates a typical beam-
45
Brick
elements
Shell
elements
Beam
elements
Figure 4.7 Continuum-beam interface showing a beam element connected to a rigid
shell element connected to eight-node brick elements.
Compatibility in element formulation between NIKE3D and DYNA3D was
maintained at the interface to facilitate the transfer of data between the two codes. The
continuum elements were of the standard eight-node formulation. The shell and beam
elements were of the Hughes-Liu formulations with compatible integration schemes.
This interface was tested with the cantilever beam model and the portal frame
model.
Maximum deflections and deflection time histories were compared between
beam solutions, continuum solutions and beam-continuum solutions for the cantilever
beam and portal models in NIKE3D and DYNA3D. The interface was also tested for a
NIKE3D to DYNA3D to NIKE3D analysis.
46
Data Translation
Another unique feature of this research-is the combination of, and translation
between, implicit and explicit finite.element techniques in dynamic structural analysis. It
is known that the response of a large structure to a localized blast load occurs in two
phases. First, a blast causes local damage to a structure. Then, the structure responds to
the localized damage by distributing gravity loads to the surviving structural members.
Recall that implicit finite element techniques are well suited for low-rate dynamic
problems, such as determining structural integrity of a damaged structure. Explicit codes
are better suited for high-rate dynamic problems, such as predicting local structural
damage resulting from blast loading. The combination of these two techniques yields an
analysis methodology ideally suited to characterize both phases in the response of
multistory civilian structures to blast loads.
As previously mentioned, the choice of the NIKE3D/DYNA3D code set was
based on the ability to transfer data between the two codes. The data transferred between
the two codes includes the deformed mesh coordinates, the associated strain field and the
kinetic energy in the model. Additionally, all material properties, boundary conditions
and load cases were transferred.
The following analysis parameters required close attention to maintain
mathematical compatibility when transferring data between the two formulations:
1. Integration techniques for both structural and continuum elements.
2.
Hourglass stabilization techniques.
3.
Material models for structural and continuum elements.
4.
Transfer sequence.
J
47
Compatibility of Integration Techniques
Several integration techniques are implemented in both NIKE3D and DYNA3D
for beam, shell and continuum elements.
The eight-node continuum element in
DYNA3D uses one-point integration over the element. By default, NIKE3D uses a
2x2x2 point Gauss quadrature rule to integrate over the eight-node continuum element.
However, continuum elements in NIKE3D can be specified to use the same one-point
reduced integration technique as is used in DYNA3D. This is specified for NIKE3D by
setting the brick element formulation to a value of ten in field five of control card eight in
the NIKE3D input deck.
The use of one-point Gauss quadrature rule to integrate continuum elements
results in zero energy deformations or “hourglass modes” within an element in dynamic
analyses. Continuum elements must be stabilized to resist hourglass modes but maintain
accurate deformations modes.
Hence the term “hourglass stabilization.”
Several
hourglass stabilization techniques are available in DYNA3D. To match the NIKE3D
formulation, the hourglass stabilization technique must be set to the Flanagan-Belytschko
stiffness form in field five of material card one in the DYNA3D input deck.
The two beam elements implemented in DYNA3D are the Belytschko-Schwer
and the Hughes-Liu. The Belytschko-Schwer beam element in not integrated over the
cross-section and is thus not compatible with the N1KE3D beam element formulations.
Alternatively, the Hughes-Liu beam element, which by default uses a 2x2 Gauss
quadrature rule to integrate over the cross-section, is compatible with the N1KE3D beam.
48
Additionally, user-defined integration points can be specified for both NIKE3D and
DYNA3D.
The Hughes-Liu, YASE, and Belytschko-Tsay shell elements are available in both
codes. The Hughes-Liu shell implemented in this research uses 2x2 Gauss integration in
the plane of the shell and a variety of integration schemes through the thickness. For
proper translation, it was observed that in DYNA3D only two integration points can be
defined through the thickness of the shell, regardless of the number defined in the
NIKE3D shells.
Material Model Compatibility
All three of the material models used for this research were compatible between
the two codes except when elements were removed in the DYNA3D analyses with the
elastoplastic-failure models. The incompatibility arose when the failed mesh was
transferred back to NIKE3D. The cause of the incompatibility was due to NIKE3D’s
inability to update the stiffness matrix based on the new mesh; therefore, all analyses
with the failure model were terminated after the explicit phase of the procedure.
It should also be noted that in addition to failure modeling, a restart capability is
available in DYNA3D that allows the deletion of element blocks based on an element
range or material number. This capability was investigated early in the research as a
method to remove failed structural members from an analysis to decrease the size of the
mesh. Unfortunately, test cases revealed that the elements were not physically deleted
and removed from the mesh. Instead, the deviatoric stress in the specified elements was
merely set to zero. It was later discovered that this is only true for the public domain
49
version of DYNA3D, as the commercial version, LS-DYNA, completely reformulates the
mesh.
Transfer Sequence
The sequence for passing data between the two codes began by initializing the
gravity loads in the structure. This included the design dead and live loads. The finite
element model was then solved implicitly with NIKE3D. At the end of the solution, a
stress/deformation file was written for the current state of the problem. This file was read
into DYNA3D as an initialization file. Once initialized, a blast load was applied to the
finite element model, which was solved explicitly with DYNA3D. After the blast and the
resulting stress waves had attenuated through the structure, the explicit analysis was
stopped and another stress/deformation file was written. The new stress/deformation file
was read into NIKE3D and the implicit analysis was resumed for the newly damaged
finite element model. Figure 4.8 shows a flow chart for the sequence.
NIKE3D
DYNA3D
NIKE3D
Initialize gravity
loads
Predict blast
damage
Determine structural
integrity
Figure 4.8 Flow chart showing the sequence of data passing from NIKE3D to
DYNA3D to NIKE3D.
The input steps involved with the transfer procedure (based on versions of NIKE3D and
DYNA3D used for this research) are as follows:
I . The model was built in ANSYS5.5 and translated to a NIKE3D and DYNA3D
input deck via the a n s 2 l l n l script.
50
2. The NIKE3D analysis was started by the command:
n ik e 3 d i = n i k e _ f i len am e s = n 3 s t r
3. Once the NIKE3D analysis completed, the DYNA3D analysis was started by
the command: d y n a 3 d
±=
d y n a _ f ilen am e m = n 3 s tr 1=20
4. After completion of the DYNA3D analysis, the NIKE3D analysis was
restarted at end of the DYNA3D analysis by the command:
n ik e S d i= n ik e _ f ile n a m e m = d 3 s tr
In the above procedure, the finite element model was preprocessed in ANSYS5.5. The
command a n s 2 l l n l converted the ANSYS5.5 model database to a NIKE3D or
DYNA3D input deck. All load cases and the total load histories were entered into both
the NIKE3D input deck and the DYNA3D input deck. A termination time for the first
stage of the analysis was entered into the NIKE3D input deck, which was executed via
the n ik e S d
i= n ik e _ f ile n a m e
s= n 3 str
command.
Where i specified the
input, n i k e f ile n a m e was the name of the NIKE3D- input file and s = n 3 s t r
specified the name of the stress/deformation file.
Once the implicit analysis completed and the stress/deformation file had been
written to disk, the explicit analysis was started.
At this stage in the analysis, the
dynamic load was applied and the stress/deformation file was read into the explicit
analysis, which was executed by the command d y n a 3 d
m=n3 s t r
i = d y n a _ file n a m e
1= 20. Where i specified the input, d y n a _ fi I ename was the name of the
DYNA3D input file and m = n 3 s tr specified the name of the stress/deformation file.
The 1=2 0 command specified the size of the output files written by DYNA3D in
megabytes. By default, NIKE3D wrote output files that were twenty megabytes in size
while DYNA3D only wrote output files that were one megabyte in size. The 1=2 0
I-
51
command forced DYNA3D to read and write output files that are twenty megabytes in
size. Additionally, two keyword control cards were included in the DYNA3D input deck.
Keyword card ten specified the start time of the analysis and keyword card eleven
specified that a NIKE3D restart file should be written at the end of the explicit analysis.
After the dynamic load had been fully applied and the finite element model was
explicitly solved, another stress/deformation file was written for final stage of the
analysis. The final stage in the analysis modeled the response of the structure due to the
damage caused by the dynamic load.
i = n i k e _ f i len am e m = d 3 str .
This stage was executed by the n ik e 3 d
Where m = d 3 s tr instructed NIKE3D to read the
DYNA3D stress/deformation file. Figure 4.9 shows the sequential commands.
n ik e 3 d i= n ik e f ile n a m e s = n 3 s t r
I
d y n a 3 d i= d y n a f ile n a m e m = n 3 s tr 1= 20
I
n ik e 3 d i= n ik e f ile n a m e m = d 3 s tr
Figure 4.9 Sequence of input commands to transfer data from NIKE3D to DYNA3D
and back to NIKE3D.
52
Blast Model
Resources for this research were concentrated on modeling structural response
due to an undisturbed blast profile. Though work has been done to characterize blast
wave interaction with complex geometries, it was not the focus of this research. Blast
pressures were calculated based on the typical charge type and weight associated with
vehicle carried terrorist bombs.
According to recent literature, Ammonium Nitrate-Fuel Oil bombs ranging from
2000-lbs to 6000-lbs have been used for terrorist attacks.
To determine peak blast
overpressure, an equivalent TNT factor of 0.56 was first applied to the ANFO charge
weight {Major, 1994). Once the equivalent TNT charge weight had been calculated, the
peak overpressure was found based on detonation height and the distance between the
point of detonation and the structure, also known as standoff distance (DOE/TIC, 1981).
For substantial blast damage to occur from ANFO bombs in the weight range mentioned
above, standoff distances must be less than approximately 50 feet. Recall that decreasing
the standoff distance can dramatically increase the effectiveness of a blast. For example,
a 5000-lb ANFO vehicle bomb placed 3-ft above the ground produces a reflected peak
overpressure of 2900-psi at a standoff distance of 20-ft. When the standoff distance is
double, the same bomb produces a reflected peak overpressure of 1250-psi.
The blast profile used for this research is based on data published by the U. S.
Department of Energy.
The negative pressure phase of the profile is neglected as
suggdsted in the literature review. Peak reflected overpressure, arrival time, and blast
duration were determined from empirical data published in DOE/TIC (DOE/TIC, 1981)
using the Hopkinson-Cranz scaling law.
An example blast profile for a 500-pound
ANFO bomb with a standoff distance of 20 feet is shown below (Figure 4.10).
53
P
(m illis e c o n d s )
Figurfe 4.10 Undisturbed blast profile for a 500-pound ANFO bomb with a standoff
distance of 20 feet.
Where Pmax is the maximum reflected peak overpressure and time is shown in
milliseconds.
Notice that the blast front traverses the standoff distance in only 3.2
milliseconds but the blast duration is 111 milliseconds with a peak reflected overpressure
of 700-psi. Though the initial blast overpressure is assumed to occur instantaneously, the
infinitely sloped initial rise in the blast profile is not mathematically compatible with
explicit analysis. This is solved in the finite element analysis by applying a very steep
slope to the blast front. Typically, the peak overpressure occurring at the blast beginning
of the blast profile is applied to the finite element model over a few tenths of a
millisecond.
The blast load was applied to the finite element models as a uniformly distributed
load with the profile shown above. That is, the peak overpressure was applied over a few
tenths of a millisecond, the peak overpressure then decayed linearly to zero over the next
54
few milliseconds.
Although complex structure-blast interactions were expected, the
magnitude of the peak overpressure was assume to be the dominant factor in the response
of the structure, particularly concerning structural damage. Therefore, the blast profile
remained undisturbed throughout the analyses.
Approach Conclusion
For the presented methodology, the four components essential to the finite
element analysis are the material models, the beam-continuum interface, compatibility
between the two finite element formulations and a reasonable approximate blast model.
When choosing a material model, plasticity and damage accumulation appropriate for the
structural material (typically either steel reinforced concrete or structural steel) must be
considered. Material modeling of steel reinforced concrete presents some difficulties due
to its anisotropic, composite nature. To reduce the size of the model and, consequently,
the compute times of analysis, a beam-continuum interface is necessary. The interface
constrains rotational degrees of freedom and ensures that plane sections remain plane
throughout the analysis.
Compatibility between the two finite element formulations
allows data to be passed from one code to the other. Compatibility is maintained between
element integration points, hourglass stabilization methods and material models. Finally,
though the blast history is independent of structure deformation throughout the analysis,
an approximate model applies the appropriate undisturbed blast profile to the structure.
This approximation is based on the assumption that the initial blast profile causes the
most severe damage to the structure. Furthermore, the deformed blast profile resulting
from the blast wave interacting with the structure is assumed to be of little consequence
once the initial damage has occurred.
55
CHAPTER FIVE
CANTILEVER BEAM AND TWO-BAY PORTAL MODELS
Cantilever Beam Model
The proposed modeling methodology was initially validated on a 72-inch long
cantilever beam with a 5000-lb point load applied to the free end. The cantilever beam
model was chosen for preliminary tests because its geometric simplicity yielded small
models that could be readily solved.
Physical Model
The dimensions of the cantilever beam were 72 inches long, 8 inches tall and 4
inches wide. The beam was assumed to be of A36 structural steel with a Young’s
modulus of 29E+06psi and a Poisson ratio of 0.29 (ASTM). Figure 5.1 shows the
dimensions of the beam, location of the applied load and the location of the momentresisting support.
X
56
5000-lbs
Figure 5.1 Cantilever beam model for preliminary tests.
Three models with different element types but identical dimensions, material
properties and boundary conditions were used to:
1. Test the beam-continuum interface for the implicit, explicit and combined finite
element formulation.
2. Validate continuity issues associated with transferring data between the explicit and
implicit formulations.
3. Illustrate the difference in compute times between the explicit, implicit and combined
finite element formulations.
The first model was built entirely of beam elements. Due to the use of structural
beam elements, only one element was needed to model the entire cross section of the
beam thus simplifying the finite element mesh. Each beam element was one inch in
length yielding a finite element model with 72 elements describing the beam. A
continuum model was also used for the cantilever beam analysis. This model required a
considerable amount of compute time to solve, as it consisted of 2304 elements, each
57
measuring I-inch by I-inch by I-inch. Finally, a model consisting of both beam elements
and continuum elements was built.
The beam-continuum interface discussed in the
previous chapter was implemented at the middle of the beam span length to maintain
continuity between the two element formulations.
This model consisted of 1152
continuum elements, 36 beam elements and 32 shell elements at the interface surface, all
with dimensions of I-inch in each direction. Figures 5.2 through 5.4 show the three finite
element models used for the cantilever beam analysis.
As previously discussed all
models were built in ANSYS, translated to DYNA3D or NIKE3D and then solved with
DYNA3D and NIKE3D.
The figures below show the applied boundary conditions,
applied loads, and the mesh geometry.
F
ANSYSI
beam validation
Figure 5.2 Cantilever beam model with beam elements.
58
AIMSYS
cont. v a l i d a t i o n
Figure 5.3 Cantilever beam modeled with continuum elements.
ANSYS
continuum-beam validation
Figure 5.4 Cantilever beam model with beam elements and continuum elements.
59
Finite Element Analyses
Nine finite element models were analyzed using the models from Figure 5.2
through Figure 5.4. Implicit analyses with the beam model, continuum model, and the
beam-continuum model were run in NIKE3D.
Explicit analyses were then run with
DYNA3D followed by three analyses combining implicit and explicit solutions. Similar
load curves were used for all solution methods. Figure 5.5 shows the load curve used for
the implicit analyses. In Figure 5.5, a load factor of one corresponds to a maximum load
of 5000-pounds.
Load Factor
NIKE3D
Step I
NIKE3D
Step 2
Time
(seconds)
Figure 5.5 Load curve for implicit analyses.
For the implicit analyses, two monotonic load steps were applied to attain the
maximum load. The monotonic load steps used for the implicit analyses were, however,
not applicable to the explicit analyses due to the conditional stability of the explicit
solution formulation. For these analyses, the average time step size, governed by the
Courant condition, remained within 32 to 33 milliseconds. After reaching the maximum
60
load value, the load was maintained there for one half of a second to attenuate dynamic
vibration in the beam. Figure 5.6 shows the load curve for the explicit cantilever
analyses.
Load factor
1.0
DYNA3D
Ramp
Load
DYNA3D
Constant
Load
lnnc
(seconds)
Figure 5.6 Load curve for explicit analyses.
For the combined solution method, a monotonic load step was applied over one
half of a second for the implicit phase of analysis. Data from the last state of the implicit
solution was then written and transferred to the explicit analysis, which ran for one half
of a second bringing the load up to its maximum value. Data for the explicit analysis
after one second on the load curve was written to a file and transferred back to the
implicit analysis where the maximum load was held constant for another one half of a
second. Figure 5.7 shows the load curve for analyses with combined implicit and explicit
solutions.
61
Load Factor
NIKE3D
Step I
DYNA3D
Step 2
NIKE3D
Step I
Time
(seconds)
Figure 5.7 Load curve for combined formulation solutions.
The deflected shapes of the cantilever beam due to the 5000-pound point load are
shown for the beam model, continuum model, and beam-continuum model for NIKE3D
solutions.
The plots shown in Figures 5.8, 5.9 and 5.10 were generated in the
NIKE3D/DYNA3D postprocessor, GRIZ (Dovey and Speck). Figure 5.8, albeit trivial,
shows the deflected shape of the beam element model for the implicit analysis due to the
5000-lb point load applied to the free end of the cantilever beam. The explicit and
combined formulation solutions for the deflected shape of the beam element model
follow a similar shape. The deflected shape of the continuum model is shown in Figure
5.9, followed by the deflected shape for the beam-continuum model in Figure 5.10.
Deflected shapes for the explicit and combined formulation solutions also follow
deflected shapes similar the implicit deflected shapes.
62
min: - I 27e-01. node 2
max: O-OOe+00, node I
Y Displacement
O-OOed-OO
-1-27e-01
Y
X
k r?
beam validation
t = I .QQOOOe+QO
Figure 5.8 Deflected shape of the beam element model for the implicit analysis due
to the 5000-lb point load applied to the free end of the cantilever beam.
63
1 26e-01. node 46
maxi 1.05e-05, node 410
min: -
Y
_
Displacement
I-Lvue—Uj
Y
X
cont validation
t = 1,00000e400
Figure 5.9 Deflected shape of the continuum element model for the implicit analysis
due to the 5000-lb point load applied to the free end of the cantilever
beam.
64
mi'n: —1 26e-01- node 2
maxi 1.05e-Q-5, node 303
Y Displacement
,
I-DSe-OS
continuum-beam validation
t = 1.QQOOQe+QG
Figure 5.10 Deflected shape of the beam-continuum model for the implicit analysis due
to the 5000-lb point load applied to the free end of the cantilever beam.
65
Nodal displacements for the beam, continuum, and beam-continuum models in
the y-direction were compared for the implicit, explicit, and combined formulation
analyses.
The nodal displacements in the y-direction as a function of time were
compared at 36 and 72 inches along the length of the beam. The final displacements for
each model were then compared at 18, 36, 54 and 72 inches along the length of the beam.
Figures 5.11 and 5.12 show nodal displacements in the y-direction as a function
of time for the NIKE3D analyses at 36 and 72 inches along the length of the cantilevered
beam. Nodal displacements due to the maximum load at 18, 36, 54 and 72 inches along
the beam are also shown in Figure 5.13.
0.000 9
-
-0.005
-
0.010
Beam Elements
■ Continuum Elements
Beam and Continuum Elements
Load Curve
.S -0.015
I -0.020
0.75
-0.025
-0.030
S -0.035
-0.040
-0.045
Time (seconds)
Figure 5.11 Nodal vertical displacement predicted by the NIKE3D solution at 36
inches along the length of the cantilever beam.
66
0.000 'V
-
0.020
.S -0.040
— Beam Elements
■ Continuum Elements
Beam and Continuum Elements
Load Curve
-0.060
0.75
a -0.080
-
0.100
-
0.120
-0.140
Time (seconds)
Figure 5.12 Nodal vertical displacement predicted by the NIKE3D solution at 72
inches along the length of the cantilever beam.
Figures 5.11 and 5.12 show that the implicitly solved vertical nodal displacements
for the beam-continuum model were in agreement with vertical displacements for the
continuum model and the beam model at each time step. As expected, the final vertical
deflections of the beam element model in Figure 5.13 below deviate slightly from the
finite element models containing continuum elements. This is a result of using only one
element in the beam element model to describe the cross-section of the cantilevered
beam.
67
♦—Beam Elements
Continuum Elements
Beam and Continuum Elements
8 -0.08
-
0.122
-
0.124
-
0.126
-
0.128
Cantilever Beam Length (inches)
Figure 5.13 Vertical nodal displacements predicted by NIKE3D.
Nodal displacements at the location of the beam-continuum interface (36 inches)
in Figure 5.13 show that the maximum vertical displacements for the beam-continuum
model were in close agreement with the beam model and the continuum model. Note,
however, the slight deviation between the beam element model and the models
containing continuum elements.
Next, the beam, continuum and beam-continuum models were analyzed with the
explicit code, DYNA3D. Figures 5.14 and Figure 5.15 show nodal displacements in the
y-direction as a function of time for the DYNA3D analyses at 36 and 72 inches along the
length of the cantilevered beam. Nodal displacements due to the maximum load at 18,
36, 54 and 72 inches along the beam are shown in Figure 5.16.
68
0.000
X
-
0.010
-
0.020
1.50
Ix
■B e a m E le m e n ts
■ C o n tin u u m E le m e n ts
B e a m an d C o n t i n u u m E le m e n ts
L o a d C urve
x.
X.x
I
X
1O
1.25
1.00
E
5
«c.
Q
0.75
-
0.030
O
SCS
■O
g
U
0.50
■a
Z
-
0.040
-
0.050
0.25
0. 00
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
Time (seconds)
Figure 5.14 Vertical nodal displacements predicted by DYNA3D at 36 inches along
the length of the beam.
0. 000
-
0.020
-
0.040
-
0.060
B e a m E le m e n ts
C o n t i n u u m E le m e n ts
B e a m an d C o n t i n u u m E l e m e n t s
L o a d C urv e
- 0.1
-
0.080
20
0.75
-0.125
-0.1 3 0
-c
Z
0.95
- 0 100
-
0.120
-
0.140
1 .0 0
1.05
1.10
Time (seconds)
Figure 5.15 Vertical nodal displacements predicted by DYNA3D at 72 inches along
the length of the beam.
69
-
0.02
■£ -0.04
Beam Elements
■ Continuum Elements
Beam and Continuum Elements
O -0.08
-
0.12
-0.14
Cantilever Beam Length (inches)
Figure 5.16 Vertical nodal displacements predicted by the DYNA3D.
Figures 5.14 and 5.15 show that the explicitly solved vertical nodal displacements
for the beam-continuum model were in agreement with vertical displacements for the
continuum model and the beam model at each time step. Again, as expected, the final
vertical deflections of the beam element model in Figure 5.16 deviate slightly from the
finite element models containing continuum elements.
Finally, the models were solved with the combined implicit and explicit codes.
The code sets ability to translate data between the two finite element formulations was
first validated on the beam and continuum models then the beam-continuum model was
tested. Figures 5.17 and Figure 5.18 show nodal displacements in the y-direction as a
function of time for the combined solution analyses at 36 and 72 inches along the length
70
of the cantilevered beam. Nodal displacements due to the maximum load at 18, 36, 54
and 72 inches along the beam are shown in Figure 5.19.
The analysis sequence for passing data between the two finite element
formulations described in Chapter Four was applied to the beam, continuum and beamcontinuum models.
The first one half second was solved with an implicit analysis
corresponding to half of the total load. Data from the implicit analyses at one half of a
second was written to a file to be read by the explicit formulation. The explicit solutions
were then used to account for the rest of the total load, which was applied over the next
one half second. Data from the explicit analyses was then written to a file to be read back
into the implicit solution, which ran for one half of a second with the full load applied
constantly.
0.000
-
0.010
—•— Beam Elements
—— Continuum Elements
*— Beam and Continuum Elements
Load Curve
S -0.020
0.75
q
-
0.030
-
0.040
-
0.050
Time (seconds)
Figure 5.17 Vertical nodal displacements predicted by the combined formulation
analyses at 36 inches along the length of the beam.
71
0.000
1.50
-— B ea m Elements
^
J
-
- — Continuum Elements
0.020
B ea m and Continuum Elem ents
1.25
L oad Curve
.= -0.040
*---------------------K
I -0.060
-
1.00 u
2
V
0.120
os
0.75 k
I
T3
■f. -0.080
M
.S
O
>>
75
-
-
0.100
0.50 J
0.130
■o
0.25
Z -0.120
-0.140
0.00
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
Time (seconds)
Figure 5.18 Vertical nodal displacements predicted by the combined formulation
analyses at 72 inches along the length of the beam.
B ea m Elem ents
«
B eam and Continuum Elements
-0.04
-0.08
-
Continuum Elements
-0.126
0.12
1 I ‘
Cantilever Beam Length (inches)
Figure 5.19 Vertical nodal displacements predicted by the combined formulation
analyses.
72
As with the previous two test cases. Figures 5.17 and 5.18 show that the
combined solution of the vertical nodal displacements for the beam-continuum model
were in agreement with vertical displacements for the continuum model and the beam
model. Additionally, all three models appear to translate well between the implicit and
explicit formulations.
Deflection Comparisons
Based on the modeling assumptions associated with structural beam elements,
nodal calculations for models containing only beam elements were expected to differ
slightly from similar models containing continuum elements. However, based on model
geometry, vertical displacements between the continuum and the beam-continuum
models should not significantly differ. It was found that the maximum relative errors
between the continuum element models and the beam-continuum models did not exceed
1% (Table 5.1), suggesting that the beam-continuum models closely approximate the
continuum elements models for each solution formulation.
Table 5.1 Relative error between continuum and beam-continuum models for NIKE3D,
DYNA3D and the combined formulation solution method.
Relative Error Between Continuum and Beam-Continuum Models
Length
(inches)
NIKE3D Solution
Relative Error (%)
DYNA3D Solution
Relative Error (%)
NIKE3D-DYNA3D Relative
Error (%)
18
0.000
0.909
0.000
36
0.000
0.750
0.000
54
0.125
0.619
0.246
72
0.000
0.000
0.000
73
Next, nodal deflections were compared for the NIKE3D, DYNA3D and NIKE3DDYNA3D formulations to determine if the solution formulation method had a significant
effect on nodal results for the beam-continuum interface. Figure 5.20 shows the vertical
nodal displacements for the NIKE3D models, DYNA3D models and NIKE3D-DYNA3D
models at 18, 36, 54 and 72 inches along the cantilevered beam for the continuum and
beam-continuum models.
-0.140
□ NIKE3D Continuum
Model
-
0.120
■ DYNA3D Continuum
Model
-5 -o.ioo
&
I
I
□ NIKE3D-DYNA3D
Continuum Model
-0.080
U
S -0.060
□ NIKE3D BeamContinuum Model
Q
.1 -0.040
-E
<u
■ DYNA3D BeamContinuum Model
>
-
0.020
0.000
18
36
54
72
Nodal Location Along Length of
Beam (inches)
□ NIKE3D-DYNA3D
Beam-Continuum
Model
Figure 5.20 Horizontal nodal displacement comparison for the cantilever beam analyses.
74
The vertical nodal displacements for the cantilever beam models using implicit,
explicit and the combined solution technique shown in Figure 5.20 vary only slightly at
each point on the beam. However, the marked variation in vertical displacements for the
implicit (NIKE3D) solutions as compared to the explicit and combined formulation
displacements should be noted.
The values for the nodal displacements for each model are given in Table 5.2.
Maximum relative error for displacements between each of the models at 18, 36, 54 and
72 inches along the beam are shown in Table 5.3. These values remained below 2%
(Table 5.3), indicating that the solution formulation had a small effect on displacement
calculations.
Table 5.2 Vertical nodal displacements for the cantilever beam models at 18, 36, 54, and
72 inches along the length of the beams
Vertical Nodal Displacements for Cantilever Beam Models
Continuum Models
Length
(inches)
Beam-Continuum Models
NIKE3D
(inches)
DYNA3D
(inches)
-0.011
-0.040
-0.081
NIKE3DDYNA3D
(inches)
-0.011
-0.040
-0.081
-0.011
-0.040
-0.080
-0.011
-0.040
-0.081
NIKE3DDYNA3 D
(inches)
-0.011
-0.040
-0.081
-0.128
-0.128
-0.126
-0.128
-0.126
NIKE3D
(inches)
DYNA3D
(inches)
18
36
54
-0.011
-0.040
-0.080
72
-0.126
75
Table 5.3 Maximum relative errors between continuum and beam-continuum models for
NIKE3D, DYNA3D and the combined formulation solution method.
Maximum Relative Error Between Continuum and Beam-Continuum
Modehfor NIKE3D, DYNA3D and NIKE3D-DYNA3D Nodal
Displacements
Maximum Relative Error (%)
Length (inches)
18
36
72
54
1.801
1.985
1.845
1.563
Although vertical deflections for the cantilevered beam models varied only
slightly, suggesting the validity of the beam-continuum interface, stress concentrations at
the interface were also a concern. However, upon investigation of principal stresses for
continuum elements and shear resultants for beam elements adjacent to the beamcontinuum interface, no significant stress concentrations were discovered in any of the
models.
Solution Time Comparisons
Solution times were compared between the implicit, explicit and combined
formulations. The comparisons illustrate the added computational efficiency resulting
from:
1. The combination of beam elements and continuum elements in the finite
element model.
2. The combination of implicit and explicit finite element formulations to
provide unconditional numerical stability (implicit formulation) while
maintaining the ability to track stress waves in the model (explicit
formulation), when necessary.
76
Figure 5.21 shows implicit, explicit and combined solution compute times for the beam
element model, continuum element model and the beam-continuum model. As expected,
the implicit solutions required the least amount of processor time while the explicit
solution required considerably more. The combined solution method with continuum
elements yielded a 68.4% decrease in solution time from the fully explicit solution. A
similar decrease of 68.4% in solution time from the fully explicit solution was also noted
for the combined solution method with beam and continuum elements. Additionally, for
both the combined solution method and the explicit solution method, the beamcontinuum model reduced compute times by 45% as compared to the continuum model.
Figure 5.21 Compute time necessary to complete analyses in seconds.
77
Two-Bay Portal Model
Three two-bay, steel portal models were used to further test the modeling
methodology. In addition to testing the beam-continuum interface and the combined
formulation method, these models were also used to test the code sets ability to account
for gravity loading, bilinear material plasticity, and material failure. These additional
properties cannot be neglected, as they play a critical role in the response of large,
dynamically loaded structures.
Physical Model
The two-bay model was assumed to be of A36 structural steel with a Young’s
modulus of 29E+06psi and a Poisson ratio of 0.29. The yield stress was assumed to be
36E+03psi, the tangent modulus was 1.0E+06psi and the hardening coefficient was 0.5.
The columns and the spandrel beams had a rectangular cross-section of eight inches by
twelve inches. The height of the structure was 168 inches and the interior span of each
bay was 180 inches. Two loads were applied to the structure. A distributed load was
applied to the top of the spandrel beam to simulate a dead load while a dynamic
distributed load was applied to the center column to simulate a blast load. Figure 5.22
shows the dimensions of the structure, the locations of the distributed loads and the
locations at which deflections were compared. Note that nodal data was recorded at each
time step for each node in the model. Points a, b, c, and d in Figure 5.22 were chosen as
representative nodes in regions where large horizontal displacements were expected.
78
150 psi
6000 psi
\\\\\\V
\\\\\\V
Figure 5.22 Two-bay portal model showing applied loads, boundary conditions and
locations where nodal data was compared.
element types. The first model consisted of two-inch structural beam elements yielding a
finite element mesh with only 414 elements. As expected, solution times for this model
were the shortest of the three models. The second model consisted of 2 x 2 x 2-inch
continuum elements, yielding a finite element mesh with a total of 9792 elements. The
third model consisted of 315 beam elements measuring two-inches in length and 2232
continuum elements measuring 2 x 2 x 2-inches. For the third model, beam elements
were used for the outer columns and most of the spandrel beams while continuum
elements were used for the inner column and at the intersection of the center column and
the spandrel beam. As can be seen in Figure 5.25, the continuum elements were used to
model the portion of the structure where the dynamic load was applied.
79
Figure 5.23 Two-bay portal modeled with beam elements.
80
Figure 5.24 Two-bay portal modeled with continuum elements.
81
ANSYS
Continuum p o rta l v a lid a tio n frame
Figure 5.25 Two-bay portal modeled with continuum and beam elements.
Finite Element Analysis
Thirteen finite element analyses were performed on the models in Figures 5.23,
5.24, and 5.25. Three implicit, bilinear plastic analyses were conducted in NIKE3D
using the beam model, the continuum model and the beam-continuum model. Three
explicit bilinear plastic analyses were conducted in DYNA3D using the same models.
82
Two additional explicit analyses were performed on the continuum and beam-continuum
models, which included bilinear plasticity and failure based on the criteria mentioned in
Chapter Four.
Three bilinear plastic analyses were conducted using the combined
formulation technique.
Finally, two additional combined formulation analyses were
performed on the continuum and the beam-continuum models, which also included
failure criteria.
Similar load curves were used for each of the analyses. Figure 5.26 shows the
load profile used for the NIKE3D, DYNA3D and combined formulation analyses. In this
figure, load (I) corresponds to the simulated dead load applied to the spandrel beam and
load (2) corresponds to the simulated blast load applied to the center column. Load steps
of 0.05 seconds were used for the dynamic, implicit analysis. Time steps for the explicit
analysis averaged about 23 microseconds. For the combined formulation analyses, a
single load step of I second was used to implicitly apply the dead load. Once the dead
load was fully applied, the model was transferred to the explicit code, which was used to
analyze the structure due to the blast load for the next 0.20 seconds. Finally, at 1.20
seconds, the model was.transferred back to the implicit code where a time step of 0.20
seconds was used to determine the final deformed state of the structure.
83
L oad F actor
Figure 5.26 Load profiles of (I) the gravity and distributed load applied to the spandrel
beams and (2) the dynamic load applied to the center column of the two-bay
portal models.
Horizontal displacement time histories were compared for each of the thirteen
models at points a, b, c, and d (Figure 5.22) to illustrate the nodal behavior resulting from
each finite element formulation and model configuration. Solution times were compared
to illustrate the decrease in compute time achieved by implementing the beam-continuum
model and mixed formulation solution method.
As expected, nodal displacements for the models that include failure deviate
significantly from nodal displacements of the bilinear plasticity models. Table 5.4 shows
that the maximum horizontal nodal displacements for each of the portal models at points
a, b, c, and d differed at most by 9%. Figures 5.27 and 5.28 show the predicted deflected
shape of the two-bay portal model using the combined formulation analysis with the
elastic-plastic and elastic-plastic-failure material models. Figures 5.29, 5.30, 5.31 and
5.32 show horizontal displacement time histories for the portal models at points a, b, c,
and d respectively. The figures illustrate variations in nodal calculations between the
implicit, explicit and combined formulation analyses.
84
Table 5.4 Maximum absolute horizontal displacements for each of the two-bay portal
models.
M a x i m u m A b s o l u t e H o r i z o n t a l D i s p l a c e m e n t in I n c h e s
Analysis Type
Beam Model
Continuum Model
DYNA3D
83.3
80.2
Beam-Continuum
Model
84.2
DYNA3D with failure
N/A
Failed
Failed
NIKE3D
84.1
86.1
815
NIKE3D-DYNA3DNIKE3D
812
80.2
84.2
NIKE3D-DYNA3DNIKE3D with failure
N/A
Failed
Failed
85
min: -■4 23e-D 3- node 1029
m o x i 7 .9 9 e+ 0 1 . node 2
X Displacement
I
I
t
i
I
I
Y
X
k rz
file
t = 1.20000e+00
Figure 5.27 Predicted deflected shape using beam and continuum elements and the
combined formulation analysis with the elastic-plastic material model.
86
min: O-OOe + OO. node I
X Displacement
max: 4.12e+0l, node 1062
4.1 2e+01
Y
X
k r?
file
t = 1,04999e+00
Figure 5.28 Predicted deflected shape using beam and continuum elements and the
combined formulation analysis with the elastic-plastic-failure material
model.
87
200.00
♦ CMM^BDBeem
I CMMaSD Q rtrujn
180.00
CMMaSDfeanQrtnum
Horizontal Displacement, inches
160.00
CMMaSDFaI Q r tr u m
140.00
I IXXXXXXXXXXXXXXXXXXXX
X DrTMaSDfaI B a a n Q r tru m
12000
+ NKBDQrttrum
-NfBDfeanQritrum
NKEDCMMaSDNKBDfean
NKEDOrTMaSDN K BD Q rtrum
NKBDOrTMaSDNKBDfean
Q rttru m
NKBDOrTMaSDNKBDfaI Q rtirum
NIBDOrTMaSDNKBDfaI Baan
Q rfiru m
Tims seconds
Figure 5.29 Horizontal nodal time histories for the two-bay portal models at point a.
88
100.00
• CJrNMDBeem
■ DyNMDCOrtnLUTi
90.00
DrNMDBeemCOrtirum
80.00
XDrNMDfaI CDrtnum
I
c
+■*
70.00
■^
S 60.00
E
.*'
™ 50.00
-TT-
• X
. - ' v 1' .
x DrNMDfaI Beem Cotrum
y
• NhEDBeem
0)
CL
+ NKEDCordrum
W
Q
• NIEDBeemCoritnum
m 40.00
- NKEDDrNMDNKEDBeem
c
O
■c
o 30.00
NIEDDrNMDNKED COrtnum
X
NKEDDrNMDNKEDBeem
COitrum
20.00
NKEDDrNMDNKEDFaI
CCrtrum
10.00
0.00
1.00
NKEDDrNMDNKEDFaI Beem
CDrtrum
1.10
1.20
1.30
1.40
1.50
Time, seconds
Figure 5.30 Horizontal nodal time histories for the two-bay portal models at point b.
89
90.00
♦ DVNASDBeem
■ DVNASDCDntiruLm
80.00
DVNASD B e a rrrC C rtiru m
^
70.00
^
_ ■ !_
____
D V N A SD faI G r t i r u m
g
JC
C 60.00
x DVNASDfaiI B e a m C d r tir u m
4-r
c0)
• M ^D B eam
E 50.00
0
:*
JS
+ M K E S D G r tir u m
o_
__ t
-40.00
1
- N K E S D B e a r n G r itr u m
X
X
-X
-N K E S D D V N A S D M K E S D B eam
X
I 30.00
o
N K E S D O V N A S D N K B D G rtiru m
X
X
if_____________ t _________________________________________________
20.00
N K E S D D rN A SD N K E SD B eam -
X
V
C d rtiru m
*
N K E SD D vN A SD N K E SD FaI
10.00
G rtru rn
N K ESD D vN A SD N K ESD FaiI Beam-
0.00
1.00
G rtiru m
1.10
1.20
1.30
1.40
1.50
Tlme1seconds
Figure 5.31 Horizontal nodal time histories for the two-bay portal models at point c.
90
70.00
♦ CMsMDBaem
failure
■ D Y lN M D Q rtrurn
J
60.00
..
DyInM D B e e m O rtn u m
tn
o
DYlNMD-FaI Q rtnuum
2 50.00
x DYlNMD-FaI B e e m Q x tm m
.E
I6
E 40.00
00)
ra
• N H ED Beem
+ N E D Q rta u n
•
Q-
tfl
-N E B D B eem Q riInuL m
Q 30.00
S
- NHEDQYlNM DlNlEDBeem
1
o 20.00
N F E D D Y T M D N E B D Q rtm m
X
*
A
NKEBDDYlNM DNEDBeem
Q rtm m
10.00
0.00
N F E D D rlN M D N E B D F aI
Q rtru m
N H E D D Y lM D N H E D F aI Beam
Q rtm m
%
1.00
1.10
1.20
1.30
1.40
1.50
Figure 5.32 Horizontal nodal time histories for the two-bay portal models at point d.
Figure 5.33 compares computation times required to solve each of the portal
models. As with the cantilever beam models, the beam-continuum portal models
required less time to solve than the continuum portal models. More significantly, the
mixed formulation solution method solved considerably faster than the fully explicit
models. For example, the mixed formulation solution for the continuum model solved
over 6 times faster than the fully explicit continuum model.
91
4 .5 0 0 E + 0 4 j
4 .0 0 0 E + 0 4
I
3 .5 0 0 E + 0 4 :
3 .0 00E + 04
■S
0
2 .5 0 0 E + 0 4
8
1
□ B eam
■ Continuum
2 .0 0 0 E + 0 4
F
□ B eam -C ontinuum
1.500E + 04
1 .000E+ 04
5 .0 00E + 03
O.OOOE+OO
DYNA3D
DYNASD-FaiI
NIKE3D
NIKE3DDYNA3DNIKE3D
NIKE3DDYNA3DNIKESD-FaiI
Figure 5.33 Compute time required to solve each of the two-bay portal models.
92
CHAPTER SIX
TEST CASE: ALFRED P. MURRAH FEDERAL BUILDING
Building Model
As a final case study, the proposed methodology was tested on a finite element
model with structural characteristics similar to a portion of the Alfred P. Murrah Federal
building near the area most affected by the blast responsible for collapsing the structure.
The methodology was expected to predict the initial stress-state in the structure due to
normal operating loads, then simulate the response of the structure due to the blast load,
and finally, predict the resulting structural integrity of the building. Ideally, failure would
be predicted in the column directly in front of the blast followed by immanent loss of
structural integrity resulting in partial collapse of the building.
Parameters
The Alfred P. Murrah Federal building in Oklahoma City, Oklahoma was a ninestory tall reinforced concrete civilian structure. The building, essentially rectangular in
shape, measured 220-feet by 100-feet with the long sides of the building facing north and
south.
A parking garage was attached to the south side of the structure and an
overhanging ceiling was built into the third floor of the north side of the structure to serve
as a recessed vestibule that could be accessed through the back of the foyer. The
overhanging ceiling was supported by 36-inch by 60-inch reinforced concrete transfer
93
girders, which in turn were supported by 24-inch by 36-inch reinforced concrete columns
located every 40-feet along the length of the 220-foot long building. These columns also
carried floor loads from the seven floors directly above them. The first and second floors
were supported by 24-inch by 24-inch reinforced concrete columns while the remaining
seven floors were supported by 20-inch by 20-inch reinforced concrete columns. The
floor system consisted of 6-inch thick, one-way, steel reinforced concrete slabs supported
by 48-inch by 20-inch reinforced concrete beams.
According to the Building Performance Assessment Team, deployed by the
Federal Emergency Management Agency, the 4000-lb ANFO bomb responsible for
catastrophically collapsing nearly half of the Alfred P. Murrah Federal building exploded
20-feet away from a 24-inch by 36-inch column that supported the third floor transfer
girders and the seven floors above it (Corely, Mlakar, Sozen and Thorton). Because it
was a critical structural member and due to a lack of structural redundancies in the
building, once the column failed, the seven floors above it collapsed in a progressive
manner.
Finite Element Model of the Alfred P. Murrah Building
Due to computational limitations, only a portion of the Alfred P. Murrah Federal
building was modeled. Six bays and four floors of the building were modeled with a mix
of beam, shell and continuum elements. A symmetry plane that bisected the structure in
the north-south direction was utilized to further simplify the model. The final model
consisted of 1843 beam elements, 12,804 continuum elements and 32,946 shell elements.
Figures 6.1 through 6.4 show row and column references used in the following discussion
94
(in these figures, G l6 corresponds to row G, column 16). The sections closest to and
most affected by the blast (sections G l6 through F24 of floors one, two and three) were
modeled with continuum and shell elements, while the remaining sections of the structure
were modeled with beam and shell elements. The beam-continuum interface presented in
the previous two chapters was applied at row F of floors one through three and between
floors three and four of sections G l6 through F24. Figure 6.5 shows a visualization of
the section modeled. Note the placement of the simulated blast load, which was applied
to the 24-inch by 36-inch beam directly in front of it. Figure 6.6 shows the final finite
element model of the structure.
(5>
(E )
Symmetry Plane
Modeled Section
0
(2>
Figure 6.1 Floor plan (first floor) of the nine-story portion of the Alfred P. Murrah
building showing the section modeled and the location of the symmetry
plane.
95
@
@
@
(M)
@
(18)
(S)
®
©
©
Figure 6.2 Floor plan (second floor) of the nine-story portion of the Alfred P.
Murrah building showing the section modeled and the location of the
symmetry plane.
9
20'-cr
---------->
©-
©
20’-cr 20 ' - 0 " 20'-cr
20’-O'
--------> ----------> <----- ><- — >|
n
ry
F®
35'-O'
11
Symmetry Plane
©
©
Figure 6.3 Floor plan (third floor) of the nine-story portion of the Alfred P. Murrah
building showing the section modeled and the location of the symmetry
plane.
©
96
Figure 6.4 Floor plan (fourth floor) of the nine-story portion of the Alfred P. Murrah
building showing the section modeled and the location of the symmetry
plane.
Figure 6.5 Visualization of the section modeled (floor slabs removed for clarity) and
the placement of the blast source. Symmetry plane applied at the middle
column in front of the point of detonation.
97
Two material models were used with the finite element model shown in Figure
6.6. The bilinear elastic-plastic material model used in the cantilever beam and two-bay
portal models was used for a fully implicit analysis and a combined formulation analysis.
Although not an ideal, failure model for reinforced concrete, the bilinear elastic-plasticfailure material model introduced with the two-bay portal model analyses was also used
for a combined formulation analysis.
The structure was assumed to consist of concrete with steel reinforcement.
However, the steel reinforcing bars were not explicitly included in the model. Instead, a
volume fraction. method was used to account for the reinforcing bars within the
continuum elements. Transformations in moments of inertia were used to include the
reinforcing bars in the beam and shell element descriptions. Table 6.1 shows the material
properties used for the concrete and the steel reinforcement. Note that these values are
approximately based on the original design values specified for the Alfred P. Murrah
Federal Building.
Table 6.1 Table showing the material properties for concrete and steel used for the
elastic-plastic and elastic-plastic with failure material models.
Material Property
Concrete
Steel
Young’s Modulus, psi
3 .6 x 1 0 "
29x10"
Poisson’s Ratio
0.17
0 .2 9
Tangent Modulus, psi
9.7xl’05
IxlO6
Yield Stress, psi
4x103
60x1O3
Density, slugs/in3
0.0007346 .
0.0002488
Strain at Failure, in/in
0.004
0.15
'
98
Finite Element Analysis
Three FE analyses were conducted using the model shown in Figure 6.6.
Bilinear elastic-plastic models were run with NIKE3D and the combined formulation
method followed by a mixed formulation analysis with failure. Nodal displacements and
compute times were compared for all three analyses. Figure 6.6 shows the location on
the model of four nodes for which data was compared.
Figure 6.6 Finite element model of section modeled.
x
99
As with the cantilever beam and portal models, similar load curves were used for
each of the analyses.
Figure 6.7 shows the load profile used for the NIKE3D and
combined formulation analyses. In this figure, dead and live loads refer to floor weight
and office furniture as well as the calculated weight of the upper stories, which were not
explicitly included in the finite element model. The blast load, calculated based on 4000
pounds of ANFO, reached a maximum of 6000psi at the peak of the blast load curve
(1.005 seconds).
Load Factor
Dead and
Live LoadsX^
Blast Load
Time
(seconds)
0.0 -----
1.0 1.01
Figure 6.7 Load profiles for dead and live loads and the applied blast load.
Automatic time stepping was used for the dynamic implicit analyses, while time
steps for the explicit analyses averaged approximately 23 microseconds.
For the
combined formulation analyses, a single load step of I second was used to statically
apply the dead load. Then, the explicit code was used to analyze the structure during the
blast load and for the following two seconds to determine the final deformed state of the
structure. Finally, at two seconds, the model was transferred back to the implicit code
100
where automatic time stepping was used to determine the final deformed state of the
structure.
Horizontal and vertical displacement time histories were compared for each of the
six models at the nodal points indicated in Figure 6.6 to illustrate the nodal behavior
resulting from each solution formulation as well as the two different material models.
Table 6.2 shows the maximum predicted vertical displacements at each of the four nodes.
Figures 6.8 and 6.9 show the deflected shapes of the structure predicted by the elasticplastic, combined formulation analysis and the elastic-plastic with failure, combined
formulation analysis after two seconds on the load curves.
Table 6.2 Maximum vertical displacements for each of the building model analyses.
Maximum Vertical Displacement in Inches
Analysis Type
NIKE3D
Bilinear Elastic-Plastic
NIKE3D-DYNA3D-NIKE3D
Bilinear Elastic-Plastic
NIKE3D-DYNA3D-NIKE3D
Bilinear Elastic-Plastic with
Failure
Node
5832
-0.189
Node
20112
-0.0539
Node
58570
-0.0650
Node
90042
-0.0807
-0.505
-0.172
-0.0647
-0.186
-1.790
-0.161
Failed
-0.339
101
Figure 6.8 Deformation of the combined formulation, bilinear elastic-plastic model
after two seconds. Note the large deflection of the column due to the blast
load.
102
I
Y
X
psuedo-murrah (B^arn. Shell and
t = 2,OOOQ3e-hOO
Figure 6.9 Deformation in the combined formulation, bilinear elastic-plastic model with
failure after two seconds. Note that the column has failed due to the blast
load and that both transfer girders are beginning to collapse.
Figures 6.10, 6.11 and 6.12 show nodal displacement time histories for the
pseudo-Murrah models at the points indicated previously.
The figures illustrate
significant variations in nodal calculations between the bilinear elastic-plastic models and
the bilinear elastic-plastic models with failure.
103
0.1000
NKESD-Hastic Nxle 90M2
0.0800
N K B D H astic Node 58570
0.0600
NKESDHastic Nxie 5832
NKESDHastic N x k 20112
-Str- NKBDDYNASDFail Nxfc 90042
0.0200
N K B D D Y N A SD Ral Nxfe 58570
E 00000 &* w WSH
w..
- S - N K B D D Y N A SD Ral Nxfe 5832
•2 -0.0200
------N K B D D Y N A SD Fal Nxfe 20112
-0.0400
------NKBDDYNASDHastic Nxfe 90042
-0.0600
- - N K B D DYNASDHasdc Nxfe 58570
NKBDDYNASDFlastic Nxfe 5832
-0.0800
- 6 - N KBDDYNASDHastic Nxfe 20112
-
0.1000
Time, seconds
Figure 6.10 Nodal displacement time history for the pseudo-Murrah models in the xdirection.
Figure 6.10 shows nodal displacement data in the x-direction from 0 to 3 seconds.
This data reflects translation in the east-west direction of the building. Note the nodal
data for node points along or near the symmetry plane are well behaved, however, the
nodal data for the node located at the outer edge of the model (node 58570) show
significant displacements during and after the application of the blast load. This suggests
a loss of lateral stability in the model away from the symmetry plane.
104
N lK E S D -P la stic N o d e 9 0 0 4 2
0.00
-
/;♦ —w
-— +—♦—
0.20
—
N IK E S D -H a stic N o d e 5 8 5 7 0
N IK E S D -H a stic N o d e 5 8 3 2
-0 .4 0
N IK E S D -H a stic N o d e 2 0 1 1 2
$ -0 .6 0
2
-0 .8 0
_
I( T
IS -loo
N IKESD-DYNASD-FaiI N o d e 9 0 0 4 2
"
NIKESD -D YN A SD -FaiI N o d e 5 8 5 7 0
- t - N IKESD-DYNASD-FaiI N o d e 5 8 3 2
£
S-I-2O
>.
/I \A x 1XhA a _ _
-1 .4 0
K V
-1 .6 0
\
-1 .8 0
W
I
x
—
N IKESD-DYNASD-FaiI N o d e 2 0 1 1 2
—
N IK E SD -D Y N A SD -H astic N o d e 9 0 0 4 2
N IK E SD -D Y N A SD -H astic N o d e 5 8 5 7 0
N IK E SD -D Y N A SD -H astic N o d e 5 8 3 2
i
N IK E SD -D Y N A SD -H astic N o d e 2 0 1 1 2
-
2.00
0 .0 0
0 .5 0
1.00
1.50
2 .0 0
2 .5 0
3 .0 0
3 .5 0
Time, seconds
Figure 6.11 Nodal displacement time history for the pseudo-Murrah models in the ydirection.
Figure 6.11 shows nodal data for displacements in the vertical direction. This
data reflects the vertical stability of the model.
All nodes experience vertical
displacements, however, note large vertical displacements of nodes 5832 and 90042 in
the both the plastic model and the model with material failure included. Also note that
node 5832 in the model with material failure included failed during the blast load
application, which can be verified by Figure 6.9. Additionally the magnitude of the
vertical displacement of node 90042 increases throughout the analysis. This indicates
initial loss of vertical stability near the failed column.
105
NIKBD-Plastic Node 90042
0.30 —
NIKBD-Plastic Node 58570
NIKBD-Plastic Node 5832
NKBD-PIastic Node 20112
NIKBD-DYNtiD-Fail Node 90042
NKBD-DYNtiD-FaiI Node 58570
E 0.00
- + - NKBD-DYNtiD-Fail Node 5832
— NKBD-DYNtiD-Fail Node 20112
— NKBD-DYNtiD-Plastic Node 90042
NKBD-DYNtiD-Plastic Node 58570
NKBD-DYNtiD-Plastic Node 5832
NKBD-DYNtiDPIastic Node 20112
Time, seconds
Figure 6.12 Nodal displacement time history for the pseudo-Murrah models in the zdirection.
Figure 6.12 shows nodal data for displacements in the vertical direction. This
data reflects the lateral stability of the model in the north-south direction. Note here that
all data is well behaved before the application of the blast load. During and after the blast
load, however, all nodes except those associated with failure oscillate semi-regularly.
Nodal displacements for the NIKESD-Plastic analysis remain relatively stable
throughout the analysis. However, combined analyses with the bilinear plasticity and
failure models show large nodal displacements during and after application of the blast
load. Of particular interest are nodal displacements for the y-direction (vertical). Plastic
106
analyses predict significant nodal displacements in the y-direction in the immediate
vicinity of the column subjected to the blast load, while vertical nodal displacements for
the analyses when failure was included predict large, steadily increasing vertical nodal
displacement magnitudes at nodes 5832 and 90042. This result suggests, at least, initial
loss of structural integrity as the vertical nodal displacement magnitudes for the analysis
with failure included were still increasing at 3.0 seconds.
I
107
CHAPTER SEVEN
CONCLUSION AND CLOSING REMARKS
A numerical methodology capable of predicting the effects of blast loads on
multistory civilian structures was presented. The presented methodology incorporated a
beam-continuum interface and a mixed solution formulation approach to reduce the
computational cost of analyzing large civilian structures under dynamic loads.
The basic mechanical behavior of multistory civilian structures under dynamic
loads was stated. This included an initial stress-state due to design loads, followed by a
dynamic response due to blast loads and, finally, the resulting loss of structural integrity
due to possible failure of structural members. For traditional structural and mechanical
response analyses, simplifications often allow each phase of the abovementioned
behavior to be considered separately. However, for analyses of blast loaded civilian
structures, the two-bay portal and the Alfred P. Murrah analyses suggested that each
phase of response was of equal importance in representing the overall integrity of a
structure after a bomb blast.
The methodology presented herein combined two different finite element
techniques in the following manner. First, an implicit finite element code, NIKE3D, was
used to determine the initial stress field in a typical multistory civilian structure due to
dead and live loads. Stresses and strains from the implicit code were passed to an explicit
FE code, DYNA3D.
Once the static stresses and strains were transferred to and
initialized for the explicit formulation, a calculated blast load was applied to
108
predetermined structural members in the form of a distributed impulse load. The explicit
formulation was then used to predict localized structural damage resulting from the blast
load. Finally, after initial dynamic vibrations in the structure dissipated, the new stress
and strain fields were passed back to the implicit formulation where a dynamic implicit
analysis was used to determine the resulting integrity of the structure.
' Specifically, the implicit and explicit modeling capabilities associated with
initializing gravity loads, predicting blast damage and tracking the resulting post-blast
stability of a structure were addressed. Translation between the implicit and explicit
codes was discussed and validated. A beam-continuum interface, used to reduce the size
of the finite element mesh, was also presented and validated. Analyses of simple steel
cantilevered beam models using a linear elastic material model were conducted to test the
beam-continuum interface.
Analyses on steel, two-bay portal models using elastic-
plastic, and elastic-plastic-failure material models were performed to test the beamcontinuum interface and to investigate a simple failure material model. Compute times
were compared between test cases to show the reduction in computational cost gained
from the proposed methodology over fully explicit and/or fully continuum based models.
Finally, analysis results from a model with structural characteristics and load conditions
similar to those of the Alfred P. Murrah Federal Building were presented. Similarities
and differences between the actual response of the Alfred P. Murrah Federal Building and
the response predicted by the model were discussed.
109
Cantilever Beam Model
I
Due to modeling assumptions associated with structural beam elements, nodal
calculations for models containing only beam elements were expected to differ slightly
from similar models containing continuum elements. However, the maximum relative
errors in nodal displacement between the continuum element models and the beamcontinuum models did not exceed 1%, suggesting that the beam-continuum cantilever
beam models closely approximated the continuum element cantilever beam models for
each solution formulation.
The vertical nodal displacements for the cantilever beam models using implicit,
explicit and the combined solution technique varied only slightly at each point on the
beam. However, some deviation in vertical displacements for the implicit solutions was
noted as compared to the explicit and combined formulation displacements. Maximum
relative error for displacements between each of the models at 18, 36, 5^ and 72 inches
along the beam remained below 2%, indicating that the solution formulation had only a
small effect on displacement calculations.
As expected, the implicit solutions required the least amount of processor time
while the explicit solution required considerably more. However, the combined solution
method with continuum elements yielded a significant decrease in solution time from the
fully explicit solution. A similar decrease in solution time from the fully explicit solution
was noted for the combined solution method with beam and continuum elements. For
both the combined solution method and the explicit solution method, the beamcontinuum model reduced compute times considerably as compared to the continuum
model.
no
Two-Bay Portal Analysis
A stress-state due to self-weight and an initial load on the spandrel beams was
generated with the implicit code and successfully transferred to the explicit code where a
dynamic load was applied for one tenth of a second. The stress-state of the structure
resulting from the applied dynamic load was also successfully transferred back to the
implicit analysis for the elastic-plastic case. However, due to a limitation in the finite
element code set, the post-blast stress-state could not be transferred back to the implicit
analysis when the failure model was used. This limitation has since been removed.
Nodal displacement variations in the two-bay portal models varied only slightly
between implicit, explicit and the combined formulation method when the bilinear
elastic-plastic material model was used. However, as expected, nodal displacements for
the models that included failure deviated significantly from nodal displacements of the
bilinear elastic-plastic models. Note that the maximum horizontal nodal displacements
for each of the portal models with the bilinear elastic-plastic material model differed at
most by 9%.
As with the cantilever beam models, the beam-continuum portal models required
less time to solve than the continuum portal models. The computational cost benefit of
the mixed formulation solution method was evident in these models. The cost benefit
was most notable in the continuum model using the mixed formulation solution, which
solved over 6 times faster than the continuum model when the fully explicit method was
used.
Ill
Alfred P. Murrah Federal Building Model
The beam-continuum interface significantly reduced the number of elements
required to accurately model the proposed structure.
An interface such as the one
'
presented for this study is essential for large, compute bound problems where mesh size
is the dominant factor in computational cost. Without the presented beam-continuum
interface, this problem would be too computationally expensive for most current
mainframe computers, even with advanced solution techniques.
An initial stress-state due to dead and live loads was generated with the implicit
code and successfully transferred to the explicit code where the blast load was applied for
one one-hundredth of a second.
The stress-state of the structure resulting from the
applied blast after two seconds was also successfully transferred back to the implicit
i
analysis for the elastic-plastic case. As with the two-bay portal model, the post-blast
stress-state could not be transferred back to the implicit analysis when the failure model
was used.
In addition to the above limitation, the failure model chosen to test the
methodology, while suitable for ductile and isotropic materials, was not ideally suited to
model failure in reinforced concrete. However, the extensive laboratory tests needed to
calibrate more complex and accurate material models available in NIKE3D and
DYNA3D were not available for this study. It is important to note that analyses that
included the chosen failure model, though not ideal for reinforced concrete, illustrated a
dramatically different response than elastic-plastic analyses, clearly suggesting the
importance of including failure in future analyses.
112
Closing Remarks
The methodology presented was successful at reducing the computational cost of
analyzing large civilian structures subjected to blast loads. Stress-states due to design
loads were characterized, plastic damage and failure resulting from an applied blast load
was predicted and the resulting post-blast structural integrity was assessed based on nodal
displacement trends. Prediction of the loss of structural integrity in the pseudo-Murrah
building model after the application of a blast load similar to the one experienced by the
Alfred P. Murrah federal building illustrates the utility of this methodology in assessing
the vulnerability of existing and future structures to malevolent bomb attacks. Finally,
although only a portion of the Alfred P. Murrah federal building was modeled, this study
suggests that given the necessary computational resources, much larger structures, more
accurate failure models and more complete load cases could be applied and solved with
the proposed methodology.
113
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116
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117
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118
APPENDIX
PSEUDO-MURRAH FE MODEL INPUT FILES
119
PSEUDO-MURRAH ANSYS INPUT FILE
/COM
**************
**********
/COM
/COM
B u ild in g
***
**********
/FIL E N A M E ,build
/ c l e a r
/TITLE,
p su e d o -m u rra h
(Beam ,
S h e ll
and
S o lid
/PR EP7
/CO M ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
/COM
*** G e o m e tric P a r a m e te r s
***
/COM* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
edim =6
/COM
***
Load
P a ra m e te rs
***
/COM* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
p r e s s
=
1000
I p r e s y
=
!
P re s s u re
Load
15
/COM* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
/COM
***
R e fe re n c e
ET_CONC
=
I
MP
=
I
24
=
2
M _24x 24
=
2
CONC
E_24
x
E_24x36a
-
3
M _24x36a
=
3
E_24x36b
=
4
M_2 4 x 3 6 b
-
4
E_48x20a
=
5
M _48x20a
=
5
E_48x20b
=
6
M_48x20b
=
6
E_48x20c
=
7
M 48x20c
=
7
E_36x60
=
8
M_36x60
=
8
E_20x48a
=
9
M _20x48a
=
9
E_20x48b
= 1 0
M _20x48b
=
10
E_2 4x 48 a
=
11
M 24x48a
=
11
P a ra m e te rs
***
E lem ents)
120
E_24x48b
=
12
M _24x48b
=
12
E_SHEL
= 1 3
M_SHEL
= 1 3
E_PLATE
=
M PLATE
= 1 4
14
E_BEAM
=
15
M BEAM
=
15
/COM* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
/COM
*** R e a l S e t N um bers ***
/COM* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
re20x20
=
I
!
U pper
re20x36
=
2
!
C olum ns
s to r y
re48x20
=
3
!
I n t e r i o r
colum ns
s u p p o rtin g
o verhang
beams
re l8 x 3 6
=
4
re36x60
=
5
re l8 x 4 8
=
re22x50
=
7
1 s t
f lo o r
re !2 x 3 6
=
8
!
2nd
and
3rd
f lo o r edge
f lo o r
re24x24
=
=
9
10 !
1 s t
and
2nd
s to r y colum ns
p l a t e
=
11
re20x48
=
6
!
end
beams
beams
12
s ymm_b
=
13
symm_c
=
14
/COM* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
/COM
*** E le m e n ts ***
/COM* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
ETf E
BEAM,BEAM4
.6E 6
m p,ex,M _B E A M ,3
m p ,alpx,M _B E A M ,0 .1 7
E T , ET_CO N C,SO LID 45
m p , ex,M P_CON C, 3 . 6 e6
m p ,nuxy,M P_CO N C, 0 .1 7 0
m p ,dens,M P_C O N C , 0 . 0 0 0 2 4 8 8
E T , E _ 2 4 x 2 4 , SOLID45
m p,e x , M 2 4 x 2 4 ,4 .07e6
m p,n u x y ,M 2 4 x 2 4 ,0 .1 7 2
m p,d e n s , M _24x24,0 .0 0 0 2 4 8 8
E T ,E _ 2 4 x 3 6 a , SOLID45
m p ,ex,M _24x36a, 4 . 3e6
m p ,nuxy,M _24x36a, 0 .1 7 4
m p ,d e n s , M 2 4 x 3 6 a , 0.0002488
ET, E _24x36b,SO L ID 45
m p,ex,M _ 2 4 x 3 6 b ,4 . 7e6
m p ,nux y ,M _ 2 4 x 3 6 b ,0.1 7 8
m p,d e n s , M _24x36b,0 .0 0 0 2 4 8 8
E T ,E _48x20a,SO L ID 45
m p,ex ,M _ 4 8 x 2 0 a,4 . 44e6
m p,n u x y , M _48x20a,0.1 7 4
m p,d e n s , M _48x20a,0.0002488
E T ,E _48x20b,SO L ID 45
m p,e x ,M _ 4 8 x 2 0 b ,4 . 02e6
m p ,nuxy,M _48x20 b , 0 .1 7 2
m p,d e n s , M _48x20b,0 .0 002488
E T ,E _48x20c,SO L ID 45
!
M a te ria l
!
Prop,
M a te ria l
Y o u n g 's
Prop,
M ajor
M od.,
M at#I,
P o is s o n 's
M agnitude
R a tio
121
m p,ex ,M _ 4 8 x 2 0 c,3 . 87e6
m p,nuxy ,M _ 4 8 x 2 0 c,0.171
m p,d e n s,M _ 4 8 x 2 0 c ,0 .0 002488
E T , E _ 3 6 x 6 0 , SOLID45
m p,ex ,M _ 3 6 x 6 0 ,4 . 86e6
m p,n u x y ,M _36x60,0.1 7 6
m p,d en s,M _ 3 6 x 6 0 ,0.0002488
ET, E _20x48a,SO L ID 45
m p,ex ,M _ 2 0 x 4 8 a,3 . 88e6
m p,n u x y ,M _ 2 0 x 4 8 a,0.1 7 1
m p,d en s,M _ 2 0 x 4 8 a ,0 .0 002488
ET, E _20x48b,S O L ID 45
m p,ex ,M _20x48b,3 . 77e6
m p ,n u x y ,M _ 2 0 x 4 8 b ,0.1 7 0
m p,d en s,M _ 2 0x48 b ,0 .0 002488
ET, E _24x48a,SO L ID 45
m p,ex ,M _ 2 4 x 4 8 a,3 . 83e6
m p ,nuxy,M _24x48 a , 0.1 7 1
m p ,d en s,M _ 2 4 x 4 8 a ,0.0002488
ET, E _24x48b,S O L ID 45
m p,ex ,M _ 2 4 x 4 8 b ,3 . 74e6
m p,n u xy,M _24x48b,0.1 7 0
m p,d ens,M _24x48 b ,0.0002488
E T , E_SH EL,SH ELL63
m p ,e x , M SHEL, 3 . 6e6
m p , e y , M _SH EL ,3 . 6 e6
m p ,ez,M _S H E L ,3 . 6e6
m p ,nuxy,M _SH E L ,0 .1 7
m p ,nuyz,M _S H E L ,0 .1 7
m p ,nuxz,M _S H E L ,0 .1 7
m p,dens,M _SH E L ,0 .0 0 0 4 3 5
E T , E_PLA TE,SH ELL63
m p ,ex,M _PL A T E ,3 . 6e6
m p ,ey ,M P L A T E ,3 . 6e6
m p ,ez,M _PLA TE , 3 . 6e6
m p , n u x y , M_PLATE, 0 . 1 7
m p ,nuyz,M _P L A T E ,0 .1 7
m p ,nuxz,M _P L A T E ,0 .1 7
m p ,dens,M _PL A T E ,0 .0 0 0 4 3 5
/COM
*** R e a l s e t p a r a m e te r s
***
/COM* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
r ,r e 2 0 x 2 0 ,4 0 0 ,2 2 8 5 4 ,2 2 8 5 4 ,2 0 ,2 0 ,0 ,0
!
a r e a , I z z , I y y , T K z , TKy
r m o re ,, , , , , 0 . 0 8 9 9 5
!
m a s s /u n it
r , re 2 0 x 3 6 ,7 2 0 ,9 2 3 1 1 ,4 2 1 7 6 ,3 6 ,2 0 ,0 ,0
r m o re ,, , ,
, , 0.16192
r, re48x20, 960, 3 7 1 31,198966,4 8 ,2 0 ,0 ,0
r m o re ,, , , , , 0 . 2 1 5 8 9
r , r e ! 8 x 3 6 ,6 4 8 ,7 8 9 4 3 ,1 9 2 1 1 ,1 8 ,3 6 ,0 ,0
r m o r e ,,,,,, 0 . 1 4 5 7 3
r , re 3 6 x 6 0 ,2 1 6 0 ,8 3 7 8 9 2 ,2 6 0 0 1 2 ,3 6 ,6 0 ,0 ,0
r m o re ,, , , , , 0 . 4 8 5 7 5
r , r e l8 x 4 8 ,8 6 4 ,1 6 5 8 8 8 ,2 3 3 2 8 ,1 8 ,4 8 ,0 ,0
rm o r e ,,,,, , 0 . 1 9 4 3 0
r, re2 2 x 5 0 , 1100,341400, 5 2 0 2 0 ,2 2 ,5 0 ,0 ,0
r m o re ,, , , , , 0 . 2 7 7 0 6
r , re l2 x 3 6 , 432, 5 1 2 1 1,5412, 1 8 ,5 6 ,0 ,0
rm o r e ,,,,, , 0 . 2 2 6 6 8
r , f l o o r , 6, 6, 6, 6, 0
r , p l a t e , 6 ,6 ,6 ,6 ,0
r, r e 2 4 x 2 4 ,5 7 6 ,4 2 3 1 4 ,4 2 3 1 4 ,2 4 ,2 4 ,0 ,0
r m o re ,,,,,,0 .1 4 3 3 3 7 6
le n g th
122
r ,r e 2 0 x 4 8 ,9 6 0 ,1 9 8 9 6 6 ,3 7 1 3 1 ,2 0 ,4 8 ,0 ,0
r m o re ,, , , , , 0 . 2 1 5 8 9
r , s ymin_b , 4 8 0 , 1 8 5 6 5 . 5 , 2 4 8 7 0 . 7 5 , 2 4 , 2 0 , 0 , 0
r m o r e ,,,,,,0 .0 4 4 9 7 5
r , sym m _c,2 8 8 ,5 2 8 9 .2 5 ,2 1 1 5 7 ,1 2 ,2 4 ,0 ,0
r m o r e ,, , ,,,0 .0 7 1 6 6 9
K ey p o in ts
/COM
/CO M ** * * * * * * * * * * * * * * * * * * * * * * * * * * * *
/C O M *****************************'
/COM
* * *
F ir s t- s e c o n d
f lo o r
* * *
/COM ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
k ,l
,2 2 8
0
,408
k,2
,228
0
,432
k, 3
,252
.0
,432
k, 4
,252
,0
,408
k, 5
,228
, 136
,408
k, 6
,228
, 136
,4 3 2
k, 7
,252
, 136
,4 3 2
k, 8
,2 5 2
, 136
,408
k, 9
,228
,156
,408
k , 10
,2 2 8
,156
,4 3 2
k , 11
,2 5 2
,156
,432
k, 12
,252
,156
,408
k, 13
,264
,136
,432
k, 14
,264
,136
,408
k, 15
,264
,156
,408
k, 16
,264
, 156
,432
k, 17
,216
,136
,432
k , 18
,216
, 136
,408
k, 19
,216
,156
,408
k, 20
,216
,156
,432
k, 21
,216
, 136
,710
k, 22
,228
,1 3 6
,7 1 0
k, 23
,252
,136
,7 1 0
k , 24
,264
,1 3 6
,710
k, 25
,264
,1 5 6
,7 1 0
k, 26
,2 5 2
,156
,710
k, 27
,228
, 156
,7 1 0
k, 28
,216
,156
,7 1 0
k, 29
,1 9 2
,156
,710
k , 30
,192
,108
,710
k, 31
,216
,108
,7 1 0
k, 32
,2 2 8
,108
,7 1 0
k, 33
,2 5 2
, 108
,710
k, 34
,264
, 108
,710
k, 35
,4 5 6
,108
,7 1 0
k, 36
,456
,136
,7 1 0
k, 37
,456
,156
,710
k, 38
,192
,108
,730
k, 39
,216
,108
,730
k, 40
,228
,108
,7 3 0
k, 41
,2 5 2
, 108
,7 3 0
k, 42
,264
,108
,7 3 0
k, 43
,456
, 108
,730
k, 44
,456
,136
,7 3 0
k, 45
,456
, 156
,730
k, 46
,264
,156
,730
k, 47
,252
,156
,730
k, 48
,228
,156
,730
k, 49
,216
, 156
,730
k, 50
,192
, 156
,7 3 0
!
Cl
123
,7 3 0
k,51
,1 9 2
, 136
k, 52
,216
, 136
,730
k, 53
,2 2 8
,136
,7 3 0
k , 54
,2 5 2
, 136
,7 3 0
k, 55
,264
, 136
,7 3 0
k, 56
,192
, 136
,7 1 0
k, 57
,468
, 468
k ,59
,492
k, 60
,492
,0
,0
,0
,0
,822
k, 58
k, 61
,468
,1 0 8
,822
k ,62
,468
,108
,858
k, 63
,492
,108
,858
k, 64
, 492
,108
,822
k, 65
,468
,1 3 6
,8 2 2
k , 66
,468
,136
,858
k , 67
,492
, 136
,858
k , 68
,492
, 136
,822
k, 69
,468
,1 5 6
,822
k, 70
,468
,1 5 6
,858
k, 71
,4 9 2
,1 5 6
,858
k, 72
,4 9 2
,156
,822
k, 73
,468
, 108
,730
k , 74
,492
,1 0 8
,730
k, 75
, 492
,136
,730
k, 76
,4 9 2
,156
,730
k, 77
,4 6 8
, 156
,730
k, 78
,468
,136
,730
,8 5 8
,858
,822
/CO M ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
*** S e c o n d - t h ir d
f lo o r
/COM
/COM* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
k, 79
,228
292
,408
k, 80
,228
292
,4 3 2
k , 81
,252
292
,432
k, 82
,252
292
,408
k, 83
,2 2 8
312
,408
k, 84
,2 2 8
312
,432
k, 85
,2 5 2
312
,432
k, 86
,2 5 2
312
,408
k, 87
,2 6 4
292
,432
k, 88
,2 6 4
292
,408
k, 89
,264
312
,408
k, 90
,264
312
,432
k, 91
,216
292
,432
k, 92
,216
292
,408
k, 93
,216
312
, 408
k, 94
,216
312
,432
k, 95
,216
292
,8 2 2
k, 96
,2 2 8
292
,8 2 2
k, 97
,2 5 2
292
,822
k, 98
,264
292
,822
k, 99
,264
312
,8 2 2
k , 100
,2 5 2
, 312
,822
k , 101
,228
312
,822
k , 102
,216
,312
,822
k, 103
,192
,312
,822
k, 104
,192
,252
,822
k , 105
,216
,252
,822
k , 106
,228
,252
,822
!
Cl
124
k, 107
,252
,252
,822
k, 108
,264
,252
,8 2 2
k, 109
,456
,252
,8 2 2
k, 110
,456
,292
,822
k, 111
,456
,312
,822
k, 112
,1 9 2
,252
,858
k, 113
,2 1 6
,252
,858
k, 114
,228
,252
,858
k, 115
,252
,2 5 2
,858
,858
k, 116
,264
k, 117
,456
,2 5 2
,252
k, 118
,456
,292
,858
k, 119
,4 5 6
,3 1 2
,858
k, 120
,264
,312
,858
k, 121
,252
,312
,858
k, 122
,228
,312
,858
k, 123
,2 1 6
,312
,858
k, 124
,192
,312
,858
k, 125
, 192
,292
,858
k, 126
,216
,292
,8 5 8
k, 127
,228
,292
,858
k, 128
,252
,292
,8 5 8
k, 129
,264
,292
,858
k, 130
,192
,2 9 2
,822
k, 131
,468
,2 5 2
,822
k, 132
,468
,2 5 2
,858
k, 133
,492
,2 5 2
,858
k, 134
,4 9 2
,2 5 2
,822
,858
k, 135
,228
,336
,408
k, 136
,228
,336
,432
k, 137
,2 5 2
,336
,432
k, 138
,252
,336
,408
k, 139
,2 2 8
,336
,822
k, 140
,2 2 8
,336
,858
k, 141
,252
,336
,858
k, 142
,252
,336
,822
second
!
beam
nub
!
beam
nub
/COM* * * * * * * * * * * * * * * * * * * * * * * 1
F i r s t
/COM***
f lo o r
beams
k , 1011
,0
,0
,0
k , 1012
,240
,0
,0
k , 1013
, 480
,0
,0
k , 1014
,7 2 0
,0
,0
k , 1015
,960
,0
,0
k , 1021
,0
,0
,420
k , 1025
, 960
,0
,4 2 0
k , 1031
,0
,0
,840
k , 1035
,960
,0
,8 4 0
I
/COM* * * * * * * * * * * * * * * * * * * * * * *
beams
/COM***
Second
f lo o r
k ,2011
,0
, 136
,0
k , 2012
,2 4 0
, 136
,0
k , 2013
,4 8 0
,136
,0
k , 2014
,720
,136
,0
k, 2015
,9 6 0
, 136
,0
k ,2020
,216
, 136
,4 2 0
k , 2021
,0
, 136
,420
to
!
new
kp
t h i r d
f lo o r
colum n
125
k , 2022
,240
, 136
k , 2122
,240
, 136
, 408
,4 2 0
k, 2023
, 480
,136
,408
k, 2123
, 480
,136
,4 2 0
k , 2024
,720
, 136
,408
k,2124
,720
, 136
, 420
k , 2025
,960
, 136
,420
!
new
kp
k ,2030
,0
, 136
,710
k , 2031
,0
, 136
,720
k , 2032
,192
, 136
,720
k , 2132
,240
,136
,720
k , 2034
,768
, 136
,720
k , 2134
,744
, 136
,720
k , 2035
,960
,136
,720
k, 2036
,216
,136
,7 2 0
!
new
kp
k , 2037
,960
, 136
,7 1 0
!
new
kp
k , 2038
,744
, 136
,4 2 0
!
new
kp
k , 2041
,0
, 136
,8 4 0
k , 2045
,960
,136
,8 4 0
***
f lo o r beam s k e y p o in ts
/CO M *** T h i r d
/COM* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
k , 3011
,0
,292
,0
k , 3012
,2 4 0
,2 9 2
,0
k, 3013
,4 8 0
,2 9 2
,0
k , 3014
,7 2 0
,292
,0
k , 3015
,9 6 0
,292
,0
k , 3021
,0
,292
,420
k , 3022
,240
,292
,420
k , 3122
,240
,336
,4 2 0
k , 3222
,240
,312
,420
k , 3023
,480
,2 9 2
,4 2 0
k, 3123
,4 8 0
,336
,4 2 0
k , 3223
,4 8 0
,3 1 2
,4 2 0
k , 3024
,7 2 0
,292
,420
k , 3124
,720
,336
, 420
k , 3224
,7 2 0
,3 1 2
,4 2 0
k, 3025
,9 6 0
,292
,4 2 0
k, 3031
,0
,2 9 2
,840
k, 3032
,192
,292
,840
k, 3132
,2 4 0
,336
,840
k, 3232
,2 4 0
,292
,840
k, 3033
,480
,336
,840
k, 3034
,768
,292
,840
k, 3134
,720
,336
, 840
k , 3234
,720
,292
,840
k, 3035
,960
,292
,8 4 0
/CO M ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
/CO M ***
F o u rth
f lo o r
beam
k e y p o in ts
***
/COM* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
k,4011
0
, 468
,0
k, 4012
240
,468
,0
k , 4013
480
,468
,0
k, 4014
720
,468
,0
k , 4015
960
,468
,0
k , 4021
0
,468
,4 2 0
k , 4022
240
,468
,420
k , 4023
480
,468
,4 2 0
k , 4024
720
,468
,4 2 0
k , 4025
960
,468
,4 2 0
,468
, 840
k , 4031
, 00
k , 4032
,2 4 0
,468
,840
k , 4033
, 480
,468
,840
k , 4034
,7 2 0
, 468
,8 4 0
k , 4035
, 960
, 4 68
, 840
/C O M ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
/COM
*** F i r s t - s e c o n d
f l o o r v o lu m e s ***
/COM* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
v,
I,
2,
3,
4,
5,
6,
7,
8
v,
5,
6,
7,
8,
9,
10,
11,
12
v,
18,
17,
6,
5,
19,
20,
10,
9
v,
8,
7,
13,
14,
12,
11,
16,
15
v,
17,
6,
10,
20,
21,
22,
27,
28
v,
6,
7,
11,
10,
22,
23,
26,
27
v,
7,
13,
16,
11,
23,
24,
25,
26
v,
30,
38,
39,
31,
56,
51,
52,
21
V,
56, 51,
52,
21,
29,
50,
49,
28
22
v,
31, 39,
40,
32,
21,
52,
53,
v,
21, 52,
53,
22,
28,
49,
48,
27
v,
32, 40,
41,
33,
22,
53,
54,
23
v,
22, 53,
54,
23,
27,
48,
47,
26
v,
33, 41,
42,
34,
23,
54,
55,
24
v,
23, 54,
55,
24,
26,
47,
46,
25
v,
34, 42,
43,
35,
24,
55,
44,
36
v,
24, 55,
44,
36,
25,
46,
45,
37
57, 58,
59,
63,
64
v,
v,
61,
60,
6 2 ,.6 3 ,
61,
64,
v,
65, 66,
67,
v,
73, 61,
64,
v,
78, 65,
68,
62,
65,
68,
66,
67,
68
71,
72
69,
70,
74,
78,
65,
68,
75
75,
77,
69,
72,
76
/CO M *1
*** S e c o n d - t h i r d
/COM
/COM* * * * * * * * * * * * *
V,
V,
V,
V,
V,
V,
V,
V,
V,
V,
V,
V,
V,
V,
V,
f lo o r
volum es
9,
10,
11,
12,
81,
82
80,
81,
82,
7 9 ,,
8 3 ,,
80,
79,
84,
85,
86
82,
81,
87,
88,
8 6 ,,
85,
90,
89
92,
91,
80,
79,
9 3 ,,
94,
84,
83
91,
80,
84,
94,
9 5 ,,
96,
101,
80,
81,
85,
84,
9 6 ,,
97,
100,
81,
87,
90,
85,
9 7 ,,
98,
99,
104,,
112,
113,
105 ,
130,,
125,
126,
95,
105,,
106,,
113,
114,
114,
115,
107 ,
115,
116,
95
123,
102
106 ,
95,
126,
127,
96
107 ,
96,
127,
128,
97
108 ,
97,
128,
129,
98
122,
101
128,
97,
101,
122,
121,
100
129,
98,
100,
121,
120,
99
96,
127,
97,
128,
109,
V,
V,
98,
129,
V,
69,
70,
71,
72 ,
V,
V,
83,
84,
85,
86 ,
117,
118,
122,
126,
124,
123,
127,
101,,
125,
103,
102,
126,
116,
101
100
96,
95,
108,
130 ,
102
H O ,
121,
98,
99,
131,
132,
135,
100,
136,
139,
/COM* * * * * * * * * * * * * * * * * * * *
Copy volum es
/COM
/COM*
e s i z e , edim
v s e l , s , v o l u , ,1 ,7
v s e l , a , v o l u , ,1 0 ,1 7
129,
120,
118,
119,
133,
137,
140,
H O
111
134
138
141,
142
127
v s e l , a , v o l u , ,2 3 ,2 9
v s e l , a , v o l u , ,3 2 ,3 9
v s e l , a , v o l u , ,4 1 ,4 2
v g e n ,2 , a l l , ,,2 4 0
v s e l , s , v o l u , ,4 3 ,5 5
v s e l , a , v o l u , ,5 8 ,7 0
v s e l , a , v o l u , ,7 3 ,7 4
v g e n ,2 , a l l , ,,2 4 0
v s e l, s, v o lu , ,8 ,9
v s e l , a , v o l u , ,3 0 ,3 1
v g e n ,2 , a l l , ,,5 5 2
a l l s e l , a l l
num m rg,kp
/COM* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
/COM
***
A reas
***
a.
157,
158,
15,
16
a,
16,
25,
37,
157
a,
89,
90,
207,
208
a.
90,
99,
111,
207
/COM* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
/COM
*** C opy a r e a s
***
/ COM* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
a s e l , s , a r e a , ,231
a s e l , a , a r e a , ,236
a s e l , a , a r e a , ,245
a s e l , a , a r e a , ,241
a g e n ,2 , a l l , ,,2 4 0
/COM* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
/COM
*** M esh v o lu m e s ***
/COM* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
a l l s e l , a l l
m at,M P_C O N T
t y p e , ET_CONT
v m e s h ,a ll
a l l s e l , a l l
/COM* * * * * * * * * * * * * * * * * * * * * * * * * * *
/COM
*** M o d ify e le m e n ts
* * *
/COM* * * * * * * * * * * * * * * * * * * * * * * * * * *
/CO M ***
m odify
colum n
I
n s e l ,s ,lo c ,x ,2 2 8 ,2 3 4
***
24x24
re b a r
assig n m e n t
n s e l,r ,l o c ,z ,4 0 8 ,4 3 2
e s l n , s , I , a l l
,
e m o d if, a ll,ty p e ,E _ 2 4 x 2 4
e m o d if , a l l , m a t , M_24x2 4
n s e l ,s ,lo c ,x ,2 4 6 ,2 5 2
n s e l , r , l o c , z , 408,432
e s l n , s , I , a l l
e m o d if, a ll,ty p e ,E _ 2 4 x 2 4
e m o d if ,a ll,m a t,M _ 2 4x24
n s e l , s , l o c , x , 228,252
n s e l , r , l o c , z , 408,414
e s l n , s , I , a l l
e m o d if ,a ll,ty p e ,E _ 2 4 x 2 4
e m o d if ,a ll,m a t,M _ 2 4x24
1*1 I
1*1
|*|*|*|*|
1*1
I 1*1
I*1*1*1*1
n s e l ,s ,l o c ,x ,2 2 8 ,2 5 2
n s e l ,r ,l o c ,z ,4 2 6 ,4 3 2
e s l n , s , I , a l l
e m o d if, a ll,ty p e ,E _ 2 4 x 2 4
e m o d if , a l l , m a t , M_24x24
/CO M ***
m odify
colum n
2
n s e l,s ,lo c ,x ,4 6 8 ,4 7 4
n s e l ,r ,l o c ,z ,4 0 8 ,4 3 2
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 2 4 x 2 4
e m o d i f , a l l , m a t , M_24x24
n s e l , s , l o c , x , 486,492
n s e l,r ,l o c ,z ,4 0 8 ,4 3 2
e s l n , s , I , a l l
e m o d if ,a ll,ty p e ,E _ 2 4 x 2 4
e m o d if, a ll,m a t,M _ 2 4x24
n s e l , s , l o c , x , 468,492
n s e l , r , l o c , z , 408,414
e s l n , s , I , a l l
e m o d if ,a ll,ty p e ,E _ 2 4 x 2 4
e m o d if,a ll,m a t,M _ 2 4x24
n s e l , s , l o c , x , 468,492
n s e l , r , l o c , z , 426,432
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 2 4 x 2 4
e m o d if ,a l l,m a t ,M 2 4 x 2 4
/CO M ***
m od ify
colum n
3
n s e l , s , l o c , x , 708,714
n s e l , r , l o c , z , 408,432
e s l n , s , I , a l l
e m o d if ,a ll,ty p e ,E _ 2 4 x 2 4
em o d if, a ll,m a t,M _ 2 4x24
n s e l , s , l o c , x , 726,732
n s e l , r , l o c , z , 408,432
e s l n , s , I , a l l
e m o d i f ,a l l , type,E _24x24
e m o d if,a ll,m a t,M _ 2 4 x 2 4
n s e l , s , l o c , x , 708,732
n s e l , r , l o c , z , 408,414
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 2 4 x 2 4
e m o d i f , a l l , m a t , M _24x24
n s e l , s , l o c , x , 708,732
n s e l , r , l o c , z , 426,432
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 2 4 x 2 4
e m o d i f , a l l , m a t , M_24x24
/CO M ***
m od ify
nub
I
**
n s e l , s , l o c , x , 228,234
n s e l , r , l o c , z , 828,852
e s l n , s , I , a l l
e m o d i f , a l l , t y p e , E
24x24
e m o d i f , a l l , m a t , M _24x24
n s e l , s , l o c , x , 246,252
n s e l , r , l o c , z , 828,852
e s l n , s , I , a l l
e m o d if ,a ll,ty p e ,E _ 2 4 x 2 4
129
emodif,all,mat,M_24x24
n s e l ,s ,l o c ,x ,2 2 8 ,2 5 2
n s e l ,r ,l o c ,z ,8 2 8 ,8 3 4
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 2 4 x 2 4
e m o d if ,a ll,m a t,M _ 2 4x24
n s e l , s , l o c , x , 228,252
n s e l ,r ,l o c ,z ,8 4 6 ,8 5 2
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 2 4 x 2 4
e m o d if , a l l , m a t , M_24x24
/CO M ***
m od ify
nub
2
***
n s e l , S , l o c , x , 468,474
n s e l , r , l o c , z , 828,834
e s l n , s , l , a l l
e m o d if,a ll,ty p e ,E _ 2 4 x 2 4
em odif, all,m a t,M _ 2 4 x 2 4
n s e l , s , l o c , x , 486,492
n s e l , r , l o c , z , 828,852
e s ln , s , l , a l l
e m o d if, a ll,ty p e ,E _ 2 4 x 2 4
e m o d i f ,a l l , m at,M _24x24
n s e l , S , l o c , x , 468,492
n s e l , r , l o c , z , 828,834
n s e l , r , l o c , y , 252,340
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 2 4 x 2 4
e m o d if ,a ll,m a t,M _ 2 4x24
n s e l , s , l o c , x , 468,492
n s e l , r , l o c , z , 846,852
n s e l , r , l o c , y , 252,340
e s l n , s , l , a l l
e m o d if, a l l ,t y p e ,E _ 2 4x24
e m o d if,a ll,m a t,M _ 2 4x24
/CO M ***
m o d ify
nub
3
***
n s e l , s , l o c , x , 708,714
n s e l, r, l o c , z , 828,852
e s l n , s , I , a l l
em odif, a ll,ty p e ,E _ 2 4 x 2 4
e m o d i f , a l l , m a t , M_24x24
n s e l , s , l o c , x , 726,732
n s e l , r , l o c , z , 828,852
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 2 4 x 2 4
e m o d if ,a ll,m a t,M _ 2 4x24
n s e l , s , l o c , x , 708,732
n s e l , r , l o c , z , 828,834
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 2 4 x 2 4
e m o d i f , a l l , m a t , M_24x24
n s e l , s , l o c , X ,708,732
n s e l , r , l o c , z , 846,852
e s l n , s , l , a l l
e m o d if,a ll,ty p e ,E _ 2 4 x 2 4
e m o d if, a ll,m a t,M _ 2 4x24
/COM
***
m o d ify
c a n t i l e v e r
nsel,s,loc,z,834,846
s u p p o rt
colum n
***
! 24x36 rebar assignment
130
n s e l , r , l o c , x , 468,474
I
n s e l, r, l o c , y , 0,2 5 2
!
e s l n , s , I , a l l
M
M
! Ia|
e m o d if,a ll,ty p e ,E _ 2 4 x 3 6 a
I b T lI
|b |
I
I
I
I
Ia
I
e m o d i f ,a l l ,m a t ,M 2 4 x 3 6a
!
n s e l , s , l o c , z , 834,846
!
Ibl
n s e l , r , l o c , x , 486,492
I
-
Ibl
I
-
Ia
-
-
n s e l , r , l o c , y , 0,2 5 2
e s l n , s , I , a l l
e m o d if, a ll,ty p e ,E _ 2 4 x 3 6 a
e m o d if, a ll,m a t,M _ 2 4 x 3 6 a
n s e l , s , l o c , z , 822,828
n s e l , r , l o c , x , 468,474
n s e l , r , l o c , y , 0,2 5 2
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 2 4 x 3 6 b
e m o d i f , a l l , m a t , M _ 2 4 x 3 6b
n s e l , s , l o c , z , 852,858
n s e l , r , l o c , x , 468,474
n s e l , r , l o c , y , 0,2 5 2
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 2 4 x 3 6 b
e m o d i f , a l l , m a t , M _ 2 4 x 3 6b
n s e l , s , l o c , z , 822,828
n s e l , r , l o c , x , 486,492
n s e l , r , l o c , y , 0,2 5 2
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 2 4 x 3 6 b
e m o d if , a l l , m a t , M_24 x 3 6b
n s e l , s , l o c , z , 852,858
n s e l , r , l o c , x , 486,492
n s e l , r , l o c , y , 0,2 5 2
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 2 4 x 3 6 b
e m o d i f , a l l , m a t , M_24 x 3 6b
/COM
***
m od ify
f lo o r
j o i s t s
n s e l , s , l o c , y , 151,156
-
seco n d
f lo o r
-
f i r s t
row
48x20
re b a r
assig n m e n t
n s e l , r , l o c , x , 216,222
n s e l , r , l o c , z , 408,710
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 4 8 x 2 0 a
e m o d if,a ll,m a t,M _ 4 8x20a
n s e l , s , l o c , y , 136,142
n s e l , r , l o c , x , 216,222
n s e l , r , l o c , z , 408,710
e s l n , s , I , a l l
em odif, a ll,ty p e ,E _ 4 8 x 2 0 c
e m o d if, a l l , m a t,M 48x20c
n s e l , s , l o c , y , 136,142
n s e l , r , l o c , x , 258,264
n s e l , r , l o c , z , 408,710
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 4 8 x 2 0 c
e m o d if,a ll,m a t,M _ 4 8x20c
n s e l , s , l o c , y , 151,156
n s e l , r , l o c , x , 2 3 4,246
n s e l , r , l o c , z , 408,710
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 4 8 x 2 0 b
e m o d if, a l l , m a t , M 48x20b
I a I I Iblbl I | a|
I I I I I I I I I
! I M M I M I
Mc | M M Mc l
***
131
n s e l,s ,l o c ,y ,1 5 1 ,1 5 6
n s e l , r , I o c , x , 258,264
n s e l , r , l o c , z , 408,710
e s l n , s , I , a l l
e m o d if, a ll,ty p e ,E _ 4 8 x 2 0 a
e m o d if, a ll,m a t,M _ 4 8 x 2 0 a
/COM
***
m odify
f lo o r
j o i s t s
-
second
f lo o r
-
48x20
re b a r
assig n m e n t
I
n s e l , s , l o c , y , 151,156
second
row
***
n s e l , r , l o c , x , 456,462
n s e l , r , l o c , z , 408,710
I a I I Ib Ib I
I I I I I I
! I I
I Id I I I
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 4 8 x 2 0 a
e m o d if ,a l l,m a t, M _48x20a
I
I
I
I
Ia I
I I
I I I I I I
I Id
n s e l , s , l o c , y , 136,142
n s e l , r , l o c , x , 456,462
n s e l , r , l o c , z , 408,710
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 4 8 x 2 0 c
e m o d i f , a l l , m a t , M _ 4 8 x 2 Oc
n s e l , s , l o c , y , 136,142
n s e l , r , l o c , x , 498,504
n s e l , r , l o c , z , 408,710
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 4 8 x 2 0 c
e m o d i f , a l l , m at,M _48x20c
n s e l , s , l o c , y , 151,156
n s e l , r , l o c , x , 474,486
n s e l , r , l o c , z , 408,710
e s l n , s , I , a l l
e m o d if, a l l , t y p e , E_48x20b
e m o d if ,a l l,m a t ,M _ 4 8 x 2 0b
n s e l , s , l o c , y , 151,156
n s e l, r , l o c , x, 498,504
n s e l , r , l o c , z , 408,710
e s l n , s , l , a l l
e m o d if,a ll,ty p e ,E _ 4 8 x 2 0 a
e m o d if,a ll,m a t,M _ 4 8x20a
/COM
***
m odify
f lo o r
j o i s t s
n s e l , s , l o c , y , 151,156
!
second
f lo o r
-
t h i r d
row
48x20
re b a r
assig n m e n t
n s e l , r , l o c , x , 696,702
n s e l , r , l o c , z , 408,710
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 4 8 x 2 0 a
e m o d i f ,a l l , m a t, M _48x20a
n s e l , s , l o c , y , 136,142
n s e l , r , l o c , x , 696,702
n s e l , r , l o c , z , 408,710
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 4 8 x 2 0 c
e m o d if ,a l l,m a t, M _48x20c
n s e l , s , l o c , y , 136,142
n s e l , r , l o c , x , 738,744
n s e l , r , l o c , z , 408,710
e s l n , s , I , a l l
e m o d if ,a l l,ty p e , E_48x20c
e m o d if,a ll,m a t,M _ 4 8 x 2 0 c
n s e l , s , l o c , y , 151,156
n s e l , r , l o c , x , 7 1 4,726
n s e l , r , l o c , z , 408,710
e s l n , s , I , a l l
I a I I Ib Ib I I I a I
I II I I I I I I I
I II I I I I I I I
! I d I I I I I | c|
***
132
emodif,all,type, E_48x20b
emodif,all,mat,M_48x20b
n s e l ,s ,l o c ,y ,1 5 1 ,1 5 6
n s e l ,r ,l o c ,x ,7 3 8 ,7 4 4
n s e l ,r ,l o c ,z ,4 0 8 ,7 1 0
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 4 8 x 2 0 a
e m o d if ,a l l,m a t, M _48x20a
/COM
***
m od ify
f lo o r
j o i s t s
-
th i r d
48x20
n s e l , s , I o c , y , 307,312
f lo o r
re b a r
-
f i r s t
row
***
a ssig n m e n t
n s e l , r , I o c , x , 215,222
n s e l , r , l o c , z , 408,822
I a I I Iblbl I I a I
I I I II I I I I
M I Il I I I I I
! | c | I I I I l | c|
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 4 8 x 2 0 a
e m o d if,a ll,m a t,M _ 4 8 x 2 0 a
n s e l , s , l o c , y , 292,297
n s e l , r , l o c , x , 216,222
n s e l , r , l o c , z , 408,822
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 4 8 x 2 0 c
e m o d i f , a l l , m a t , M _ 4 8 x 2 Oc
n s e l , s , l o c , y , 292,297
n s e l , r , l o c , x , 258,264
n s e l , r , l o c , z , 408,822
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 4 8 x 2 0 c
e m o d if ,a l l,m a t, M _48x20c
n s e l , s , l o c , y , 307,312
n s e l , r , l o c , x , 2 34,246
n s e l , r , l o c , z , 408,822
e s l n , s , I , a l l
em odif, a l l , ty p e , E_48x20b
e m o d if ,a l l,m a t ,M _ 4 8 x 2 0b
n s e l , s , l o c , y , 307,312
n s e l , r , l o c , x , 258,264
n s e l , r , l o c , z , 408,822
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 4 8 x 2 0 a
e m o d if ,a ll,m a t,M _ 4 8x20a
/COM
***
m od ify
f lo o r
j o i s t s
n s e l , s , l o c , y , 307,312
-
f i r s t
I
48x20
f lo o r
re b a r
-
seco n d
row
a ssig n m e n t
n s e l , r , l o c , x , 456,462
n s e l , r , l o c , z , 408,822
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 4 8 x 2 0 a
e m o d i f ,a l l ,m a t , M_48x20a
n s e l , s , l o c , y , 292,297
n s e l , r , l o c , x , 456,462
n s e l , r , l o c , z , 408,822
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 4 8 x 2 0 c
e m o d i f , a l l , m a t , M_48 x 2 0 c
n s e l , s , l o c , y , 292,297
n s e l , r , l o c , x , 498,504
n s e l , r , l o c , z , 408,822
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 4 8 x 2 0 c
e m o d if ,a l l,m a t, M _48x20c
nsel,s,loc,y,307,312
Ial
I Iblbl I I a I
I II I I I I I I I
I II I I I I I I I
! | c| I I I I I | c|
* * *
133
n s e l , r , l o c , x z474,486
n s e l ,r ,l o c ,z ,4 0 8 ,8 2 2
e s l n , s , I , a l l
e m o d if, a ll,ty p e ,E _ 4 8 x 2 0 b
e m o d if, a l l , m a t , M _48x20b
n s e l ,s ,l o c ,y ,3 0 7 ,3 1 2
n s e l , r , I o c , x , 498,504
n s e l,r ,l o c ,z ,4 0 8 ,8 2 2
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 4 8 x 2 0 a
e m o d if,a ll,m a t,M _ 4 8 x 2 0 a
/COM
***
m od ify
f lo o r
j o i s t s
-
f i r s t
n s e l , s , I o c , y , 307,312
!
n s e l , r , I o c , x , 696,702
!
f lo o r
48x20
-
t h i r d
re b a r
row
assig n m e n t
n s e l , r , I o c , z , 408,822
!
e s l n , s , I , a l l
! |a| I Iblbl I Ial
! M I M M I I
e m o d if,a ll,ty p e ,E _ 4 8 x 2 0 a
! M M M M I
e m o d if,a ll,m a t,M _ 4 8 x 2 0 a
Mc M
M
M
Icl
n s e l , s , I o c , y , 292,297
n s e l , r , l o c , x , 696,702
n s e l , r , l o c , z , 408,822
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 4 8 x 2 0 c
e m o d i f , a l l , m a t , M _ 4 8 x 2 Oc
n s e l , s , l o c , y , 292,297
n s e l , r , l o c , x , 738,744
n s e l , r , l o c , z , 408,822
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 4 8 x 2 0 c
e m o d if ,a l l,m a t, M _48x20c
n s e l , s , l o c , y , 307,312
n s e l , r , l o c , x , 714,726
n s e l , r , l o c , z , 408,822
e s l n , s , I , a l l
e m o d if ,a ll,ty p e ,E _ 4 8 x 2 0 b
e m o d if,a ll,m a t,M _ 4 8 x 2 0 b
n s e l , s , l o c , y , 307,312
n s e l , r , l o c , x , 738,744
n s e l , r , l o c , z , 408,822
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 4 8 x 2 0 a
e m o d i f , a l l , m a t , M _ 4 8 x 2 Oa
/COM
***
m odify
second
f lo o r
c a n til e v e r
n s e l , s , l o c , z , 710,730
!
n s e l , r , l o c , y , 151,156
!
20x48
beam
re b a r
e s l n , s , I , a l l
I
e m o d if,a ll,ty p e ,E _ 2 0 x 4 8 a
I Ia Ia Ia Ia I
e m o d if,a ll,m a t,M _ 2 0x 4 8a
n s e l , s , l o c , z , 710,730
n s e l , r , l o c , y , 108,114
e s l n , s , I , a l l
e m o d if, a ll,ty p e ,E _ 2 0 x 4 8 b
l
l
l
l
l
/COM
***
m odify
t h i r d
f lo o r
Mi
M i
Mi
Mi
Mi
!
Ib lb lb lb l
!
n s e l , s , l o c , z , 822,858
n s e l , r , l o c , y , 307,312
e s ln , s , I , a l l
e m o d if,a ll,ty p e ,E _ 3 6 x 6 0
c a n til e v e r
!
20x48
assig n m e n t
! Mi l l
l
l
l
l
l
!
!
!
!
!
e m o d if ,a l l,m a t ,M _ 2 0 x 4 8b
***
M
i
beam
re b a r
l
l
***
a ssig n m e n t
!
! I*l*l*l*l*l*l
***
134
emodif,all,mat,M_36x60
n s e l ,s ,l o c ,z ,8 2 2 ,8 5 8
n s e l ,r ,l o c ,y ,2 5 2 ,2 5 8
e s l n , s , I , a l l
I
M i l
e m o d if,a ll,ty p e ,E _ 3 6 x 6 0
e m o d if, all,m a t,M _ 3 6 x 6 0
/COM
m od ify
* * *
seco n d
f lo o r
beam
from
24x48
n s e l , s , I o c , z , 730,822
colum n
re b a r
to
a ssig n m e n t
n s e l , r , I o c , y , 151,156
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 2 4 x 4 8 a
I
Ia Ia Ia Ia I
I
I II I I I
II I I I
I I I I I I
e m o d if ,a l l,m a t, M _24x48a
n s e l , s , l o c , z , 730,822
Illlll
n s e l , r , l o c , y , 108,114
e s l n , s , I , a l l
e m o d if,a ll,ty p e ,E _ 2 4 x 4 8 b
e m o d i f , a l l , m a t , M _ 2 4 x 4 8b
/COM
***
M esh
f lo o r
a re a s
I
I
II I I I
II I I I
I II I I I
I Ib Ib Ib Ib I
***
/CO M ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
a l l s e l , a l l
m at,M _SH EL
t y p e , E_SHEL
r e a l , f l o o r
a s e l , s , l o c , y , 156
a s e l , u , a r e a , ,11
a s e l , u , a r e a , ,61
a s e l , u , a r e a , ,247
a s e l , u , a r e a , ,1 0 3
a s e l , u , a r e a , ,94
a s e l , u , a r e a , ,206
a s e l , u , a r e a , ,353
a s e l , u , a r e a , ,394
am e sh ,a l l
a s e l , s , l o c , y , 312
a s e l , u , a r e a , ,113
a s e l , u , a r e a , ,168
a s e l , u , a r e a , ,274
a s e l , u , a r e a , ,3 2 0
a s e l , u , a r e a , ,4 1 2
a s e l , u , a r e a , ,458
a m e s h ,a ll
a l l s e l , a l l
num m rg,no d e
/COM
*****************************
/COM
/COM
*** M esh i n t e r f a c e
p la te s
* * *
*****************************
m a t , M_PLATE
type,E _P L A T E
r e a l , p l a t e
asel,s,loc,x,192
c a n t i l e v e r
***
135
a s e l , a , l o c , x , 768
a s e l , a , l o c , y , 336
am esh ,a l l
a s e l , s , l o c , z , 408
a s e l , u , a r e a , ,189
a s e l , u , a r e a , ,107
a s e l , u , a r e a , ,5
a s e l , u , a r e a , ,336
a s e l , u , a r e a , ,268
a s e l , u , a r e a , ,200
a s e l , u , a r e a , ,465
a s e l , u , a r e a , ,406
a s e l , u , a r e a , ,347
a m e s h ,a ll
a l l s e l , a l l
/COM
/COM
* * *
C re a te beam l i n e s
***
*****************************
/COM
* * *
F ir s t- s e c o n d
f lo o r
colum ns
***
1 . 1011.2011
1 . 1012.2012
1 . 1013.2013
1 .1 0 1 4 .2 0 1 4
1 . 1015.2015
1 . 1021.2021
1 ,1 0 2 5 ,2 0 2 5
1 .1 0 3 1 .2 0 4 1
1 . 1035.2045
/COM
***
Second
f lo o r
Back
beam s
f lo o r
j o i s t s
f lo o r
c a n t i l e v e r
***
1 , 2011,2012
1 .2 0 1 2 .2 0 1 3
1 .2 0 1 3 .2 0 1 4
1 .2 0 1 4 .2 0 1 5
/COM
***
Second
***
1 . 2011.2021
1 , 2012,2022
1 .2 0 1 3 .2 0 2 3
1 .2 0 1 4 .2 0 2 4
1 .2 0 1 5 .2 0 2 5
1 .2 0 2 1 .2 0 3 1
1 .2 0 3 1 .2 0 4 1
1 ,2 0 2 5 ,2 0 3 5
1 .2 0 3 5 .2 0 4 5
/COM
***
Second
beam
***
1 .2 0 3 1 .2 0 3 2
1 ,2 0 3 5 ,2 0 3 4
/COM
***
S e c o n d -th ird
1 .2 0 1 1 .3 0 1 1
1 .2 0 1 2 .3 0 1 2
1 ,2 0 1 3 , 3013
1 .2 0 1 4 .3 0 1 4
1 .2 0 1 5 .3 0 1 5
1 ,2 0 2 1 ,3 0 2 1
f lo o r
colum ns
***
1 ,2 0 2 5 ,3 0 2 5
1 . 2041.3031
1 ,2 0 4 5 , 3035
/COM
***
T h ird
f lo o r
Back
beams
f lo o r
j o i s t s
f lo o r
c a n t i l e v e r
***
1 .3 0 1 1 .3 0 1 2
1 . 3012.3013
1 .3 0 1 3 .3 0 1 4
1 .3 0 1 4 .3 0 1 5
/COM
***
T h ird
* * *
1 .3 0 1 1 .3 0 2 1
1 .3 0 1 2 .3 0 2 2
1 .3 0 1 3 .3 0 2 3
1 .3 0 1 4 .3 0 2 4
1 .3 0 1 5 .3 0 2 5
1 .3 0 2 1 .3 0 3 1
1 .3 0 2 5 .3 0 3 5
/COM
***
T h ird
beam
1 .3 0 3 1 .3 0 3 2
1 . 3034.3035
/COM
***
T h ird -F o u rth
f lo o r
colum ns
1 .3 0 1 1 .4 0 1 1
1 .3 0 1 2 .4 0 1 2
1 .3 0 1 3 .4 0 1 3
1 .3 0 1 4 .4 0 1 4
1 . 3015.4015
1 .3 0 2 1 .4 0 2 1
1 .3 1 2 2 .4 0 2 2
1 . 3123.4023
1 . 3124.4024
1 . 3025.4025
1 .3 0 3 1 .4 0 3 1
1 .3 1 3 2 .4 0 3 2
1 . 3033.4033
1 .3 1 3 4 .4 0 3 4
1 .3 0 3 5 .4 0 3 5
/COM
***
F o u rth
f lo o r
Back
beams
f lo o r
j o i s t s
***
f lo o r
f r o n t
beams
***
1 .4 0 1 1 .4 0 1 2
1 .4 0 1 2 .4 0 1 3
1 .4 0 1 3 .4 0 1 4
1 .4 0 1 4 .4 0 1 5
/COM
***
F o u rth
1 .4 0 1 1 .4 0 2 1
1 . 4012.4022
1 .4 0 1 3 .4 0 2 3
1 . 4014.4024
1 .4 0 1 5 .4 0 2 5
1 .4 0 2 1 .4 0 3 1
1 . 4022.4032
I , 4023,4033
1 .4 0 2 4 .4 0 3 4
1 . 4025.4035
/COM
***
F o u rth
1 ,4 0 3 1 ,4 0 3 2
***
137
1 . 4032.4033
1 . 4033.4034
1 . 4034.4035
/COM
*****************************
/COM
/COM
**** C r e a te
f lo o r a re a
****
*****************************
a , 2 0 1 1 ,2 0 2 1 ,2 1 2 2 ,2 0 1 2
a , 2 0 1 2 ,2 1 2 2 ,2 1 2 3 ,2 0 1 3
a , 2 0 1 3 ,2 1 2 3 ,2 1 2 4 ,2 0 1 4
a , 2 0 1 4 ,2 1 2 4 ,2 0 2 5 ,2 0 1 5
a , 2 0 2 1 ,2 0 3 0 ,2 1 ,2 0 2 0
!
a , 2 0 2 1 ,2 0 3 1 ,2 1 3 2 ,2 1 2 2
a , 2 0 3 0 ,2 0 3 1 ,2 0 3 6 ,2 1
!
n u ll
a , 2 0 3 8 ,2 7 3 ,2 0 3 7 ,2 0 2 5
!
a ,2 1 2 4 ,2 1 3 4 ,2 0 3 5 ,2 0 2 5
a , 2 7 3 ,2 1 3 4 ,2 0 3 5 ,2 0 3 7
a , 3 0 1 1 ,3 0 2 1 ,3 0 2 2 ,3 0 1 2
a , 3 0 1 2 ,3 0 2 2 ,3 0 2 3 ,3 0 1 3
a , 3 0 1 3 ,3 0 2 3 ,3 0 2 4 ,3 0 1 4
a , 3 0 1 4 ,3 0 2 4 ,3 0 2 5 ,3 0 1 5
a , 3 0 2 1 ,3 0 3 1 ,3 2 3 2 ,3 0 2 2
a , 3 0 2 4 ,3 2 3 4 ,3 0 3 5 ,3 0 2 5
a , 4 0 1 1 ,4 0 2 1 ,4 0 2 2 ,4 0 1 2
a, 4 0 1 2 ,4 0 2 2 ,4 0 2 3 ,4 0 1 3
a , 4 0 1 3 ,4 0 2 3 ,4 0 2 4 ,4 0 1 4
a , 4 0 1 4 ,4 0 2 4 ,4 0 2 5 ,4 0 1 5
a , 4 0 2 1 ,4 0 3 1 ,4 0 3 2 ,4 0 2 2
a, 4 0 2 2 ,4 0 3 2 ,4 0 3 3 ,4 0 2 3
a , 4 0 2 3 ,4 0 3 3 ,4 0 3 4 ,4 0 2 4
a, 4 0 2 4 ,4 0 3 4 ,4 0 3 5 ,4 0 2 5
/COM
***
M esh
a re a s
***
/COM ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
nununrg, kp
a l l s e l , a l l
m at,M _SH EL
type,E _SH E L
r e a l , f l o o r
a s e l , s , a r e a , ,383
a s e l , a , a r e a , ,437
a s e l , a , a r e a , ,452
a s e l , a , a r e a , ,4 7 3
a s e l , a , a r e a , ,478
a s e l , a , a r e a , ,484
a s e l , a , a r e a , ,4 8 9
a s e l , a , a r e a , ,4 9 4 ,5 0 8
am e sh ,a l l
/COM* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
/COM
***
M esh
beams
***
/COM* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
/COM
/CO M ***
C olum ns
***
/COM
m a t , M B E AM
t y p e ,EBEAM
re a l,re 2 4 x 2 4
l s e l , s , l i n e , ,4 5 2 ,4 5 3
138
l s e l , a , l i n e , , 458,460
l s e l , a , l i n e , , 472,473
l s e l , a , l i n e , , 555
l s e l , a , l i n e , , 566
l s e l , a , l i n e , , 710
l s e l , a , l i n e , , 716,718
l s e l , a , l i n e , , 724
l s e l , a , l i n e , , 7 28,730
l s e l , a , l i n e , , 736
l s e l , a , l i n e , , 7 55,769
lm e s h ,a ll
/COM
/COM
***
back
beams
/COM
re a l,re 2 0 x 4 8
l s e l , s , l i n e , , 570,572
l s e l , a , l i n e , , 577
l s e l , a , l i n e , , 737,738
l s e l , a , l i n e , , 744,745
l s e l , a , l i n e , , 770,773
lm e s h ,a ll
/COM
/COM
***
f r o n t
beams
/COM
r e a l,r e 3 6 x 6 0
l s e l , s , l i n e , ,, 7 5 3 , 7 5 4
lm e s h ,a ll
r e a l ,r e l8 x 3 6
l s e l , s , l i n e , ,7 8 4 ,7 8 7
lm e s h ,a l l
r e a l,r e ! 8 x 4 8
l s e l , s , l i n e , , 708,709
lm e s h ,a ll
/COM
/COM
***
s id e
beam s
***
/COM
re a l,r e 2 2 x 5 0
l s e l , s , l i n e , , 578
l s e l , a , l i n e , , 658
l s e l , a , l i n e , , 678
l s e l , a , l i n e , , 657
l s e l , a , l i n e , ,
l s e l , a , l i n e , ,
795
i
lm e s h ,a ll
r e a l,r e l8 x 4 8
l s e l , s , l i n e , , 677
l s e l , a , l i n e , , 704
lm e s h ,a ll
r e a l ,r e l2 x 3 6
l s e l , s , l i n e , ,746
l s e l , a , l i n e , ,7 5 0 ,7 5 2
*********************************
139
l s e l , a , l i n e , ,774
l s e l , a , l i n e , , 7 7 8 , 7 7 9
l s e l , a , l i n e , ,7 8 3
lm e s h ,a l l
/COM
/COM
***
f lo o r
j o i s t s
***
/COM
re a l,re 4 8 x 2 0
l s e l , s , l i n e , ,6 4 1
l s e l , a , l i n e , ,6 5 2
l s e l , a , l i n e , ,656
l s e l , a , l i n e , ,7 4 7 ,7 4 9
l s e l , a , l i n e , ,7 7 5 ,7 7 7
l s e l , a , l i n e , ,7 8 0 ,7 8 2
lm e s h ,a ll
a l l s e l , a l l
num m rg, n o d e , 2 .9 5
n s e l , s , l o c , y , 0
d , a l l , a l l
n s e l , s , l o c , z , 858
n s e l , r , l o c , x , 468,492
s f , a l l , p r e s s , p r e s _ z
/C O M *****
F lo o r
Loads
n s e l , s , l o c , x , 0
n s e l , r , l o c , y , 468
n s e l , r , l o c , z , 0
f , a l l , f y , -226000
n s e l , s , l o c , x , 240
n s e l , r , l o c , y , 468
n s e l , r , l o c , z , 0
f , a l l , f y , -433000
n s e l , s , l o c , x , 480
n s e l , r , l o c , y , 468
n s e l , r , l o c , z , 0
f , a l l , f y , -216500
n s e l , s , l o c , x , 0
n s e l , r , l o c , y, 468
n s e l , r , l o c , z , 420
f , a l l , f y , -342000
n s e l , s , l o c , x , 240
n s e l , r , l o c , y , 468
n s e l , r , l o c , z , 420
f , a l l , f y , -671000
n s e l , s , l o c , x , 480
n s e l , r , l o c , y , 468
n s e l , r , l o c , z , 420
f , a l l , f y , -335500
n s e l , s , l o c , x , 0
n s e l , r , l o c , y , 4 68
n s e l , r , l o c , z , 840
f , a l l , f y , -217000
***
140
n s e l , s , l o c , x , 240
n s e l , r , l o c , y , 468
n s e l , r , l o c , z , 840
f , a l l , f y , -420000
n s e l , s , l o c , x , 480
n s e l , r , l o c , y , 468
n s e l , r , l o c , z , 840
f , a l l , f y , -210000
a l l s e l , a l l
/COM* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
/COM
*** S ym m etry ***
/COM* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
m odm esh,n o ch eck
n s e l , s , l o c , x , 481,960
e s l n , s , , a l l
e d e l e ,a l l
n d e l e ,a l l
n s e l , s , l o c , x , 480
dsym m ,sym m ,x
a l l s e l , a l l
n s e l , s , l o c , z , 0
!
M odify
colum ns
!
M odify
beams
on
sym m etry
p la n e
n s e l , r , l o c , x , 480
e s l n , s , I , a l l
e m o d if, a ll,r e a l,s y m m _ c
n s e l , s , l o c , z , 420
n s e l , r , l o c , x , 480
n s e l , r , l o c , y , 336,468
e s l n , s , I , a l l
e m o d if, a ll,re a l,s y m m _ c
n s e l , s , l o c , z , 840
n s e l , r , l o c , x , 480
n s e l , r , l o c , y , 3 3 6 , 4 68
e s l n , s , I , a l l
em odif, a ll,re a l,s y m m _ c
n s e l , s , l o c , y , 468
on
sym m etry
p la n e
n s e l , r , l o c , x , 480
e s l n , s , I , a l l
e m o d if,a ll,re a l,s y m m _ b
n s e l , s , l o c , x , 480
n s e l , r , l o c , y , 292
n s e l , r , l o c , z , 0,4 0 2
e s l n , s , I , a l l
e m o d if, a l l , r e a l , sym m b
n s e l , s , l o c , x , 480
n s e l , r , l o c , y , 136
n s e l , r , l o c , z , 0,4 0 2
e s l n , s , I , a l l
e m o d if,a ll,re a l,s y m m _ b
a l l s e l , a l l
/COM* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
/COM
*** S o lu ti o n
***
/COM* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
/SOLUTION
lo u t p r ,a l l , I
!
To
o u tp u t
f i l e ( . o u t ) ,
a l l
r e s u l t s ,
LS
fre q .
141
!o u t r e s , a l l , I
!save
!
To
r e s u l t
f i e l ( . r s t ) ,
!
Save
to
D ata b ase
!
Save
to
D atabase
! SOLVE
!save
I a l l s e l , a l l
!e p lo t
/COM
**************
/COM
/COM
*** F i n i s h
***
**************
f in i s h
!/d e v ic e ,v e c to r ,o n
!/e s h a p e ,I
/EOF
<«
a l l
r e s u l t s ,
LS
fre q .
142
PSEUDO-MURRAH NIKE INPUT FILE
(Nodal location and element data omitted)
p su e d o -m u rra h
*
N ike3D
*
$ I d :
(Beam ,
in p u t
S h e ll
2nd
Wed
C ard
C o n tro l
#nodes
FL
101405
*
*
*
3 rd
*
# t
E lem ents)
2 1 :5 7 :5 1
ladeanm
N ode/E lem ent
-
# b riq
#beam
Es
.
*
# sh e l
-
Tim e
S tep
Specs
d t
TSF
ATSC
# i t r
30
I. 00E-01
C ard
0
E s#lD SL
*
*
#
#w
s i
*
*
0
0
0
*
*
*
*
*
*
*
d t
RATL
0
10
max
d t
0.0 0 1
*
*
*
0
*
*
*
*
*
*
*
4 th
C o n tro l
-
Load
Specs
*
# lc
m lcp
# c l
#dl
#dBC
#ADL
#NCC
BAFx
BAFy
BAFz
AVFx
AVFy
AVFz
NSBC
NFBC
2
10
9
118
0
0
0
0
I
0
0
0
0
0
0
*
*
*
*
MAug
IGPF
C ard
*
*
C o n tro l
C ard
F i l e / P r i n t
-
*
5 th
*
P r .F r e q .|- # t - H i s t o r y
P r in t
— >
F lag s
* o frq
p d fq
node
b r iq
beam
s h e l
# s rr
# s r f
ShDF
ISST
AcDF
-5
I
0
0
0
0
0
0
I
3
I
*
*
*
6th
*
C ard
C o n tro l
S o lu tio n
-
*
Specs
B lo c k s - I—
*
0
*
*
*
l s t o l
BWMF
#tsR
# tsE
M#ER
M#Ts
d to l
e to l
r t o l
I
I
I
I
10
15
a1 . 0 0 1
0.01
1E+10
*
*
C ard
C o n tro l
7th
IV F
ITE f
IP IF
#Eig
I
0
★
0
0
0
*
C o n tro l
s h f t
N IntP arm l
0
0 .5
8 th
E -fo rm u la tio n s
*
Mem
E _ b u ff
DDES
BFGS
BqEF
BqSF
ShEF
0
0
I
I
10
I
10
*
*
*
*
9 th
*
C o n tro l
* #ULS
SlnM
*
*
*
10 th
*LESO
C o n tro l
*
0.0 0 1 0
*
C o n tro l
*
C ard
TargSR
*
-
Specs
0
0
*
*
Specs
DSOp
*
*
e
*
*
BmEF
BmSF
0 .25
*
ShSF
*
0
*
1
*
*
*
*
*
#BIP
*
#SIR
#SIP
*
*
*
*
*
*
*
(C ont.)
1
*
-
*
1
*
S o lu tio n
*
SPF
M inSR
*
a p p ro x .
HGCP
*
#BIR
LBuf PrOp
0
*
(C ont.)
ALDO
*
C ard
0
I l t h
*
*
DynaSD' S
*
ACCM
0
*
(C ont.)
m atch
*
S o lu tio n
I te r C to l
*
Specs
*
A rcL
1
*
ILLS
*
-
A rcC
0
*
0
*
C ard
N#DC
1
S o lu tio n
(BqEFsShEF=IO )
0.9
*
*
N IntParm 2
*
*
*
-
*
*
( C o n t .)
Specs
f
*
*
C ard
*
S o lu tio n
-
eAnTy
*
*
Specs
e NESM
*
2000
DEIF#RN&F
ssp
0
m in
11
*
*
*
32946
*
s te p s
C o n tro l
M ST
0 8 :4 9 :0 0
ladeanm $
lk**************
Specs
Es
1892
12804
8
Mar
Exp
*
*
*
*F#mt
24
S o lid
1.1..1 .1 9 I 2 0 0 0 /0 2 /2 3
a n s 2 1 1 n l,v
e
*
and
deck
*
C o n tro l
*
*
*
*
*
*
*
MaxP
CoLC
CoM#
*
*
[cc>3:9]
MaxSR
P C _ti
Ramp_t
Top%El
1 1
********************************************************************************
*
M a te r ia l
S p e c i f ic a t io n s
[p g .4 -1 ,
c c > 2 :2]
********************************************************************************
*
M a te r ia l
I
*
In
m odel
*
ID#
*
ANSYS
1
*
=>
type= 2,
m typ
m ass_dens
3
0.0002488
*
*
*
m at= 2,
E typ
*
0
T re f
*
0 .0
*
r e a l= l
R D _alpha
*
0 .0
*
R D b e ta
*
0 .0
*
*
*
*
*
*
143
S e t
I:
=>
B i a s t i c - I s o t r o p i c
4.07E + 06
0.1 7 2
4589
9 . 7e+05
0.5
*
M a te ria l
2
*
In
m odel
*
ID#
m typ
2
3
S e t
ANSYS
2:
=>
=>
ty p e = I,
m at= l,
:
RD
b e ta
dens
E typ
T re f
R D _alpha
0.0002488
0
0.0
0.0
0.0
R D _alpha
b e ta
0.0
0.0
m ass
E la s t i c - I s o t r o p i c
3.6E +06
0.17
4000
9 . 7e05
0 .5
3
In
m odel
*
ID#
m typ
3
3
S e t
ANSYS
3:
m ass
=>
type= 6.
dens
E typ
0.0002488
0
m a t= 6,
T re f
O
M a te ria l
O
*
*
E la s t i c - I s o t r o p i c
=>
4 . 02E+06
0.1 7 2
4530
0 .5
9 . 7e05
M a te ria l
4
In
m odel
ANSYS
=>
ty p e = 7 ,
m at=7,
re a l= l
ID#
m typ
m ass_dens
E typ
T re f
R D _alpha
4
3
0.0002488
0
0.0
0.0
S et
4:
=>
RD
b e ta
0.0
E l a s t i c - I s o t r o p i c
3.88E + 06
0.1 7 1
4350
9 . 7e05
0 .5
*
*
M a te ria l
5
*
In
m odel
*
ID#
m typ
5
3
ANSYS
=>
type= 5,
m at= 5,
dens
E typ
T re f
0.0002488
0
0.0
m ass
I
RD
b e ta
0.0
0.0
*
S et
5:
=>
E la s t i c - I s o t r o p i c
4.44E + 06
0.1 7 4
5060
9 . 7e05
0 .5
*
*
M a te ria l
6
*
In
m odel
*
ID#
m typ
6
3
ANSYS
*
S et
6:
=>
=>
Inat=IO l
r e a l= l
E typ
T re f
R D _alpha
0.0002488
*
*
0
*
0 .0
0.0
E la s t i c - I s o t r o p i c
3.77E + 06
0 .17
4216
9 . 7e05
type= 10 ,
den s
m ass
0 .5
RD
b e ta
0.0
144
*
*
*
*
7
*
In
m odel
*
ID#
m typ
7
3
ANSYS
S et
7:
=>
=>
type= 9,
m at= 9,
dens
E typ
T re f
0.0002488
0
0 .0
m ass
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
r e a l= l
RD
RD_ b e t a
a lp h a
0 .0
O
M a te ria l
O
*
E la s t i c - I s o tto p i c
3.88E + 06
0.1 7 1
4350
9 . 7e05
0 .5
M a te ria l
8
In
m odel
ANSYS
=>
ty p e = 4 ,
m at= 4,
re a l= l
RD
b e ta
ID#
m typ
m ass_dens
E typ
T re f
R D _alpha
8
3
0.0002488
0
0.0
0.0
0.0
J b e ta
S et
8:
=>
E la s t i c - I s o t r o p i c
4.7E + 06
0.1 7 8
5380
9 . 8e05
0 .5
M a te r ia l
9
In
m odel
ANSYS
=>
ty p e= 3 ,
m at= 3,
re a l= l
ID#
m typ
m ass_dens
E typ
T re f
R D _alpha
9
3
0.0002488
0
0.0
0.0
S et
9:
=>
"
0.0
E l a s t i c - I s o t r o p i c
4.3E + 06
0.174
4883
9 . 8e05
0 .5
*
*
M a te ria l
10
*
In
m odel
*
ID#
m typ
10
3
ANSYS
S e t
10:
=>
=>
ty p e= 1 2 ,
m at= 12,
dens
E typ
T re f
0.0002488
0
0 .0
m ass
*
r e a l= l
RD
RD_ b e t a
a lp h a
0 .0
0 .0
*
*
*
*
*
*
*
*
*
*
*
*
*
*
RD
b e ta
*
*
*
*
*
E l a s t i c - I s o t r o p i c
3.74E + 06
0.17
4179
0 .5
9 . 7e05
*
M a te ria l
11
*
In
m odel
*
ID#
m typ
11
3
S et
ANSYS
11:
=>
=>
ty p e = ll,
m a t= !!.
dens
E typ
T re f
0.0002488
0
0 .0
m ass
re a l= l
RD
a lp h a
0 .0
0 .0
*
*
RD
b e ta
E la s t i c - I s o tr o p ic
3.83E + 06
0.1 7 1
4290
0 .5
9.7 e0 5
*
*
*
*
*
M a te ria l
12
*
In
m odel
*
ID#
m typ
m a s s d e n s
E typ
T re f
12
3
0.0002488
0
0 .0
ANSYS
=>
type= 8.
m at= 8,
*
*
re a l= l
RD
a lp h a
0 .0
0 .0
145
S et
12:
=>
B i a s t i c - I s o t r o p i c
4 . 86E+06
0.1 7 6
5590
9 .7 e0 5
0 .5
M a te r ia l
13
In
m odel
ANSYS
=>
type= 13,
ID#
m typ
m ass_dens
E typ
13
I
0.000435
2
S e t
13:
=>
m at= 13,
re a l= 9
T re f
RD
R D _alpha
0 .0
b e ta
0.0
0 .0
E la s t i c - I s o t r o p i c
3.6E + 06
0 .17
S et
13:
S h e ll
X -s e c tio n
6.00
*
M a te ria l
14
*
In
m odel
*
ID#
m typ
14
20
ANSYS
S et
14:
p a r a m e te r s :
3
0
6 .00
6. 00
6.00
=>
ty p e = 1 4 ,
m at= 14,
dens
E typ
T re f
0.0 0 0 4 3 5
2
0 .0
m ass
=>
(re a l)
2
O
H*
*
H ughes-L iu
0 .0
0 .0
r e a l = l l
RD
a lp h a
RD
b e ta
0 .0
0 .0
E la s t i c - I s o t r o p i c
3.6E + 06
0 .17
*
S et
14:
S h e ll
X -s e c tio n
1 .0
6.00
6.00
M a te r ia l
15
In
m odel
*
ID#
m typ
m a s s d e n s
E typ
15
3
0.000248
I
S et
15:
=>
type= 15,
H ughes-L iu
0
6.00
*
=>
p a r a m e te r s :
3
*
ANSYS
(re a l)
2
6.00
m at= 15,
re a l= 1 0
T re f
R D a lp h a
0 .0
0.0
0.0
R D b e ta
0.0
0 .0
E la s t i c - I s o t r o p i c
3.6E + 06
0.17
4000
9 . 7e05
*
S et
15:
0 .5
Beam
X -s e c tio n
0 .833
(re a l)
2 .0
24
24
24
*
M a te ria l
16
*
In
m odel
*
ID#
m typ
m a s s d e n s
E typ
16
3
0.000248
I
S et
ANSYS
16:
=>
=>
0 .17
4000
9 . 7e05
ty p e= 1 5 ,
E la s t i c - I s o t r o p i c
3.6E + 06
0 .5
p a ra m e te rs:
H ughes-L iu
0 .0
24
m at= 15,
real= 1 4
T re f
R D _alpha
0 .0
0.0
0 .0
0 .0
RD
b e ta
0.0
146
*
*
*
S et
16:
IB e a m
*
0.8 3 3
2 .0
12
12
*
*
*
*
*
In
*
ID#
m typ
17
3
m odel
ANSYS
m ass
*
17:
*
(re a l)
*
p a r a m e te r s :
*
*
*
*
*
0 .0
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
H ughes-L iu
0 .0
24
*
*
24
0 .0
*
17
M a te ria l
S et
*
X -s e c tio n
=>
=>
type= 15,
m at= 15.
E typ
T re f
0 .000248
*
*
I
*
0 .0
*
*
re al= 1 2
RD
dens
a lp h a
RD
b e ta
0 .0
0 .0
E l a s t i c - I s o t r o p i c
3 . 6E+06
0.17
4000
9 . 7e05
0 .5
*
*
*
S et
17:
Beam
X - s e c tio n
(re a l)
0 .0
20
48
*
*
*
M a te ria l
18
*
In
m odel
*
ID#
m typ
18
3
ANSYS
m ass
=>
m at= 15,
ty p e= 1 5 .
E typ
T re f
0.000248
I
0 .0
*
*
18:
=>
0 .0
re a l= 5
RD
den s
*
S e t
48
*
O
2 .0
20
H ughes-L iu
O
0.8 3 3
*
p a ra m e te rs :
a lp h a
RD
b e ta
0 .0
0.0
E la s t i c - I s o t r o p i c
3.6E + 06
0 .17
4000
0 .5
9 . 7e05
*
*
*
S et
18:
(re a l)
0.8 3 3
2 .0
0.0
36
36
60
*
*
*
X- s e c t i o n
Beam
*
*
M a te ria l
19
*
In
m odel
*
ID#
m typ
19
3
ANSYS
*
S et
19:
=>
=>
type= 15,
*
*
p a r a m e te r s :
m at= 15.
60
*
*
0.0
*
0 .0
*
*
b e ta
r e a l- 4
dens
E typ
T re f
R D _alpha
RD
0 .000248
*
I
0 .0
*
0 .0
*
*
m ass
*
H u g h es--Liu
*
0.0
*
E la s t i c - I s o t r o p i c
3.6E + 06
0.17
4000
0 .5
9 . 7e05
*
*
*
S et
19:
Beam
X -s e c tio n
(re a l)
0.8 3 3
2 .0
0 .0
18
18
36
*
*
*
M a te ria l
20
*
In
m odel
*
ID#
m typ
20
3
ANSYS
m ass
=>
type= 15,
dens
E typ
0.000248
I
*
S e t
=>
H ughes-L iu
0.0
0 .0
36
*
m at= 15,
T re f
*
20:
*
p a r a m e te r s :
0 .0
*
r e a l- 6
RD
a lp h a
0 .0
RD
b e ta
0 .0
E la s t i c - 1s o tr o p ic
3.6E + 06
0 .17
4000
9.7 e0 5
0 .5
* Set 20: Beam X-section (real) parameters: Hughes-Liu
147
O
*
*
*
*
In
ID#
m typ
21
3
m odel
ANSYS
type= 15 ,
=>
m at-15,
E typ
T re f
0.000248
I
0 .0
*
*
*
=>
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
r e a l - 7
RD
dens
m ass
RD_ b e t a
a lp h a
°
*
*
21:
*
21
M a te ria l
S et
*
O
*
48
*
*
O
48
*
*
O
18
O
2 .0
18
O
0.8 3 3
0 .0
*
B i a s t i c - I s o t r o p i c
3.6E + 06
0 .17
4000
9 .7 e0 5
0 .5
*
*
*
S et
21:
*
Beam
*
*
*
M a te ria l
22
*
In
m odel
*
ID#
m typ
22
3
ANSYS
*
H ughes-L iu
=>
ty p e -1 5 ,
0 .0
0 .0
50
50
*
*
*
m at-15,
E typ
T re f
0.000248
*
*
I
*
0 .0
*
*
r e a l - 8
RD
d en s
m ass
*
*
p a r a m e te r s :
0 .0
22
*
22
22:
*
(re a l)
2 .0
0.8 3 3
S e t
*
X -s e c tio n
RD
a lp h a
b e ta
0 .0
0 .0
E la s t i c - I s o t r o p i c
=>
3.6E + 06
0 .17
4000
0 .5
9 . 7e05
*
*
*
S e t
22:
*
X- s e c t i o n
Beam
(re a l)
0 .833
2 .0
0 .0
18
18
56
*
*
*
*
*
In
*
ID#
m typ
23
3
=>
m odel
ANSYS
*
H ughes-L iu
0.0
0 .0
56
*
*
*
=>
m at-15,
ty p e -1 5 .
r e a l - 3
RD
dens
E typ
T re f
R D _alpha
0.000248
*
I
0.0
*
0 .0
*
m ass
*
23:
*
23
M a te ria l
S et
*
p a r a m e te r s :
*
*
b e ta
0 .0
E l a s t i c - I s o t r o p i c
3.6E + 06
0 .17
4000
9.7 e0 5
0 .5
*
*
*
S et
23:
Beam
*
0.8 3 3
2 .0
48
48
*
★
*
*
M a te ria l
24
*
In
m odel
*
ID#
m typ
24
3
ANSYS
*
S e t
24:
=>
*
X -s e c tio n
=>
*
(re a l)
*
p a ra m e te rs :
0 .0
ty p e -1 5 ,
*
m at-15,
E typ
T re f
0 .000248
*
*
I
*
0 .0
*
*
0.0
0 .0
20
20
*
*
dens
m ass
H ughes-L iu
*
*
*
*
r e a l- 1 3
RD
RD
a lp h a
b e ta
0 .0
0 .0
E la s t i c - I s o t r o p i c
3 . 6E+06
0 .17
4000
0 .5
9 . 7e05
*
*
*
s e t
*
24:
*
Beam
0 .8 3 3
*
*
*
*
*
*
*
p a ra m e te rs :
*
H ughes-L iu
0 .0
24
*
*
(re a l)
2 .0
24
*
*
X -s e c tio n
20
*
*
20
0.0
0.0
148
***************************************
[p g .4 -4 7 ,
* Node S p e c i f i c a t i o n s
*******************************
cc> 2:3]
NODE AND ELEMENT DATA HERE
********************************************************************************
*
Load
[p g .4 -7 3 ,
C urve
c c > 4 :1]
*******************************************
* lcID
n p ts
I
3
*
lo a d _ s f
tim e
0
I
I
0
I
3
* lc ID
n p ts
2
5
*
l o a d s f
tim e
0
0
6
0
0
0
I
1.0 0 5
1.01
3
*
C o n c e n tra te d
*N odeID #
75741
75742
75812
75852
78652
78692
87172
87242
90042
*
do f
2
2
2
2
2
2
2
2
2
D is tr ib u t e d
*lcID
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
Loads
IcX D
[p g .4 -7 4 ,
cc>4:3]
[p g .4 -7 6 ,
c c > 4 :4]
I c s f
I
- 2 . 26e+05
I
- 3 . 42e+05
I
- 6 . 71e+05
I
- 4 . 33e+05
1 - 3 .355e+05
1 - 2 .165e+05
I
- 2 . 17e+05
I
- 4 . 2e+05
I
- 2 . le+05
Loads
nodi
nod2
nod3
nod4
5122
5129
5303
5157
5129
5130
5320
5303
5157
5303
5304
5158
5303
5320
5321
5304
5158
5304
5305
5159
5304
5321
5322
5305
5159
5305
5306
5160
5305
5322
5323
5306
5160
5306
5307
5161
5306
5323
5324
5307
5161
5307
5308
5162
5307
5324
5325
5308
5162
5308
5309
5163
5308
5325
5326
5309
5164
5163
5309
5310
5309
5326
5327
5310
5164
5310
5311
5165
5310
5327
5328
5311
5165
5311
5312
5166
5311
5328
5329
5312
5166
5312
5313
5167
5312
5329
5330
5313
5167
5313
5314
5168
5313
5330
5331
5314
5168
5314
5315
5169
5314
5331
5332
5315
Ic
S fl
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
I c
s f 2
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
Ic
s f 3
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
Ic
sf4
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
149
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
"2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
5169
5315
5316
5170
5315
5332
5333
5316
5170
5316
5317
5171
5316
5333
5334
5317
5172
5171
5317
5318
5317
5334
5335
5318
5172
5318
5319
5173
5318
5335
5336
5319
5173
5319
5300
5156
5319
5336
5301
5300
5156
5300
5829
5787
5300
5301
5833
5829
5787
5829
5830
5788
5829
5833
5834
5830
5788
5830
5831
5789
5830
5834
5835
5831
5789
5831
5832
5790
5831
5835
5836
5832
5790
5832
5826
5786
5832
5836
5827
5826
5786
5826
5996
5962
5826
5827
5999
5996
5962
5996
5997
5963
5996
5999
6000
5997
5963
5997
5998
5964
5997
6000
6001
5998
5964
5998
5993
5961
5998
6001
5994
5993
5961
5993
14467
14337
14467
5993
5994
14482
14337
14467
14468
14338
14467
14482
14483
14468
14338
14468
14469
14339
14468
14483
14484
14469
14339
14469
14470
14340
14469
14484
14485
14470
14340
14470
14471
14341
14470
14485
14486
14471
14341
14471
14472
14342
14471
14486
14487
14472
14342
14472
14473
14343
14472
14487
14488
14473
14343
14473
14474
14344
14473
14488
14489
14474
14344
14474
14475
14345
14474
14489
14490
14475
14345
14475
14476
14346
14475
14490
14491
14476
14346
14476
14477
14347
14476
14491
14492
14477
14347
14477
14478
14348
14477
14492
14493
14478
14348
14478
14479
14349
14478
14493
14494
14479
14349
14479
14480
14350
14479
14494
14495
14480
14351
14350
14480
14481
14480
14495
14496
14481
14351
14481
14464
14336
14481
14496
14465
14464
14336
14464
23764
23664
14464
14465
23770
23764
23664
23764
23765
23663
23764
23770
23771
23765
23663
23765
23766
23662
23765
23771
23772
23766
23662
23766
23767
23661
23766
23772
23773
23767
23661
23767
23768
23660
23767
23773
23774
23768
23660
23768
23769
23659
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000 /
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
150
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
23768
23774
23775
23769
23659
23769
23761
23658
23769
23775
23762
23761
23658
23761
24111
24059
23761
23762
24114
24111
24059
24111
24112
24058
24111
24114
24115
24112
24058
24112
24113
24057
24112
24115
24116
24113
24057
24113
24108
24056
24113
24116
24109
24108
24056
24108
27071
27037
24108
24109
27074
27071
27037
27071
27072
27038
27071
27074
27075
27072
27038
27072
27073
27039
27072
27075
27076
27073
27039
27073
27068
27036
27073
27076
27069
27068
27069
27068
27068
27036
0
0
D isp la c e m e n t
*N odeID #
*
Base
* lcID
d o f
* * *
End
Ic
IcID
Sf
386
In p u t
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
0
0
1000
1000
1000
T ooo
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
0
0
(N ike3D )
***
c c > 4 :4]
SIF
[p g .4 -7 9 ,
a c c e l_ s f
o f
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
[p g .4 -7 8 ,
B C s
A c c e le r a tio n s
I
0
0
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
c c > 4 :7->9]
151
PSEUDO-MURRAH DYNA INPUT FILE
(Nodal location and element data omitted)
p su ed o -m u rrah
*
DynaSD
(Beam ,
S h e ll
and
deck
[ p g .61-
)
in p u t
* $ I d : a n s 2 1 1 n l,v 1 .1 .1 .2 0
**************************
S o lid
in p u t
2 0 0 0 /0 3 /2 0
2 1 :1 9 :4 8
*
*
2nd
C o n tro l
If n o d e s
24
101405
3rd
*
#
C o n tro l
Tim e
*
5 th
*
#Ic
B ff
0
*
o u t
d t
sf
0 .0 1
I
*
*
*
*
*
*
F l a g s — I SAND
Ip p f
ED /f
0
I
0
100
*
‘
*
c so
Ncf
ncsd
0E 20.0
0
NRBC
d t
ATBf
CVS
0
0
0
Itnc
IC f
Itsi
x b af
ybaf
zb a f
xbvf
ybvf
zb v f
ft E m d
Itdp
0
0
0
0
0
0
I
0
0
0
0
0
0
d t
s i
p s s f
te o
IRQ
SCFT
0
0
C ard
h i s t
-
p l o t
Specs
i n i t
d t
rd n
rrd n
1.0E -02
0
0
lp f
rbw i
s s o f
HLuo
StCO
0
0
0
0
m nip
ib c c
0 .0
0 .0
0
d s e f
n rb s
,
C ard
s s e i
t b s l
0
0
0
*
*
*
tnw f
m
d t
0
0
s b i r
m nip
0
0
0
*
*
*
SC ft
ts s b
C ard
r f i n i t
d t
s s i r
d r f
C to l
*
C o n tro l
#cs
Specs
T im e /H isto ry
d t
1.0E -02
C o n tro l
*
C ard
d tp f
0
0
*
0
116
0
IHQ
ItIFS
0
9
0
10th
Es
ttrw
ttcs
*
Es
*
Load
rb en
*
tttsh l
*
-
C ard
C o n tro l
9 th
*
ttv/a
*dofc
*
*
# d l
C o n tro l
*pspa
*
ttcl
C o n tro l
8t h
*
C ard
0
0
*
0
0
Itdp
7 th
*
32946
r f p f
srT
0
* rb jd
Itshel
Es
- I- P r i n t
t s h l
0
‘ k i l l . tim e
3 .0
*
B locks
s h e l
ttfsp
6t h
la d e a n m Exp $
**********************************
*
1892
ftsbp
2
*
la rg e
la rg e
C ard
0
C o n tro l
4 th
‘ n u ll
Itbeam
Es
12804
beam
0
0
*
Itbriq
H is to r y
b r ig
‘ node
fo rm a t
C ard
*#mat
*
88
->88
E lem ents)
C o n tro l
damp
Rdca
d rd f
0
m rot
mbdf
0
C ard
QH
[ I f
IRQ
( c c 6 :9)
qbvc
IBQ
*
ir
*
*
*
*
*
*
*
*
*
= 1]
Ibvc
*
*
*
.
k***************
*
K eyw ord
C o n tro l
C ards
[ p g .72]
********************************************************************************
*
F l a g - > i n i t i a l i r a t i o n
*
o=>(0),
i r e s t t
1= > ( u s e
r e s t a r t
tim e
tim e :
from
i r e s t t =
m = in i_ f ile ) ,
2= > { i n c _ d t )
I
n i k e f i l e
d 3 s tr
e n d fre e
********************************************************************************
*
M a te r ia l
S p e c i f ic a t io n s
[p g .8 9 ,
c c > 2 :3]
********************************************************************************
152
*
M a te ria l
S et
*
In
m odel
*
ID#
m typ
I
13
ANSYS
S et
I:
ETyp
=>
m ass
=
B ric k
m at= 2 ,
type= 2,
dens
r e a l= l
IHQ
e q s t
QH
IBQ
qbvc-Q l
lbvc-Q 2
E typ
g ra v
Efrm
0
4
0.0002488
=>
3
***
I,
0
E la s t i c - I s o t r o p i c
*****
sigm a_o
**
E_T
***
e p s ilo n
**
f a i l
p re s s
fo r
re b a r
(te n sio n )
I . 74E+06
4589
9.7e+ 05
0 .04
-5031
***
************************************************************************
**
2 . 06e+06
f
s t f d i n
*
f a i l
I
*
*
*
*
M a te ria l
*
In
*
ID#
*
S et
*
2,
=>
m ass
13
*
*
ETyp
m odel
m typ
2:
*
S et
ANSYS
2
*
pirsss
*
=
*
*
B ric k
ty p e = l,
dens
m at= l,
e q s t
0.0002488
*
*
=>
***************************************************
I
r e a l= l
IHQ
IBQ
QH
lbvc-Q 2
qbvc-Q l
*
*
g ra v
E typ
Efrm
0
4
*
0
*
E la s t i c - I s o t r o p i c
1.5E + 06
4000
9 . 7e05
-4000
0.04
1.8E +06
I
*
*
*
I
*
*
*
M a te ria l
S et
*
In
m odel
*
ID#
ANSYS
m typ
3
*
*
S et
*
ETyp
dens
*
*
B ric k
m at= 6,
e q s t
0.000 2 4 8 8
*
*
=>
*
=
ty p e = 6,
=>
m ass
13
*
3:
3,
r e a l= l
IHQ
IBQ
QH
lbvc-Q 2
qbvc-Q l
E typ
*
*
g ra v
Efrm
0
0
4
*
*
E la s t i c - I s o t r o p i c
I . 72E+06
4530
9.7 e0 5
4928
0 .04
2 . 04e+06
I
*
*
I
*
*
*
*
M a te ria l
S et
*
In
m odel
*
ID#
m typ
4
13
S et
ANSYS
4:
4,
=>
m ass
*
ETyp
=
*
ty p e = ? ,
dens
e q s t
*
m at= ?,
*
*
*
*
*
*
re a l= l
IBQ
QH
IHQ
0.0002488
=>
*
B ric k
lbvc-Q 2
qbvc-Q l
E typ
g ra v
Efrm
0
0
4
E la s t i c - I s o t r o p i c
I . 66E+06
4350
-4613
0.04
9.7e05
I . 97e+06
I
*
*
*
I
*
*
M a te ria l
*
In
*
ID#
m typ
5
13
S et
S e t
ANSYS
5:
*
5,
m odel
m ass
*
ETyp
=>
*
=
type= 5,
dens
*
e q s t
m at=5,
*
*
r e a l= l
QH
IHQ
0.0002488
=>
*
B ric k
IBQ
lbvc-Q 2
qbvc-Q l
E typ
0
4
g ra v
Efrm
0
B ia s t i c - I s o t r o p i c
1.89E + 06
5060
0.04
9.7e05
-5856
2.26E + 06
1
I
*
*
*
*
*
*
6,
M a te ria l
S e t
*
In
m odel
*
ID#
ANSYS
m typ
*
ETyp
=>
m ass_dens
=
*
ty p e= 1 0 ,
e q s t
*
*
*
*
*
*
*
*
*
*
B ric k
m at= 10,
IHQ
r e a l= l
QH
IBQ
qbvc-Q l
lbvc-Q 2
E typ
g ra v
Efrm
153
6
13
6:
S et
0.000 2 4 8 8
=>
4
B i a s t i c - I s o t r o p i c
4216
I . 61E+06
9 . 7e05
-4362
0.04
I . 90E+06
I
I
*
M a te ria l
S e t
*
In
m odel
*
ID#
m typ
7
13
ANSYS
S et
7:
7,
ETyp
=>
m ass
=
ty p e= 9 ,
dens
=>
m at=9,
e q s t
0.000 2 4 8 8
*
*
*
*
*
E typ
g rav
Efrm
B ric k
r e a l= l
IHQ
QH
IBQ
qbvc-Q l
lbvc-Q 2
*
0
0
4
*
*
*
*
*
*
*
*
*
E typ
g ra v
Efrm
E la s t i c - I s o t r o p i c
4350
I . 66E+06
9 . 7e05
-4613
0.04
I . 97E+06
I
I
8,
*
M a te r ia l
S et
*
In
m odel
*
ID#
m typ
8
13
ANSYS
8 :
S e t
ETyp
=>
m ass
=
B ric k
ty p e = 4 ,
dens
e q s t
m at= 4,
0.000 2 4 8 8
=>
r e a l= l
IHQ
QH
IBQ
qbvc-Q l
lbvc-Q 2
0
4
0
*
*
*
*
*
*
E typ
g ra v
Efrm
E la s t i c - I s o t r o p i c
5380
1.99E + 06
9 . 8e05
-6375
0.04
2.43E + 06
I
I
*
*
*
M a te ria l
S et
*
In
m odel
*
ID#
m typ
9
13
ANSYS
S e t
9:
9,
*
ETyp
=>
m ass
*
=
*
B ric k
ty p e= 3 ,
d en s
m at=3,
e q s t
r e a l= l
IHQ
0.000 2 4 8 8
=>
*
QH
IBQ
qbvc-Q l
lbvc-Q 2
0
0
4
*
*
*
*
*
*
E typ
g rav
Efrm
E la s t i c - I s o t r o p i c
4883
I . 83E+06
9 . 8e05
-5546
0.04
2 . 20e+06
I
I
*
M a te ria l
S e t
*
In
m odel
*
ID#
m typ
10
13
S et
ANSYS
10:
=>
10,
ETyp
m ass
=
B ric k
ty p e = 12,
=>
dens
0.000 2 4 8 8
*
*
e q s t
I
*
*
M a te ria l
S e t
In
m odel
*
ID#
m typ
m a s s d e n s
11
13
0.0002488
=>
E la s t i c - I s o t r o p i c
1.94E + 06
I
*
*
0
*
*
*
E typ
g ra v
Efrm
-4314
0.04
I
*
11:
lbvc-Q 2
0
9.7 e0 5
*
I . 64E+06
qbvc-Q l
4
4179
I . 90E+06
S et
r e a l= l
IBQ
QH
B i a s t i c - I s o t r o p i c
1.60E + 06
ANSYS
m a t= 12,
IHQ
11,
ETyp
=>
=
B ric k
ty p e = ll,
4290
e q s t
m a t= ll,
IHQ
QH
IBQ
qbvc-Q l
4
9.7 e0 5
I
re a l= l
0.04
-4508
lbvc-Q 2
0
0
154
*
M a te ria l
S e t
*
In
m odel
*
ID#
m typ
12
13
0.0002488
=>
E la s t i c - I s o t r o p i c
ANSYS
S et
12:
12,
ETyp
m ass
=
dens
e q s t
m at= 8,
re a l= l
IHQ
IBQ
QH
lbvc-Q 2
qbvc-Q l
E typ
*
9 . 7e05
*
g ra v
O
4
5590
2.07E + 06
B ric k
ty p e = 8,
=>
Efrm
O
*
•6783
0.04
2 . 48e+06
I
I
*
*
*
*
S e t
*
*
M a te r ia l
*
In
*
ID#
m typ
m ass_dens
13
I
0.0 0 0 4 3 5
ANSYS
*
*
S e t
13,
m odel
*
13:
=>
*
ETyp
=>
*
*
=
*
*
*
*
*
*
*
*
*
ty p e= 1 3 ,
e q s t
m at=13,
re a l= 9
IHQ
QH
IBQ
qbvc-Q l
lbvc-Q 2
E typ
4
*
*
S h e ll
*
g ra v
2
*
*
*
*
*
*
*
*
Efrm
1
*
*
*
E l a s t i c - I s o t r o p i c
3.6E + 06
0 .17
*
4000
*
9 . 7e05
*
0 .5
S et
13:
S h e ll
X -s e c tio n
1 .0
6 .0 0
*
*
*
*
M a te r ia l
S e t
In
m odel
*
ID #
m typ
14
20
*
*
*
S e t
14:
=>
14,
*
m ass
=
*
e q s t
0 .0 0 0 4 3 5
*
*
*
m at= 14,
*
g ra v
Efrm
r e a l = l l
IHQ
QH
IBQ
qbvc-Q l
lbvc-Q 2
*
E typ
2
4
*
*
S h e ll
ty p e= 1 4 ,
dens
0 .0
6 .0 0
*
ETyp
->
H ughes-L iu
0
6 .0 0
*
*
p a ra m e te rs:
3
6 .0 0
*
ANSYS
(re a l)
2
*
*
I
*
E l a s t i c - I s o t r o p i c
3.6E + 06
0 .17
*
*
S e t
*
14:
*
S h e ll
*
1 .0
6 .0 0
*
*
*
M a te r ia l
S et
In
m odel
*
ID#
m typ
15
3
*
S e t
15:
=>
m ass
15,
*
*
p a ra m e te rs :
3
*
ETyp
=>
dens
*
0.0002488
*
*
*
Beam
type= 15,
e q s t
0 .0
6 .0 0
*
=
H ughes-L iu
0
6 .0 0
*
*
*
*
2
*
*
*
(re a l)
6 .0 0
*
ANSYS
*
X -s e c tio n
m at= 15,
re al= 1 0
IHQ
QH
IBQ
qbvc-Q l
lbvc-Q 2
*
*
*
*
*
E la s t i c - I s o t r o p i c
3.6E + 06
0 .17
4000
9 . 7e05
0 .5
S et
15:
Beam
1.000
24
X -s e c tio n
(re a l)
2.0
0.0
24
24
E typ
I
0
p a ra m e te rs:
24
H ughes-L iu
0.0
0.0
g ra v
Efrm
I
155
*
S et
15:
Beam
X -s e c tio n
(re a l)
p a r a m e te r s :
B ely tsch k o -S ch w er
1.00
*
*
576
4.23e+ 04
*
M a te ria l
S et
*
In
m odel
*
ID#
m typ
m ass_dens
16
3
0.0002488
ANSYS
S et
16:
=>
16,
4.23e+ 04
ETyp
=>
=
0
0
Beam
ty p e= 1 5 ,
e q s t
m at=15,
IHQ
real= 1 4
QH
qbvc-Q l
IBQ
lb v c -0 2
0
E typ
g ra v
Efrm
E typ
g ra v
Efrm
E typ
g ra v
Efrm
I
I
E la s t i c - I s o t r o p i c
3.6E + 06
0.17
4000
9 . 7e05
0 .5
S et
16:
Beam
X -s e c tio n
1.000
12
*
S et
16:
Beam
1.00
*
288
M a te r ia l
S e t
In
m odel
*
ID#
m typ
m ass_dens
17
3
0.0002488
=>
17,
H ughes-L iu
=
0.0
0 .0
p a ra m e te rs :
2 . 12e+04
ETyp
=>
24
(re a l)
5 .29e+ 03
*
17:
24
X -s e c tio n
*
ANSYS
p a r a m e te r s :
0.0
12
*
S et
(re a l)
2.0
B ely tsch k o -S ch w er
0
0
Beam
ty p e= 1 5 ,
e q s t
m at= 15,
real= 1 2
QH
IHQ
IBQ
qbvc-Q l
lbvc-Q 2
0
I
I
E la s t i c - I s o t r o p i c
3.6E + 06
0 .17
4000
9 . 7e05
0 .5
S e t
17:
Beam
X -s e c tio n
1.000
20
*
S et
17:
Beam
1.00
*
960
M a te ria l
S e t
In
m odel
*
ID#
m typ
18
3
18:
=>
18,
m ass
H ughes-L iu
=
e q s t
0.0002488
*
*
B e ly tsch k o -S ch w er
0
0
Beam
ty p e= 1 5 ,
dens
0.0
0 .0
p a ra m e te rs :
3.71e+ 04
ETyp
=>
48
(re a l)
I . 99e+05
*
ANSYS
48
X -s e c tio n
*
p a ra m e te rs :
0.0
20
*
S et
(re a l)
2.0
m at= 15,
re a l= 5
QH
IHQ
IBQ
qbvc-Q l
lbvc-Q 2
0
*
*
I
I
*
E l a s t i c - I s o t r o p i c
3 . 6E+06
0 .17
4000
9 . 7e05
0 .5
S e t
18:
Beam
X -s e c tio n
1.000
36
*
S et
18:
Beam
*
1.00
*
2 . 16e+03
0.0
36
60
X -s e c tio n
M a te ria l
S e t
*
In
m odel
19,
ETyp
*
ID#
m typ
m ass_dens
19
3
0.0002488
=>
p a ra m e te rs:
B ely tsch k o -S ch w er
0
0*
Beam
type= 15,
e q s t
0.0
0 .0
p a r a m e te r s :
2 . 6e+05
=
H ughes-L iu
60
(re a l)
8 . 38e+05
*
ANSYS
(re a l)
2.0
m at= 15,
IHQ
0
real= 4
QH
IBQ
qbvc-Q l
lbvc-Q 2
E typ
I
g ra v
Efrm
I
156
*
*
S et
*
19:
*
=>
*
*
*
*
*
*
*
*
*
*
*
*
*
B i a s t i c - I s o tr o p ic
3 . 6E+06
0.17
4000
9 . 7e05
0 .5
19:
S et
Beam
S et
36
18
19:
Beam
p a ra m e te rs :
H ughes-L iu
0.0
2.0
18
*
(re a l)
X -s e c tio n
1.000
X -s e c tio n
36
(re a l)
0.0
0 .0
p a ra m e te rs :
B e ly tsc h k o -S c h w e r
1.00
*
*
*
*
648
7 . 89e+04
*
*
*
M a te ria l
S e t
*
In
m odel
*
ID#
m typ
20
3
ANSYS
1.92e+ 04
*
20,
*
ETyp
=>
m ass
*
«
m at= 15,
IHQ
e q s t
20:
=>
0
*
*
*
r e a l =6
IBQ
QH
lbvc-Q 2
qbvc-Q l
*
*
E typ
g ra v
Efrm
*
*
*
E typ
g ra v
Efrm
I
0
0.0002488
*
S et
*
Beam
type= 15,
den s
0
*
I
*
E la s t i c - I s o t r o p i c
3.6E + 06
0 .17
4000
9 . 7e05
0 .5
*
S et
*
*
20:
Beam
*
*
1.000
*
*
S et
*
20:
*
Beam
*
*
p a r a m e te r s :
*
*
*
H ughes-L iu
0.0
18
*
*
(re a l)
2.0
18
*
*
X -s e c tio n
48
*
*
48
*
X -s e c tio n
*
(re a l)
0 .0
*
*
0 .0
*
p a ra m e te rs :
*
*
B e ly tsc h k o -S c h w e r
1.00
*
*
*
864
I . 66e+05
*
*
*
M a te ria l
S e t
*
In
m odel
*
ID#
m typ
21
3
*
ANSYS
S et
21:
21,
m ass
=>
2.33e+ 04
*
*
ETyp
=>
*
=
*
0
*
*
*
*
Beam
type= 15,
dens
0
*
m at= 15,
IHQ
e q s t
re a l= ?
IBQ
QH
9
S
*
qbvc-Q l
*
*
I
I
0
0.0002488
*
*
*
*
*
*
B i a s t i c - I s o t r o p i c
3.6E +06
0 .17
4000
9 . 7e05
0 .5
S et
21:
Beam
X - s e c tio n
1.000
22
*
S et
21:
(re a l)
2.0
22
Beam
p a ra m e te rs:
H ughes-L iu
0.0
50
X -s e c tio n
50
(re a l)
0.0
0 .0
p a ra m e te rs:
B ely tsch k o -S ch w er
1 .0 0
l.le + 0 3
*
*
3 .4 le+ 05
*
*
M a te ria l
S e t
In
m odel
ANSYS
m typ
22
*
3
Set
*
22:
=>
3.6E +06
0 .17
4000
9 . 7e05
0 .5
m ass
ETyp
=>
dens
0.0002488
*
*
=
*
ty p e= 1 5 ,
e q s t
m at= 15,
*
*
*
E typ
g ra v
Efrm
r e a l =8
QH
IHQ
IBQ
qbvc-Q l
*
E la s t i c - I s o tr o p ic
I
I
0
*
*
Beam
I
ID#
22,
0
0
5.2e+ 04
*
*
8
*
*
*
*
*
*
*
157
S e t
22:
Beam
X - s e c tio n
1.000
18
*
S e t
(re a l)
2.0
18
22:
Beam
p a r a m e te r s :
H ughes-L iu
0.0
56
X -s e c tio n
56
(re a l)
0.0
0 .0
p a ra m e te rs :
B e ly tsch k o -S ch w er
1.00
*
*
432
5 . 12e+04
*
M a te r ia l
S e t
*
In
m odel
*
ID#
m typ
m ass_dens
23
3
0.000 2 4 8 8
S e t
ANSYS
23:
=>
23,
5 .41e+ 03
ETyp
=>
=
0
Beam
type= 15,
e q s t
0
m at=15,
IHQ
re al= 3
QH
IBQ
qbvc-Q l
lbvc-Q 2
0
E typ
g ra v
Efrm
E typ
g ra v
Efrm
I
I
E la s t i c - I s o tto p i c
3.6E + 06
0 .1 7
4000
9 . 7e05
0 .5
S et
23:
Beam
X - s e c tio n
1.000
48
*
S e t
(re a l)
2.0
48
23:
Beam
p a r a m e te r s :
H ughes-L iu
0.0
20
X -s e c tio n
20
(re a l)
0.0
0 .0
p a r a m e te r s :
B ely tsch k o -S ch w er
1.00
*
*
960
3 . 71e+04
*
M a te ria l
S et
*
In
m odel
*
ID#
m typ
m ass_dens
24
3
0.000 2 4 8 8
S et
ANSYS
24:
=>
24,
1.99e+ 05
ETyp
=>
»
0
Beam
type= 15,
e q s t
0
m at= 15,
IHQ
re a l= 1 3
QH
IBQ
qbvc-Q l
lbvc-Q 2
0
I
I
E la S t i c - I s o t r o p i c
3.6E + 06
0.17
4000
9 . 7e05
0 .5
S et
24:
Beam
X -s e c tio n
1.000
24
*
S e t
24:
(re a l)
2.0
24
Beam
*
1.00
*
480
p a ra m e te rs :
H ughes-L iu
0.0
20
X -s e c tio n
I . 86e+04
(re a l)
20
0.0
0 .0
p a r a m e te r s :
2.49e+ 04
0
B ely tsch k o -S ch w er
0
**********************
*
Node
[p g .2 8 3 ,
S p e c i f ic a t io n s
c c > 2
:
2
]
NODE AND ELEMENT DATA HERE
*****************************************
* Load C urve
*************************************
* lcID
I
*
n p ts
3
tim e
0
I
3
lo a d
s f
0
I
I
(p g .311,
c c > 5 : 1]
158
* lcID
n p ts
2
5
tim e
lo a d
0
I
*
s f
0
0
1.0 0 5
6
1.01
0
3
0
C o n c e n tra te d
*N odeID #
do f
2
2
2
2
2
2
2
2
2
75741
75742
75812
75852
78652
78692
87172
87242
90042
*************************
[p g .314,
Loads
IcID
Ic
nod
s f
I
-2 .2 6 e+ 0 5
I
- 3 . 42e+05
I
- 6 . 71e+05
I
- 4 . 33e+05
m2
nod
m3
1 - 3 .355e+05
1 - 2 . 165e+05
I
- 2 . 17e+05
I
- 4 . 2e+05
I
- 2 . le+05
***********
**********4
* D is tr ib u t e d
***********
*lcID
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
c c > 5 :2]
[p g .316,
Loads
n o d i
n od 2
nod3
nod4
5122
5129
5303
5157
5129
5130
5320
5303
5157
5303
5304
5158
5303
5320
5321
5304
5158
5304
5305
5159
5304
5321
5322
5305
5159
5305
5306
5160
5305
5322
5323
5306
5160
5306
5307
5161
5306
5323
5324
5307
5161
5307
5308
5162
5307
5324
5325
5308
5162
5308
5309
5163
5308
5325
5326
5309
5163
5309
5310
5164
5309
5326
5327
5310
5164
5310
5311
5165
5310
5327
5328
5311
5165
5311
5312
5166
5311
5328
5329
5312
5166
5312
5313
5167
5312
5329
5330
5313
5167
5313
5314
5168
5313
5330
5331
5314
5169
5168
5314
5315
5314
5331
5332
5315
5169
5315
5316
5170
5315
5332
5333
5316
5170
5316
5317
5171
5316
5333
5334
5317
5171
5317
5318
5172
5317
5334
5335
5318
5172
5318
5319
5173
5318
5335
5336
5319
5173
5319
5300
5156
5319
5336
5301
5300
5156
5300
5829
5787
5300
5301
5833
5829
5787
5829
5830
5788
5829
5833
5834
5830
5788
5830
5831
5789
5830
5834
5835
5831
5789
5831
5832
5790
5831
5835
5836
5832
5790
5832
5826
5786
Ic
S fl
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
Ic
s f 2
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
Ic
sf3
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
I c
c c > 5 :3]
sf4
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
159
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
23664
23764
23765
23663
23764
23770
23771
23765
23663
23765
23766
23662
23765
23771
23772
23766
23662
23766
23767
23661
23766
23772
23773
23767
23661
23767
23768
23660
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
23767
23773
23774
23768
1000
23660
23768
23769
23659
23768
23774
23775
23769
23659
23769
23761
23658
23769
23775
23762
23761
24059
5832
5836
5827
5826
5786
5826
5996
5962
5826
5827
5999
5996
5962
5996
5997
5963
5996
5999
6000
5997
5963
5997
5998
5964
5997
6000
6001
5998
5964
5998
5993
5961
5998
6001
5994
5993
5961
5993
14467
14337
14467
5993
5994
14482
14337
14467
14468
14338
14467
14482
14483
14468
14338
14468
14469
14339
14468
14483
14484
14469
14339
14469
14470
14340
14469
14484
14485
14470
14340
14470
14471
14341
14470
14485
14486
14471
14341
14471
14472
14342
14471
14486
14487
14472
14342
14472
14473
14343
14472
14487
14488
14473
14343
14473
14474
14344
14473
14488
14489
14474
14344
14474
14475
14345
14474
14489
14490
14475
14345
14475
14476
14346
14475
14490
14491
14476
14346
14476
14477
14347
14476
14491
14492
14477
14347
14477
14478
14348
14477
14492
14493
14478
14348
14478
14479
14349
14478
14493
14494
14479
14349
14479
14480
14350
14479
14494
14495
14480
14350
14480
14481
14351
14480
14495
14496
14481
14351
14481
14464
14336
14481
14496
14465
14464
14336
14464
23764
23664
14464
14465
23770
23764
23658
23761
24111
23761
23762
24114
24111
24059
24111
24112
24058
24111
24114
24115
24112
24058
24112
24113
24057
24112
24115
24116
24113
24057
24113
24108
24056
24113
24116
24109
24108
24056
24108
27071
27037
24108
24109
27074
27071
27037
27071
27072
27038
27071
27074
27075
27072
27038
27072
27073
27039
27073
27072
27075
27076
27039
27073
27068
27036
27073
27076
27069
27068
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
160
*
*
2
2
27069
27068
27068
27036
0
0
1000
1000
0
0
1000
1000
*******************
**************
*
C o n ta c t
S u rfa c e s
[p g .3 2 9 ,
c c > 5 :8]
********************************************************************************
NSS
NMS
s ty p
c o e f
s f
0.3
* Base A c c e le r a tio n s
********************************
* lcID
I
a c c e l_ s f
386
*************************
* End o f In p u t
(Dyna3D)
*
*************************
c o e f
d f
0.2
c o e f
ed
0.5
IPEN
o u ts
outm
s c f
m pssf
1.0
1.0
*****************************************
[pg.366, c c >5:9->11]
8
9