NONLIN
Nonlinear Dynamic Time History Analysis
of Single Degree of Freedom Systems
developed by
Finley A. Charney, Ph.D., P.E.
Advanced Structural Concepts, Inc.
2221 East Street Golden, CO 80401
Phone (303) 278-6234
Fax (303) 278-6235
Email Address: advstrcon@aol.com
Introduction
NONLIN is a Microsoft Windows based application for the dynamic
analysis of single degree of freedom structural systems. The
structure may be modeled as elastic, elastic-plastic, or as a
yielding system with an arbitrary level of secondary stiffness.
The secondary stiffness may be positive, to represent a strain
hardening system, or negative, to model P-Delta effects. The
dynamic loading may be input as an earthquake accelerogram acting
at the base of the structure, or as a linear combination of sine,
square, or triangular waves applied at the roof of the structure.
The program uses a step-by-step method to solve the incrementally
nonlinear equations of motion. See Clough and Penzien [1] for a
theoretical description of the solution technique.
While NONLIN may be used for professional practice or academic
research, the fundamental purpose of the program is to provide a
visual basis for learning the principles of earthquake engineering,
particularly as related to the concepts of structural dynamics,
damping, ductility, and energy dissipation.
Program Design and Concepts
All input for NONLIN is carried out interactively through the use
of the computer keyboard and the mouse. For the current version,
plots are written to the screen in several different “windows” and
tabular output information can be written to four different output
file types that can be saved to disk. These files include a text
file with the .OUT extension which summarizes the latest run and
three tab-delimited files with the .XL1, .XL2 and .XL3 file
extensions. These tabular data files are intended for use with
a spreadsheet program such as Microsoft Excel. This allows you to
perform further processing of the data or to graph the output data
for inclusion in reports and other documents. The .Xlx files can
be viewed or printed from a simple text processing program such as
Microsoft WordPad. Graphical screen plots of several different
types are produced during program execution. Hard copies of any of
the screen plot windows may be obtained as described later in this
manual.
After the structural properties and loading have been input, you
may obtain the following information:
Loading Type Input Time History Fourier Amplitude Spectrum
Wave Form n n n n n n n
Earthquake n n n n n n n n
Response Spectrum Computed Time Histories Computed Hysteresis Plots
Computed Energy Time Histories Result Summaries
Animate StructureResponse
System Requirements
NONLIN must be run on a 80486 or Pentium system running under DOS
and Microsoft Windows 3.0 or higher, Windows 95 and Windows NT.
The computer should have a minimum of 4 MB main memory, and at least
4.0 MB free on the fixed disk.
For best results, your system’s video should be set to 800 by 600
resolution, displaying not less than 256 simultaneous colors.
However, resolutions as low as 640 by 480 and as high as 1024 by
768 will work. The computer must be equipped with a Microsoft
compatible mouse, trackball, or other pointing device.
Installing NONLIN Using the SETUP Utility
To install NONLIN, run the SETUP utility provided on disk one of
the program disk set. The installation procedure is given below
for the Windows 3.x, Windows NT and the Windows 95 operating systems
.
Windows 3.x or Windows NT Users:
1. Insert disk one in the appropriate drive, A: or B:.
2. From the File menu of the Program Manager or File Manager,
choose Run.
3. Type a:setup (or b:setup).
4. Follow the setup instructions on the screen. NONLIN and
associated compressed files are expanded and placed in the newly
created \NONLIN directory by default. You can change the directory
name if you choose during the setup process.
5. You can run NONLIN from the File menu of the Program Manager
by choosing Run then typing c:\nonlin\nonlin.exe
or:
6. You can place the NONLIN program icon in an applications
group of your choosing. To run NONLIN, double click on the icon.
Windows 95 Users:
1. Insert disk one in the appropriate drive, A: or B:.
2. From the Start Menu on the Taskbar, choose Run.
3. Type a:setup (or b:setup).
4. Follow the setup instructions on the screen. NONLIN and
associated compressed files are expanded and placed in the newly
created \NONLIN directory by default. You can change the directory
name if you choose during the setup process.
5. You can run NONLIN from the Start button on the Taskbar,
highlighting Programs, and then clicking on the NONLIN icon,
or:
6. You can drag the NONLIN program icon to your desktop. A
Shortcut icon is created in the dragging process. To run NONLIN,
double click the shortcut icon.
If you choose to browse the newly created \NONLIN directory, you
will notice that there are several files that possess an .ACC file
name extension. These are earthquake acceleration records that are
supplied with the program. Appendix A of this document lists the
acceleration records as well as pertinent facts about the records.
The records supplied with your disk may be different from those lis
ted in Appendix A. The acceleration records are written in a
special format, as described in Appendix B.
The SETUP utility also places several files in your C:\WINDOWS\
SYSTEM directory. These files MUST be present for NONLIN to run.
These files include:
CMDIALOG.VBX
MHPFST.VBX
MHRUN400.DLL
SPIN.VBX
THREED.VBX
VBRUN300.DLL
Do not delete or move these files. If any or all of these files
are accidentally deleted from the C:\WINDOWS\SYSTEM directory, you
will have to run SETUP again to replace them.
Part One Inputting Data
Description of the User Interface
After NONLIN is started, the NONLIN Version 5.2 : filename window
(hereafter referred to as the “NONLIN” window) and the STRUCTURE
PROPERTIES INPUT window automatically appear. The filename is
“untitled” when you first start the program and becomes the problem
file name when a problem is created or loaded from disk.
These windows are shown in Figure 1.
Figure 1. The NONLIN and STRUCTURE PROPERTIES INPUT windows.
The NONLIN window consists of a title bar, a menu bar, and a button
bar. The NONLIN window is always open, and serves as a “container”
for all other windows used by the program. Closing the NONLIN
window terminates the program, and minimizing the window reduces
the entire NONLIN environment to an icon. The title bar displays
the active problem file name to the right of the colon.
The Menu Items
The menu bar as shown in Figure 1 has menu items File, Parameters,
Quik Quake, Quik Wave, Window, View, and Help. These menus items
are available whenever the STRUCTURE PROPERTIES INPUT window is the
active window. The underlined character indicates that the menu
may be opened by holding down the Alt key in combination with the
underlined letter. For example, the File menu may be opened by
pressing Alt-F. Any menu item may also be opened by clicking the
item with the mouse. Some of the menu items in the NONLIN window
menu bar will change depending upon which one of several other
windows is currently the active.
(Note: This manual shows menu items as they appear if your
computer is running Windows 95. These items may appear slightly
different if your computer is running Windows 3.x. In either case,
the menu item functions are the same.)
The File menu displays the following submenus when the STRUCTURE
PROPERTIES INPUT window is open:
You can save individual problems in separate files. You create
problem files which contain all necessary input data to run a
NONLIN analysis. All problem files have the .NLN file name
extension. The first four submenus allow the creation, storage
and retrieval of problem files. In addition, the file names of
past problem runs will appear below the Exit submenu as shown
above. This is typical of many Windows applications. Clicking
the problem file name will load the problem. Clicking on Exit
immediately terminates the program.
If a secondary input or output window, such as those which display
screen plots of acceleration, velocity and so on, is open, the File
menu changes to display one or two sub-menus, depending upon which
secondary window is open. For example, when you have opened the
Computed Time Histories or the Computed Hysteresis windows to view
the structural response, the File menu takes the following form:
.
Print Form produces a printer plot of the open window, which usually
contains one or more plots. The Create File option, if clicked,
causes an output file to be created which is stored in the NONLIN
directory. The output file is always called NONLIN.XL1 when the
Summary of Computed Results window is open. Anytime the NONLIN.XL1
file is created, it overwrites any existing file of the same name.
This file is a tab-delimited file for use with a spreadsheet program.
One use for this file and any other .Xlx file is to obtain a smooth
plot of the output data for inclusion in a report using the plotting
features of Microsoft Excel.
When the Summary of Computed Results window (described later) is
open, the File menu takes this form:
The two print options either print all result pages or the current
result page, depending upon which option you choose. The Create
File option is the same as described above.
The Create File option is also active when the Computed Energy
Plots window is open. If you choose to create a file in this case,
the NONLIN.XL2 file contains values of strain + kinetic, damping,
hysteretic and total energy. Anytime the NONLIN.XL2 file is created
, it overwrites any existing file of the same name. This file is
a tab-delimited file for use with a spreadsheet program.
Finally, the Create File option is also active when the Earthquake
Response Spectrum of Input window shows a spectrum plot. If you
choose to create a file in this case, the program writes spectral
displacement, velocity, and acceleration to the file NONLIN.XL3.
Anytime the NONLIN.XL3 file is created, it overwrites any existing
file of the same name. This is also a tab-delimited file for use
with a spreadsheet program.
Anytime that you create a .XL1, .XL2 or .XL3 file, you can view
the contents of the file in a window on the screen by positioning
the cursor inside the active window and clicking the right mouse
button. The tab-delimited file appears in a separate window.
As described earlier, clicking on Exit in any form of the File
menu immediately terminates the program after asking if you are sure
that you want to exit and asking if you want to save the current
problem in a file for future use.
The Parameters menu is only displayed when the STRUCTURE PROPERTIES
INPUT window is open. It contains three submenus as shown here:
The Step Factor X submenu asks for the digitization step factor X
which is used in controlling program accuracy. Reducing X will
increase solution speed, but may reduce accuracy. It is recommended
that X not be set to a value less than 50. The default value of X is
100. The Input Mass As submenu asks you if you want to enter the
mass of the structure as a mass in mass units (e.g., k-sec2/in), a
mass in weight (e.g., lbs), or as a period. If you enter the mass
of the structure as a weight, the program converts the weight to
mass units, and if you input the period, the mass will be calculated
(in mass units) using the assigned stiffness value K1. The Input
Damping As submenu asks for the damping either as a constant (e.g.,
k-sec/in) or as a percent of critical value. Damping values are
explained in more detail in the Entering Structural Properties
section.
The Quik Quake menu is only displayed when the STRUCTURE PROPERTIES
INPUT window is open. Quik Quake is a shortcut method of bringing
earthquake data into NONLIN for use in a simulation. Clicking Quik
Quake displays a list of the earthquake ground acceleration record
file names supplied with the program. Clicking one of the acceleration
file names immediately loads the appropriate acceleration record to be
applied to the structure. The name of the earthquake record is
displayed at the bottom of the STRUCTURE PROPERTIES INPUT window.
Choosing an earthquake acceleration automatically changes the dynamic
force to be applied as a ground acceleration for analysis by the
program. The Quik Quake option will appear in gray if no acceleration
records (i.e., the .ACC files) are present in the NONLIN directory.
A more powerful method of defining earthquake accelerations is built
into NONLIN. You can obtain time history, FFT and response spectrum
plots as well as modify the accelerations of a particular record.
These features are available through the use of the Earthquake Ground
Acceleration Input window. Its features are described in a later
section.
The Quik Wave menu is only displayed when the STRUCTURE PROPERTIES
INPUT window is open. It displays a separate window that allows you
to define the forcing function wave. You can select one of three
different wave types, sine, square and sawtooth by clicking on the
appropriate button. Then, within this window, you can define the
Total Time of the time history plot, the DigiTization Interval (DT),
the Amplitude, the Period and the Duration that the forcing function
wave is applied to the structure. Defining a forcing function wave
automatically changes the dynamic force to be applied as a forcing
function for analysis by the program.
The Quik Wave provides a quick way to define a wave forcing function.
A WAVE GENERATOR window is available to you under the Forcing Function
option in the Dynamic Force Applied as... window. This window gives
you many options for creating your own wave forcing function. This
option is described in more detail later in this manual.
The Window menu contains the sub-menu items Cascade, Tile, and Arrange
Icons. These items indicate how the active windows or icons will be
displayed. The Window menu will also list the names of all windows
that are currently open, with a check mark to the left of the window
that is currently active. To access a non-active window (including
one that has been minimized) click on the name of the window in the
window list.
The View menu has a single item, which when clicked which will display
(or remove) a small panel showing a brief summary of the latest
analysis results. This small panel is located between the columns
of the structure, under the mass icon. Figure 1 shows the structure
window with the results panel activated. Note that the View menu is
available only when the STRUCTURE PROPERTIES INPUT Window is active.
The Help menu contains only contains four submenu topics. Selecting
Contents from the Help menu displays an alphabetical list of the
contents of this help file. You can also search for a specific help
topic by selecting Search. How to use Help displays the standard
Windows Help on Help text for users unfamiliar with the Windows help
system. The last item in this menu is About NONLIN. Click on this
menu item to contain basic information about the program.
The Button Bar
The button bar contains seven buttons, each of which is briefly
described below:
Structure Restore Button
Press this button to restore the STRUCTURE PROPERTIES INPUT window
if it has been closed. In most cases, you will keep this window open
at all times.
GO/NO GO Analysis Buttons
When NONLIN is first loaded, the NO GO button shown at the left will
appear with a red square in the center. This indicates that not all
of the required data has been input. If the button is pressed before
the data is completely entered, the program will provide a window
that lists the portions of data that are missing.
Once all of the data has been correctly entered, the red NO GO button
will change to a green triangle, the GO button, indicating that the
program is ready to perform an analysis run. Once the button has been
pressed, the analysis will proceed, and results will be available for
viewing.
The green GO button also appears when you have loaded a problem file
with the Open Problem... option in the File menu or highlighting a
problem name in the lower potion of the File menu.
To the right of the GO/NO GO button is the RUN frame which displays
the number of the latest analysis run executed by NONLIN.
View Computed Time Histories Button
After the analysis has been run, you may click the Time History button
to display the computed time-histories of displacement, spring force,
and yield event codes, with additional plot types available as
explained later. This button is inactive when the Start Analysis
button contains a red square. If the structure data, units, or
loading has changed since the last run, NONLIN will request that the
Start Analysis button be clicked before reviewing plots.
When the time history window is the active window, selecting the menu
options File and then Print Form will send a copy of the plots to a
printer.
View Computed Hysteresis Plots Button
After the analysis has been run, you must click this button to display
the computed hysteresis curves. Three hysteresis curves are displayed
: inertial force versus displacement, damping force versus displacement
, and spring force versus displacement, with additional plot types
available as explained later. If the structure data, units, or loading
has changed since the last run, NONLIN will request that the green GO
button be clicked before reviewing plots.
When the hysteresis plot window is the active window, selecting the
menu options File and then Print Form will send a copy of the plots to
a printer.
View Computed Energy Plots Button
Press this button to display the relative or absolute dissipated energy
time history plot. This plot shows how the earthquake input energy
is dissipated through structural kinetic, recoverable strain, damping,
and hysteretic energy. By moving the mouse laterally while the plot
is displayed, the relative percent of structural energy for each
structural energy type is displayed. For a reference on computing
energy time-histories, see Uang and Bertero [2].
If the structure data, units, or loading has changed since the last
run, NONLIN will request that the green GO button be clicked before
reviewing plots.
When the energy window is the active window, pressing the menu options
File and then Print Form will send a copy of the plots to a printer.
Review Summary of Computed Results Button
Press this button to obtain a summary of computed results. The
window displayed shows the current contents of the NONLIN.OUT output
file. When the summary window is the active window, you can obtain
a hardcopy of the output file contents. An example of the Summary of
Computed Results Window is shown in Part Two of this manual.
Animate Button
Press this button to view an animated representation of the structure
displacing from side to side. This represents the response of the
structure to the ground acceleration or forcing function wave.
Entering Structural Properties
The structural properties are entered through the STRUCTURE PROPERTIES
INPUT window, which is shown in Figure 1. This window contains
seven parts or frames:
· The Unit Type input frame
· The Length Units input frame
· The Force Units input frame
· The Dynamic Force Applied as... input frame
· The Constitutive Properties input frame (which includes the structure
diagram)
· The Dynamic Properties output frame
· The Summary of Latest Run output frame
The Unit Type, Length Units and Force Units Frames
These three frames are input frames - you are expected to click on the
appropriate buttons within these frames. NONLIN can operate in either
U.S. Customary or metric units. Unit types are toggled by the two
option buttons in the Unit Type frame. For U.S. Customary units,
lengths may be entered in the Length Units frame as inches or feet
and forces may be entered in the Force Units frame in pounds or kips.
When metric units are selected, lengths are centimeters or meters and
forces are either Newtons or kiloNewtons. You may switch from one
unit type to another at any time. Data that has already been entered
is automatically converted as soon as you select the appropriate
units.
When the applied dynamic force is an earthquake ground acceleration,
NONLIN automatically converts the acceleration units into units which
are expressed as a fraction of the acceleration due to gravity. The
acceleration of gravity in the current computational units is always
shown on the Gravity line (the last line) of the Dynamic Properties
frame. Note that these units automatically change when the
computational units are altered via the option buttons in the Unit
Type, Length Units and Force Units frames.
If a wave type forcing function is used, the forcing function
amplitude is assumed to be in units of force consistent with the
unit types selected using the Unit Type, Length Units and Force Units
frames.
The Constitutive Properties Frame
This frame includes both the Constitutive Properties frame and the
structure diagram. Six general items of input corresponding to five
large icon buttons and one small button, are expected in order to
analyze your problem.
The structure is idealized as a single degree of freedom system, as
shown schematically in Figure 1. For linear analysis, the following
properties are required:
> MASS
> DAMPING
> INITIAL STIFFNESS K1
For nonlinear analysis two additional properties are required:
> SECONDARY STIFFNESS K2
> YIELD STRENGTH Fy
Structural properties are entered by clicking the three structure
stiffness buttons located within the Constitutive Properties frame
and the mass and damping buttons located above and below the structure
mass in the structure diagram. Data input is described for each button
as follows:
Structural Mass/Weight/Period Button
This button either represents a mass with an “M” in the icon, a weight
with a “W” in the icon, or a sine wave. NONLIN changes the icon to
match the Input Mass As choice that you made in the Parameters menu.
To enter structural mass or weight, press the MASS/WEIGHT icon. An
input window will open to prompt for the appropriate data. The
structural mass or weight must be greater than zero.
If you choose mass units, the weight of the structure is displayed in
the next to last line of the Dynamic Properties frame. If you choose
weight units, the mass is displayed on this line. Masses are derived
from weights by dividing the weight by the acceleration due to gravity
. NONLIN converts the units internally once the mass or weight has
been input.
Example: If a structure has a weight of 55 kips, NONLIN will
internally calculate the mass by dividing by 32.2 ft/sec2 times 12
inches per foot as follows:
mass = 55.0 / 386.1 = 0.142 kip-sec2/inch
Sometimes it is useful to enter a structure with a known period.
This option allows this to be done by entering the period on the MASS
box. When the STIFFNESS is entered, this is used together with the
period to compute a corresponding mass value.
Structural Damping Button
To enter structural damping, press the DAMPER icon. Damping can be
input either as a percent of critical or as a damping constant. The
Damper icon will display a small % or a “c” to indicate which case is
active. Critical damping is defined as the smallest amount of damping
required to prevent an oscillatory motion (no zero displacement
crossings) after a system is given an initial displacement and then
released. Critical damping is mathematically defined as follows:
where m is the system mass (in mass units), and is the structural
circular frequency in radians/second, computed as
and K1 is the initial stiffness of the system, as described in the
following section.
In NONLIN, a nondimensional damping value is entered as
The 100 in the above equation converts the damping into a percent.
NONLIN will allow damping values from 0 to 100 percent critical.
However, damping values of 2 to 7 percent critical are commonly used
for analysis of structures responding to earthquake ground motions,
where it is anticipated that the response will go into the nonlinear
(inelastic range). Note that lower values of damping may be
appropriate for computation of the response of systems which are
intended to remain elastic. High damping values (20 to 30% critical)
may be used to represent structures with added viscous damping.
Example: Assume a structure has an initial stiffness of 70 kips/inch,
and a weight of 55 kips. The mass of the structure is 55/386.1 =
0.142 kip-sec2/inch. The circular frequency = [70/0.142]0.5 = 22.2
radians/sec. If a damping of 5 percent critical is desired, enter 5.0
at the prompt. The damping coefficient c used in the analysis is
(5.0/100)cc = 0.05(2)(0.142)(22.2) = 0.315 kip-seconds/inch.
As previously mentioned, the damping constant may be entered directly.
Initial Stiffness K1 Button
To enter the initial stiffness, press the INITIAL STIFFNESS icon. The
initial stiffness K1 is illustrated below. K1 has units of
force/length. For nonlinear analysis, the unloading stiffness is
assumed to be equal to the initial stiffness.
After both the mass and the initial stiffness have been entered,
NONLIN will compute and display the structure’s dynamic properties,
which include the circular frequency (radians/second), the cyclic
frequency f (Hertz) , and the period of vibration T (seconds).
Secondary Or Yielding Stiffness K2 Button
The secondary stiffness is the first of two properties required for
nonlinear analysis. To enter the secondary stiffness, press the
SECONDARY STIFFNESS icon and respond to the prompt. The secondary
stiffness is the slope of the post-yielding portion of the
force-displacement response of a structure. The value may be positive
, representing strain hardening, zero, representing an elastic-perfectly
plastic response, or negative, representing P-Delta effects. The
secondary stiffness K2 is illustrated below. Note that K2 must be
less than the initial stiffness of the structure.
If a negative secondary stiffness is used to represent P-Delta
effects, you must be careful to enter initial stiffness and yield
strength values that include such effects. Assume a structure without
P-Delta effects considered has an initial stiffness Ko, a yield strength
Fy,o, and a strain hardening stiffness of zero. (Yield strength is
described in the following section.) The structure is shown in the
figure on the next page.
Under a gravity force P (compression positive), the structure has
an initial stiffness K1=Ko+KG, where KG, the P-Delta stiffness,
is computed as follows:
For this structure, you should enter an initial stiffness
K1=Ko-(P/h), and a secondary stiffness K2 = -P/h. If the yield
strength of the structure without P-Delta effects is Fy,o, you
should enter a modified yield strength Fy as follows:
Example: Assume a structure in absence of a vertical force P has
an initial stiffness of 50 kips/inch, and after yielding at a lateral
force of 20 kips, has a strain hardening stiffness of zero. If the
column height h is 10.0 feet, and the total vertical force P is
480 kips, determine the initial stiffness, the secondary stiffness,
and the yield strength to be used for a nonlinear P-Delta analysis.
Secondary stiffness K2 = - P/h = -480/(10x12) = -4.0 kips/inch
Initial stiffness K1 + K2 = 50 +(-4) = 46 kips/inch
Yield Strength = Fy = Fy,0(1-P/(Koh)) = 20(1-480/(50x23x10)) = 18.4 k/in
Yield Strength Fy Button
The system yield strength is the second of two properties required
for nonlinear analysis. To enter the yield strength, press the
YIELD STRENGTH icon and respond to the prompt. The yield strength,
which is illustrated below, is given in force units.
Linear/Nonlinear Analysis Buttons
Just below the Yield Strength button are two small buttons (also
called radio buttons) which you can use to define whether you want
a linear or nonlinear analysis of the defined structure. If you
choose a linear analysis, the secondary stiffness and yield strength
values are ignored because they do not apply to a linear analysis.
Dynamic Properties Output Frame
This frame is located in the lower right corner of the STRUCTURE
PROPERTIES INPUT window. The frame echoes the structure properties
input values. Except for the Gravity line, the frame will contain
no values until the structure properties have been defined either
by defining a new problem or loading a problem file.
Summary of Latest Run Output Frame
This frame is located inside the structure diagram in the STRUCTURE
PROPERTIES INPUT window. It provides several items of output data
that updated after every run. The frame contains no values until
an analysis run has been executed.
Dynamic Force Applied as... Input Frame
As previously mentioned, the forcing function may be either a
prerecorded earthquake, a linear combination of up to five sine,
square, or triangular waves, or a free vibration. As shown in
Figure 1, the type of dynamic force is toggled by clicking on the
appropriate option button in the Dynamic Force Applied as... input frame.
Defining a Ground Acceleration
You can bring an earthquake acceleration record into NONLIN through
the Quik Quake menu option or you can use the more sophisticated
Ground Acceleration input function. When the Ground Acceleration
button is activated, the icon in the Dynamic Force Applied as...
input frame resembles an accelerogram. Clicking on this icon, shown
below, opens a special frame for inputting and plotting data associated
with the selected ground motion.
Upon pressing the accelerogram icon, the EARTHQUAKE GROUND
ACCELERATION INPUT frame appear as illustrated in Figure 2 below.
In Figure 2, the STRUCTURE PROPERTIES INPUT window has been
minimized so that only the NONLIN window and the EARTHQUAKE
GROUND ACCELERATION INPUT windows frames are visible.
To select a pre-recorded earthquake, click the File Open icon
which resides in the upper left of the window. The icon looks like this:
All of the pre-recorded earthquake files have a name in the
format FILENAME.ACC, where FILENAME is a one to eight character
name, and ACC is the default extension for the accelerograms.
When installing NONLIN, several acceleration files were copied
to the NONLIN directory of the hard disk. In Figure 2, the
file which has been opened is NRIDGE1.ACC.
For NONLIN to be able to read an acceleration record, it must
be in a special format. This format is described in detail in
Appendix B of this documentation.
After the file has been opened, NONLIN displays a description
of the file, and shows the pertinent aspects of the record,
including the number of points in the record, the digitization
interval, the duration, and minima and maxima of acceleration,
displacement, and velocity, if present in the record. NONLIN
also shows the units at which the record was loaded. As mentioned
earlier, the record will be nondimensionalized by dividing by the
appropriate acceleration of gravity before being sent to the
computational unit of NONLIN.
Figure 2. The EARTHQUAKE GROUND ACCELERATION INPUT window
The acceleration record may be used as-is, or may be revised
by changing the maximum acceleration, reducing the number of
points to be included in the NONLIN analysis, or changing the
discretization interval. In Figure 2, these quantities have
been changed to 400 mm/sec, 2000 points, and 0.01 seconds,
respectively. The revised values will be used by NONLIN unless
the RESET to Original button is clicked prior to clicking the
USE for ANALYSIS button. When the USE for ANALYSIS button is
clicked, the EARTHQUAKE GROUND ACCELERATION INPUT window is
minimized, and NONLIN will be ready to run (if all structural
properties have been previously entered).
Before describing the plotting options, it is very important
to note that changing the digitization interval of a record
does not rediscretize the accelerogram. The effect is to
compress or expand the time scale, as shown below.
Original Record
Revised Record
It should be noted that the velocity and displacement time histories
are also affected by a change in the discretization timestep.
There are two circumstances where you may want to change the
digitization interval. The first is to change the frequency
content of the earthquake ground. The second reason to change
the accelerogram is for dimensional similitude as required in
model studies. For a true scale model with a dimensional scale
factor of n (n = 5 for a 1/5 scale model), the time digitization
interval should be divided by the square root of the scale factor.
Displaying Ground Acceleration Plots
Using the plotting options, you may plot the ground acceleration,
velocity, and displacement, develop an elastic response spectrum,
or plot a Fourier amplitude spectrum. The plots are obtained by
clicking one of the three buttons in the lower right hand corner
of the EARTHQUAKE GROUND ACCELERATION INPUT window. Note that
either the original or the revised data may be plotted. Recall
however, that if the ground motion characteristics have been
revised, the revised motion will be used by NONLIN unless the
Reset To Original button has been clicked.
The acceleration, velocity, and displacement plots are self
explanatory, and will not be described further. Is should be
noted, however, that hard copies of the plot may be obtained by
clicking the File menu, and then clicking the Print Form menu item.
By selecting the Response Spectra box, response spectra will be
plotted for up to six different damping values. The damping
values are selected from the Damping Values frame that appears
after you have pressed the PLOT DATA button. After pressing the
button, the input frame on the left side the Earthquake Response
Spectrum of Input window as shown in Figure 3 appears.
Figure 3. Earthquake Response Spectrum of Input Window.
The five damping values shown, plus one additional value may be
used. The response spectrum is plotted on a logarithmic plot,
with either 10, 20, 40, 80, 160, or 320 equally spaced points
being plotted per logarithmic decade (points per decade) Click
the appropriate check boxes and radio buttons, and then click the
Plot Spectrum button. Pressing the Plot Spectrum button computes
the spectrum for the selected damping values. The spectrum is
plotted versus structural period, or structural frequency, at your
option. The plot type is by default Tripartite, as shown in the
center of Figure 3. On this logarithmic plot type, logarithmic
axes for displacement and acceleration are superimposed at an
angle to the orthogonal period and velocity axes. This is a
common method of presenting the spectrum.
You will notice that if you drag the cursor through the Tripartite
plot, the Spectral Coordinates in the frame at the top of the
window change to indicate the values at the cursor location.
By choosing the Separate Plot Type option, the program displays
three plots: displacement versus period, pseudo velocity versus
period and pseudo acceleration versus period. The Separate Plots
may be Log-Log, Log-Arithmetic or Arithmetic-Arithmetic. Example
Separate Plots are shown in Figure 4.
Figure 4. Separate Plots of Sample Spectrum
As with the Tripartite plot, the Spectral Coordinates in the frame
at the top of the window change to indicate the values at the
cursor location if you drag the cursor through any of the plots.
The third type of plot available from this screen is the Demand
Spectrum plot. A demand spectrum is an elastic response spectrum
plotted with the spectral displacement on the horizontal axis, and
the pseudoacceleration on the vertical axis. Radial lines represent
the square of the circular frequency, but for convenience are
labeled as period values. The structure’s force-deformation
response (capacity spectrum) may be superimposed on the demand
spectrum to provide useful design information. Demand-Capacity
spectra are a major feature of the ATC-33 Recommendations for
Rehabilitation of Existing Buildings. An example of this type
of plot is show in Figure 5.
Figure 5. Example Demand Spectum Plot
If you choose the Create File menu option at this point, the
NONLIN.XL3 file is written to disk. This is a tab-delimited
file that can be manipulated with a spreadsheet program. Any
of these types of Response Spectrum plots may be printed by
selecting the Print Form option from the File menu. Note that
you also have the option of printing a blank tripartite plot.
Since the response spectrum can take some time to compute,
the spectrum plot window does not immediately show the plot.
Instead, a Compute Spectrum button appears, which must be
clicked prior to computing and displaying the spectrum plot
(s). While the spectrum is being computed, a progress bar
is displayed for each damping value selected. The spectra
are computed by a piecewise exact integration scheme per
Chopra.[3].
After the spectrum has been computed, the Compute Spectrum
button changes to the Plot Spectrum button. You can change
plot types and display the corresponding plot. The spectrum
does not have to be recomputed as long as you do not change
the damping values. If you do change the damping values,
the Compute Spectrum button reappears and you must click
the button to recompute the spectrum.
As mentioned previously, a Fourier amplitude spectrum can
also be generated and printed. In NONLIN, the transform is
normalized to have a maximum value of 1.0. The frequency
that has a Transform ordinate of 1.0 is the dominant frequency
in the ground motion. The plot is useful in viewing the energy
content of a forcing function wave or earthquake at different
frequencies. For example, the majority of the energy of the
Imperial Valley Earthquake as measured at El Centro in May
1940 was focused between 1 and 2.25 Hertz.
A Fourier transform (often referred to as FFT, which is
technically incorrect because the FFT is a method, whereas the
transform itself is a result) converts a time function into a
frequency function. A Fast Fourier Transform (FFT) is a preferred
numerical method to compute the Fourier transform. An FFT requires
that the number of time-amplitude data points passed to the routine
be a power of 2. This is automatically taken care of in NONLIN.
Different segments of an earthquake may have different frequency
content. The Traveling FFT provides a method for determining the
frequency content of segments of the ground motion (or computed
response) consisting of 128, 256, or 512 contiguous points in the
motion. An example of this screen is show in Figure 6.
Figure 6. Traveling FFT Window
Dragging the cursor through the total plot shown in the FFT
window changes the values of frequency and amplitude shown in
separate boxes in a frame located just to the lower right of
the total FFT plot. the lower left corner of the window.
Defining a Wave Forcing Function
When Forcing Function is activated, the icon in the Dynamic
Force Applied as... frame resembles a complex wave form.
Clicking on this icon, shown below, opens a special window
for inputting and plotting a forcing function which consists
of a linear combination of simple sine, square, or triangular waves.
The WAVE GENERATOR window is shown in Figure 7.
Figure 7. The WAVE GENERATOR Window
The WAVE GENERATOR window consists of five frames plus four buttons.
In the Signal Length and Digitization Frame, you enter the total
wave duration and the discretization interval. The number of time
steps is then automatically computed and displayed.
To create a signal, move to the Frequency Data Frame, and select
the wave type for each component of a one to five part wave.
Individual wave components may be sine, square, or triangular
in type. At least one wave must be active at all times.
For each wave activated, the Period, the Amplitude, the Phase
Lag, and the Duration of each wave component must be specified.
The duration of any or all waves may be set to a value less than
the total length of the signal. The phase lag shifts the entire
wave to the right by an amount equal to the time entered. The
phase lag must be set to a value less than the period for the
particular wave. If all waves are shorter in duration than
the total wave length, the structure will enter into free
vibration once all the signals have terminated.
In the Startup Ramp Frame, you may enter a value between 2 and
100 to gradually increase (from zero) the magnitude of the wave
form over the initial portion of the total time period selected.
For example, a 10 second signal with a startup ramp of 20% will
cause a gradually increasing wave over the first two seconds of
the function. The last eight seconds of the signal will not
be affected by the ramp.
In the Random Noise Frame, you may superimpose a random noise
on the combined wave form. The maximum magnitude of the random
noise may be from 0 to 50 percent of the maximum wave amplitude
(without noise).
The Signal Description input frame is used to enter a title for
the wave form. This title will appear on all plots produced by
the program.
You also have the option of applying the forcing function as a
ground motion. When this box is checked, the forcing function
is treated as a ground motion during the calculations (only).
The amplitude is then taken as an acceleration represented as
a fraction of gravity. This is useful to when trying to model
specific ground motion characteristics that are not present in
the earthquake files supplied with NONLIN.
Displaying Wave Generator Plots
After all wave parameters have been set, click on the Generate
Signal to create the waveform. When the wave is ready, the
Time-History Plot and the FFT Plot buttons become active, and
when clicked, cause the program to display the corresponding plot.
The Time-History plot shows the force amplitude versus time.
If the Plot Total Wave Only box is checked, the intermediate waves
will not be plotted. The FFT (Fast Fourier Transform) plot transforms
the wave from the time domain to the frequency domain so that the
normalized energy content of the wave versus frequency can be seen.
To obtain a hard copy of a plot, click the File menu, followed by
the Print Form menu.
When you are ready to use the waveform in response computation,
press the USE for ANALYSIS button, at which time the WAVE GENERATOR
window will automatically minimize. If all structural data has
been previously input, you are now ready to proceed with an
analysis of the structure. Part Two of this manual describes
the execution of the program to obtain analysis results.
Part Two Program Output
Program Execution Results
NONLIN’s primary function is to model the response of a single
degree of freedom structural system to a dynamic loading. To this
point, this manual has described the process of providing input
data to NONLIN in order to run the program to obtain numerical and
graphical output describing the response. A brief summary of
typical input actions follows:
· Define the units
· Define the properties of the model structure
· Define the forcing function by choosing an earthquake or defining
a wave forcing function
· Define the type of analysis desired, that is, linear or nonlinear
or
· Open a problem file in which input information has been saved and
make modifications, if necessary
This section of the manual addresses the actual running of the
program to produce the output results.
Running the Analysis
Running the analysis of the model structure to obtain the dynamic
response is very simple. After you have entered all data necessary
input data, the red NO GO button gives way to the green GO button.
The presence of the GO button gives you an indication that necessary
and sufficient input data has been entered.
To produce an analysis run, simply click the GO button.
A progress bar will appear at the bottom of the STRUCTURE
PROPERTIES INPUT window to indicate that the run is progressing.
The speed of progression depends largely on the speed of your
computer, the length of the record and step factor. When the
analysis is complete, a run number indicator in the NONLIN window
increments, e.g., RUN0 is replaced with RUN1 and so on. The
Summary of Latest Run frame in the STRUCTURE PROPERTIES INPUT
window is updated. You are now ready to view, save and/or print
the computed time histories plots, the computed hysteresis plots,
the computed energy plots and/or the summary of computed results.
You can also view an animated representation of structural
displacement.
Click on:
to view the COMPUTED TIME HISTORIES plots.
to view the COMPUTED HYSTERESIS PLOTS.
to view the COMPUTED ENERGY PLOTS.
to view the SUMMARY OF COMPUTED RESULTS.
to view an ANIMATION of the structural response.
Each of these output features is described in more detail in the
following sections.
Computed Time Histories
Perhaps the first item of interest after running the analysis is
to view the COMPUTED TIME HISTORIES plots. You can open this
window by clicking the appropriate button as described above.
The window always displays three plots which default to displacement
, velocity and yield code versus time. Example time histories
plots are presented in Figure 8.
Figure 8. Example COMPUTED TIME HISTORIES Window
You can change any of the plots to one of nine different time
histories by clicking the buttons above each plot. If you change
one or more of the time histories, the plots will be automatically
updated with the new information.
Both the COMPUTED TIME HISTORIES window and the COMPUTED HYSTERESIS
PLOTS window have one icon button in the upper left corner of the
their respective windows. This button performs the same function
in either window, as follows:
The RESIZE button expands the plots to the limits of the
graph so that maximum values are readily apparent. If you click
on the RESIZE button again, the vertical and horizontal axes unit
values change back to convenient values beyond the maxima.
Both the COMPUTED TIME HISTORIES window and the COMPUTED HYSTERESIS
PLOTS window possess an additional feature. When either of these
two windows is the active window, the menu bar in the NONLIN
window presents an Options menu item. A Plot Points submenu is
presented when the Options menu item is clicked. You can choose
to have every point, every second point, every fourth point, every
sixth point or every eight point plotted. Your choice here does
not effect the screen plotting of the time histories or the
hysteresis plots. The feature is added to NONLIN to allow for a
smaller plot file to be transferred to your printer in the event
that your printer cannot handle the amount of data sent with a
“plot every point” plot. You may have to experiment to find the
largest number of points (i.e., the highest resolution) that your
printer can handle.
The COMPUTED TIME HISTORIES plots possess a helpful feature. If
you drag the cursor across any of the three plots, the cursor
becomes a double headed arrow with a vertical line through the
middle. You will notice that changing data values are given above
each plot that corresponds to the position of the cursor.
You can obtain a hardcopy of the plots by clicking the File menu
and choosing Print Form. If you choose the Create File menu option,
the NONLIN.XL1 tab-delimited file is written to disk. Uses for
this file are the same as the other .Xlx files already described.
Additionally, for all time history results except Yield Codes you
can view the time history calculated as a Fourier Transform in the
FFT window by clicking the FFT button to the right of each plot.
Computed Hysteresis Plots
Generally, the next output view of interest are the COMPUTED
HYSTERESIS PLOTS. The plots are useful to view various forces
in the system versus displacement, acceleration or velocity.
Clicking the appropriate button opens the window which always
displays three plots. The plots show inertial force, damping
force and spring force versus displacement by default. An example
of the hysteresis plots are presented in Figure 9.
Figure 9. Example of COMPUTED HYSTERESIS PLOTS.
You can change the ordinates to one of five different force types
and the abscissas to displacement, acceleration or velocity by
clicking the down-arrow boxes above and below each plot. If you
change any of the values, the plots will automatically be updated.
The COMPUTED HYSTERESIS PLOTS window contains the RESIZE button.
The function of this button is identical to the function described
in the COMPUTED TIME HISTORIES section above.
You can obtain a hardcopy of the plots by clicking the File menu
and choosing Print Form.
Computed Energy Plots
This plot shows the total energy dissipated over the time span of
the earthquake or forcing function event. The energy contributions
of the kinetic+strain, damping and hysteretic energies as well as
the total energy are shown. An example of the energy plot is shown
in Figure 10.
Figure 10. Example Computed Energy Plots Window
The dark vertical line in the example plot indicates the position
of the cursor. Note that the percentages of the energy types
change as you drag the cursor through the plot. The vertical blue
lines in the hysteretic energy are the yield events. If the
analysis is based on an earthquake and is nonlinear, you can view
either the relative (default) or the absolute energies. The energy
time histories allow for the input energy to be computed on the
basis of relative velocities or total absolute velocities. This
affects the magnitude of computed kinetic energy, as well as the
magnitude of total energy. It has been shown in a paper by Uang
and Bertero ["Evaluation of Seiemic Energy in Structures",
Earthquake Engineering and Structural Dynamics, pp 77-90, Vol.
19, No. 1, 1990] that for structural period ranges of about 0.3
to 4.0 seconds, relative and absolute energy maxima are almost
identical. Significant differences can occur for very low or
very high period structures. These differences can be very
important when computing energy spectra and using these spectra
for design.
The thin blue line at the top of the plot is the total energy
calculated separately. If the blue line does not closely
follow the top the cumulative energy curve, set the Step value
in the Parameters menu to a higher value. Note that this total
energy line does not show up on the printed output of the
energy plot.
Note that if the analysis is based on a user defined wave for
the forcing function (even if that forcing function is being
treated as a ground motion), or a linear analysis is being used,
you will only be able to view the relative energy.
You can obtain a hardcopy of the plot or create the .XL2 file
by clicking the File menu and choosing Print Plot or Create
File, respectively.
It is worth noting that the hysteretic energy is an indication
of structural damage resulting from the application of the
dynamic loading. The higher the percentage contribution of
the hysteretic energy to the total energy, the greater the
damage to the structure.
Summary of Computed Results
The Summary of Computed Results window is provided to give
you a summary of numerical results from your analysis runs.
Clicking the appropriate button as described above opens
the window. The problem filename, analysis type (linear
or nonlinear), structural properties, forcing function
properties and a summary of response maxima are presented.
The window shows the current contents of the filename.OUT
output file. When the window is opened, the file is
positioned to the last run executed. Use the scroll bar
at the right of the window to view the results of earlier
runs. The scroll bar moves in discrete jumps from run
summary to run summary, not in a continuously smooth,
scrolling manner.
When the summary window is the active window, clicking
the File menu and then Print All Pages or Print Current
Page will send the appropriate portions of the .OUT file
to the printer.
Figure 11. Example Summary of Computed Results Window.
As previously mentioned, the Create File menu option writes
the NONLIN.XL1 file to disk when this window is active.
Animation
A unique feature of the program is the Animation Window.
When opened by clicking the animation button, a representation
of the model structure and five plots are produced and
displayed in time increments. You can control the display
progress and speed through the use of a recorder control in
the upper left corner of the window. The recorder control
looks like this:
You can stop, start, reverse, fast reverse, fast forward
the progress of the simulated response. You can also
reverse to start and forward to end. A separate Animation
Speed slider is provided to control the speed of the simulation.
A Time Value slider is also provided so that you can move
to any point in time in the duration of the simulation.
The Time Value slider moves to indicate the relative point
in time in the progressing simulation.
By default, the structure roof displaces but the structure
foundation remains fixed. Note that the Relative Displacement
radio button is set. By choosing the Total Displacement
radio button, you can change the display to simulate ground
motion as well as structure motion. Clicking on the
Undeformed Shape check box in the upper right corner of
the window produces a stationary reference shadow representing
the original position of the structure before the application
of the dynamic loading.
Three time history plots of Input Ground Acceleration,
Displacement and Yield Code versus time are constantly
updated and displayed in the center portion of the window.
To right of the time histories plots, you see two
hysteretic plots: Damping and Spring force versus displacement.
Figure 12. Example Animation Window.
A yellow line appearing at the top or bottom of the
two structure columns indicates yielding of the structure.
A printed of the animation window is not directly
available. However, if you press Print Screen on your
computer keyboard, the current screen image is saved
to the Windows Clipboard. If you close or minimize NONLIN
and open a drawing program such as Paint, you can Paste
the image to the drawing program workspace by using the
Edit menu. From this point, you modify the image, print
it or save to a file.
References
1) Clough, Ray.W., and Penzien, J., Dynamics of Structures,
Volume 2, McGraw Hill, New York, N.Y., 1993.
2) Uang, C., and Bertero, V.V., “Evaluation of Seismic
Energy in Structures”, Earthquake Engineering and
Structural Dynamics, Volume 19, pp 77-90.
3) Chopra, A.K., Dynamics of Structures, Prentice
Hall, Upper Saddle River, N.J., 1995.
Acknowledgments
NONLIN was developed by Dr. Finley A. Charney of Advanced
Structural Concepts, Denver, Colorado. The developer would
like to thank Mr. Michael Valley of J.R. Harris & Company,
Denver, Colorado, for his assistance in verifying the results
of the program, and for making helpful suggestions throughout
the development process. Coding of the program was produced
by Dr. Finley Charney and Mr. Brian Barngrover. Mr. Scott
Harper assisted in the writing of the manual. Funding was
provided through a grant from the Federal Emergency Management
Agency (FEMA).
NONLIN was written in Microsoft Visual Basic Professional
Version 3.0. The files MHPFST.VBX and MHRUN400.DLL are
part of the IOTech VisuaLab-GUI system.
APPENDIX A
Summary of Ground Motion Records Supplied with NONLIN
Filename Description Max. Accel.[cm/sec2] Max. Veloc.[cm/sec] Max. Displ.[cm] Number of Points Duration[sec]
impval1.acc Imperial ValleyEl CentroMay 18, 1940270 degrees 3417.0 32.323 10.86 2688 53.74
impval2.acc Imperial ValleyEl CentroMay 18, 1940180 degrees 2101.0 -36.473 -19.783 2674 53.46
loma-p1.acc Loma PrietaOakland Outer WharfOctober 17, 1989270 degrees 270.361 -37.574 -7.999 2000 39.98
mexcit1.acc Mexico City Station 1September 19, 1985270 degrees -97.965 38.739 19.123 9006 180.1
mexcit2.acc Mexico CityStation 1September 19, 1985180 degrees -167.92 -60.499 21.936 9006 180.1
nridge1.acc Northridge Sylmar County Hosp.January 17, 199490 degrees 592.639 -76.936 -15.217 3000 59.98
nridge2.acc NorthridgeSanta Monica, City Hall GroundsJanuary 17, 199490 degrees -865.97 41.751 -14.316 3000 59.98
Summary of Ground Motion Records Supplied with NONLIN (continued)
Filename Description Max. Accel.[cm/sec2] Max. Veloc.[cm/sec] Max. Displ.[cm] Number of Points Duration[sec]
nridge3.acc NorthridgeArleta and Nordhoff Fire StationJanuary 17, 199490 degrees 337.318 -40.362 8.878 3000 59.98
oakwh1.acc Loma PrietaOakland Outer WharfOctober 17, 1989270 degrees 270.361 -37.574 -7.999 2000 39.98
oakwh2.acc Loma PrietaOakland Outer WharfOctober 17, 19890 degrees -215.50 -35.378 8.871 2000 39.98
pacoima1.acc San FernandoPocoima DamFebruary 9, 1971196 degrees 1054.9 -57.499 -10.801 2086 41.70
pacoima2.acc San FernandoPocoima DamFebruary 9, 1971286 degrees -1148.1 -113.23 37.538 2091 41.80
park040.acc ParkfieldCholame, ShandonJune 27, 196640 degrees -232.60 10.842 4.41 1310 26.18
park130.acc ParkfieldCholame, ShandonJune 27, 1966130 degrees -269.60 11.759 -3.933 1308 26.14
sanfern1.acc San Fernando8244 Orion Blvd.February 9, 197190 degrees -250.0 -29.745 -14.789 2975 59.48
Summary of Ground Motion Records Supplied with NONLIN (continued)
Filename Description Max. Accel.[cm/sec2] Max. Veloc.[cm/sec] Max. Displ.[cm] Number of Points Duration[sec]
sanfern2.acc San Fernando8244 Orion Blvd.February 9, 1971180 degrees -131.7 23.933 13.843 2980 59.58
s_monica1.acc NorthridgeSanta Monica City Hall GroundsJanuary 17, 199490 degrees -865.97 41.751 -14.316 3000 59.98
s_monica2.acc NorthridgeSanta Monica City Hall GroundsJanuary 17, 19940 degrees -362.93 24.910 6.525 3000 59.98
whitt01.acc WhittierEaton Canyon ParkOctober 1, 198790 degrees -157.88 -4.832 -.510 2000 39.98
whitt03.acc WhittierFremont SchoolOctober 1 , 1987180 degrees 286.159 -21.718 -2.443 2000 39.98
Note: The distribution diskette that came with your version of NONLIN may have more or less earthquake records than are indicated in this table.
APPENDIX B
Format of NONLIN Acceleration Records
NONLIN comes with a selection of earthquake accelerograms taken from a variety of sources. Each acceleration record consists of the following lines of data:
ntitles
“title 1”
“title 2”
.
.
“title ntitles”
nacc dtacc nplacc unitacc
nvel dtvel nplvel unitvel
ndis dtdis npldis unitdis
Acceleration header
nacc acceleration values, nplacc values per line
Velocity header
nvel velocity values, nplvel values per line
Displacement header
ndis displacement values, npldis values per line
The first line contains the entry ntitles, which designates how many title lines follow. Each title line must be in double quotation marks. NONLIN uses the first title line as a descriptor for each plot produced.
Following the title lines are three lines listing the number, timestep, number of values per line, and length units used for the following acceleration, velocity, and displacement data blocks which are listed below. Each data block begins with a header, which is read but otherwise ignored by NONLIN.
An partial listing of the file LOMAP1.ACC is given below. The lines with “.” in column 1 indicate data that was eliminated from the record for brevity.
Example Acceleration Record for Loma Prieta Earthquake:
4
"LOMA PRIETA EARTHQUAKE - OAKLAND OUTER HARBOR WHARF"
"OCTOBER 17, 1989, 17:04 PDT"
"CORRECTED ACCELEROGRAM, CHANNEL 1, 270 DEGREES, CDMG QL89A472 "
" SOURCE: NISEE, U.C. BERKELEY, CALIFORNIA"
2000 0.02 8 CM
2000 0.02 8 CM
2000 0.02 8 CM
2000 POINTS OF ACCEL DATA EQUALLY SPACED AT .020 SEC. (UNITS: CM/SEC/SEC)
-2.257 -.708 .339 -.139 1.199 3.213 3.521 2.479
-1.153 -4.317 -5.423 -6.067 -4.769 -.936 3.444 7.283
9.006 6.764 3.293 3.135 1.264 .210 1.797 .486
.
.
.
3.088 5.707 1.915 -3.141 -7.087 -10.550 -11.959 -11.184
2000 POINTS OF VELOC DATA EQUALLY SPACED AT .020 SEC. (UNITS: CM/SEC)
-.106 -.136 -.139 -.137 -.126 -.081 -.014 .047
.060 .006 -.091 -.206 -.313 -.370 -.344 -.236
-.072 .086 .188 .253 .297 .313 .334 .358
.
.
.
.395 .484 .561 .550 .449 .274 .049 -.182
2000 POINTS OF DISPL DATA EQUALLY SPACED AT .020 SEC. (UNITS: CM)
-.021 -.023 -.026 -.029 -.032 -.034 -.035 -.035
-.034 -.033 -.034 -.037 -.042 -.049 -.056 -.062
-.065 -.065 -.062 -.058 -.052 -.046 -.040 -.032
.
.
.
-.025 -.016 -.005 .006 .016 .024 .027 .026
End of File
Index
.
.ACC file, 3
.NLN file, 5
.XL1, 1
.XL2, 1, 28
.XL3, 1
A
acceleration, 11, 17, 18, 19, 36
acceleration records, 3, 7
accelerogram, 1, 16, 18
Amplitude, 1, 7, 22
ANIMATE BUTTON, 10
Animation, 29, 30, 31
B
Button Bar, 8
C
Compute Spectrum, 20
Computed Energy Plots, 6, 10, 27
Computed Hysteresis Plots, 1, 9, 25, 26, 27
Computed Time Histories, 1, 6, 9
Constitutive Properties, 11, 12
CREATE FILE, 6
Create File option, 6
Critical damping, 12
D
DAMPING, 7, 11, 12
displacement, 9, 12, 14, 17, 18, 19, 36
Duration, 8, 22, 33, 34, 35
dynamic, 1, 7, 8, 11, 13, 16, 24, 30
Dynamic Force, 10, 16, 21
Dynamic Force Applied As, 7, 8
E
earthquake, 1, 3, 7, 10, 11, 13, 16, 17, 18, 35, 36
Earthquake Response Spectrum of Input window, 6
energy dissipation, 1
Entering Structural Properties, 7, 10
F
FFT Plot, 23
File menu, 2, 5, 6, 7, 9, 19, 23, 26, 27, 28, 29
Force Units, 10, 11
free vibration, 16, 22
frequency content, 18
G
GO/NO GO, 8, 9
Ground Acceleration, 16, 18
H
HELP window, 8
I
INITIAL STIFFNESS, 11, 12, 13, 14, 15
INPUT DAMPING AS, 7
INPUT MASS AS, 7
Inputting Data, 4
Installing NONLIN, 2
L
Length Units, 10, 11
linear, 1, 11, 16, 21, 24, 28
Linear/Nonlinear Analysis, 16
logarithmic plot, 19
M
MASS, 7, 11, 12
Menu Items, 5
Microsoft Windows, 1, 2
N
Newtons, 11
NONLIN.OUT, 1, 10, 29
NONLIN.XL1, 6
NONLIN.XL2, 6
nonlinear, 1, 11, 13, 14, 15, 16, 24, 28
P
Paint, 31
PARAMETERS, 5, 7, 12
P-Delta effects, 1, 14, 15
Period, 8, 22
PLOT DATA, 18
Plot Spectrum, 20
Print Form, 1, 6, 9, 10, 19, 23, 26, 27
pseudo velocity, 20
Q
QUIK QUAKE, 5, 7
QUIK WAVE, 5, 7, 8
R
radio button, 30
Random Noise Frame, 23
REPAINT, 25, 26, 27
RESIZE, 26, 27
response, 10, 13, 14, 18, 19, 20, 23
response spectra, 19
Results, 6, 10, 24, 29, 31
RUN0, 24
S
secondary stiffness, 1, 11, 14, 15, 16
SETUP Utility, 2
slider, 30
Spectral Coordinates, 20
START ANALYSIS BUTTONS, 8
Startup Ramp Frame, 22
STEP FACTOR X, 7
strain hardening, 1, 14, 15
structural energy, 10
STRUCTURE PROPERTIES INPUT, 4, 8, 10, 17, 21, 23, 24
STRUCTURE RESTORE BUTTON, 8
Summary of Computed Results, 6, 10
System Requirements, 2
T
Taskbar, 3
the EARTHQUAKE GROUND ACCELERATION INPUT frame, 16
the STRUCTURE PROPERTIES INPUT, 5, 7
Tripartite, 19, 20
U
User Interface, 4
V
velocity, 17, 18, 19, 36
VIEW menu, 8
W
Wave Forcing Function, 21
WAVE GENERATOR, 8, 21, 22, 23
WINDOW menu, 8
Windows 3.x, 2
Windows 95, 2, 3, 5
Windows Clipboard, 31
WordPad, 1
Y
YIELD STRENGTH, 11, 15