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