UserGuide

Department of Civil Engineering COMPUTER PROGRAM LIBRARY

Program name:–RUAUMOKO2D

Program type:–Inelastic Dynamic Analysis

Program code:–ANSI Fortran77

Author:–Athol J Carr

Date:–25 September 2004

RUAUMOKO

The Maori God of Volcanoes and Earthquakes

Volume 2: User Manual for the 2-Dimensional Version, Ruaumoko2D

Copyright \ Athol J. Carr, University of Canterbury, 1981-2004. All Rights reserved.

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Running the program RUAUMOKO-2D.

The program is designed to run in an interactive mode or in a batch mode with an input data file that may beprepared using a word-processor, a spreadsheet or a text editor. If a word-processor or spreadsheet is usedto prepare a data file then the data MUST be saved as a plain ASCII text file. In the default form the programwill prompt the user for the input data. The input data supplied may be logged so that it can be used for lateranalyses and prepared data files may be used for all or part of the input data. For further details on the use ofthe command processor used in the program type $HELP at any prompt. Complete all responses by pressingthe RETURN/ENTER key.

To run the program call the program by the method appropriate to your operating system. On a personalcomputer just type RUAUMOKO2D assuming that the file RUAUMOKO2D.EXE and FQWIN.HLP are in yourcurrent directory or path.

In Microsoft Windows operating systems another option is to create a shortcut on the desktop and for thispurpose a suitable icon for RUAUMOKO, Ruaumoko2D.ico, is supplied with the program.

The program prompts for responses to a series of questions. Default responses, where appropriate, areenclosed in square brackets, [ ]. File names must match the conventions of your operating system but filenames, with paths where necessary, must not exceed 60 characters in length and must not contain blanks.

The first question asks for the name of the output file. The default is the computer console or terminal screen.

The next two questions are for names of the files containing the earthquake accelerograms or the excitationhistories. The default value assumes that the excitations are appended to the rest of the input data. If thereare less than three inputs records just hit the RETURN key for the subsequent requests. If the file names areincluded in the excitation part of the data file then just hit the RETURN key at each prompt.

The next question asks for the name of the DYNAPLOT post-processor file. This file will only be opened ifrequested by a greater than zero value of the variable KPA later in the data. This file is automatically giventhe extension .RES or .RAS if required, or if the name shown, which uses the filename of the output file, isacceptable, just hit the RETURN key.

The next question asks for the selection of on-screen graphics. Any answer not of the form Y, YE or YES(upper or lower case) will suppress the graphics. If the answer was YES and the screen supports colourgraphics you will later be asked if you want COLOUR graphics or not. Note; if on-screen graphics is enabledthe screen cursor is invisible at the end of all future prompts.

The next question asks if this is a data check run only. If so type Y, YE or YES. In the case of the data checkrun the analysis is terminated at the completion of the modal analysis and just before the start of the time-history analysis. The total storage requirements for the time-history analysis is checked.The program then displays information on logging or adding data files

The next prompt is for the title name of your analysis which is the first line of the data described in thefollowing sections of this manual. If the user already has a data file ready then type $ADD filename, wherefilename is the name and path if necessary of the data file, followed by RETURN. If the user is going to keythe data in as prompted, it is suggested that the all of the data be logged in a file for later use and to save re-supplying this data in the event of a data error by giving the command $LOG filename, where filename is thename of the file where data is to be logged, followed by RETURN. Note that all responses prior to this one willnot be logged even if logging had been enabled at an earlier prompt.

At the completion of reading and checking of all of the input data for the analysis, the program, if it is runningin an interactive mode and the on-screen graphics is enabled, the user will be prompted as to whether colourgraphics is wanted.

The on-screen graphics draws a picture of the structure with all members numbered and the analysis pausesuntil the RETURN key is pressed. If you want a hard copy use the pull-down menu at the top left of thewindow to print the picture or to save it as a The program will next plot the accelerograms or excitationhistories scaled to the magnitudes used in the analysis. These are cleared by pressing the RETURN key.

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After the modal analysis is complete the user is asked if the mode shapes are to be displayed in an animateddisplay. Respond by typing the mode number followed by RETURN. Five and a quarter cycles of vibrationare displayed unless a different number of cycles is specified. The default response END terminates theplotting of mode shapes and starts the time-history analysis.

During the time-history, on-screen pictures of the deformed shape of the structure showing the locations ofinelastic behaviour are presented but require no user action because the pictures are replaced automaticallyas soon as a new picture is ready. Excessive use of the screen capture during the time-history may cause thesystem to crash.

Running the program RUAUMOKO-2D in Batch Mode.

The program RUAUMOKO-2D may be run in a batch mode as well as the interactive mode described above.In the batch mode the graphics is disabled and the test data option is also disabled.

The .BAT file has the command line as follows:

START/w RUAUMOKO2D outputfile inputfile quake1file quake2file

The START/w is only required for Windows95 or Windows98 operating systems to prevent the system fromattempting to multi-task following command lines. For WindowsNT, Windows2000 or WindowsXP this itemshould be removed.

If the RUAUMOKO-2D executable file RUAUMOKO2D.EXE is not in your path then the path should be part ofthe command.

The outputfile is the name (including the path) of the output file. This file must NOT exist. If the file doesexist the analysis will terminate immediately. The post-processor file, if requested in the input data, will havethe same file name (and path) but with the extension .RES or .RAS .

The inputfile is the name (including path) of the input data file (in the form required in the following part of thismanual) and the file MUST exist. If the file cannot be found, because the name or path is incorrect then theanalysis will terminate.

The files quake1file and quake2file are the names (including paths) of the excitation files. These file namesare optional, if they are missing or the word INPUT (in upper case) is supplied instead than they are assumedto be part of the inputfile above. If files names are supplied then the files MUST exist or the analysis will beterminated.

If there are less than two arguments following the command RUAUMOKO2D then the programs will run in thenormal interactive mode.

As many such command lines may be arranged in a .bat file, the best example was a visitor to the departmentwho set up 475 runs in a batch file and went away for days skiing. The only real limitation is the amount ofdisk required for the output files, especially if the post-processing file is also output.

Enviroment Settings.

RUAUMOKO-2D makes great use of a local random access scratch file during th analysis. At each time-stepand in each iteration a read and a write operation is carried out for each member in the structure. The defaultlocation for this file RUAUMOKO.SCR is in the users current working directory. When the analysis iscompleted this file is deleted by the program, however, if the program is terminated prematurely by the userthis file may be left in the directory. This will not cause any difficulties as it will over-written the next time theprogram runs. However, if the program is being run over a network and the users working directory is on aserver, then a very large penalty will be paid for the network traffic and the program may appear to run atabout 40% of its normal speed. The tmp and temp environment variable should be set to a local hard disk onthe computer where the analysis will actually take place. On all of the Windows workstations in the School ofEngineering, University of Canterbury, computer laboratories these variables are set to C:\TEMP which is a

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local scratch directory on each workstation. If the programs are being run on a single personal computer thereis no necessity to set the environment variables.

On the latest personal computer version of RUAUMOKO-2D most of the scratch file is emulated in memorywhich has increased the execution speed of the program by factors of up to 8. However, should the numberof sectors required for the scratch file exceed the memory allocated the remainder of the disk sectors will bewritten to the hard disk file mentioned above. In all cases, even if it is not used, the file RUAUMOKO.SCR willbe created at the start of the program execution and deleted at the end of the analysis. (This disk in memoryapproach has been successfully used in VMS and unix workstations since 1989).

Do not attempt to carry out simultaneous executions of the program unless they are run from differentdirectories and the environment variable are not set as the scratch file would be accessed by the differentanalyses with great confusion as the result.

Note: In the following user guide, each line of required data is indicated by a box containing the data items.Below each box is a description of the data items. The data items on each line may be separated by commasor blank spaces. The format for the items are indicated by the letter at the end of each descriptive line with Aindicating a character string, I indicating an integer value and F indicating a floating point number. A floatingpoint number may or may not have a decimal point and may also take a scientific or exponent form such as1.5E6 which could also be expressed as 1500000.0. Character strings will be upper-cased unless enclosed indouble or single quotes and will terminate at the first blank space unless the string is enclosed in quotes.

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OVERVIEW OF THE DATA FOR "RUAUMOKO-2D"

The analysis data for the structure is described by the following sequence of input lines or card images. Eachdata set consists of the following items of data.

1 Title for the Analysis - one line - see section 1

2 Analysis Control Parameters - one line - see section 2

3 Structural Parameters - one line - see section 3

4 Output and Plotting Parameters - one line - see section 4

5 Iteration and Travelling wave parameters - one line - see section 5

6 NODES - one line - see section 7This is followed by one line for each nodal point giving the coordinates, the boundary condition flags,displacement slaving flags and the output control flag. The nodes must be in ascending numericalsequence. If lines are omitted their data will be interpolated.

7 ELEMENTS - one line - see section 8This is followed by one line for each member in the structure giving the property-set number, the fournodal point numbers that define the location, or connectivity, of the member and the output control flag.the members must be in ascending numerical order. Lines may be omitted with interpolation giving theproperties of the intervening members.

8 PROPS - one line - see sections 9,10,11,12,13,14,15,16,17,18,19 and 20.This is followed by lines for each of the sections in the properties table together with data on strengthand stiffness degradation covered in Appendices A and B.

9 WEIGHTS - one line - see section 21This is followed by one line for each node that has a specified point, or lumped, weight for the massmatrix.

10 LOADS - one line - see section 22This is followed by one line for each node that has a static load applied to it.

11 SHAPE - one line - see section 23This section only applies to dynamic load histories and not to earthquake analyses.This is followed by one line for each node that has a contribution to the dynamic forcing function that willact on the structure. The magnitudes of the loads are multiplied by the dynamic loading history which isdescribed in the following section. One set is required for each loading pattern, i.e. if there is a secondloading pattern repeat all of this section for the second loading pattern.

12 EQUAKE - one line - see section 24. This is only required if dynamic excitation is applied.This is followed by a line with the parameters for the accelerogram or the loading history.This then may be followed by the accelerogram or loading history though in most cases theaccelerogram is read from a separate file.

13 EQUAKE - one line - see section 24. This is only required if there are two components of theaccelerogram or loading history.This is followed by a line with the parameters for the accelerogram or the loading history.This then may be followed by the accelerogram or loading history though in most cases theaccelerogram is read from a separate file.

14 EQUAKE - one line - see section 25. This data is only required for a Cyclic Adaptive Pushover Analysis.This is followed by a line with the parameters for the application of the displacement history.This then may be followed by the displacement history though in many cases the history may be readfrom a separate file.

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15 SPECTRA - one line - see section 26. This is only required if the analysis is for a Response SpectraAnalysis.This is followed by a line with the parameters for the Acceleration Response Spectra.This then may be followed by the data for the response spectra though the spectra could be read from aseparate file.

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THE DATA FILE FOR "RUAUMOKO-2D"

The analysis data for the structure is described by the following sequence of input lines or card images.

1 Description of the Analysis

Description of the structure (up to 79 alphanumeric characters)

2 Principal Analysis Options

IPANAL IFMT IPLAS IPCONM ICTYPE IPVERT INLGEO IPNF IZERO ORTHO IMODE

IPANAL = 0 ; Static Analysis (with iteration for in-elastic behaviour) I= 1 ; Static (with iteration for in-elastic behaviour) and Modal Analyses= 2 ; Dynamic Time-history using Newmark constant average acceleration = 3 ; Dynamic Time-history using Central Difference explicit method= 4 ; As for IPANAL=2 above but see note below.= 5 ; As for IPANAL=3 above but see note below. = 6 ; Adaptive Push-Over= 7 ; Cyclic Adaptive Push-Over= 8 ; Multiple Input Ground Displacement Histories.= 9 ; As for IPANAL=8 above but see note below.=10 ; Response Spectrum Analysis

IFMT = 0 ; Binary post-processor file with extension .RES I= 1 ; ASCII binary post-processor file with extension .RAS

IPLAS = 0 ; Elastic Time-history Analysis only I= 1 ; In-elastic Time-history Analysis

IPCONM = 0 ; Lumped mass matrix used in Time-history I= 1 ; Diagonal mass matrix used in Time-history= 2 ; Consistent mass matrix used in Time-history

ICTYPE = 0 ; Initial Stiffness Rayleigh Damping I= 1 ; Tangent Stiffness Rayleigh Damping= 2 ; Linear variation of damping with elastic natural frequencies = 3 ; Tri-linear variation of damping with elastic natural frequencies = 4 ; User specified modal damping= 5 ; Material specific Rayleigh Damping

IPVERT = 0 ; X-direction earthquake only I= 1 ; Y-direction earthquake only = 2 ; Both X and Y direction earthquakes= -1 ; One component dynamic loading history= -2 ; Two component dynamic loading history

INLGEO = 0 ; Small displacement analysis assumed. I= 1 ; Large displacement effects included= 2 ; P-Delta effects included (after the static analysis the stiffnesses

are modified and INLGEO is reset to 0)IPNF = 0 ; Modal analysis is carried out after the static analysis (Normal Case) I

= 1 ; Natural frequencies and Mode Shapes are NOT calculated= 2 ; Modal analysis is carried out before the static analysis

IZERO = 0 ; All zero output is omitted (normal case) I= 1 ; All zero output is printed

ORTHO = 0 ; Mode shape orthogonality check not carried out. I= 1 ; Mode shape orthogonality check printed

IMODE = 0 ; Householder QR eigenvalue algorithm used (Default) I= 1 ; Jacobi eigenvalue algorithm used= 2 ; Sub-space iteration eigenvalue algorithm used

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Notes: If IPANAL is greater than 0, a static analysis is carried out if any static loads are specified and thenthe modal analysis is performed unless suppressed, or the order of the operations is reversed, by thevariable IPNF.

Limits on valid ranges for variable IPVERT If IPANAL = 1,2,3,4 or 5, IPVERT = 0,1 or 2, or >-100

If IPANAL = 6 or 7, IPVERT = -1 If IPANAL = 8 or 9, IPVERT < 100

If IPANAL = 10, IPVERT = 0,1 or 2

For IPANAL = 4 or 5. Degrees of Freedom flagged as for travelling wave input are treated as fixed forthe static and modal analyses and are then released at the start of the relative displacement timehistory integration.

For IPANAL = 9. Degrees of Freedom flagged as input nodal displacement degrees of freedom arefixed for the static and modal analyses and are then released at the start of the total displacementtime history integration.

IPANAL = 6 is for an Adaptive Push-Over Analysis where the input load pattern is adapted as thestructure deforms and the analysis will terminate when the limit displacement is reached, the factoredelastic displacement is reached or the structure stiffness reduces to 0.1% of the initial stiffness.

IPANAL = 7 is for a Cyclic Adaptive Push-Over Analysis where the input load pattern is adapted asthe structure deforms and when the change points in the prescribed displacement history is reachedthe loading again reverts to the initial loading pattern but in the opposite direction and the adaptiveloading again continues until the next reversal point in the displacement history is reach. The analysiswill terminate when the displacement history is completed or the structure stiffness reduces to 0.1% ofthe initial stiffness.

IPANAL = 8 is for the case for simulating a laboratory excitation where a displacement is applied tothe structure at a particular degree of freedom or a set of degrees of freedom. In this case thedegrees of freedom where the displacements are to be applied are treated as free for the static andmodal analyses, i.e. gravity and free-vibration cases and then the displacement histories are appliedto these degrees of freedom. The analysis is a Relative Displacement formulation.

IPANAL = 9 is for the case for the analysis of a structure where the ground is to be subjected to a setof specified ground displacement histories. This would be appropriate if the different motions are tobe applied at different parts of the foundation or at different depths in the foundation. For the staticand modal analyses these degrees of freedom need to be fixed to prevent rigid body displacements ofthe structure. The analysis is a Total Displacement formulation

IPANAL = 10 is for the case for the analysis of a structure where the ground motion is based on anacceleration response spectra. The data for a normal dynamic analysis is read but then the analysisis reset to linear elastic, the damping model is reset to Rayleigh damping, the mass matrix is reset todiagonal and the analysis is set to small displacement theory. There may be separate spectra for theeach earthquake direction or the same spectra may be use for all earthquake component. Theanalysis is a Relative Displacement formulation.

ORTHO is a flag that enables the user to show the orthogonality of the mode shapes computed withrespect to the mass matrix. Ideally the diagonal terms of the orthogonality matrix should be 1.0 andthe off-diagonal terms should be 0.0.. This check is normally only used if, for some reason, there is asuspicion that the modes computed are not orthogonal with respect to the mass or stiffness matrices.

IMODE is used to select the eigenvalue algorithm used to compute the natural frequencies and modeshapes of free-vibration. The default is the Householder and QR algorithm that has been used sincethe mid-1960s. This has always been reliable but in 2001 3 instances were reported where non-orthogonal modes were computed The Jacobi algorithm is the most stable algorithm available but isslow, and if any mode shapes are required they all have to be found, recommended for smallproblems only. The Sub-space iteration method is suitable for very large problems but must be usedwith care if parts of the structure have very small masses with small stiffnesses to match as theiteration process may then be unpredictable. The iteration uses a generalised Jacobi eigenvalueroutine.

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Rayleigh or Proportional Damping Model ICTYPE=0 or 1

Linear or Tri-linear Damping Model ICTYPE=2 or 3

User Specified Modal Damping ICTYPE=4

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3 Frame Control Parameters

NNP NMEM NTYPE M MODE1 MODE2 GRAV C1 C2 DT TIME FACTOR

NNP Number of nodal points in the structure INMEM Number of members in the structure INTYPE Number of different cross-section in the section table IM Number of mode-shapes required to be printed in the modal analysis IMODE1 The mode number at which the first damping ratio is applied. IMODE2 The mode number at which the second damping ratio is applied IGRAV The acceleration of gravity FC1 The percentage of critical damping at mode MODE1 FC2 The percentage of critical damping at mode MODE2 FDT The time-step (Time units, usually seconds) FTIME The length of time-history to be run (Time units, usually seconds) FFACTOR A scale factor applied to the time-history input (Default = 1.0) F

Note: If both MODE1 and MODE2 above are zero then the coefficients C1 and C2 are to be taken as theconstants " and $ of the Rayleigh damping model. If there is only one dynamic degree of freedom then if MODE1=1 and MODE2=0 then massproportional damping is modelled.If there is only one dynamic degree of freedom then if MODE1=0 and MODE2=1 then stiffnessproportional damping is modelled.If ICTYPE = 4, User specified Modal damping, then MODE1 is the number of modes for whichdamping is specified, 1 # MODE1 # 10. Note that MODE2, C1 and C2 should be zero.

4 Output Intervals and Plotting Control Parameters

KP KPA KPLOT JOUT DSTORT DFACT XMAX YMAX NLEVEL NUP IRESID KDUMP

KP = 0; Time-history output suppressed I= k; Time-history output every k time-steps

KPA = 0; Post-processor DYNAPLOT output suppressed I= k; Post-processor DYNAPLOT output every k time-steps

KPLOT = 0; Plastic Hinges plotted at every status change I= k; Plastic Hinges plotted every k time-steps

JOUT Not used any longer, supply 0 (zero) IDSTORT Not used any longer, supply 1.0 (one) FDFACT Displacement multiplying scale factor for on-screen graphics. $ 1.0 F XMAX Maximum X displacement for use in the on-screen graphics FYMAX Maximum Y displacement for use in the on-screen graphics FNLEVEL Number of levels for computed inter-storey drifts, i.e. number of storeys+1 I If NLEVEL is less than 2 then inter-storey drifts are not output.NUP Vertical axis for inter-storey drifts, 1=X axis or 2=Y axis. IIRESID =1, Residual displacements and forces output at end of time-history output. I

=0, Residual displacements and forces not output.KDUMP = 0; Mass and Stiffness matrices output suppressed I

= k; Mass and Stiffness matrices output every k time-steps

Note: The variables JOUT and DSTORT are no longer used in Ruaumoko but are retained to maintainbackwards compatibility of the data files.If KP is zero for a response spectra analysis (IPANAL=10) then only the combined modal responsewill be output whereas if KP is greater than zero each modal response will also be output.

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5 Iteration Control and Wave Velocities

MAXIT MAXCIT FTEST WAVEX WAVEY THETA DXMAX DYMAX D OMEGA F

MAXIT Maximum number of cycles of Newton-Raphson iteration per Time-step IIf =0 : no iteration If IPANAL = 3 (explicit integration) MAXIT is the number of sub-steps per time-step DT in the integration of the equations of motion i.e. the actual integration time-step = DT/MAXIT

MAXCIT Maximum number of cycles of iteration/solution step for damping models IICTYPE = 2, 3 or 4 that have coefficients outside the skyline of the stiffnessmatrix. In other values of ICTYPE use 0

FTEST Norm of the out-of-balance force vector relative to the incremental force Fvector for the Newton-Raphson or damping iteration.The value is the square of the iteration tolerance required. i.e. 0.0001 implies a tolerance of 1% in the residual vector.

WAVEX Wave velocity of propagation in the x-direction (if = 0.0 taken as infinite) FWAVEY Wave velocity of propagation in the y-direction (if = 0.0 taken as infinite) FTHETA Angle of Earthquake X and Y direction to structure X and Y directions F

degrees (default =0.0)DXMAX X displacement to terminate analysis FDYMAX Y displacement to terminate analysis FD Traveling Wave Dispersion Factor I

0.0 implies no dispersion (D = infinity)1.0 Maximum dispersion.100.0 Minimum dispersion

OMEGA Earthquake Characteristic Frequency (radians/second) used for dispersion. FF Scale factor for dispersion (default = 0.10) F

Notes: 1. If IPVERT is negative then travelling wave models are not permitted.2. If the ground wave velocities WAVEX and/or WAVEY are input as zero they are treated as

infinite.3. When the Central Difference marching method is being used for the time-history integration

then the actual time-step DT/MAXIT must be less than half the shortest natural period of thestructure if numerical instability is to be avoided in the time-history integration.

4 The Displacement limits are absolute values in that only positive numbers are used.5 The default value for FTEST used when either one or both of MAXIT and/or MAXCIT are

specified is 0.00001. Note that the squares of the vector norms are used in the test so that0.001 implies a 3% tolerance and 0.0001 implies a 1% tolerance.

6 If the variable MAXCIT is applicable the maximum number should lie in the range of 1 to 3.As a rule, experience has shown that very seldom is more than one cycle of iterationrequired.

7 As a general observation not more than about 5 Newton Raphson iterations should beneeded in any time-step

8 If Dispersion is applied to the travelling wave, then the amount of dispersion applied to theaccelerogram applied to nodes after the first node to receive the input depends on the wavevelocity, the distance between the nodes (i.e. the time delay) and the dispersion parameter Dand the characteristic earthquake frequency OMEGA. The dispersion is in the form of awhite noise which is designed not to significantly alter the response spectra of the inputground motion. The first node to receive the input motion has no dispersion applied to itsinput motion.

9. The dispersion amplitude may be scaled by the factor F.

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5a User Specified Modal Damping Parameters (Only if ICTYPE = 4)

MODE1 DAMP1 MODE2 DAMP2 .. .. MODEn DAMPn

MODEi Mode number. Must be in ascending numerical order, IDAMPi Percentage of Critical Damping for MODEi F

Notes:1. Number of Modes n specified must equal MODE1 of line 2, Principal analysis options.2. Damping for modes less than the first mode above is taken as DAMP1 and damping for modes

greater than the last above is taken as DAMPn. This model may be considered as a variation of thetrilinear damping model.

3. For modes with numbers in-between the modes specified, the Percentage of Critical damping isinterpolated with respect to the modal frequencies of the modes at the beginning and end of the gapin the mode numbers.

6 Time-History Output Control

Output control during the time-history integration is under the control of the parameters KP and KPA on theSection 4 above. If the parameter KP is non-zero, = J, the results are written to the output file, or device, everyJ time steps starting at step 0. Likewise, if KPA is non-zero, = I, then results go to the post-processingDYNAPLOT disk file every I time steps starting at step zero.

The control of which nodes or members have their results output is determined by the parameter IOUTassociated with each of the nodes or members in the following data sections.

The value of IOUT lies in the range of 0 to 3;

IOUT = 0; if required, the results will be sent to both the output file and written to the DYNAPLOT file.= 1; if required, will only be written to the DYNAPLOT file= 2; if required, will only be sent to the output file.= 3; will neither be printed or written to the DYNAPLOT file or to the output file.

Default values of IOUT are set on the lines with the words NODES or MEMBERS in Sections 7 or 8 below andthese values will apply for all nodes or members unless over-ridden by new values on the data for that node ormember. Interpolated nodes or members take the value for the first node or member in the sequence.

At every time step the following information may be written to the DYNAPLOT post-processing file.

1. The time, ground accelerations and the inertia, damping and elastic energies, the external work doneby the applied loads and the plastic work.

2. For every requested node, the nodal displacements, velocities, accelerations, damping forces, inertiaforces and applied forces.

3. For every requested member, the member forces, the member deformations, the member actionstiffness flags as a percentage of the elastic stiffness. (axial, flexure at end 1, flexure at end 2) or(longitudinal displacement, transverse displacement and moment). For the four-hinge beam membersthe moments, curvatures and stiffness flags for the internal hinges are also output. For Frame andWall members the shear forces at each end are also output.

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7 Nodal Point Input

One input line with the word NODES starting in column 1.

NODES IOUT

IOUT Output control flag (see section 6 above) I

One input line required per nodal point, except that the presence of sequential nodal points with equallyspaced nodal point coordinates need only be implied by the presence of the first and last nodal points of thesequence. Boundary conditions will be taken (except for the last nodal point in the sequence) as beingidentical to those of first nodal point in the sequence. Coupling nodes will also be interpolated between thefirst and last nodal points in the sequence.

N X(N) Y(N) NF1 NF2 NF3 KUP1 KUP2 KUP3 IOUT

N Nodal point number IX(N) X-coordinate of node N FY(N) Y-coordinate of node N FNF1 = 0; x-displacement is unconstrained I

= 1; x-displacement is zero i.e. fixedNF2 = 0; y-displacement is unconstrained I

= 1; y-displacement is zero i.e. fixedNF3 = 0; Z-rotation is unconstrained I

= 1; Z-rotation is zero i.e. fixedKUP1 = 0; no coupling of the X-displacement degree of freedom I

= J; X-displacement of this node is coupled to that of node J= -1; Support node for travelling wave input for x component of input.

(NF1 must = 0) = -k; Only if IPANAL = 8 or 9. Input k displacement at this degree of

freedomKUP2 = 0; no coupling of the Y-displacement degree of freedom I

= J; Y-displacement of this node is coupled to that of node J= -1; Support node for travelling wave input for y component of input.

(NF2 must = 0)= -k; Only if IPANAL = 8 or 9. Input k displacement at this degree of

freedomKUP3 = 0; no coupling of the Z-rotation degree of freedom I

= J; Z-rotation of this node is coupled to that of node J (Caution must be exercised here as the rotational coupling couples only the rotational degree of freedom and does not make any allowance for the distance between the nodes)

= -k; Only if IPANAL = 8 or 9. Input k displacement at this degree of freedom


Note: There is no restriction of the ordering of master and slave nodes in the program and daisy chaining ofslaving has also been used. However, care must be exercised to ensure that circular chaining doesnot occur, i.e. that the node is not effectively slaved back to itself. The unconstrained equations arenumbered and then the program works out the equation numbers of the slaved nodes. Once themember data has been input the equations are automatically renumbered to maximise the executionspeed in the subsequent equation solving. This means that if one later wishes to apply foundationcompliance to what was a fixed-base structure then the original node numbering does not have to bechanged, the new numbers for the foundation nodes are just appended to the existing nodesequence. Similarly, adjoining frames in a pounding study can be numbered sequentially rather thannumbering across floors of both structures to minimise band-width. Dummy nodes may be left in thedata set as long as they are fully fixed.

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7a. Inter-storey Drift Input. (Only if NLEVEL on data line 5 is greater than 2)

One input line with the word DRIFT starting in column 1.

DRIFT

This is followed by a line or lines with a list of a list of NLEVEL nodal point numbers starting with a node pointat the ground level and then with a node point at each storey progressing upwards from the bottom of thestructure. If the nodes cannot be listed on one line then take as many lines as is necessary. The program willcontinue reading data lines until all NLEVEL numbers have been read.

N1 N2 N3 . . . Ntop

N1 Nodal point number at ground floor, or first level, of the structure. IN2 Nodal point number at the second level of the structure. IN3 Nodal point number at the third level of the structure. I. . . Nodal point numbers at intermediate levels INtop Nodal point at the top level of the structure I

Notes: The total number of nodes must be NLEVEL

15

Four Node Member

Quadrilateral Elements and Panel Elements

16

8 Member Topology or Geometry

One input line with the word ELEMENTS starting in column 1.

ELEMENTS IOUT


One input line is required per member in ascending order, except that sequential members with a nodal pointnumbering that uniformly increments may be implied by the provision of the first and last member in thesequence. The member type for all interpolated members will be taken as that for the first member in thesequence.

N MT NODE1 NODE2 NODE3 NODE4 IOUT

N Member number IMT Member type number, refers to the member properties that follows INODE1 Nodal point number at end 1 of the member INODE2 Nodal point number at end 2 of the member INODE3 Inner nodal point at end 1 of the member I

(if NODE3 is zero or blank it is reset = NODE1) NODE4 Inner nodal point at end 2 of the member I

(if NODE4 is zero or blank it is reset = NODE2) IOUT Output control flag (see section 6 above) I

Notes: The 4-node members are connected to NODE1 and NODE2 only with no stiffness contributions tonodes NODE3 and NODE4. These latter two nodes NODE3 and NODE4 are purely for a geometricdefinition (they are assumed to be connected to nodes NODE1 and NODE2 respectively by rigid linkswith the flexible section of the member lying between the inner nodes). The boundary conditions forthe inner nodes NODE3 and NODE4 must be fully fixed.In a large displacement analysis the coordinates of nodes NODE3 and NODE4 are updated from theincremental displacements and rotations of nodes NODE1 and NODE2.

All four nodal points are required and must be distinct for the quadrilateral finite elements and themasonry panel elements. The nodal points must be given in an anti-clockwise sequence around theelement.

17

9 Member Property Tables

One input line with the word PROPS starting in column 1.

PROPS

10 Section Property Information

One set of input for every different cross-section type (this may be due to the different initial load conditionsetc.). These must be arranged in ascending section number order and each must be one of the followingsection types;

N MTYPE LABEL

N Section Number I MTYPE = FRAME => Beam or Beam-Column member A

= SPRING => Translational and Rotational Spring member= WALL => Taylor Structural-Wall member = DAMPER => Viscous Damping member = TENDON => Active Tendon or Constant Force member= CONTACT => Contact or Impact member= QUAD => Quadrilateral Finite Element.= PANEL => Masonry In-fill Panel= GROUND => Foundation Element= MULTISPRING => Multi-Spring Hinge Element.

LABEL Maximum 30 character label for section. If you wish to retain case or if the Alabel contains blank characters enclose the label in single or double quotes.

The MTYPE may be supplied with just enough letters to be distinct , in this case just the first letter is sufficient.

The above line for each section shall be followed by the remaining data for the appropriate member types.See the following sections.

SECTION 11 = FRAME type members SECTION 12 = SPRING type members SECTION 13 = WALL type members SECTION 14 = DAMPING type members SECTION 15 = TENDON type members SECTION 16 = CONTACT type membersSECTION 17 = QUAD type elements.SECTION 18 = PANEL type elementsSECTION 19 = GROUND type elementsSECTION 20 = MULTI-SPRING elements

18

Beam Sign Convention

Frame Member

11 FRAME type member properties

Order of all of the components required for Frame Members are: 1 Basic Section Properties see section 11a 2 Elastic properties see section 11b 3 Member bi-linear factors and hinge lengths only is IHYST > 0, see section 11c 4 Material Specific Damping Parameters, (only if ICTYPE = 5 on line 2) see section 11d 5 Member initial conditions, or fixed end forces, only if ICOND > 0, see section 11e 6 Yield Forces and Moments Except when IHYST = 0, see sections 11f to 11i 7 Shear Yield data, only if IGA > 0, see sections 11j or 11k 8 Strength Degradation Parameters, only if ILOS > 0, see section 11l 9 Stiffness Degradation Parameters, only if IHYST > 0, see section 11m10 Damage Index data, only if IDAMG > 0, see section 11n

19

Giberson One Component Beam Model

Two Component Beam Model

Four-Hinge Beam Model

Variable Flexibility Beam Member

20

11a. Basic section properties

ITYPE IPIN ICOND IHYST ILOS IDAMG ICOL IGA

ITYPE = 1; One Component (Giberson) BEAM member I= 2; Concrete BEAM-COLUMN member= 3; Steel BEAM-COLUMN member= 4; General quadratic BEAM-COLUMN member= 5; Two-component BEAM member= 6; Variable Flexibility BEAM member= 7; Four-Hinge BEAM member

IPIN = 0; Member built-in to joint (Normal case) I= 1; End 1 pinned (internally) to the joint= 2; End 2 pinned (internally) to the joint= 3; Both ends pinned (internally) to the joint

ICOND = 0; No initial loads applied I= 1; Initial Fixed-end forces or Prestress are applied. See section 11e.

IHYST = n; Hysteresis rule. See Appendix B IILOS = 0; No strength degradation. See Appendix A I

= 1; Strength reduction in each direction based on its ductility factor= 2; Strength reduction based on number of cycles= 3; Strength reduction based on maximum ductility= 4; Strength reduction as for ILOS=1 above but strength reduction also with

number of inelastic cycles.= 5; Strength reduction as for ILOS=4 above but strength reduces suddenly

at ultimate ductility.= 6; Strength reduction as for ILOS=3 above but strength reduction also with


at ultimate ductility.IDAMG = 0; No damage indices computed I

= m; Damage indices computed (m integer > 0 used as weight)ICOL = 0; Column ductilities computed at balance point of axial force I

= 1; Column ductilities computed at static axial force= 2; Column ductilities computed at zero axial force= 3; Column ductilities computed at each time-step using current axial force

IGA = 0; Shear deformation is elastic (only option if ITYPE=7) I= 1; In-elastic Shear deformation with SINA hysteresis= 2; In-elastic Flange Shear-Link model

Note:1. If ITYPE above is 6 or 7 then IHYST may not be 1, 5, 18 or 19, IPIN must be 0 and the bi-linear factor

RF in section 11c must have a value greater than or equal to 0.01.

2. If the member is linearly elastic then there is no effective distinction between members ITYPE 1 to 6.

3. To represent truss members either IPIN = 3 or I (in section 11b) is set equal to zero. The latter option ispreferred as then all beam hysteresis rules can be used for the truss behaviour. If the first option is usedthen only the elasto-plastic and bi-linear rules may be used.

4. The value of IDAMG is used as a weight when computing the weighted damage index for the wholestructure. Only integer values are accepted. If all damage index flags are 1 then the weighted damageindex for the structure is the average damage index.

21

11b. Elastic section properties

E G A AS I WGT END1 END2 FJ1 FJ2

E Elastic (Young's) Modulus of member material FG Shear Modulus of member material FA Cross-sectional AREA of the member section FAS Effective SHEAR AREA of the member section F

(if AS=0.0 then shear deformations in the section are suppressed)I MOMENT of INERTIA (2nd Moment of Area) of section FWGT Weight/(unit length) of the member FEND1 Length of Rigid End-block at End 1 of member FEND2 Length of Rigid End-block at End 2 of member FFJ1 Joint flexibility at End 1 (radians/unit moment) FFJ2 Joint flexibility at End 2 (radians/unit moment) F

Note: The weight/unit length is used to compute the member mass and does not contribute to the static loadson the member or the structure.The end-block lengths END1 and END2 are within the beam between nodes NODE3 and NODE4.

11c. Member Bi-linear Factors and Hinge Properties (only if IHYST above not equal 0)

RA RF H1 H2 H3 H4 H5 H6 H7

RA Bi-linear factor (or Ramberg-Osgood r) (Axial) FRF Bi-linear factor (or Ramberg-Osgood r) (Flexure) FH1 Plastic Hinge Length at End 1 FH2 Plastic Hinge Length at End 2 F H3 Plastic Hinge Length at Hinge 3 (4-Hinge Beam only) FH4 Plastic Hinge Length at Hinge 4 (4-Hinge Beam only) F H5 Fraction of length Hinges 1 to 3 (4-Hinge Beam only) FH6 Fraction of length Hinges 4 to 2 (4-Hinge Beam only) FH7 Fraction of Central EI to Section EI (4-Hinge Beam only) F

Notes:1. For One-Component and Four-Hinge Beams and all Beam-Columns the plastic hinge lengths are reset

to 1.0 if 0.0 is specified making the plastic curvature the same as the plastic hinge rotation.2. The plastic hinge lengths are not used for the Two-Component Beam members.3. The plastic hinge lengths for Variable Flexibility Beams should be between 0.1 and 0.5 of the member's

clear span.4. The Fractions of length to the interior plastic hinges of the Four-Hinge Beam member should be between

0.1 and 0.4, the default is 0.3.5. The Central Stiffness ratio is the fraction of the end stiffnesses that is used by the central region between

hinges 3 and 4. The minimum is 0.1. All stiffness quantities, AE, EI and GA are adjusted by the samescale factor.

22

11d. Material Specific Damping (only if ICTYPE = 5 in section 2)

This option allows different sections to have their own values of ALPHA and BETA for Rayleigh Damping. Thisis useful if one is modelling a pounding study between two adjoining buildings where the buildings have differentdamping characteristics or where different parts of the system have different damping characteristics, i.e. in soil-structure interaction studies. Damping matrix C is given by

where M = Mass, = Initial Elastic Stiffness, = Current Tangent Stiffness.

BETA0 BETAT ALPHA

BETA0 Multiplier associated with Initial Stiffness FBETAT Multiplier associated with Tangent Stiffness FALPHA Multiplier associated with Mass F

23

Frame Member Initial Fixed End Force Sign Convention

11e. Member Initial Fixed End Forces (only if ICOND = 1)

M1 M2 V1 V2 AXIAL AXPS IOP

M1 Fixed-end moment at End 1 F M2 Fixed-end moment at End 2 F V1 Fixed-end shear force at End 1 FV2 Fixed-end shear force at End 2 FAXIAL Axial force applied to member F AXPS Axial prestress in the member FIOP = 0; Axial prestress has no effect of the structure (see note below) I

= 1; Axial prestress also implies loads acting on the nodes at the endsof the member.

Note: The prestress force which is Tension positive affects only the internal member axial force used in thedetermination of yield states and has no effect on the static analysis of the structure.

The Axial force applied to the member is positive if it acts in the direction NODE3 to NODE4 and one halfof this force is applied to each of the nodes at the ends of the member.

Positive member moments cause tensile stresses on the bottom fibres and positive shear forces act in the localy direction on the positive local x face of the beam section. Tensile axial forces are positive. As an example ifa downward load is applied to the above member M1, M2 and V1 are negative while V2 is positive.

24

11f. BEAM Yield Conditions

PYT PYC MY1+ MY1- MY2+ MY2- MY3+ MY3- MY4+ MY4-

PYT Axial force for tensile yield ( $ 0.0) FPYC Axial force for compression yield ( # 0.0) FMY1+ Positive yield moment (End 1) ( $ 0.0) FMY1- Negative yield moment (End 1) ( # 0.0) FMY2+ Positive yield moment (End 2) ( $ 0.0) FMY2- Negative yield moment (End 2) ( # 0.0) FMY3+ Positive yield moment (Hinge 3) ( $ 0.0) FMY3- Negative yield moment (Hinge 3) ( # 0.0) FMY4+ Positive yield moment (Hinge 4) ( $ 0.0) FMY4- Negative yield moment (Hinge 4) ( # 0.0) F

Note: Yield moments for hinges 3 and 4 are only required for the Four-hinge BEAM members. If both yieldmoments at a hinge are zero then the hinge remains elastic. If both PYC and PYT are zero then axialyield is suppressed. If both positive and negative yield moments at a hinge are zero then yield at thathinge is suppressed.There is no interaction between axial forces and the yield moments.

25

Concrete Beam-Column Yield Interaction Surface

11g. Concrete BEAM-COLUMN Yield Surface at End 1 of member

PYC PB MB M1B M2B M0 PYT IEND

PYC Axial compression yield force ( < 0.0) FPB Axial compression force at B ( < 0.0) FMB Yield moment at B ( > 0.0) FM1B Yield moment at P=(2/3)*PB ( > 0.0) FM2B Yield moment at P=(1/3)*PB ( > 0.0) FMO Yield moment at P=0.0 ( > 0.0) FPYT Axial tension yield force ( > 0.0) FIEND = 0; End 2 of the member has the same yield surface I

= 1; A further line will be required to supply the parameters PYC to PYT for End 2 of the member.

Note: If M1B = M2B = 0.0 then a straight line is used between the points (PB, MB) and (0.0, MO) and not thecubic curve. The interaction is symmetric about the M = 0.0 axis.

26

Steel Beam-Column Yield Interaction Surface

11h. Steel BEAM-COLUMN Yield Surface at End 1 of member

PYC PB MB M0 PC MC PYT IEND

PYC Axial compression yield force ( < 0.0) FPB Axial compression force at B ( < 0.0) FMB Yield moment at B ( > 0.0) FMO Yield moment at P=0.0 ( > 0.0) FPC Axial tension force at C ( > 0.0) FMC Yield moment at C ( > 0.0) FPYT Axial tension yield force ( > 0.0) FIEND = 0; End 2 of the member has the same yield surface I


Note: The interaction is symmetric about the M=0.0 axis.

27

Quadratic Beam-Column Yield Interaction Surface

11i. Quadratic BEAM-COLUMN Yield Surface at End 1 of member

PYC PB MB PC MC PYT IEND

PYC Axial compression yield force ( < 0.0) FPB Axial force at B (PYT > PB > PYC) FMB Yield moment at B ( > 0.0) FPC Axial force at C (PYT > PC > PYC) F MC Yield moment at C ( < 0.0) FPYT Axial tension yield force ( > 0.0) F IEND = 0; End 2 of the member has the same yield surface I


28

SINA Hysteresis

11j. In-elastic Shear Parameters (Only if IGA on line 11a is 1)

One line for in-elastic shear for flexure about the local z-z axis.

Vy Vcr Vcc Alfa R Duct1 Duct2 Vres Phi1 Phi2 Pres Ido

Vy Shear yield strength ( > 0.0) FVcr Shear cracking strength ( > 0.0) FVcc Shear crack closing corce ( > 0.0) FAlfa Bi-linear factor, cracking to yield ( R < Alfa < 0.0) FR Tri-linear factor after yield ( > 0.01) FDuct1 Shear ductility where strength degradation starts F

If less than 1.0 then no shear strength degradationDuct2 Shear ductility where shear strength degradation stops ( > Duct1) FVres Residual shear strength as proportion of Vy (0.01 # Vres < 1.0) FPhi1 Flexural ductility where shear strength degradation starts F

If less than 1.0 then no shear strength degradationPhi2 Flexural ductility where shear strength degradation stops ( > Phi1) FPres Residual shear strength as proportion of Vy (0.01 # Pres < 1.0) F

(Note: Vres*Pres*Vy must be somewhat greater than Vcr)Ido = 0; In-elastic shear yield may occur (default) I

= 1; Retrofit assumed, message printed, shear remains elastic.= 2: Failure assumed, message printed, analysis terminated.

Notes: The flexural ductility used for the strength degradation is based on the flexural ductilities at the hingesat the ends of the member.

The action taken on the reaching of the shear yield strength follows the rules of Satyarno in his study onthe behaviour of shear-flexure interaction in framed structures.

The in-elastic shear follows the SINA hysteresis rule. Please see the Appendices. Beta = Alfa and the rule assumes symmetry in both force and displacement axes.

If Vy, the shear area or the shear modulus are less than or equal to 0.0 then in-elastic shear is disabled

29

Shear Link Behaviour

11k. In-elastic Flange Shear-Link Parameters (Only if IGA on line 11a is 2)

One line for in-elastic shear for flexure about the local z-z axis.

Flex Bear V1 V2 V3

Flex Shear Link Initial Flexibility (Radians/unit moment) ( > 0.0) FBear Shear Link Flexibility after bolts bear ( < Flex) FV1 Shear where flange splice first slips ( > 0.0) FV2 Shear where bolt bearing begins ( > 1.1*V1) FV3 Shear where splice slips in later cycles ( > 0.0) F

Notes: The joint flexibilities specified at the ends of the member are complemented by the shear link flexibilitycomputed for the shear link. The shear force at each end of the member is used to adjust the jointflexibility at that end of the member.

30

11l. Strength Degradation Parameters (only if ILOS is > 0) (See Appendix A)

11m. Stiffness Degradation Parameters (only is IHYST > 0) (See Appendix B)

For those rules which require sets of data such as SINA or Muto etc., then there are 2 sets of such data:1: Flexure at End 1

2: Flexure at End 2

11n. Damage Index data (Only if IDAMG > 0).

MUT MUC MU1+ MU1- MU2+ MU2- MU3+ MU3- MU4+ MU4- BETA1 BETA2

MUT Positive axial ultimate ductility FMUC Negative axial ultimate ductility FMU1+ Positive ultimate ductility (End 1) FMU1- Negative ultimate ductility (End 1) FMU2+ Positive ultimate ductility (End 2) FMU2- Negative ultimate ductility (End 2) FMU3+ Positive ultimate ductility (Hinge 3) FMU3- Negative ultimate ductility (Hinge 3) FMU4+ Positive ultimate ductility (Hinge 4) FMU4- Negative ultimate ductility (Hinge 4) FBETA1 Park and Ang Beta Axial (Default = 0.05) FBETA2 Park and Ang Beta Flexural (Default = 0.05) F

Notes: Ductility data for hinges 3 and 4 is to be provided only for the Four-hinge Beam members. All ultimate ductilities must be greater than 1.0.

The ultimate ductilities have no effect on the dynamic analysis but are only used at the end of theanalysis to compute the damage indices.See Appendix B for information on which hysteresis rules can allow damage indices to be computed.

31

Spring Member

Spring Member Sign Convention

12 SPRING type member properties

Order of all of the components required for Spring Members.

1 Basic Section Properties see section 12a2 Material Specific Damping parameter (only if ICTYPE = 5 in line 2) see section 12b3 Yield Forces and Moments Except when IHYST = 0, 18, 19, 33 or 37.

see sections 12c, 12d, 12e, 12f or 12g4 Strength Degradation Parameters, only if ILOS > 0, see section 12h5 Stiffness Degradation Parameters, only if IHYST > 0, see section 12i6 Damage Index data, only if IDAMG > 0, see section 12j

32

12a. Basic Section properties

ITYPE IHYST ILOS IDAMG KX KY GJ WGT RF RT PSX PSY PSZ THETA ITRUSS IOP

ITYPE = 1; No interactions between X, Y or Theta Z components I= 2; Elliptic interaction between yield forces in the X and Y directions,

no interaction with rotation.= 3; Interaction between Rotation and Y forces. (Flexure-Shear interaction)

(SINA hysteresis assumed for Y components)= 4; Interaction between Axial Force and Yield Moments= 5; Friction Interaction between Axial Force and Transverse Force

IHYST = n; Hysteresis rule. See Appendix B I(If ITYPE=2 Hysteresis is tri-linear).

ILOS = 0; No strength degradation (If ITYPE=2 then ILOS=0) I= 1; Strength reduction in each direction based on ductility in that direction.= 2; Strength reduction based on number of cycles= 3; Strength reduction based on maximum ductility= 4; Strength reduction as for ILOS=1 above but strength reduction also with


at ultimate ductility.= 6; Strength reduction as for ILOS=3 above but strength reduction also with


at ultimate ductility.IDAMG = 0; No damage indices computed I

= m; Damage indices computed (If ITYPE=2 then IDAMG=0)KX Spring Stiffness in the local X-direction FKY Spring Stiffness in the local Y-direction FGJ Rotational stiffness of the member section FWGT Weight/(unit length) of the member FRF Bi-linear Factor, or Ramberg-Osgood r, for spring forces F

(This is only used if ITYPE=1)RT Bi-linear Factor, or Ramberg-Osgood r, rotation FPSX Pre-load force in the local X-direction FPSY Pre-load force in the local Y-direction FPSZ Pre-load moment about the Z-axis FTHETA Angle from Global X axis to local x axis. (Degrees). (Over-rides Note 2 below) F

(This angle is only used if spring length is zero)ITRUSS = 0; Stiffness coefficients used as input I

= 1: Stiffness coefficients divided by member length (Default=1.0) (Truss action)IOP = 0; Pre-load forces and moments are internal to the member only. I

= 1; Pre-load forces and moments act as pre-loads that also affect the nodalForces acting on the nodes at the ends of the member in the static analysis of thestructure.

Notes:1. The weight/unit length is used to compute the member mass and does not contribute to the static loads

on the member or the structure.2. If the length of the member is zero then the local X and Y axes coincide with the global axes.3. The ITYPE=2 model may be used to model the horizontal x and y behaviour of say a bridge pier where

the bridge is modelled in plan and the pier acts in flexure with the vertical axis in the z directionperpendicular to the model of the structure. The behaviour of the pier represents the yield forceinteraction in the x and y directions where the yield forces would be the yield moments about the y-y andx-x axes at the base of the pier multiplied by the height of the pier.

4. The pre-load forces are internal to the member and have no contribution to the forces acting on thestructure. They affect only the initial member deformation before any structure deformations areimposed.

33

5. This member may be used to represent truss members where the local X-direction represents the trussaction. The stiffness KX should equal the AE/L of the truss member.

6. If the Crisafulli hysteresis rule 33 is to be used to model in-fill panels then the AREAs asked for by therule, (see IHYST=33, Appendix B), are used to set up the stiffness of the spring at each time step.However, the spring member does not use the length of the strut in forming the stiffness and so theAREAs should be the strut cross-sectional areas divided by the strut length. Also, the stiffness KX isused for the initial stiffness of the strut until the stiffness is checked to find its status in the hysteresis rulebehaviour, this is in the static analysis, where static loads are applied or at time = 0.0 if not. This meansthat an initial estimate of KX should be made. In general the Crisafulli model does not carry significanttensile forces which means that normally two strut members are required acting along opposite diagonalsand each would only act in the longitudinal, or X, direction.

7. IDAMG, m is used as a weight when adding member damage indices to obtain structure damage index,see notes for Frame members , section 11a.

8. If ITYPE= 5 then the transverse yield force is a function of the axial force. The transverse hysteresis iselasto-plastic representing the transverse friction. The other actions in the axial direction and rotationare linearly elastic. There must be axial and transverse stiffness but the rotational stiffness may be zero.

12b. Material Specific Damping (only if ICTYPE = 5 in section 2)

This option allows different sections to have their own values of ALPHA and BETA for Rayleigh Damping. Thisis useful if one is modelling a pounding study between two adjoining buildings where the buildings have differentdamping characteristics or where different parts of the system have different damping characteristics, ie.e. in soil-structure interaction studies. Damping matrix C is given by


BETA0 BETAT ALPHA


34

Spring Member Yield Interaction Surfaces

12c. Yield Surface ( ITYPE = 1 ) (Not if IHYST = 0, 18, 19, 33 or 37)

FX+ FX- FY+ FY- MZ+ MZ-

FX+ Positive spring yield force in the X direction FFX- Negative spring yield force in the X direction FFY+ Positive spring yield force in the Y direction FFY- Negative spring yield force in the Y direction FMZ+ Positive torsional yield FMZ- Negative torsional yield F

Note: There is no interaction between torsion and spring yield and there is no interaction between the springyield in the rotation, x or y directions.

12d. Yield Surface ( ITYPE = 2 ) (Not if IHYST = 0, 18, 19, 33 or 37)

FX1 FY1 FX2 FY2 MZ+ MZ- RX1 RY1 RX2 RY2

FX1 Cracking force in the X direction FFY1 Cracking force in the Y direction FFX2 Yield force in the X direction FFY2 Yield force in the Y direction FMZ+ Positive torsional yield moment F MZ- Negative torsional yield moment FRX1 Bi-linear factor in the X direction FRY1 Bi-linear factor in the Y direction FRX2 Tri-linear factor in the X direction FRY2 Tri-linear factor in the Y direction F

Note: There is an elliptic interaction curve between x and y yield force in each quadrant of the diagram below.The force-displacement curve in this case is tri-linear, it is modelled by two elasto-plastic members andone elastic member in parallel. The yield forces are symmetric about the origin. There is no interactionbetween yield in rotation and the x and y directions. The rotational component follows a bi-linearhysteresis rule.

35

12e. Yield Surface ( ITYPE = 3 ) Flexure-Shear interaction. (Not if IHYST = 0, 18, 19, 33 or 37)

FX+ FX- FY+ FY- MZ+ MZ- FCRY FCCY ALFA HINGE DUCT1 DUCT2 RES DUCT3 I

FX+ Positive Yield force in the X direction ($ 0) FFX- Negative Yield force in the X direction (# 0) FFY+ Positive Yield force in the Shear (or Y) direction ($ 0) FFY- Negative Yield force in the Shear (or Y) direction (# 0) FMZ+ Positive rotational yield moment ($ 0) F MZ- Negative rotational yield moment (# 0) FFCRY Cracking Shear Force in the Y direction (> 0) FFCCY Crack Closing Shear Force in the Y direction (> 0) FALFA Bi-linear factor from cracking to yield in the Y direction (0.4#ALFA#0.8) FHINGE Plastic Hinge Length (Default = 1.0) FDUCT1 Flexural ductility at which Shear strength starts to degrade ($1) FDUCT2 Flexural ductility at which Shear strength reaches residual strength F

(Minimum value is 1.5 DUCT1)RES Residual Shear strength when flexural ductility is greater than DUCT2 FDUCT3 Flexural Ductility when strength = 1% of original F

= 0; Strength = RES*FYI = 0; No shear strength degradation. I

= 1; Shear strength degradation.= 2; Shear strength degradation but Retrofit Assumed, No shear yield occurs.= 3: Shear strength degradation, Shear yield terminates analysis.

Notes:1. The SINA hysteresis rule governs the Shear (or Y action). The cracking forces in the Y direction are

symmetric about the origin. The strength loss in the Y direction is based on the absolute values of therotational component ductility.

2. The Shear Stiffness KY = G AS / L where G is the shear modulus, AS is the Shear Area and L is theplastic hinge length. The Flexural Stiffness GJ = E I / L where E is the elastic modulus and I is thesecond moment of area of the equivalent beam section. To get curvatures from the rotations divide therotations by the plastic hinge length L.

3. If I above is non-zero then shear strength degradation will also occur with shear ductility. A line with thedegradation data as for Appendix A of this manual must immediately follow this line. The normal strengthdegradation controlled by the variable ILOS will apply to the x and rotational actions in the springmember. The case of I above is 2 is for columns where retrofit is assumed to have been applied andthe sequence of shear failure is to be shown. When I is 3 is the case where retrofit is assume not to occurand shear failure in a column implies failure of the structure.

4. These last two cases of I = 2 or 3 are really applicable to columns, 2 informs the user that shear yield hasoccurred but implies a retrofit has been applied so one can see where the next yield will occur. Option3 covers the case for columns without retrofit where failure of a column implies failure of the structure.

36

12f. Yield Surface ( ITYPE = 4 ) Axial Force - Yield Moment interaction (Not if IHYST = 0, 18, 19, 33 or 37)

FY+ FY- PYC PB MB M1B M2B M0 PYT

PYT Axial tension yield force ( > 0.0) FPYC Axial compression yield force ( < 0.0) FFY+ Positive Yield Force in Shear ( > 0.0) FFY- Negative Yield Force in Shear ( < 0.0) FPB Axial compression force at B ( < 0.0) FMB Yield moment at B ( > 0.0) FM1B Yield moment at P=(2/3)*PB ( > 0.0) FM2B Yield moment at P=(1/3)*PB ( > 0.0) FMO Yield moment at P=0.0 ( > 0.0) F

Note: The interaction is symmetric about the M = 0.0 axis.The axial force is the local x component action. A cubic curve describes the moment variation from PBto the moment axis. A linear variation of moment occurs outside this region.

37

12g. Yield Surface ( ITYPE = 5 ) Axial Force - Transverse Force interaction (Not if IHYST = 0, 18, 19, 33 or 37)

F0 MU IOP

F0 Constant Component of Friction Force ( > 0.0) FMU Coefficient of Friction ( > 0.0) FIOP = 0; Friction Force limit = F0 -MU*(Axial force) ( > 0.0) I = 1; Friction Force limit = F0+MU*Abs(Axial force)

Note: The axial force is the local x component action. The friction force acts in the local y direction.

12h. Strength Degradation Parameters (only if ILOS > 0) (See Appendix A)

12i. Stiffness Degradation Parameters (only if IHYST > 0) (See Appendix B.)

For those rules which require sets of data, such as SINA or Muto, then there are 2 sets of such data.ITYPE=1

1: Longitudinal or X direction action. (The same parameters are used for rotational action)2: Transverse or Y direction action.

ITYPE=31: Longitudinal or X direction action.2: Rotation or Theta-Z action.

For the Widodo hysteresis (IHYST = 19) a third set of data is used for the rotational action.

12j. Spring Damage Index data (Only if IDAMG > 0).

MUX+ MUX- MUY+ MUY- MUR+ MUR- BETA1 BETA2

MUX+ Positive ultimate ductility (Longitudinal or X direction) FMUX- Negative ultimate ductility (Longitudinal or X direction) FMUY+ Positive ultimate ductility (Transverse or Y direction) FMUY- Negative ultimate ductility (Transverse or Y direction) FMUR+ Positive rotational ultimate ductility FMUR- Negative rotational ultimate ductility FBETA1 Park and Ang Beta X and Y (Default = 0.05) FBETA2 Park and Ang Beta rotation (Default = 0.05) F

Notes: All Ultimate Ductilities must be greater than 1.0.The ultimate ductilities have no effect on the dynamic analysis but are only used at the end of theanalysis to compute the damage indices.See Appendix B for information on which hysteresis rules can allow damage indices to be computed.

38

Wall Member

13 STRUCTURAL-WALL type properties

13a. Basic section properties [Taylor 1977]

NSECT NIP ICOND IHYST WGT AMAX IMAX H1 H2

NSECT Number of Lobatto integration sections along the member (3, 4, 5, 6 or 7) IThere is an exception for a special 2-hinge Beam-Column NSECT = 2

NIP Number of segments in section (3 # NIP # 20) IFor Standard Wall sections maximum number of segments is 18

ICOND = 0; Standard Wall section input I= 1; Numerical Wall section input

IHYST = 0; Member remains perfectly elastic I= 1; Taylor material properties, linear stress-strain to SIGA= 2; Kent & Park material properties, quadratic stress-strain to SIGA

WGT Weight/(unit length) of the member FAMAX Maximum fraction of Gross Section Area used FIMAX Maximum fraction of Gross Second Moment of Area used FH1 Hinge Length End 1 (only for special 2 hinge member) FH2 Hinge Length End 2 (only for special 2 hinge member) F

Notes:1. The weight/unit length is used to compute the member mass and does not contribute to the static loads

on the member or the structure.2. Wall members usually require smaller time-steps than most other structures, i.e. 0.001 to 0.0001 seconds

compared with 0.01 seconds and Newton-Raphson iteration, say 3 cycles, should be provided. Changesin the flexural stiffness also lead to large changes in the axial stiffness and the movement of the neutralaxis implies coupling between the axial and flexural actions as well.

3. If the member is in-elastic and Newton-Raphson iteration has not been enabled the variable MAXIT isautomatically reset to a maximum of 3 cycles of iteration and FTEST to 0.10. It has been found that asmaller value of FTEST would be more appropriate.

4. The original Taylor element had a mid-length node with an hierarchical axial degree of freedom so that

39

the longitudinal strains due to the axial displacements had a quadratic variation with length as do thelongitudinal strains due to the beam-like cubic flexural displacement with length. It has been found thatthe mid-length degree of freedom was never excited in the analyses and this seventh deformation degreeof freedom has been deleted.

5. At each section along the length the centre-line axial strain is computed, the curvature computed as afunction of the end rotations and assuming that the cross-section remains plane the longitudinal strainin each segment of the section is computed. For each segment in the cross-section the concrete andsteel stresses and tangent modulii are computed and then the moment and axial force on the section arecalculated and the new effective cross-sectional area, second moment of area and the location of theneutral axis is computed.

6. The section properties are integrated along the length using a Lobatto integration rule to get the memberstiffnesses. Three point Lobatto integration is identical to a three point Simpson’s rule.

7. Taylor sometimes used up to three elements to represent the wall over a single storey height.8. IMAX < 1 is accounted for by intially cracking the section from both extreme segments inwards so that

the effective I is less than or equal to IMAX*IGROSS. AMAX is no longer used but as the flexural stiffnessreduces with the pre-cracking of the section the effective cross-sectional area also reduces.

9. NSECT = 2 is for an Giberson type beam-column model with an elastic central region with the plastichinge zones modelled by a Taylor-like segmental section. This allows for the neutral axis to move withinthe hinge zone.

Wall Member Sign Convention

40

Taylor’s Concrete Stress-Strain Relationships

13b. Concrete and Steel Properties

EMODC EMODS SIGA SIGB EPSB SIGCR SIGYS SBILIN ALFA

EMODC Elastic Modulus of the Concrete ( > 0.0) FEMODS Elastic Modulus of the Steel ( > 0.0) FSIGA Concrete Peak Stress f'c ( < 0.0) FSIGB Concrete Ultimate Stress ( < 0.0) FEPSB Concrete Ultimate Strain ( < 0.0) FSIGCR Concrete Cracking Stress ( > 0.0) FSIGYS Steel Yield Stress ( > 0.0) FSBILIN Steel Bi-linear Factor ( > 0.0) FALFA Steel Bounding Surface Onset (Only if IHYST=2, see note 4 below) F

Notes:1. The concrete is assumed to carry no tensile stress once the material has cracked and the concrete is

assumed to carry no tensile stress once the compressive strain has exceeded EPSB.2. IHYST = 0, The uncracked section properties are used for all time-steps.3. IHYST = 1, The concrete elastic modulus is assumed to be a constant EMODC until the stress SIGA is

reached. The peak strain EPSA = SIGA/EMODC. The steel assumes a bi-linear stress-strain hysteresis.This follows the original Taylor Element-A model

4. IHYST = 2, The concrete stress-strain law follows a quadratic rule until the stress SIGA is reached. Thepeak strain EPSA = 2.0*(SIGA/EMODC). The steel hysteresis rule has an elasto-plastic first yieldexcursion but subsequent cycles follow the Al-Bermani Bounding Surface rule with "=$=0.3 to modelthe Bauschinger effect. This default value of ALFA may be overridden by specifying a different valuein the range 0.0 to 1.0 in the data above where ALFA = 1.0 implies a bi-linear hysteresis. The steel bi-linear factor SBILIN, used to define the in-elastic bounding surface, takes a minimum of 0.0001 for theBounding Surface algorithm to work.

41

‘Kent and Park’ Concrete Stress-Strain Relationship

Bilinear Steel Hysteresis

Al Bermani Steel Hysteresis

42

13c Material Specific Damping (only if ICTYPE = 5 in section 2)



BETA0 BETA ALPHA


43

Geometry of the Standard Wall Section

13d. Input for Standard Wall Section (ICOND = 0)

B D B1 B2 D1 D2 D3 D4 AS1 AS2 AS3

B Thickness of the Wall FD Width (length) of the wall FB1 Width of the outstanding flange at flange 1 FB2 Width of the outstanding flange at flange 2 FD1 Distance to the left face of flange 1 FD2 Distance to the right face of flange FD3 Distance to the left face of flange 2 FD4 Distance to the right face of flange 2 FAS1 Cross-sectional Area of Steel uniformly distributed in the main wall FAS2 Cross-sectional Area of Steel uniformly distributed in flange 1 FAS3 Cross-sectional Area of Steel uniformly distributed in flange 2 F

Note: All distances D1, D2, D3 and D4 are measured from the left side of the wall when the section is vieweddown the member in the -X direction The structural axis of the member is assumed to be at D/2

44

Numerical Definition of Wall Cross-Section

13e. Input for Numerical Wall Section (ICOND = 1)

One line is required for each of the sub-areas in the section. NIP lines required.

I X(I) AS(I) AC(I)

I Sub-area number IX(I) Location of centre of sub-area I FAS(I) Area of steel in sub-area I FAC(I) Area of concrete in sub-area I F

Note: The member structural axis is assumed to be at (X(1) + X(NIP))/2

45

Dashpot Member

14 DAMPER (dash-pot) type member properties

ITYPE C1 C2 C3 GAP+ GAP- ALFA C4 C5 C6 ALFA- THETA

ITYPE = 0 Linear Dashpot I= 1 Non-Linear Dashpot = 2 Non-Linear Dashpot with different properties in Positive and Negative

directions.C1 Longitudinal coefficient FC2 Transverse coefficient FC3 Rotational coefficient FGAP+ Positive Gap FGAP- Negative Gap FALFA Velocity Power Factor (ALFA > 0.0) (Default=1.0) (ITYPE > 0) FC4 Longitudinal coefficient (negative direction) (ITYPE = 2) FC5 Transverse coefficient (negative direction) (ITYPE = 2) FC6 Rotational coefficient (negative direction) (ITYPE = 2) FALFA- Velocity Power Factor ALFA in the negative direction. (ITYPE = 2) FTHETA Angle between Global X and Local x axes (Degrees) F

Notes:1. C1, C2 and C3 are the dash-pot coefficients (force / unit velocity) for the different actions in the member.

These act in the positive direction only if ITYPE = 2.

2. These members are only included in the time-history analysis if IPANAL = 2 or more when theircontributions are added to the damping matrix of the structure.

4. Sign Conventions are the same as those for the SPRING member types, see section 12.

5. If the length of a DAMPER type member is zero then the local X and Y axes coincide with the global axesunless a non-zero value has been specified for THETA above.

6. If the member deformation is within the range of the gap then the dashpot has no resisting force.

46

Member Sign Convention

7. For Non-linear dash-pots all components use the same ALFA. The dash-pots show no hysteresis in theirForce-Velocity relationship, it is a non-linear elastic force-velocity relationship. The dash-pot force forcomponent i is related to the dash-pot velocity by the following equation

8. If ITYPE = 2 the dashpot has different properties in the positive and negative directions and the rulesfor the data in the negative direction are the same as those for the positive direction components.

9. If IPLAS = 0, Elastic time-history analyses only, (see section 2, Principal analysis options), then the initialgaps are reset to zero and ITYPE is reset to 0 after all the input data has been read.

47

Constant Force Member

Tendon Member

15 TENDON type member properties

Either Constant Force member

ITYPE FPP FPN FNN FNP GAP+ GAP- THETA

ITYPE = 0 ; Simple Constant Force Tendon Member IFPP Force, Positive Displacement and Displacement Increasing FFPN Force, Positive Displacement and Displacement Decreasing FFNN Force, Negative Displacement and Displacement Decreasing FFNP Force, Negative Displacement and Displacement Increasing FGAP+ Positive Gap, No Force if Displacement less than this ($ 0) FGAP- Negative Gap, No Force if Displacement greater than this (# 0) FTHETA Angle between Global X and Local x axes (Degrees) F

Notes: 1. These members are only included in the time-history analysis IPANAL > 1 when they are considered in

the dynamic equilibrium equations. 2. Sign Convention: This is the same as for the SPRING members. Tensile forces and member elongations

are positive.3. If the member is of zero length then the TENDON local member axis is assumed to coincide with the

global x axis unless a non-zero has been specified for THETA above. THETA is only used for zero lengthmembers.

48

Or Active Tendon Force member

ITYPE DELAY THETA

ITYPE = N ; Number of Contributions to Tendon Force ( N > 0 ) IDELAY Time Delay on Response (seconds). (Maximum of 100 time-steps) FTHETA Angle between Global X and Local x axes (Degrees) F

Note: The time delay is internally converted to an integer number of time-steps

Contribution of each component - N lines required

NODE NDOF NTYPE FACTOR

NODE Node Number INDOF = 1 ; X component at Node I

= 2 ; Y component at Node= 3 ; 2Z component at Node

NTYPE = 1 ; Nodal Acceleration I= 2 ; Nodal Velocity= 3 ; Nodal Displacement

FACTOR Multiplier of Action F

Notes:1. These members are only included in the time-history analysis IPANAL > 1 when they are considered in

the dynamic equilibrium equations. 2. Sign Convention: Tensile forces and member elongations are positive.3. If the member is of zero length then the local member axis is assumed to coincide with the global x axis

unless a non-zero value has been specified for THETA above. THETA is only used for zero lengthmembers.

4. Care must be taken when setting out the magnitude and sign of the multiplier as an inept choice maylead to very large displacements and loss of precision and failure of the analysis. The deformation andforce in the member is tension positive. The tendon member in tension pulls on both joints with equal andopposite forces. It is worth noting that if the displacement of the structure has an equivalent circularfrequency T (radians/sec) then the magnitude of the velocities are of the order of T times the magnitudeof the displacements and the magnitude of the accelerations is T2 times the magnitude of thedisplacements.

49

Or Semi-Active Tendon, Resettable Actuator, member

ITYPE STIFF FPP DELAY THETA

ITYPE = -1 ISTIFF Equivalent stiffness (Force per unit displacement) F FPP Saturation Force (Same value used in tension and compression) F DELAY Time Delay on Response (seconds). (Maximum of 92 time-steps) FTHETA Angle between Global X and Local x axes (Degrees) F


the dynamic equilibrium equations. 2. Sign Convention: Tensile forces and member elongations are positive.3. If the member is of zero length then the local member axis is assumed to coincide with the global x axis

unless a non-zero value has been specified for THETA above. Theta is only used for zero lengthmembers.

4. The force displacement relationship follows the Resettable Actuator Hysteresis rule IHYST=43, pleasesee Appendix B. The equivalent yield values are Fy+ = +FPP and Fy- = -FPP where FPP is thesaturation force.

5. The time-delay is internally converted to an integer number of time-steps

50

Or Variable Force member

ITYPE STIFF ALFA DAMP BETA

ITYPE = -2 ISTIF Equivalent stiffness coefficient (Force per unit displacement) F ALFA Power factor for element displacement (ALFA > 0.0) F DAMP Equivalent damping coefficient (Force per unit velocity) FBETA Power factor for element velocity (BETA > 0.0) F


the dynamic equilibrium equations. 2. Sign Convention: Tensile forces and member elongations are positive.3. The force in the member is given by the following relationship. The displacement is the elongation of the

member and the velocity is the rate of change of member length.

Force = STIF*(displacement)ALFA + DAMP*(velocity)BETA

4. This member is very useful where a damper or spring member is required where the power factors ALFAand BETA are less than 1.0. In these cases the equivalent tangent stiffness or damping coefficients tendto infinity when the displacement or the velocity tend to zero leading to numerical difficulties in theanalyses. In these limiting cases the forces are usually small and large stiffness or damping coefficientsare not a problem as the tendon member has neither stiffness or damping coefficients

51

Contact Member

16 CONTACT type member properties


ITYPE IHYST KX CX MU FL M1 M2 THETA INIT

ITYPE = 0; Damping Coefficient specified. I= 1; Percentage Fraction of Critical Damping specified. = 2; Coefficient of Restitution specified.

IHYST = n; Hysteresis rule. See Appendix B. (only IHYST = 5 or 19 allowed) IKX Spring Stiffness in the local X-direction FCX Damping Coefficient in the local X-direction (see ITYPE above) FMU Coefficient of Friction (Transverse or Y-direction) FFL Friction stiffness is FL*KX (Default FL = 1.0 if MU > 0 else FL = 0.0) FM1 Mass at End 1 (Only if ITYPE is 1 or 2) FM2 Mass at End 2 (Only if ITYPE is 1 or 2) FTHETA Angle between Global X and Local x axes (Degrees) FINIT =0; Member does not act during the static analysis I

=1; Member acts during static analysis. (Only the KX term is active)

Notes:1. If the length of the member is zero then the local X and Y axes coincide with the global axes unless a

non-zero value has been specified for THETA above.2. These members stiffness and damping matrices are only included in the time-history part of the analysis

when IPANAL = 2 or 3.3. The Coefficient of restitution r (supplied as CX above) is related to the Percentage of Critical damping

8 by the following formula

4. The Effective End masses are only required if ITYPE is 1 or 2 and are used to generate the equivalentfraction of critical damping in the member. The masses are usually taken as the mass in the frame atthe floor at that end of the member.

5. The transverse friction force is proportional to the transverse displacement since the onset of contact orthe reversal of transverse displacement and is limited to MU times the contact force.

6. The friction forces only exist if there is a non-zero contact force.

52

Contact Member Sign Convention

7. The Fractions of Critical Damping (for ITYPE = 1, or 2 using 8 in note 3) are related to the DampingCoefficient c in the axial deformation mode of the member by the following expression where k is thecurrent member tangent stiffness and the masses m1 and m2 are the masses at the ends of the member(When ITYPE is 0 the damping coefficient c is CX)

16b. Yield Surface (only required if IHYST = 5)

PX+ PX- RTEN

PX+ Positive spring yield force in the X direction FPX- Negative spring yield force in the X direction FRTEN Bi-Linear Factor in Tension F

16c. Hysteresis data . See section 14 for the data required. This will complete the data for this member type.

53

Quadrilateral Finite Element

Quadrilateral Stress Sign Convention

17 QUADRILATERAL type member properties

Order of all of the components required for Quadrilateral Members.

1. Basic Section Properties see section 17a.

2. Material Specific Damping, see section 17b.

54


ITYPE E NU THICK WGT

ITYPE = 0; Plane Stress I= 1; Plane Strain

E Elastic Modulus FNU Poisson's Ratio FTHICK Thickness of the element FWGT Weight/(unit volume) of the element F

Notes:1. The weight/(unit volume) is used to compute the member mass and does not contribute to the static

loads on the member or the structure.2. The element is a Hybrid Stress Type 2 quadrilateral finite element. All four nodes must be distinct (i.e.

no triangles). The stress distribution is assumed to have a cubic variation in both the x and y directionsand the element edge displacements are assumed to vary linearly along the element edge for thetangential displacement and to have a cubic variation along the edge for the normal displacement. Theelement actually assumes a linear variation of thickness between nodes but in the application within theprogram a constant thickness is assumed. Three point Guass quadrature is used in each direction tointegrate the flexibility matrix and three point Guass quadrature is used for the integrals along theelement edges. Any reduction of the order of integration gives inaccurate integrals and a higher ordergives no change in the integrals.

3. The element is assumed, at present, to be linearly elastic.

17b. Material Specific Damping (only if ICTYPE = 5 on section 2)



BETA0 BETAT ALPHA


55

Masonry Panel Elements

18 MASONRY PANEL ELEMENTS

These elements are designed to represent the behaviour of an unreinforced masonry panel infill in a reinforcedconcrete frame. The model assumes that the infill is such that there are no gaps between the frame and thepanel. As generally constructed in South America the frame is often placed after the panel is erected (Crisafulli,1997).

The panel is modelled with two parallel struts in each diagonal to represent the thrust carried across the panelin diagonal compression. A fifth strut, which acts between the two opposite diagonal carriers on the diagonalcarrying compression, transfers the shear force between the top and bottom of the panel.

In general, the panel elements are rectangular but other geometries are permitted .

Four or Three lines of data required. An extra line will be required if the Material Specific Damping model is beingused.

1. Geometric Data2. General Properties3. Strut Data (2 lines or 1 line)4. Material Specific Damping Data (if ICTYPE=5 only)

56

Interior to Exterior Node Dimensions

18a. Geometric Data

IHYST HZ XO1 YO1 XO2 YO2 XO3 YO3 XO4 YO4

IHYST = 0 ; Member is elastic only. I= 1 ; Member is inelastic (IHYST actually =33)

HZ Vertical separation between struts FXO1 X distance from external node to internal node 1 FYO1 Y distance from external node to internal node 1 FXO2 X distance from external node to internal node 2 FYO2 Y distance from external node to internal node 2 FXO3 X distance from external node to internal node 3 FYO3 Y distance from external node to internal node 3 FXO4 X distance from external node to internal node 4 FYO4 Y distance from external node to internal node 4 F

Diagonal Strut Area Displacement Relationship

57

18b. Properties 18a

TO MU TMAX SSF KTF TH WGT

TO Bond shear strength FMU Coefficient of friction FTMAX Maximum shear stress $ TO FSSF Shear stress factor "s FKTF Shear stiffness factor (s FTH Panel thickness t FWGT Weight/unit volume F

Notes:The input data required for the application of the panel element includes the parameters described in for definingthe cyclic axial behaviour of masonry and the properties of the equivalent strut. In addition, the following variablesneed to be defined in relation to the shear behaviour of the masonry panel:

Vertical separation between struts, hz: values of hz between z/3 and z/2 seems to lead to adequate results,where z is the contact length between the panel and the frame.

Horizontal and vertical offset, xoi and yoi: these parameters define the horizontal and vertical distance,respectively, measured from the external nodes to the internal nodes. This is intended to represent the reductionof the dimensions of the panel due to the depth of the frame members.

Bond shear strength, and coefficient of friction, :: these parameters are usually obtained from direct sheartests or following design specifications. It is recommended, however, the use of the reduced values resulting fromthe modified shear theory proposed by Crisafulli. This theory takes into account the complex stress state in thepanel due to the composite nature of masonry.

Maximum shear stress, : this is the maximum shear stress permissible in the masonry panel, whose valuecan be selected from the shear failure envelope of masonry. This is to avoid a large shear strength due to highaxial forces in the struts.

Shear stress factor, "s: this parameter defines the ratio of the maximum shear stress to the average stress inthe masonry panel. It normally varies from 1.40 to 1.65.

Shear stiffness factor, (s: this factor represents the fraction of the total stiffness assigned to the shear spring,usually ranging from 0.5 to 0.75 but should not exceed 0.85 to 0.90. The remaining part, , is assigned tothe struts. The total stiffness of the panel element is controlled by the strut area and the elastic modulus.

Thickness of the panel, t: this is assumed to be constant over the panel.

Weight per unit volume: this is used to calculate the mass of the panel and is used only to form the structuremass matrix. It does not contribute to loads on the structure.

58

18c. Either Strut Hysteresis (see also Appendix B IHYST=33)

FC FT UC UUL UCL EMO GUN ARE

FC Compressive strength (stress units) (FC < 0.0) FFT Tensile strength (stress units) (FT > 0.0) FUC Strain at FC (UC < 0.0) FUUL Ultimate strain (UUL < 0.0) (UUL # 1.5 UC) FUCL Closing strain FEMO Initial masonry modulus (EMO $ 2 FC/UC) FGUN Stiffness unloading factor (GUN $ 1.0) FARE Strain reloading factor (ARE > 0.0) F

18.d Strut areas

AREA1 AREA2 R1 R2 IENV

AREA1 Initial strut cross-sectional area (AREA1 > 0.0) FAREA2 Final strut cross-sectional area (AREA2 # AREA1) FR1 Displacement at 1 (R1 < 0.0) FR2 Displacement at 2 (R2 # R1) FIENV = 0 ; Sargin stress-strain envelope descending branch I

= 1 ; Parabolic stress-strain envelope descending branch

or Elastic Properties

EMO AREA1

EMO Elastic modulus FAREA1 Initial area of strut F

59

Notes:FC The compressive strength f'

m2 is the main parameter controlling the resistance of the strut. It must benoted that FC does not represent the standard compressive stress of masonry but should be adoptedtaking into account the inclination of the compressive principal stresses and the mode of failure expectedin the masonry panel. See Crisafulli 1997.

FT Tensile strength f't represents the tensile strength of the masonry or the bond strength of the panel-frameinterface, whichever is smallest. The consideration of the tensile strength has been introduced in themodel in order to gain generality. However, results obtained from different examples indicate that thetensile strength, which is generally much smaller than the compressive strength, has no significantinfluence on the overall response. Therefore, in the absence of more detailed information, the tensilestrength can be assumed to be zero.

UC The strain at maximum stress g'm usually varies between -0.002 and -0.005 and its main effect on theoverall response of the infilled frame is the modification of the secant stiffness of the ascending branchof the stress-strain curve.

UUL The ultimate strain gu is used to control the descending branch of the stress-strain relationship. Whena large value is adopted for, example gu = 20 g'm , a smooth decrease of the compressive stress isobtained.

UCL The closing strain gcl defines the limit strain at which the cracks partially close and compressive stressescan be developed. Values of the closing strain ranging between 0 and 0.003 lead to results which agreeadequately with experimental data. If a large negative value is adopted, for example gcl = gu , this effectis not considered in the analysis.

EMO The elastic modulus Emo represents the initial slope of the stress-strain curve and its value can exhibita large variation. Various expressions have been proposed for the evaluation of the elastic modulus ofmasonry. It is worth noting, however, that these expressions usually define the secant modulus at astress level between 1/3 and 2/3 of the maximum compressive stress. In order to obtain an adequateascending branch of the strength envelope it is assumed that Emo $ 2 f'm2 / g'm .

GUN The unloading stiffness factor (un controls the slope of the unloading branch. It is assumed to be greaterthan or equal to 1.0 and usually ranges from 1.5 to 2.5.

ARE The reloading strain factor "re defines the point where the reloading curves reach the strength envelope.The calibration of the hysteretic model for the axial behaviour of masonry showed that good results areobtained using values ranging between 0.2 and 0.4. However, higher values, for example 1.5, arerequired to model adequately the cyclic response of the infilled frames. This is because other sourcesof nonlinear behaviour, such as sliding shear, need to be indirectly considered in the response of themasonry struts.

Four parameters are required to represent the cross-sectional area of the masonry strut. These are the initial areaAms1 = AREA1 and final area Ams2 = AREA2 and the axial displacements at which the cross-sectional areachanges, )R1 = R1 and )R2 = R2. In a simplified model, it can be assumed that AREA1 and AREA2 are thesame using a low value of the strut area to avoid an excessive increase in the axial strength. In a more refinedanalysis, a higher value of the initial area can be adopted, whereas the final area can be reduced by about 10%to 30%. The displacement R1 and R2 can be estimated as g'm dm/5 and g'm dm (where dm is the length of themasonry strut) respectively, at least until more precise information becomes available. Several empiricalexpressions, which are described in section 6.2.1.3 of the reference, have been proposed for the evaluation ofthe equivalent width of the masonry strut, whose value normally ranges from 0.1 to 0.25 of the diagonal lengthof the infill panel.

IENV The descending branch of the stress-strain curve is usually modelled with a parabola instead of the curveassociated with Sargin's equation in order to obtain a better control of the response of the strut after themaximum stress has been reached.

60

18e. Material Specific Damping (only if ICTYPE = 5 on section 2)



BETA0 BETAT ALPHA


61

Foundation Member Sign Convention

Beam Sign Convention

19 GROUND type member properties

Foundation Members

These members can be regarded as a form of beam member and may be used to represent the flexibility of thesoil continuum beneath foundation beams and footings. The elements have a cubic variation of normal thrustand a linear variation of axial shear along their lengths so their edge displacements are fully compatible withbeam members. Three possible representations of the soil are included:

Vlazov Foundation General Two-Parameter Foundation (Pasternak model)Vogt Foundation

The normal force-deflection relationship of both the Vlazov and the General Two-Parameter Foundation membersare governed by the following equation (Selvadurai,1979):

q(x) = k.w(x) – G(d2w/dx2)

In the Vlazov soil model, the parameters k and G are derived from the elastic properties of the soil and specifiedconstraints to the variation of normal displacement of the soil with depth.

In the General Two-Parameter soil model, k and G are input directly by the user.

The Vogt foundation model was derived using Boussinesq’s formulas and has been used in the past for modellingarch dams (Holand, 1968; Clough,1973). In two-dimensional analyses, the normal force-deflection relationshipfor the Vogt model is similar to that of the Vlazov and General Two-Parameter soil models, but does not containa shear term. This model is analogous to a distributed Winkler spring. The models can be regarded as ‘Pseudo-Dynamic’ foundation compliance models. They do not automaticallyaccount for the frequency dependence of the dynamic stiffness of the soil. Such effects can be included byappropriately scaling the input parameters to account for the fundamental period of the combined soil-structuresystem.

The effects of radiation damping are incorporated into the Vlazov model by way of dashpots, placed in parallelwith the soil springs. Radiation damping is highly dependent on frequency and should only be included if thefundamental period of the combined soil-structure system is below the fundamental period of the site.Appropriate scale factors for radiation damping and the elastic stiffness of the soil, as a function of thefundamental frequency of the soil-structure system, can be obtained from Wolf (Wolf, 1994)

62

Foundation members should be placed beneath foundation beams and footings and additional members shouldbe provided to model the soil surface adjacent to the structure being modelled. These members should extendeither side of the structure at least two to three times the width of the structure.

References:

Clough, Ray W et al,. ADAP – a computer program for static and dynamic analysis of arch dams. University ofCalifornia, Berkeley, California, 1973

Holand, Ivar and Aldstedt, Erik, Arch Dam Analysis by Finite Element Analysis, Institute for Structural Mechanics,University of Trondheim, Norway, January 1968

Selvadurai, A. P. S., Elastic Analysis of Soil-Foundation Interaction. Developments in Geotechnical EngineeringVol. 17, Elsevier Scientific Publishing Company, The Netherlands, 1979.

Wolf, John P., Foundation Vibration Analysis Using Simple Physical Models. Prentice Hall , Englewood Cliffs,NJ, 1994.

Order of all data components required for Ground Members is:

General Data for Foundation Member see section 19a.Data for Soil Model

Vlazov Soil Model, ITYPE = 1, see section 19b.Vlazov Soil Model, ITYPE = 2, see section 19c.Vlazov Soil Model, ITYPE = 3, see section 19d.Two-Parameter Soil Model, ITYPE = 4, see section 19e.Vogt Foundation Model, ITYPE = 5, see section 19f.

Data for Non-linear foundation behavior, Only if IHYSTA, IHYSTK or IHYSTG > 0, see section 19g.

Data for soil element consistent mass matrix, Only if ISTF = 1, see section 19h.

Data for soil element radiation damping matrix, Only if IRAD = 1, see section 19i.

Data for Longitudinal Strength Degradation Parameters, see section 19j.Data for Longitudinal Stiffness Degradation Parameters, see section 19k.Data for Normal Strength Degradation Parameters, see section 19l.Data for Normal Stiffness Degradation Parameters, see section 19m.Data for Shear Strength Degradation Parameters, see section 19n.Data for Shear Stiffness Degradation Parameters, see section 19o.Data for Material Specific Damping (only if ICTYPE = 5), see section 19p.

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19a. General Data for Foundation Member

ITYPE ISHEAR IHYSTA IHYSTK IHYSTG ILOSA ILOSK ILOSG ISTF IRAD

ITYPE = 1; Vlazov Soil Model (Linear – shallow soils) I= 2; Vlazov Soil Model (Hyperbolic – deep soils)= 3; Vlazov Soil Model (Exponential – very deep soils)= 4; General Two-Parameter Soil Model (Pasternak)= 5; Vogt Soil Model

ISHEAR = 0; Shear term G(d2w/dx2) included I= 1; Shear term ignored (this is automatic with the Vogt model)

IHYSTA = n; Longitudinal Spring Hysteresis rule. See Appendix B IIHYSTK = n; Normal Spring Hysteresis rule. See Appendix B IIHYSTG = n; Shear Spring Hysteresis rule. See Appendix B IILOSA = 0; No Longitudinal spring strength degradation I

= 1; Longitudinal spring strength degradation varying with ductility= 2; Longitudinal spring strength degradation with varying cycle number= 3; Longitudinal spring strength degradation varying with absolute ductility

ILOSK Normal Spring strength degradation parameter (as for ILOSA) IILOSG Shear Spring strength degradation parameter (as for ILOSA) IISTFS = 0; No scale factors for stiffness terms I

= 1; Scale factors for stiffness termsIRAD = 0; No radiation damping included I

= 1; Radiation damping included

Note:IHYSTA, IHYSTK and IHYSTG can take on values of 0,1,2,3,4,8,10,11,12,13,14,20,21,23,26 and 28 seeAppendix B.

19b. Data for Vlazov Soil Model. Only if ITYPE = 1(Linear Variation of Displacement with Depth – shallow soils)

EM MU DEPTH WEFF DENS

EM Elastic Modulus of soil FMU Poisson’s Ratio of soil FDEPTH Depth of soil layer above bedrock FWEFF Effective Width of Foundation FDENS Mass density of soil F

Notes:A linear variation of displacement with depth is only appropriate for shallow soil layersThe model is formulated assuming that Plane Strain conditions apply.

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19c. Data for Vlazov Soil Model. Only if ITYPE = 2(Hyberbolic Variation of Displacement with Depth – deep soils)

EM MU DEPTH GAMA LENGTH WEFF DENS

EM Elastic Modulus of soil FMU Poisson’s Ratio of soil FDEPTH Depth of soil layer above bedrock FGAMMA Effective Constant Defining Exponential Variation (0.001 # GAMMA # 1) FLENGTH Characteristic Length FWEFF Effective Width of Foundation FDENS Mass density of soil F

19d. Data for Vlazov Soil Model. Only if ITYPE = 3(Exponential Variation of Displacement with Depth – very deep soils)

EM MU MUB WEFF DENS

EM Elastic Modulus of soil FMU Poisson’s Ratio of soil FMUB Exponential Variation Parameter (1 < MUB*WEFF < 2) F

(MUB*WEFF = 1.06 for infinitely long beams)WEFF Effective Width of Foundation FDENS Mass density of soil F

19e. Data for Pasternak General Two-Parameter Soil Model. Only if ITYPE = 4.

AS KS GS WEFF

AS Axial Stiffness of Soil Spring FKS Modulus of Subgrade Reaction of soil FGS Shear Modulus of soil FWEFF Effective Width of Foundation F

Note: KS has units of force-per-length-cubed and GS has units of force

19f. Data for Vogt Soil Model. Only if ITYPE = 5

EMF PR KFACT WEFF

EMF Effective Elastic Modulus of soil layer FPR Poisson’s Ratio of soil layer FKFACT Vogt ‘k’ Factor (2 <= k <= 2.5) FWEFF Effective Width of Foundation F

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19g. Data for Non-linear Foundation Behaviour (only if IHYSTA, IHYSTK or IHYSTG > 0)

PYTA PYCA PYT PYC TY BFA BFP BFT

PYTA Tensile Strength of Longitudinal Soil Spring FPYCA Compressive Strength of Longitudinal Soil Spring FPYT Tensile Strength of Normal Soil Spring FPYC Compressive Strength of Normal Soil Spring FTY Shear strength of Shear Soil Spring FBFA Bilinear Factor (or Ramberg Osgood r) for Longitudinal Spring FBFP Bilinear Factor (or Ramberg Osgood r) for Normal Spring FBFT Bilinear Factor (or Ramberg Osgood r) for Shear Spring F

Note: PYTA, PYCA, PYT, PYC and TY are in units of force per unit area

19h. Soil Mass Stiffness Scaling Parameters (Only if ISTF = 1)

AMASS KMASS GMASS

AMASS Scale factor for mass associated with Longitudinal springs FKMASS Scale factor for mass associated with Normal springs FGMASS Scale factor for mass associated with Shear springs F

Note: AMASS, KMASS and GMASS can take values between 0.0 and 1.0

19i. Radiation Damping Input Parameters (Only if IRAD = 1)

ADAMP KDAMP GDAMP

ADAMP Scale factor for damping associated with Longitudinal springs FKDAMP Scale factor for damping associated with Normal springs FGDAMP Scale factor for damping associated with Shear springs F

Notes:ADAMP, KDAMP and GDAMP can take values between 0.0 and 1.0Radiation damping is highly frequency dependent and scale factors should be evaluated according tofundamental frequency of the soil structure system.

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19j. Longitudinal Strength Degradation Parameters (only if ILOSA > 0), see Appendix A.

19k. Longitudinal Stiffness Degradation Parameters (only if IHYSTA > 0), see Appendix B.

19l. Normal Strength Degradation Parameters (only if ILOSK > 0) see Appendix A.

19m. Normal Stiffness Degradation Parameters (only if IHYSTK > 0), see Appendix B.

19n. Shear Strength Degradation Parameters (only if ILOSG > 0), see Appendix A.

19o. Shear Stiffness Degradation Parameters (only if IHYSTG > 0), see Appendix B.

19p. Material Specific Damping (only if ICTYPE = 5 in section 2)



BETA0 BETAT ALPHA


67

h

Node 1

Node 3

Node 4

Node 2

Spring Typ 1

Spring Typ 2

Spring Typ 3

Spring Typ 4

Spring Typ 5

h1

h5h4

h3

h2

Multi-Spring Element

Multi-Spring Member Sign Convention

20 MULTI-SPRING type member properties

If the Bi-Linear with Slackness hysteresis rule is used, then this element will become unstable if the wholeelement goes into tension. This is because the element has no stiffness if all the multi-springs have positive(tensile) displacements. To prevent this instability a compressive force should be imposed across the membereither by loads applied to the structure or by other prestressed members acting across the member.

The individual springs making up the multi-spring member have a sign convention where tensile deformationsand forces are positive.

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20a. Control Parameters.

IHYST ILOS KLOS IDAMG HS WGT THETA

IHYST = 0 Linear Element I= 1 Bi-linear with Gap Hysteresis (see IHYST = 5)= 2 Bi-linear Hysteresis (see IHYST = 2)= 3 Ramberg-Osgood Hysteresis (Original) (see IHYST = 3)= 4 Ramberg-Osgood Hysteresis (Bounded) (see IHYST = 40)= 5 Ramberg-Osgood Hysteresis (Pyke) (see IHYST = 41)= 6 Origin Centered Hysteresis (see IHYST = 38)= 7 Bi-linear Elastic Hysteresis (see IHYST = 15)= 8 Bi-linear with gap lift-off disconnects shear (see IHYST = 5)

ILOS = 0 No Longitudinal Strength Degradation I= 1 to 7 Longitudinal Strength Degradation

KLOS = 0 No Shear Strength Degradation I= 1 to 7 Shear Strength Degradation

IDAMG = 0 No Damage Indices calculated I= m Damage Indices computed with weight m (note: m =1 gives average)

HS Height of Multi-Spring member FWGT Weight of Multi-Spring member FTHETA Angle between Global X and Local x axes (Degrees) F

Note: The THETA term is only used for zero length members. In all other cases the local axial or longitudinalaxis is defined as being along the member length.The IHYST in the notes above refers to the Appendices A and B covering the hysteresis models

20b. Section Properties.

NS ITYPE SA SV YT YC YP YN RA RV

NS Number of springs (NS = 2,4,6,8 or 10) IITYPE = 1 Lobatto Quadrature (i.e. spacing and weighting of springs) I

= 2 Gaussian Quadrature= 3 Trapezoidal Rule Integration= 4 Uniform distribution and stiffness of springs

SA Axial Stiffness of Multi-spring unit (i.e. sum of all springs stiffnesses) FSV Shear Stiffness FYT Axial Yield in Tension for Multi-spring unit (YT= 0.0 for IHYST = 1) FYC Axial Yield in Compression for Multi-spring unit FYP Shear Yield Force (Positive) FYN Shear Yield Force (Negative) FRA Bi-linear factor for Axial Stiffness Multi-spring unit FRV Bi-linear factor for Shear Stiffness F

Note: If IHYST > 0 and YP > 0.0 or YN < 0.0 then a Bi-linear Hysteresis is used for the Shear Spring.

20c. Longitudinal Strength Degradation Parameters (only if ILOS > 0), see Appendix A.

20d. Shear Strength Degradation Parameters (only if KLOS > 0) see Appendix A.

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20e. Material Specific Damping (only if ICTYPE = 5 in section 2)



BETA0 BETAT ALPHA


20f. Multi-Spring Damage Index data (Only if IDAMG > 0).

MUX+ MUX- MUY+ MUY- MUR+ MUR- BETA1 BETA2

MUX+ Positive ultimate ductility (Longitudinal or X direction) FMUX- Negative ultimate ductility (Longitudinal or X direction) FMUY+ Positive ultimate ductility (Transverse or Y direction) FMUY- Negative ultimate ductility (Transverse or Y direction) FMUR+ Positive rotational ultimate ductility FMUR- Negative rotational ultimate ductility FBETA1 Park and Ang Beta X and Y (Default = 0.05) FBETA2 Park and Ang Beta rotation (Default = 0.05) F

Notes: All Ultimate Ductilities must be greater than 1.0.The ultimate ductilities have no effect on the dynamic analysis but are only used at the end of theanalysis to compute the damage indices.See Appendix B for information on which hysteresis rules can allow damage indices to be computed.

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21 Lumped Weights at the nodes

WEIGHTS INTERP

WEIGHTS Word WEIGHTS AINTERP = 0 ; Omitted Nodes have no point weight I

= 1 ; Omitted Nodes have weight of First Node in sequence repeated.

One input line is required for each nodal point. However, if any nodal points are omitted and INTERP above isnon-zero, the omitted nodes will be assumed to have the same weights as those of the nodal point on theprevious input line. The information for the last nodal point should be supplied. The nodal point numbers mustbe provided in an ascending order. It must be noted that the nodal weights and that the self-weight computedfrom the member weights are not added to the static load analysis.

N WX WY WM

N Nodal point number IWX Lumped nodal weight acting in the X direction FWY Lumped nodal weight acting in the Y direction F WM Lumped nodal weight acting in rotation at Node F

Note: If only a static analysis is to be carried out, then the nodal weights may be omitted. Similarly the weightmay be provided by self-weight of the members (see the section tables in part 10 of this manual). Notethat these weights are converted to masses internally within the program.

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22 External (static) nodal loads

LOADS

One input line with the word LOADS starting in column 1

One input line is required for each nodal point. The information for the last nodal point should be supplied evenif it is not loaded. The nodal point numbers must be provided in an ascending order. It must be noted that thenodal forces are independent of the nodal weights and that a self weight will not be computed from the nodalmasses and added to the static analysis.

N FX FY FM

N Nodal point number IFX Static load at node N in the X direction FFY Static load at node N in the Y direction FFM Static moment at node N about the Z axis F

72

23 Dynamic load factors (Only if IPVERT is less than 0).

One set of data if IPVERT = -1, two sets if IPVERT = -2, etc.

One input line with the word SHAPE starting in column 1

SHAPE ALPHA

ALPHA Multiplier of Shape Vector. (Only if IPANAL = 6) (ALPHA > 2.0) F

One input line is required for each loaded nodal point. The last nodal point should be provided even if no loadsare applied to it or a line with node number 0 will terminate the input.

The load components will be multiplied by the loading, or excitation, history (see section 23). The first componentis multiplied by the first excitation history and the second component by the second excitation history.

The units of these load shapes are force units.

This enables a maximum of three component loading, a constant static component and two time-varyingcomponents

N FX FY FM

N Nodal point number IFX Load Factor X direction FFY Load Factor Y direction FFM Load Factor 2 direction F

If there is more than a single loading pattern repeat all of the above SHAPE data for the second loading pattern

73

24. Earthquake Accelerograms, Displacement Time-Histories or Dynamic Load Time-Histories.(Only for IPANAL = 2, 3, 4, 5, 8 or 9)

The following set of input lines is required for each earthquake or dynamic loading component.There is 1 component if IPVERT = -1, 0 or 1There are n components if IPVERT = -n or n

For Earthquake Accelerograms the components act in the directions specified in the Earthquake Transformationmatrix supplied in section 2b of this manual.

For Dynamic loading patterns each component multiplies each of the load vectors described under the SHAPEdata sets.

For Input Displacement Histories (IPANAL = 8 or 9) the excitations act at the degrees of freedom specified inthe Nodal Point Boundary Condition data. The displacement must be scaled, via the divisor ASCALE to havethe displacement units chosen for the structure.

24a. Excitation Flag

One input line with the word EQUAKE starting in column 1

EQUAKE FILE

FILE Name of File where excitation is to be found (Maximum of 60 characters) AIf less than 2 excitations this name is usually supplied in response to the the prompts when the programs starts, or in Batch mode as arguments on the command line. If a file name is supplied here it over-rides those supplied at the prompts or on the command line. If no name is supplied then the excitation is assumed to follow this line in the supplied data. In this user may use word INPUT.This name MUST be supplied after the second excitation if abs(IPVERT) > 2 unless the excitations are part of the input data file.

74

24b. Control parameters for Accelerogram, Displacement Time-History or Loading Time-History

IBERG ISTART DELTAT ASCALE END VEL DIS TSCALE

IBERG = 0; Excitation in BERG Format I= 1; Excitation in CALTECH Format= 2; Excitation in NCEER Format= 3; Excitation in FREE Format (One point per line)= 4; Excitation in CSMIP Format= 5; Excitation in EXCEL Format= 6, Excitation in PEER Format= 7; Excitation in SAC Format

ISTART The number of the first line of the excitation that is to be used. IThis is usually = 1 but by using greater values enables the start of therecord to be ignored. This line number is counted from the START line.

DELTAT Excitation data interval FBERG Format records = Time step at which the record will be digitized.

The default value is the time-step for the integration DT. This may mean large memory requirements for very small time-steps. It is suggested that something of the order of 0.01 seconds be used for most records is a larger interval is desired.

CALTECH Format records the record time-interval (usually 0.025, 0.02, 0.01 or 0.005 seconds)

NCEER Format records the record time-interval (usually 0.02 seconds)

FREE Format records (see BERG Format records) CSMIP Format records the record time-interval

(usually 0.02 seconds)EXCEL Format records (see BERG Format records)PEER Format records the record time-interval

(usually 0.004 seconds)SAC Format records the record time-interval

(usually 0.020 seconds)ASCALE 1/(Scale factor) for the record. F

BERG, FREE or EXCEL Format records omit or set equal to 1.0 CALTECH records are usually in units of acceleration multiplied by a constant as the F6.0 format is usually an Integer I6 format and the decimal point ismissing with about 5 integer digits for the largest numbers. The values mustbe converted units of the acceleration of gravity . If the record is in the unitsof mm/sec/sec and if g = 9.81 m/sec/sec. then ASCALE = 9810.0.NCEER and CSMIP records are usually in cm/sec/sec and ASCALE = 981.0 to bring the record to units of the acceleration of gravity.

END Determines action if End-of-File is found before spanning duration of F excitation, DUR in line 3 of the data (Frame Control Parameters).

= 0 ; End of File implies data error= -1 ; Any missing part of record is padded with zero values= T ; After T seconds record is set to zero. Allows for a free vibration of

TIME-T seconds at the end of the earthquake excitation.VEL Initial Ground Velocity (Default = 0.0) F

Added to all degrees of freedom at beginning of Time-history analysis forearthquake analysis only. Only important in travelling wave analyses or wheretotal instead of relative displacements are being used

DIS Initial Ground Displacement (Default = 0.0) FAdded to all degrees of freedom at beginning of Time-history analysis forearthquake analysis only. (Not normally of any importance to the analysis)

TSCALE Time scale for the record (Default = 1.0) FThe times implied in the record are effectively divided by TSCALE. IfTSCALE = 2.0 then if the duration of the analysis is 10 seconds at least20 seconds of excitation must be provided unless END = -1

75

The rest of the input for the accelerogram (sections 24c and 24d) is in the Accelerogram File, the DisplacementHistory File or the Force History File specified by the user in the initial file name prompts at the beginning of theprogram execution or on the line with the word EQUAKE. The default response is that the accelerograms, orexcitation is appended to the above data file.

24c. Accelerogram, Displacement History or Load-History flag. This line is the start of the accelerogram etc. forall but the PEER or SAC format records.

The PEER format records are preceded by 4 lines of header information and this START line is not required.The SAC format records are preceded by 2 lines of header information and this START line is not required

One input line with the word STAR, START or DATA: (the colon is mandatory) starting in column 1 and the wordmust be in upper case. This line may be preceded by as many header lines as desired.

START

24d. Accelerogram, Displacement History or Load-History

The remainder of the input is the Acceleration, Displacement History or Load-history record itself. The record isin the form of a series of lines each of which starts with a Line Sequence Number (which must be in anascending order) followed by either (i) a group of 4 or 1 successive time-acceleration points (BERG or FREEor EXCEL Formats), or (ii) a sequence of 10, 8, 5 or 6 uniformly time spaced acceleration values at DELTAT timeintervals apart, the (CALTECH, NCEER or CSMIP Formats).

Note that the NCEER, CSMIP, EXCEL or PEER records do not have a sequence number. The analysisacceleration record, or forcing function, will begin at the first time on or implied by the beginning of theaccelerogram line ISTART and there must be sufficient lines remaining to span the analysis time-history lengthTR.

If the input is a force history IPVERT < 0 then the so-called accelerations are the actual force multiplier valueswhich will multiply the input load shape patterns (see section 24 above).

If the input are Displacement Histories (IPANAL = 8) these histories are applied to the degrees of freedomspecified in the Nodal Point Boundary Conditions.

The record must be on one of the following formats depending on the value of IBERG on section 25b. TheFORTRAN format is provided in parentheses for each case.

The I3 format implies 3 characters for the number which is right justified, 6X implies 6 blank characters. The F8.4implies 8 characters for the number and if omitted the decimal point is located in front of the 4th to last characterin the 8 character set which is assume to be right justified, if the decimal point is provided the number may belocated anywhere in the 8 character space. A number preceding the format, i.e. 10F8.4 means that there are10 numbers each having an 8 character field. Each format starts on a new line.

76

(1) BERG FORMAT (I3,4(F8.4,F9.6)) (Default filename extension is .eqb)

ISEQ T1 G1 T2 G2 T3 G3 T4 G4

ISEQ Line sequence number I 3Ti Time of point on accelerogram (seconds) F 8.4 Gi Acceleration (decimal fraction of gravity) F 9.6

If the line sequence number is greater than 999 it is not read or checked by the program.

(2) CALTECH FORMAT (I4,6X,10F6.0) or more precisely (I4,6X,10I6)(Default filename extension is .eqc)

ISEQ G1 G2 G3 G4 G5 G6 G7 G8 G9 G10

ISEQ Line sequence number I 4Gi 10 Accelerations (multiplied by ASCALE) at intervals of DELTAT I 6

If the line sequence number is greater than 9999 it is not read or checked by the program.

(3) NCEER FORMAT (10F8.2) (Default filename extension is .eqn)

G1 G2 G3 G4 G5 G6 G7 G8 G9 G10

Gi Acceleration (multiplied by ASCALE) at intervals of DELTAT F 8.2

(4) FREE FORMAT ( * ) (Default filename extension is .eqf)

ISEQ T1 G1

ISEQ Line sequence number I T1 Time of point on accelerogram (seconds) F G1 Acceleration (decimal fraction of gravity) F

The three items may be placed anywhere on the line and separated by at least one blank column or a comma.The lines must be in consecutive order with ISEQ starting at 1 and increasing line by line. This format isparticularly useful where the excitation record has been generated on a spreadsheet. It is, however, not ascompact a format as the NCEER format.

77

(5) CSMIP FORMAT (8F10.3) (Default filename extension is .eqs)

G1 G2 G3 G4 G5 G6 G7 G8

Gi 8 Accelerations (multiplied by ASCALE) at intervals of DELTAT F 10.3

(6) EXCEL FORMAT ( * ) (Default filename extension is .eqe)

T1 G1

T1 Time of point on accelerogram (seconds) F G1 Acceleration (decimal fraction of gravity) F

The two items may be placed anywhere on the line and separated by at least one blank column or a comma.The times MUST be in ascending order but do not have to be at equal intervals. This format is particularly usefulwhere the excitation record has been generated on a spreadsheet. It is, however, not as compact a format asthe NCEER format.

(7) PEER FORMAT (5E15.7) (Default filename extension is .eqp)

G1 G2 G3 G4 G5

Gi Acceleration (multiplied by ASCALE) at intervals of DELTAT E 15.7

Note DELTAT is usually 0.004 seconds. The records are usually in the units of acceleration of gravity.

(8) SAC FORMAT (6E13.5) (Default filename extension is .eqk)

G1 G2 G3 G4 G5 G6

Gi Acceleration (multiplied by ASCALE) at intervals of DELTAT E 13.5

Note DELTAT is usually 0.020 seconds. The records are usually in the units of acceleration of gravity.

78

25. Cyclic Adaptive Push-Over Displacement Time-History. (Only if IPANAL = 7)

The following set of input lines is required for the required displacement history. This displacement history actsas a control on the displacement at the node and direction specified on line 25b.

25a. Excitation Flag

One input line with the word EQUAKE starting in column 1

EQUAKE FILE

FILE Name of File where excitation is to be found (Maximum of 60 characters) AIf less than 2 excitations this name is usually supplied in response to the the prompts when the programs starts, or in Batch mode as arguments on the command line. If a file name is supplied here it over-rides those supplied at the prompts or on the command line. If no name is supplied then the excitation is assumed to follow this line in the supplied data. In this user may use word INPUT.

25b. Control parameters for Displacement History.

NSTEP NODE NDOF SCALE IPRINT

NSTEP Number of Points in Displacement History. INODE Nodal Point where Displacement History is Measured. INDOF Direction in which Displacement History is Measured. A

If the displacement is measured in the global X direction use X, x or 1If the displacement is measured in the global Y direction use Y, y or 2

SCALE Scale factor for the record. (Default value is 1.0) FIPRINT = 0; Displacement History is not printed in output file. I

= 1; Displacement History is printed in output file.

79

The rest of the input for the accelerogram (sections 25c and 25d) is in the Displacement-History File the nameof which is specified by the user in the initial file name prompts at the beginning of the program execution. Thedefault response is that the accelerograms, or excitation is appended to the above data file.

25c. Displacement History flag


START

25d. Displacement History

The remainder of the input is the Displacement History record itself. The record is in the form of a series of lineseach of which contains a sequence of displacements at which the Adaptive Load Sequence reverses. Each ofthese values is read under the FORTRAN Free Format so that the numbers are separated by one or more blanksor a comma. All NSTEP points MUST be supplied. The initial 0.0 is implied and should not be supplied. Thesequence of displacement values should have alternating signs. Use as many lines as are necessary to spanall NSTEP points.

D1 D2 D3 .. ... Di ... .. Dnstep

Di The ith displacement in the Displacement History. *

80

26. Acceleration Response Spectra. (Only if IPANAL =10)

The following set of input lines is required for the acceleration response spectra. These spectral accelerationsare assumed to apply to the base of the structure and will apply to all earthquake excitation directions asspecified by the parameter IPVERT in line 2 of the data set.

26a. Spectra Flag

One input line with the word SPECTRA starting in column 1

SPECTRA FILE

FILE Name of File where excitation is to be found (Maximum of 60 characters) AIf less than 2 excitations this name is usually supplied in response to the the prompts when the programs starts, or in Batch mode as arguments on the command line. If a file name is supplied here it over-rides those supplied at the prompts or on the command line. If no name is supplied then the excitation is assumed to follow this line in the supplied data. In this user may use word INPUT.

26b. Control parameters for Displacement History.

NSTEP IPRINT ISAME ICOMB SDAMP

NSTEP Number of Points in Acceleration Response Spectra. IIPRINT = 0; Response Spectra is not printed in output file. I

= 1; Response Spectra is printed in output file.ISAME = 0; All IPVERT earthquake components use the same response spectra. I

= 1; IPVERT response spectra are supplied.ICOMB = 0; SRSS modal combinations are used. I

= 1; CQC modal combinations are used (Not available yet).= 2; DSC modal combinations are used (Not available yet).= 3; Humar modal combinations are used (Not available yet).

SDAMP % damping used in modal combination method. (0.0 # SDAMP # 20.0) F(Not required for SRSS modal combinations)

Notes: The Acceleration Response Spectra are supplied in the units of Acceleration of Gravity (g). Theresponse spectra are then multiplied by the gravitational constant GRAV supplied in line 3 of the dataset.The spectra are supplied in the following section with one line required for each natural period of free-vibration. The first line must be for the zero natural period of free-vibration. The total number of linesis NSTEP.In the response spectra calculations if the natural period of a mode is greater than the value of theNSTEPth natural period the spectral acceleration is assumed to remain constant for all greater naturalperiods.

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The rest of the input for the response spectra (sections 26c and 26d) is in the Response Spectra File the nameof which is specified by the user in the first excitation file name prompt at the beginning of the program execution.The default response is that the spectra is appended to the data file following lines 26a and 26b above.

26c. Response Spectra file flag


START

26d. Spectral Accelerations.

The remainder of the input is the Response Spectra.. The record is in the form of a series of lines each of whichcontains the natural period of free-vibration and the necessary spectral values. Each of these values is readunder the FORTRAN Free Format so that the numbers are separated by one or more blanks or a comma. AllNSTEP lines MUST be supplied. The number of spectral accelerations required on each line depends on thevalues of IPVERT in line 2 of the data set and on the value of ISAME in line 26b above. If IPVERT = 0 or 1, orISAME = 0 then there must be only one spectral acceleration on each line. If IPVERT > 1 and ISAME = 1thenthere must be IPVERT spectral accelerations on each line. Use as many lines as are necessary to span allNSTEP points.

T(I) SA(i,1) SA(i,2)

T(i) The ith natural period of free-vibration. *SA(i,1) The ith spectral acceleration for the first earthquake component. *SA(i,2) The ith spectral acceleration for the second earthquake component (if required). *

End

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1


Program name:–DYNAPLOT

Program type:–Post-Processor for RUAUMOKO



Date:–September 25, 2004

DYNAPLOT

Result plotting for RUAUMOKO-2D and RUAUMOKO-3D

Purpose

This program is designed to plot the time history results or the hysteresis loops computer by the non-lineardynamic analysis programs RUAUMOKO-2D and RUAUMOKO-3D. The output is in the form of time-historyplots of nodal displacements or forces or member actions or deformations or combinations of the abovequantities. Alternatively hysteresis loops may be plotted for members or nodes.

Method of Analysis

The program generates each graph, one by one, requesting the control information for each graph thenscanning the Post-processor file generated by RUAUMOKO-2D or RUAUMOKO-3D to select the requiredfunction to plot. The program can only plot the results from one non-linear analysis at a time.

Data for DYNAPLOT

All data for DYNAPLOT is prompted for by the program using the TinyCLIP command processor. For help onthe input data type $HELP at any prompt. To get help on the use of the DYNAPLOT programme type HELPor ? At any prompt.

Control Data for Post-Processor Files

The number of nodes and members with data stores in the .RES file is recorded at the beginning of the filetogether with the time-step between stored items are recorded as the first item in the .RES file. The structuregeometry and mode shapes are also saved at the beginning of the file. Running the post-processor program DYNAPLOT.

2

To run the program call the program by the method appropriate to your operating system. On a personalcomputer just type DYNAPLOT assuming that the files DYNAPLOT.EXE and FQWIN.HLP are in your currentdirectory or path.

In Microsoft Windows operating systems another option is to create a shortcut on the desktop and for thispurpose a suitable icon for DYNAPLOT, Dynaplot.ico, is supplied with the program.

The program prompts for responses to a series of questions. Default responses, where appropriate, areenclosed in square brackets, [ ]. File names must match the conventions of your operating system but filenames, with paths where necessary, must not exceed 60 characters in length and must not contain blanks.

The first question asks for the name of the output file. The default is the computer console or terminal screen.This is normally the response for most users, however if an output file is created then the envelope values ofeach graph line drawn is output to that file.

The second question asks for the name of the DYNAPLOT post-processor file, do not supply the extensionpart of the name. This file has been given the extension .RES or .RAS by RUAUMOKO-2D or RUAUMOKO-3D and DYNAPLOT will attempt to open a file with the extension .RES but if that does not exist will attempt toopen the file with the extension .RAS. If a file with the given name and path with either extension cannot befound the program will again prompt for the file name, and path. Once the file has been found DYNAPLOTwill scan the file to determine whether it was created by RUAUMOKO-2D or RUAUMOKO-3D. The programDYNAPLOT will also scan the file to find the duration of the data stored in the file and if this is less that theduration TIME supplied in the RUAUMOKO data the user is informed of the duration that is available forplotting. The program will then ask if colour graphics is wanted. The program then prompt following thenormal options in DYNAPLOT. Please see the manual pages for DYNAPLOT.

Hard copies of the plots.

In Microsoft Windows operating systems to get hard copies of the graphs use the pull down ‘file’ menu andselect the Print or Save options to send the graph to the printer or to save the plot as a bitmap file (.BMP). On unix systems using GKS graphics select the Hard-copy option from the Choice window

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Output from RUAUMOKO-2D post-processor file

The data that can be plotted consists of the data stored in the RUAUMOKO-2D post-processor file for whichthe default name is RUAUMOKO.RES or RUAUMOKO.RAS. The content of the file is controlled by theparameter IOUT in the program RUAUMOKO. At every time-step stored in the post processor file thefollowing data is stored.

a. Analysis Data (17 items+Time)1 = X and Y ground accelerations (non-zero only for accelerogram input)2 = X and Y ground velocities (non-zero only for accelerogram input)3 = X and Y ground displacements (non-zero only for accelerogram input)4 = Kinetic Energy5 = Damping Work Done6 = Strain Energy7 = Applied Work8 = Plastic Work9 = Ductility (only meaningful for Adaptive Pushover)

10 = Effective X and Y displacement (only meaningful for Adaptive Pushover) 11 = Total X and Y Applied Forces 12 = Total Z Applied Moment

b. For each node the following items are stored: (controlled by IOUT in RUAUMOKO-2D)(18 items)

1 = X and Y displacements, Z rotation2 = X and Y velocities, Z rotational velocity 3 = X and Y accelerations, Z angular acceleration4 = X and Y applied forces, Z applied moment.5 = X and Y damping forces, Z damping moment6 = X and Y inertia forces, Z inertia moment

c. For each member the following items are stored: (controlled by IOUT in RUAUMOKO-2D)

For Frame (Beam) members (14, 18 or 22 items)1 = Axial force, Axial Strain, % Stiffness, Energy2 = Moment, Curvature, % Stiffness, Energy, (at End 1)3 = Moment, Curvature, % Stiffness, Energy, (at End 2)4 = Shear-end1, Shear-end2,5 = Moment, Curvature, % Stiffness, Energy, (at Hinge 3)6 = Moment, Curvature, % Stiffness, Energy, (at Hinge 4)7 = Shear Dis1, Shear Dis2, % Shear Stiff, Shear Energy8 = Theta-1, Theta-2, % Flex-1, % Flex-2

Note: Groups 5 and 6 are for 4 Hinge Beam only. Group 7 are for In-elastic Beam-Shear option only Group 8 are for In-elastic Shear-Link model only.

For Spring members (12 items)1 = x and y forces, z moment2 = x and y displacements, z rotation3 = x and y % stiffnesses, z % rotational stiffness4 = x and y energies, z rotational energy

For Damper members (9 items)1 = x and y forces, z moment2 = x and y velocities, z rotational velocity3 = x and y % stiffnesses, z % rotational stiffness

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For Wall members (13 items)1 = Axial force and 2 = Bending Moments at End 1 and End 23 = Axial strain4 = Curvatures at End 1 and End 25 = % axial stiffness6 = % flexural stiffness at End 1 and End 27 = Shear Forces at End 1 and End 28 = Neutral axis eccentricities at End 1 and End 2

For Tendon members (2 items)1 = Longitudinal or x Force2 = Longitudinal or x Deformation

For Contact members (5 items)1 = Contact or axial force2 = Damping Force3 = Friction force4 = Displacement in contact direction5 = % stiffness of spring

For Hybrid Quadrilateral finite elements (12 items)1 = F-xx, F-yy, J-xy, at node I2 = F-xx, F-yy, J-xy, at node J3 = F-xx, F-yy, J-xy, at node K4 = F-xx, F-yy, J-xy, at node L

For Masonry Panel Elements (15 items)1 = Force, Displacement and % Stiffness for Strut 12 = Force, Displacement and % Stiffness for Strut 23 = Force, Displacement and % Stiffness for Strut 34 = Force, Displacement and % Stiffness for Strut 45 = Force, Displacement and % Stiffness for Shear Strut

For Foundation Beam Elements (24 items)1 = Force, Deformation, % stiffness at Axial spring point 12 = Force, Deformation, % stiffness at Axial spring point 13 = Force, Deformation, % stiffness at Normal spring point 14 = Force, Deformation, % stiffness at Normal spring point 25 = Force, Deformation, % stiffness at Normal spring point 36 = Force, Deformation, % stiffness at Normal spring point 47 = Force, Deformation, % stiffness at Shear spring point 18 = Force, Deformation, % stiffness at Shear spring point 2

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Output from RUAUMOKO-3D post-processor file

The data that can be plotted consists of the data stored in the RUAUMOKO-3D post-processor file for whichthe default name is RUAUMOKO.RES or RUAUMOKO.RAS. The content of the file is controlled by theparameter IOUT in the program RUAUMOKO-3D. At every time-step stored in the post processor file thefollowing data is stored.

a. Analysis Data (24 items+Time)1 = X, Y and Z ground accelerations (non-zero only for accelerogram input)2 = X, Y and Z ground velocities (non-zero only for accelerogram input)3 = X, Y and Z ground displacements (non-zero only for accelerogram input)4 = Kinetic Energy5 = Damping Work Done6 = Strain Energy7 = Applied Work8 = Plastic Work9 = Ductility ( o n l y m e a n i n g f u l f o r A d a p t i v e

Pushover)10 = Effective X, Y and Z displacements ( o n l y m e a n i n g f u l f o r A d a p t i v e

Pushover) 11 = Total X, Y and Z Applied Forces 12 = Total X, Y and Z Applied Moments

b. For each node the following items are stored: (controlled by IOUT in RUAUMOKO-3D)(36 items)

1 = X, Y and Z displacements, X, Y and Z rotations2 = X, Y and Z velocities, X, Y and Z rotational velocities3 = X, Y and Z accelerations, X, Y and Z angular accelerations4 = X, Y and Z applied forces, X, Y and Z applied moments.5 = X, Y and Z damping forces, X, Y and Z damping moments6 = X, Y and Z inertia forces, X, Y and Z inertia moments

c. For each member the following items are stored: (controlled by IOUT in RUAUMOKO-3D)

For Frame (Beam) members (28 or 36 items)1 = Axial force, Axial Strain, % Stiffness, Energy2 = Moment-zz, Curvature-zz, % Stiffness, Energy, (at End 1)3 = Moment-zz, Curvature-zz, % Stiffness, Energy, (at End 2)4 = Torque, Twist, % Stiffness, Energy5 = Moment-yy, Curvature-yy, % Stiffness, Energy, (at End 1)6 = Moment-yy, Curvature-yy, % Stiffness, Energy, (at End 2)7 = Shear-y-1, Shear-y-2, Shear-z-1, Shear-z-28 = (-y at 1 (-y at 2, (-z at 1, (-z at 29 = % Stiff-y, %Stiff-z, Energy-y, Energy-z10 = Theta-y-1, Theta-y-2, Theta-z-1, Theta-z-211 = % Flex-y-1, % Flex-y-2, % Flex-z-1, % Flex-z-2

Note: Groups 8 and 9 are for the In-elastic Beam-Shear option only Groups 10 and 11 are for the In-elastic Shear-Link model only.

For Spring members (24 items)1 = x, y and z forces, x, y and z moments2 = x, y and z displacements, x, y and z rotations3 = x, y and z % stiffnesses, x, y and z % rotational stiffnesses4 = x, y and z energies, x, y and z rotational energies

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For Damper members (18 items)1 = x, y and z forces, x, y and z moments2 = x, y and z velocities, x, y and z rotational velocities3 = x, y and z % stiffnesses, x, y and z % rotational stiffnesses

For Tendon members (2 items)1 = Longitudinal or x Force2 = Longitudinal or x Deformation

For Contact members (6 items)1 = Contact or axial force2 = Damping Force3 = y and z Friction forces5 = Displacement in contact direction6 = % stiffness of spring

For Hybrid Quadrilateral finite elements, Forces and Moments per unit length.(24 items)1 = N-xx, N-yy, N-xy, M-xx, M-yy, Mxy at node I2 = N-xx, N-yy, N-xy, M-xx, M-yy, Mxy at node J3 = N-xx, N-yy, N-xy, M-xx, M-yy, Mxy at node K4 = N-xx, N-yy, N-xy, M-xx, M-yy, Mxy at node L

For Masonry Panel Elements (27 items)1 = Force, Displacement and % Stiffness for Strut 12 = Force, Displacement and % Stiffness for Strut 23 = Force, Displacement and % Stiffness for Strut 34 = Force, Displacement and % Stiffness for Strut 45 = Force, Displacement and % Stiffness for Shear Spring6 = Plate Bending Moments M-xx, M-yy, Mxy at node I7 = Plate Bending Moments M-xx, M-yy, Mxy at node J8 = Plate Bending Moments M-xx, M-yy, Mxy at node K9 = Plate Bending Moments M-xx, M-yy, Mxy at node L

For Foundation Beam Elements (24 items)1 = Force, Deformation, % stiffness at Axial spring point 12 = Force, Deformation, % stiffness at Axial spring point 13 = Force, Deformation, % stiffness at Normal spring point 14 = Force, Deformation, % stiffness at Normal spring point 25 = Force, Deformation, % stiffness at Normal spring point 36 = Force, Deformation, % stiffness at Normal spring point 47 = Force, Deformation, % stiffness at Shear spring point 18 = Force, Deformation, % stiffness at Shear spring point 2

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Control data for DYNAPLOT

DYNAPLOT prompts for the following information:

c. The name of the output file, the default being the output screen. If you wish the results to beoutput to a file then give the name (with path if necessary).

d. The name of the Post-processor file output by RUAUMOKO-2D or RUAUMOKO-3D, thedefault name of which is RUAUMOKO. The file must have the extension .RES or .RAS.

e. If you have a colour monitor you will be prompted to ask if you wish to use colour. If you arealso going to hard-copy the plots and you have only a mono-chromatic printer then answer Nor NO as all lines would appear as solid black lines. In monochromatic systems different linestyles are used for each line.

f. What sort of graph do you want? Minimum of the first character required.)

ACCN => Response Spectra from Nodal AccelerationsBASE => Hysteresis plot of combined inputsCOMB => Time history plot of combined inputsDISP => Snap-shots of deflected shapesENVL => Envelope Nodal ResultsFREE => Plot mode shapes of free vibrationHYST => Hysteresis plotINPT => Plot of input excitationMOVE => RUAUMOKO movie-like displaced shapes and plasticityNODE => Plot of Node Points in MeshPLOT => Plot of Element Mesh (In 3D data can redefine view axes)TIME => Time history plotVARY => Time history plot of Inter-nodal data (i.e. inter-storey drifts)WORK => Time history of work or energiesKEEP => Save last graph plotted to an ASCII fileOPEN => Restart DYNAPLOT with a new (.RES) input data setREDO => Redraw the Last Plot on the screenSTOP => Terminate DYNAPLOT

Each graph then asks for its own appropriate data.

The time ranges used in the plots must not exceed the time range stored in the post-processor file. If therange is exceeded then a message like “Ran out of RUAUMOKO results” will appear on the screen.

There is a maximum of ten lines in any time-history plot.There is only one line in a hysteresis loop or Base option plot.There is a maximum of five lines in an energy or work plot.

Graph titles which are to contain lower case letters or consist of more than one word must be enclosed insingle or double quotes and in any case must not contain more than 32 characters, including blanks. Note: Plots for which the horizontal axis is time will have the text “Time (Seconds)” appended to the title

supplied by the user for the horizontal axis.

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Time-History Plots

The program prompts for the following information:a. Number of lines N to be plotted.b. Whether Nodal data or Member data are to be plotted.c. Which item of the modal or member data is to be plotted. (x, y or rotation etc.)d. Which N nodes or members are to be plotted on the N lines.e. Step interval for vertical grid lines.f. First and last grid lines. If the grid step was 1.0 seconds and the graph was to plot from 0 to 10

seconds then the response would be 0 10.g. Graph vertical grid interval. If zero is selected then an automatic grid spacing is used.h. The bottom and top horizontal grid line IYN IYP. The lowest graph value is IYN* (grid interval)

and the top value is IYP* (grid interval). Note IYN MUST be less than IYP.i. Graph height and width. Default values fit A4 sheet.j. Title along bottom of plot.k. Title along vertical axis at left of graph.

The example below plots two lines of nodal data with a time interval of 1.0 with the first and last grid linesbeing 1 and 10 and IYN and IYP being -1 and 1 respectively.

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Hysteresis Plots

The program prompts for the following information:a. Whether Nodal data, or Member data is to be plotted.b. Which item of the nodal or member data is to be plotted on the vertical axis. (Moment etc.)c. Which item of the nodal or member data is to be plotted on the horizontal axis. (Curvature etc.)d. Which node or member is to be plotted.e. Start time for hysteresis plot.f. Finish time for hysteresis plot.g. Graph vertical grid interval. If zero is selected then an automatic grid spacing is used.h. The bottom and top horizontal grid lines IYN IYP. The lowest graph value is IYN* (grid interval)

and the top value is IYP* (grid interval). Note: IYN MUST be less than IYP.i. Graph horizontal grid interval. If zero is selected then an automatic grid spacing is used.j. The left and right horizontal grid lines IXN IXP. The left graph value is IXN* (grid interval) and

the right value is IXP* (grid interval). Note: IXN MUST be less than IXP.k. Graph height and width. Default values fit A4 sheet.l. Title along bottom of plot.m. Title along vertical axis at left of graph.

The example below plots the hysteresis curve for moment versus curvature. Note that although the memberis bi-linear the results file has only stored data at every 5 time-steps and hence some loops appear to havehad the corners cut off

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Combination Time-History Plots

This option enables combinations of node and/or member results to be combined into one plot line. Otheraspects are identical to that of the Time-History plots. The maximum number of contributions to any one plotline is 50.

The program prompts for the following information:

a. Number of Lines on Plot?b. For each line:

1: Number of Contributions?2: For each Contribution:

i Which node or member contributes to line?iii Is it a Node or Member?iv Which node or member item contributes to the line?v Multiplier for contribution.

c. Step interval for vertical grid linesd. First and last grid lines. If the grid step was 1.0 seconds and the graph was to plot from 0 to 10

seconds then the response would be 0 10e. Graph vertical grid interval. If zero is selected than an automatic grid spacing is used.f. The bottom and top horizontal grid lines IYN IYP. The lowest graph value is IYN* (grid interval)

and the top value is IYP* (grid interval). Note IYN MUST be less than IYP.g. Graph height and width. Default values fit A4 sheet.h. Title along bottom of plot.i. Title along vertical axis at left of graph.

In the example below the Base Shear is obtained by summing the shears in the two ground floor columns.

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Base Shear Combination Hysteresis Plots

This option enables combinations of node and/or member results to be combined into one plot line and to beplotted in the form of a Hysteresis plot by plotting the combined results against a second set of combinedresults. An example would be the plot of base-shear (a combined input) versus the interstorey drift (a secondcombined input). In the example below the Base Shear is plotted against the top floor displacement. Themaximum number of contributions to each axis value is 50.


a. For the Vertical axis: 1 Number of Contributions?2 For each Contribution:

i Which node or member contributes to line?ii Is it a Node or Member?iii Which node or member item contributes to the line?iv Multiplier for contribution.

b For the Horizontal axis:1 Number of Contributions?2 For each Contribution:

i Which node or member contributes to line?ii Is it a Node or Member?iii Which node or member item contributes to the line?ii Multiplier for contribution.

c Graph vertical grid interval. If zero is selected than an automatic grid spacing is used.d The bottom and top horizontal grid lines IYN IYP. The lowest graph value is IYN* (grid interval)

and the top value is IYP* (grid interval). Note IYN MUST be less than IYP.e Graph horizontal grid interval. If zero is selected then an automatic grid spacing is used.f The left and right horizontal grid lines IXN IXP. The left graph value is IXN* (grid interval) and

the right value is IXP* (grid interval). Note IXN MUST be less than IXP.g Graph height and width. Default values fit A4 sheet.h Title along bottom of plot.i Title along vertical axis at left of graph.

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Work-Energy History Plots

This option enables the Time-history of work or energies to be plotted. An option is to plot rate-of-change ofwork or “power” to be plotted.


a Whether Work-Energy or Power is to be plotted.b Number of lines to be plotted.c The five energy contributions multiplied by the factors below and are summed for each line:

1 Five multipliers (numbers) for each line are:i Multiplier for Kinetic Energyii Multiplier for Damping Work doneiii Multiplier for Strain Energy including Plastic workiv Multiplier for External Applied Workv Multiplier for Plastic Work?

d Time Step interval for vertical grid lines.e First and last grid lines. If the grid step was 1.0 seconds and the graph was to plot from 0 to 10

seconds then the response would be 0 10f Graph vertical grid interval. If zero is selected then an automatic grid spacing is used.g The bottom and top horizontal grid lines IYN IYP. The lowest graph value is IYN* (grid interval)

and the top value is IYP* (grid interval). Note IYN MUST be less than IYP.h Graph height and width. Default values fit A4 sheet.i Title along bottom of plot.j Title along vertical axis at left of graph.

The example below plots four lines, the bottom line is the kinetic energy, the second line is the kinetic energyand damping work done, the third line is the sum of the kinetic energy, the damping work done and the strainenergy. The fourth line is the External Applied Work. The vertical grid spacing is 1.0 seconds and the first andlast grids being 0 and 10 respectively. The vertical spacing was the default 0.0 and IYN and IYP are 0 and 1respectively.

If one selects the Default option then the following energy plot is produced without the necessity of specifyingall the data items above.

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Snap-shots of Deflected Shapes

This option enables the displaced shape of the structure to be plotted at various time-steps.

The program prompts for the following information:a The item to be plotted. For a building, usually the x-displacement. See table b in the section on

‘Output from RUAUMOKO post-processor file’.b Number of storeys or levels in plot. The number of storeys, or levels, in building plus one.c List of nodes, one required for each level. If the list cannot be fitted on a single input line the line

may be continued by placing an isolated ampersand (&) at the end of the line and the programwill prompt for the remaining nodes.If the first node is zero then the displacement for that node will be taken as zero.If any other nodes are zero then linear interpolation will be used for that level using the nearestavailable nodes from the adjoining levels.The node for the last level must be provided.

d Graph horizontal grid interval. If zero is selected then an automatic grid spacing is used.e The left and right vertical grid lines IYN IYP. The left graph value is IYN* (grid interval) and the

right value is IYP* (grid interval). Note IYN MUST be less than IYP.f Graph height and width. Default values fit A4 sheet.g Title along bottom of plot. Usually Displacement.h Title along vertical axis at left of graph. Usually Leveli The number of displaced shapes to be shown on the one plot (maximum of 10).j The times at which the deflected shapes are to be plotted. These must be in ascending time

sequence and the minimum separation is the time-step at which results are stored in the .RESfile. If the interval is too small the program will increment the steps automatically. The actualtimes used will be the first available step on or after the time specified.

The example below plots two lines, the solid line is the deflected shape at 2.0 seconds, the dashed line is thedeflected shape at 2.5 seconds. The data was stored for nodes 1, 3, 5, 7 and 9.

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Movie-like Presentation of Deflected Shapes and Plasticity

The option presents the movie-like displays of deflected shapes and plasticity. This show the same deformedmesh pictures that are able to be displayed in RUAUMOKO as it carries out the time-history analysis.However, in DYNAPLOT they may be displayed picture by picture so that hard copies of the plots may beproduced.

The program prompts for the following information:a. Whether continuous or stepped effectsb. Start time for the movie-like motionc. Finish time for the movie-like motion.

If continuous effects are selected then no further action is required until the sequence finishes except that onsome systems a key-press will stop the sequence and a second key-press will then terminate the plot. Forstepped effects press the Enter key to proceed to the next picture. In the later case the sequence mustproceed to the end of the sequence to terminate. The user is then asked if a further sequence is to be shown.

This feature is only available if all nodes and all members have had their results saved to the .RES post-processor file.

Mode Shapes of Free Vibration

The option presents the movie-like displays of the modes shapes of free vibration. This is similar to thedisplays in RUAUMOKO except that here if the number of cycles is S (upper or lower case) rather than thenumber of cycles then the mode shape is displayed only in its maximum plotted position so that a hard copymay be produced.


Plotting the Member or Element Mesh.

This produces the plot of the mesh as is shown in Ruaumoko. However, in this case you are asked for therange of members, or elements that are to be shown in the plot. The default range is for all elements. Forthree-dimensional structures, i.e. the data has come from Ruaumoko3D, you are also asked if you wish tochange that plot view axes.


Plotting the Nodal Point, or Joint, Mesh.

This produces the plot of thenodal points or joints in the mesh. As in the case for plotting the element mesh,case you are asked for the range of nodes or joints that are to be shown in the plot. The default range is forall nodes.


Redrawing of the Last Plot

This option enables the user to redraw the last graph plotted. This is normally used where the Enter key hasbeen pressed before the user obtained a hard-copy. This enables the graph to be redrawn without goingthrough the selection of the data items again.

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Keeping the Last Graph

This enables to user to save the graph data into an ASCII file so that it may be retrieved into the programCOMBPLOT or into a spreadsheet etc. for combining with other graphical information. For Hysteresis dataeach output line saves the coordinates of the points on the plot. For Time-history plots the first item on theline for each point is the time and this is followed by the values of each line at that time. The last two itemssaved are the x and y titles for the graph. There are several choices for the output format, one fitting an 80column line another a 132 column line as well as formats suitable for spreadsheet input such as for MicrosoftExcel.

There is an option for a single line Time-history graph and that is to save the file as a Caltech Formataccelerogram. This is particularly useful if the graph is for the total acceleration for node in the structure and ifone wishes to analyze a substructure located at that point in the structure or if one wants a Response Spectrafor the motion at that point. The resulting file may be input to RUAUMOKO or SPECTRA as a Caltech formataccelerogram.

Restarting with a new post-processor file.

If one selects the OPEN option from the main menu, DYNAPLOT restarts and prompts for the name of a newpost-processor (.RES or .RAS) file.

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Program name:–RUAUMOKO

Program type:–In-elastic Time-History Analysis



Date:–September 25, 2004

APPENDICESfor programs

RUAUMOKO2D, RUAUMOKO3D, HYSTERES & INSPECT

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APPENDIX A - STRENGTH DEGRADATION

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APPENDIX B - STIFFNESS DEGRADATIONHysteresis Loop data

Copyright \ Athol J. Carr, University of Canterbury, 1981-2004. All Rights reserved.

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APPENDIX A

DEGRADING STRENGTH parameters (Only if ILOS > 0)

DUCT1 DUCT2 RDUCT DUCT3 RCYC

DUCT1 Ductility at which degradation begins ( > 1.0) FDUCT2 Ductility at which degradation stops ( > DUCT1) FRDUCT Residual Strength as a fraction of the Initial Yield Strength FDUCT3 Ductility at 0.01 initial strength ( blank or > DUCT2) FRCYC % reduction of strength per cycle of inelastic behaviour (ILOS = 4, 5, 6 or 7 only) F

Notes:1. ILOS, the parameter that controls the strength degradation (see Properties tables)

ILOS = 0, No Strength Degradation.ILOS = 1, Strength loss in each direction is a function of the ductility in that direction.ILOS = 2, Strength loss in each direction is a function of the number of inelastic cycles.ILOS = 3, Strength loss in each direction is a function of the maximum ductility.ILOS = 4, As for ILOS = 1 above but strength loss is also proportional to the number of inelastic

cycles.ILOS = 5, As for ILOS = 4 above but strength loss is also proportional to the number of inelastic cycles

and the strength due to ductility for ductilities greater than DUCT2 remains at the level ofRDUCT until the ductility reaches DUCT3 when the strength suddenly reduces to 1% of theoriginal strength.

ILOS = 6, As for ILOS = 3 above but strength loss is also proportional to the number of inelasticcycles.

ILOS = 7 As for ILOS = 6 above but strength loss is also proportional to the number of inelastic cyclesand the strength due to ductility for ductilities greater than DUCT2 remains at the level ofRDUCT until the ductility reaches DUCT3 when the strength suddenly reduces to 1% of theoriginal strength.

2. If Strength Loss is based on cycle number rather than the ductility then DUCT1 is the cycle number thatthe strength starts to reduce and DUCT2 is the cycle number at which the strength reaches the residualvalue. It must be noted that the cycle number is computed as the number of times the hysteresis ruleleaves the post-yield back-bone or skeleton curve divided by 2 and this might be greater than thenumber of cycles of hysteresis particularly if there has been a one sided ratchet-like behaviour of thehysteresis. The minimum value permitted for RDUCT is 0.01. If the strength was to reduce to 0.0,Ruaumoko would then take the member behaviour as elastic which would not be the intention of theuser.

3. If a number is provided for the variable DUCT3 above then the strength decreases linearly from RDUCTtimes the initial strength at DUCT2 to 0.01 of the initial strength at ductility (cycle number) DUCT3. Ifthis number is omitted then the strength remains constant after DUCT2 is reached.

4. See Appendix B for information on which Hysteresis rules are able to accept strength degradation.5. If ILOS is greater than 0 then as the strength is reduced the stiffness is reduced to match. This means

that the yield displacement, rotation or curvature remains constant as the strength decreases makingthe definition of member ductility consistent. If the hysteresis loop being used has other strengthparameters such as a cracking force or moment then these are also reduced proportionally to the yieldstrength. If this is not done then some of the hysteresis loops may be impossible to follow where theyield strength would become less than the cracking strength.

6. If ILOS is supplied as a negative number, i.e. -5, the strength degradation rule would follow that forILOS=5 but the stiffness would not be reduced and other hysteresis rule actions would also not bereduced. This means that the definition of ductility would be difficult to follow as the yield displacement.rotation or curvature, which is the denominator in the expression for ductility, would decrease as thestrength decreases. Care would also be necessary insetting the levels of strength degradation toensure that the hysteresis loop does not become impossible to follow. See the note below.

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Strength Reduction Variation

In earlier versions of Ruaumoko when the strength degraded the stiffness remained using its input values.This causes problems with the definition of ductility in that as the yield force reduces and the stiffnessremains constant the yield displacement reduces and therefore for a given member deformation the apparentductility increases. This has shown up in that the residual strength, or the 1% strength, is reached at muchsmaller displacements, or curvatures, than the user had expected. The program has now been modified suchthat as the yield forces, or moments, degrade the stiffness also degrades. This means that the yielddisplacements remain constant and the definitions of ductilities remain more consistant. As some hysteresisrules have other force, or moment quantities such as cracking forces, or intercept forces (see Appendix B),which can also cause difficulties when the yield strength degrades, such that the yield strength may reduce toa smaller level than say the cracking moment leading to confusion within the hysteresis rule, such forcequantities are now also degraded as the yield strength degrades. This is more likely to be realistic than theearlier operation of the strength degradation in that for most member sections the yield point is defined by theextreme fibre yield strain and given the section properties the yield strain, or curvature, is more likely toremain constant than is the yield force or moment. There are still some difficulties when there are differentdegradations in each direction, ILOS =1, 4 or 5 as the stiffness will vary depending whether the memberdisplacement is positive or negative.

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APPENDIX B

STIFFNESS DEGRADATION parameters

Hysteresis Rules for Inelastic Member Behaviour

Each of the rules is designated by the number as shown below.

0 = Elastic (default) 1 = Elasto-plastic 2 = Bi-linear 3 = Ramberg-Osgood 4 = Modified Takeda Degrading Stiffness 5 = Bi-linear with Slackness 6 = Kivell Degrading Stiffness 7 = Origin Centered Bi-linear Hysteresis 8 = SINA Degrading Stiffness 9 = Stewart Degrading Stiffness with Slackness10 = Bi-linear Degrading Stiffness11 = Clough Degrading Stiffness12 = Q-HYST Degrading Stiffness13 = Muto Tri-linear Degrading Stiffness14 = Fukada Tri-linear Degrading Stiffness15 = Bi-linear Elastic16 = Non-linear Elastic (Un-Reinforced Masonry)17 = Degrading Elastic18 = Ring-Spring Isolator or Damper19 = Hertzian Contact Non-linear Spring20 = Mehran Keshavarzian's Degrading Stiffness21 = Widodo Foundation Compliance 22 = Li Xinrong Reinforced Concrete Column Degrading Stiffness 23 = Bouc Degrading Stiffness24 = Remennikov Out-of-plane Buckling Steel Brace25 = Takeda with Slip Degrading Stiffness26 = Al-Bermani Bounding Surface Hysteresis27 = Peak Oriented Hysteresis28 = Matsushima Strength Decay model29 = Kato Shear model30 = Elastomeric Damper Spring31 = Composite Section, modified SINA model32 = Different Stiffness in Positive and Negative directions. Modified Bi-linear rule33 = Masonry Strut Hysteresis34 = Hyperbolic Hysteresis 35 = Degrading Bi-linear with Gap Hysteresis36 = Bi-linear with Differing Positive and Negative Stiffness Hysteresis37 = Non-linear Elastic Power Rule Hysteresis 38 = Revised Origin Centred Hysteresis39 = Dodd-Restrepo Steel Hysteresis40 = Bounded Ramberg-Osgood Hysteresis41 = Modified (Payne) Ramberg-Osgood Hysteresis42 = HERA-SHJ Steel Hinge unit.43 = Resetting Origin Loop44 = Pampanin Reinforced Concrete Hinge hysteresis45 = Degrading Stiffness Ramberg-Osgood Hysteresis46 = Dean Saunders Reinforced Concrete Column47 = Multi-linear Elastic48 = Isotropic/Kinematic Strain Hardening Bi-Linear49 = Isotropic/Kinematic Strain-Hardening Ramberg-Osgood50 = Flag-shaped Bi-linear Hysteresis

5

Use of Hysteresis Rules for Frame members in RUAUMOKO-2Dand RUAUMOKO-3D

IHYST HysteresisRule

1cptbeam

R-Ccol.

Steelcol.

Gencol.

2cptbeam

VFlexbeam

0 Elastic Yes Yes Yes Yes Yes Yes

1 Elasto-Plastic Yes Yes Yes Yes Yes No

2 Bi-linear Yes Yes Yes Yes Yes Yes

3 Ramberg-Osgood Yes Yes Yes Yes Yes Yes

4 Takeda Yes Yes* Yes* Yes* Yes Yes

5 Bi-linear - Slackness Yes Yes Yes Yes Yes Yes

6 Kivell Yes Yes Yes Yes Yes Yes

7 Origin-Centered Yes Yes Yes Yes Yes Yes

8 SINA Yes Yes Yes Yes Yes Yes

9 Stewart Yes Yes Yes Yes Yes No

10 Degrading Bi-linear Yes Yes Yes Yes Yes Yes

11 Clough Yes Yes* Yes* Yes* Yes Yes

12 Q-HYST Yes Yes* Yes* Yes* Yes No

13 Muto Yes Yes Yes Yes Yes Yes

14 Fukada Yes Yes Yes Yes Yes Yes

15 Bi-linear Elastic Yes Yes Yes Yes Yes Yes

16 Non-Linear Elastic Yes Yes Yes Yes Yes Yes

17 Degrading Elastic Yes Yes Yes Yes Yes Yes

18 Ring-Spring Yes No No No No No

19 Hertzian Contact No No No No No No

20 Keshavarzian Yes Yes Yes Yes Yes No

21 Widodo Foundation Yes Yes Yes Yes Yes No

22 Li-Xinrong Column No Yes No No No No

23 Bouc Yes No No No Yes Yes

24 Remennikov Yes No Yes No No No

25 Takeda with slip Yes No No No Yes No

26 Al-Bermani Bound-Surface Yes Yes Yes Yes Yes Yes

27 Peak Oriented Yes Yes Yes Yes Yes Yes

28 Matsushima Degrading Yes Yes Yes Yes Yes Yes

29 Kato Degrading Shear Yes Yes No No Yes No

30 Elastomeric Spring No No No No No No

31 Composite Section Yes No No No Yes Yes

32 Different +/- Stiffness Yes No No No Yes Yes

33 Masonry Strut No No No No No No

34 Hyperbolic Yes Yes Yes Yes Yes Yes

35 Degrading Bi-linear Yes No No No Yes No

36 Bi-linear Differing +/- Stiffness Yes Yes Yes Yes Yes Yes

37 Non-linear Elastic Power Yes Yes Yes Yes Yes Yes

38 Revised Origin Centred Yes Yes Yes Yes Yes Yes

39 Dodd-Restrepo Steel Yes Yes Yes Yes Yes Yes

40 Bounded Ramberg-Osgood Yes Yes Yes Yes Yes Yes

41 Payne Ramberg-Osgood Yes Yes Yes Yes Yes Yes

42 HERA-SHJ Yes No No No Yes No

43 Resetting Origin No No No No No No

6

Use of Hysteresis Rules for Frame members in RUAUMOKO-2Dand RUAUMOKO-3D

IHYST HysteresisRule

1cptbeam

R-Ccol.

Steelcol.

Gencol.

2cptbeam

VFlexbeam

44 Pampanin Yes Yes Yes Yes Yes Yes

45 Degrading Ramberg-Osgood Yes Yes Yes Yes Yes Yes

46 Dean Saunders Conc. Column Yes Yes Yes Yes Yes Yes

47 Multi-linear Elastic Yes Yes Yes Yes Yes Yes

48 Isotropic Strain Hard. Bi-linear Yes Yes Yes Yes Yes Yes

49 Isotropic Strain Hard. Ramberg Yes Yes Yes Yes Yes Yes

50 Flag-shaped Bi-linear Yes Yes Yes Yes Yes Yes

7

Use of Hysteresis Rules for Spring members in RUAUMOKO-2D

IHYST Hysteresis Rule ITYPE = 1,3 or 4

0 Elastic Yes

1 Elasto-Plastic Yes

2 Bi-linear Yes

3 Ramberg-Osgood Yes

4 Takeda Yes

5 Bi-linear - Slackness Yes

6 Kivell Yes

7 Origin-Centered Yes

8 SINA Yes

9 Stewart Yes

10 Degrading Bi-linear Yes

11 Clough Yes

12 Q-HYST Yes

13 Muto Yes

14 Fukada Yes

15 Bi-linear Elastic Yes

16 Non-Linear Elastic Yes

17 Degrading Elastic Yes

18 Ring-Spring Yes

19 Hertzian Contact Yes

20 Keshavarzian Yes

21 Widodo Foundation Yes

22 Li-Xinrong Column No

23 Bouc Yes

24 Remennikov No

25 Takeda with slip Yes

26 Al-Bermani Bound-Surface Yes

27 Peak Oriented Yes

28 Matsushima Degrading Yes

29 Kato Degrading Shear Yes

30 Elastomeric Spring Yes

31 Composite Section No

32 Different +/- Stiffness Yes

33 Masonry Strut Hysteresis Yes

34 Hyperbolic Hysteresis Yes

35 Degrading Bi-linear Hysteresis Yes

36 Bi-linear Differing +/- Stiffness Yes

37 Non-linear Elastic Power Yes

38 Revised Origin Centred Yes

39 Dodd-Restrepo Steel Yes

40 Bounded Ramberg-Osgood Yes

41 Payne Ramberg-Osgood Yes

42 HERA-SHJ Yes

43 Resetting Origin Yes

8



44 Pampanin Yes

45 Degrading Ramberg-Osgood Yes

46 Dean Saunders Concrete Column Yes

47 Multi-linear Elastic Yes

48 Isotropic Strain Hard Bi-linear Yes

49 Isotropic Strain Hard Ramberg Yes

50 Flag-shaped Bi-linear Yes

9



0 Elastic Yes


2 Bi-linear Yes


4 Takeda Yes

5 Bi-linear - Slackness Yes

6 Kivell Yes

7 Origin-Centered Yes

8 SINA Yes

9 Stewart Yes


11 Clough Yes

12 Q-HYST Yes

13 Muto Yes

14 Fukada Yes


16 Non-Linear Elastic Yes

17 Degrading Elastic Yes

18 Ring-Spring Yes

19 Hertzian Contact Yes

20 Keshavarzian Yes



23 Bouc Yes

24 Remennikov No

25 Takeda with slip Yes


27 Peak Oriented Yes


29 Kato Degrading Shear Yes

30 Elastomeric Spring Yes



33 Masonry Strut Hysteresis Yes






39 Dodd-Restrepo Steel Yes



42 HERA-SHJ No

43 Resetting Origin Yes

10



44 Pampanin Yes




48 Isotropic Strain Hard. Bi-lineaqr Yes

49 Isotropic Strain Hard. Ramberg Yes


11

Use of Hysteresis Rules for Foundation members in RUAUMOKO-2D and RUAUMOKO-3D

IHYST Hysteresis Rule ITYPE = 1, 2, 3, 4 or 5

0 Elastic Yes


2 Bi-linear Yes


4 Takeda Yes

5 Bi-linear - Slackness No

6 Kivell No

7 Origin-Centered No

8 SINA Yes

9 Stewart No


11 Clough Yes

12 Q-HYST Yes

13 Muto Yes

14 Fukada Yes


16 Non-Linear Elastic No

17 Degrading Elastic No

18 Ring-Spring No

19 Hertzian Contact No

20 Keshavarzian Yes



23 Bouc Yes

24 Remennikov No

25 Takeda with slip No


27 Peak Oriented No


29 Kato Degrading Shear No

30 Elastomeric Spring No



33 Masonry Strut Hysteresis No






39 Dodd-Restrepo Steel No



42 HERA-SHJ No

43 Resetting Origin No

12

Use of Hysteresis Rules for Foundation members in RUAUMOKO-2D and RUAUMOKO-3D

IHYST Hysteresis Rule ITYPE = 1, 2, 3, 4 or 5

44 Pampanin Yes




48 Isotropic Strain Hard. Bi-linear Yes

49 Isotropic Strain Hard. Ramberg Yes


13

Use of Strength Degradation and Damage Indices in RUAUMOKO-2D and RUAUMOKO-3D

IHYST Hysteresis Rule Strength Degradation Damage Indices

0 Elastic No No

1 Elasto-Plastic Yes Yes

2 Bi-linear Yes Yes

3 Ramberg-Osgood Yes Yes

4 Takeda Yes Yes

5 Bi-linear - Slackness Yes Yes

6 Kivell Yes Yes

7 Origin-Centered Yes Yes

8 SINA Yes Yes

9 Stewart Yes Yes

10 Degrading Bi-linear Yes Yes

11 Clough Yes Yes

12 Q-HYST Yes Yes

13 Muto Yes Yes

14 Fukada Yes Yes

15 Bi-linear Elastic No No

16 Non-Linear Elastic No No

17 Degrading Elastic No No

18 Ring-Spring No No

19 Hertzian Contact No No

20 Keshavarzian Yes Yes

21 Widodo Foundation No Yes

22 Li-Xinrong Column No Yes

23 Bouc No* Yes

24 Remennikov No Yes

25 Takeda with slip Yes Yes

26 Al-Bermani Bound-Surface Yes Yes

27 Peak Oriented Yes Yes

28 Matsushima Degrading No* Yes

29 Kato Degrading Shear No Yes

30 Elastomeric Spring No No

31 Composite Section Yes Yes

32 Different +/- Stiffness Yes Yes

33 Masonry Strut Hysteresis No Yes

34 Hyperbolic Hysteresis Yes Yes

35 Degrading Bi-linear Hysteresis No No

36 Bi-linear Differing +/- Stiffness Yes Yes

37 Non-linear Elastic Power No No

38 Revised Origin Centred Yes Yes

39 Dodd-Restrepo Steel No Yes

40 Bounded ramberg-Osgood Yes Yes

41 Payne Ramberg-Osgood Yes Yes

42 HERA-SHJ Yes No

43 Resetting Origin No No

14

Use of Strength Degradation and Damage Indices in RUAUMOKO-2D and RUAUMOKO-3D

IHYST Hysteresis Rule Strength Degradation Damage Indices

44 Pampanin No No

45 Degrading Ramberg-Osgood Yes Yes

46 Dean Saunders Concrete Column Yes Yes

47 Multi-linear Elastic Yes No

48 Isotropic Strain Hard. Bi-linear No Yes

49 Isotropic Strain Hard. Ramberg No Yes

50 Flag-shaped Bi-linear Yes Yes

15

Notes on notation for hysteresis rules:

In all of the diagrams associated with the hysteresis rules the following notation is used.

F is the force or moment in the member.d is the deformation or curvature in the member.K0 is the initial elastic stiffness, i.e. the EI of a flexural beam or beam column, the AE/L for the axialstiffness of a beam or beam column, or the stiffness K of a spring member.Fy is the yield force or moment. r is the bi-linear factor or Ramberg-Osgood factor.: is the ductility where : = d / dy where, in general, the yield displacement dy = Fy / K0

Some of these rules require further data which is described in the following pages.

Notes on the preceding tables:

If a hysteresis rule is selected and the rule is not allowed for that member then an error message isprinted in the output for the section properties and the analysis will be terminated.

Yes* implies that the hysteresis rule is now allowed for column members. However, the effects on thesmall-cycle hysteresis loops of the yield moments varying with the changes in the axial force in themember have not been studied.

If both Strength Degradation and Damage Indices are selected then the effects of Strength Degradationon the computed Damage Indices is uncertain and a warning is printed after reading the memberproperties.

If Strength Reduction or Damage Indices are not allowed for the specified Hysteresis Rule and they arespecified in the input data, the data is read and then the control parameters ILOS and/or IDAMG arereset to zero. Warnings of these re-settings are printed in the output.

No*. The Bouc and Matsushima Hysteresis rules have their own strength degradation capability.

Damage indices for the masonry strut hysteresis only outputs the hysteretic work done.

For the Ruaumoko (2D) version Spring member ITYPE=2 is tri-linear hysteresis only. If ITYPE=3 thenthe SINA hysteresis is used for the transverse (local y) direction.

For the Ruaumoko (2D) version the Frame member ITYPE=7, the four hinge beam has the allowablehysteresis table that follow the same rules as that for the variable flexibility beam.

16

Linear Elastic Hysteresis

DEGRADING STIFFNESS parameters

IHYST = 0 Linear Elastic. - No further data required.

17

Elasto-Plastic Hysteresis

IHYST = 1 Elasto-Plastic Hysteresis. - No further data required.

Note: This rule is not available for Variable Flexibility Beam Members.

18

Bi-Linear Hysteresis

IHYST = 2 Bi-Linear Inelastic. - No further data required.

19

Ramberg-Osgood Hysteresis

IHYST = 3 RAMBERG-OSGOOD Hysteresis [Kaldjian 1967] - No further data required.

Note: The bi-linear factor in the section data is used as the Ramberg-Osgood factor r and must begreater than or equal to 1.0

20

It must be noted that the Ramberg-Osgood loop works well when large cycle loops are exercised but an off-set of the forces can occur in some small cycles as is shown in the diagram above. In 1984 the Ramberg-Osgood hysteresis loop in Ruaumoko was modified to bound the forces within an envelope obtained by theloops from the maximum and minimum displacements. In the year 2000 the Ramberg-Osgood loop revertedto its original definition and the bounded version was moved to IHYST = 40.

21

Modified Takeda Hysteresis

IHYST = 4 Modified TAKEDA Hysteresis [Otani 1974].

Modified Takeda rule.

ALFA BETA NF KKK

ALFA Unloading stiffness (0.0 # ALFA # 0.5) FBETA Reloading stiffness (0.0 # BETA # 0.6) FNF Reloading stiffness power factor (NF $ 1) IKKK =1; Unloading as in DRAIN-2D I

=2; Unloading as by Emori and Schnobrich

Note: Increasing ALFA decreases the unloading stiffness and increasing BETA increases the reloadingstiffness. The power factor NF is usually taken as 1.0

22

Bi-Linear with Slackness Hysteresis

IHYST = 5 Bi-linear with Slackness Hysteresis.

The bi-linear with slackness model can be used to represent diagonal braced systems where yield in in onedirection may stretch the members leading to slackness in the bracing system. The model allows for eitheryield in compression, in say a cross-braced system, or for a simple elastic buckling in compression whichwould be more appropriate in a single brace member.

Bi-linear with Slackness rule.

GAP+ GAP- IMODE RCOMP C EPS0 ILOG

GAP+ Initial slackness, positive direction. ( > 0.0) F GAP- Initial slackness, negative direction ( < 0.0) FIMODE = 0; Default case, normal rule holds I

= 1; Bi-linear elastic buckling in compression.= 2; Bi-linear Elastic in Tension and Compression

RCOMP Bi-linear Factor r in Compression FC Strain-Rate Constant (if # 0.0 Strain-rate effects are ignored) FEPS0 Quasi-static Strain-rate (if # 0.0 then C = 0.0) FILOG = 0; Natural Logarithms are used for Strain-rate effects I

= 1; Base 10 Logarithms are used for Strain-rate effects

Notes:1 Concrete and Steel Beam-column sections require GAP+ = - GAP-.2 If no value is prescribed for RCOMP, i.e. there are less than four items on the line or RCOMP is the

word DEFAULT or D then the bi-linear factor in compression is the same as that for tension. 3 For the SPRING members the hysteresis data is the same for all actions. If different properties are

desired in the different actions then separate members should be used for the different actions. Thedefault bi-linear factor is that for the force components.

4 If the strain rate constant C is non zero then the positive and negative yield forces are multiplied by thefactor

where is the current strain rate and is the quasi-static strain rate EPS0.

23

Kivell Degrading Hysteresis

HYST = 6 KIVELL Degrading Stiffness [Kivell 1981].

The pinching model of Kivell was designed to represent the behaviour of the nails in steel nail-platesconnecting timber members together at the joints. The assumed cubic unloading-reloading curve isrepresented by three straight lines.

Kivell Degrading rule.

ALFA

ALFA Unloading stiffness (0.0 # ALFA # 0.4) F

24

Origin-Centred Hysteresis

IHYST = 7 Origin-Centered Bi-linear Hysteresis - No further data is required,

On unloading and on subsequent reloading the path is on a line passing through the origin.

25

SINA Degrading Tri-linear Hysteresis

IHYST = 8 SINA Degrading Tri-linear Hysteresis. [Saiidi 1979].

SINA Degrading Tri-linear rule.

ALFA BETA FCR(i)+ FCR(i)- FCC(i)

ALFA Bi-linear factor (positive cracking to yield) FBETA Bi-linear factor (negative cracking to yield) FFCR(i)+ Cracking moment or force at i ( > 0.0) FFCR(i)- Cracking moment or force at i ( < 0.0) FFCC(i) Crack closing moment or force at i ( > 0.0) F

Notes:1. The i refers to the different actions on the member, see the member data descriptions for the number of

actions and which action they refer to.2. Concrete and Steel Beam-column sections require symmetry in moments and thus

FCR(i)- = - FCR(i)+ etc. and that ALFA = BETA

26

Wayne Stewart Degrading Hysteresis

IHYST = 9 Wayne Stewart Degrading Stiffness Hysteresis. [Stewart 1984].

This very general rule was initially developed by Wayne Stewart for the representation of timber framedstructural walls sheathed in plywood nailed to the framework. The model allows for initial slackness as well assubsequent degradation of the stiffness as the nails enlarged the holes and withdrew themselves from theframework.

Stewart Degrading with slackness rule.

FU FI PTRI PUNL GAP+ GAP- BETA ALPHA LOOP

FU Ultimate force or moment ( > 0.0) FFI Intercept force or moment ( > 0.0) FPTRI Tri-linear factor beyond ultimate force or moment FPUNL Unloading stiffness factor ( > 1.0) FGAP+ Initial slackness, positive axis ( > 0.0) FGAP- Initial slackness, negative axis ( < 0.0) FBETA Beta or Softening factor ( $ 1.0) FALPHA Reloading or Pinch power factor ( # 1.0) FLOOP =0 Loop as defined I

=1 Modified loop

Notes: Concrete and Steel Beam-column sections require GAP+ = - GAP- and that all othercomponents maintain symmetry about the zero force or moment axis

This rule is not available for the Variable Flexibility or 4-Hinge Beam members.

Modified loop; Member section yield values are taken as Fu+ and Fu- and the Fu on this line is taken as Fy+ and Fy-.This modification allows the use of strength degradation. In the original model strength degradationaffects only the cracking moments Fy and not Fu. Also the PTRI (read as part of this data line) and r(read as part of the member section data) are interchanged.

27

Operation of Wayne Stewart Hysteresis rule Note: Vos = Fi etc.

28

Wayne Stewart used the following hysteresis values in his plywood wall examples [Stewart 1984].

FU = 1.5 times yield force or momentFI = 0.25 times yield force or momentPTRI = 0.0PUNL = 1.45BETA = 1.09ALPHA = 0.38

Example: The diagram below shows the use of the modified Wayne-Stewart hysteresis loop to model a pre-1970 reinforced concrete column hinge where plain round longitudinal reinforcement bars are used[Liu,2001]. The two loops compare the observed experimental loop with that computed using theprogram HYSTERES using the following parameters

Section Stiffness propertiesK0 = 51.1 kN/mmR = 0.001FY+ = +58.4 kNFY- = -58.4 kN

IHYST=9 Stiffness Degradation parameters (see preceding pages)FRC (i.e. FU) = 27.6 kNFI = 6.0 kNPTRI = 0.14PUNL = 1.1GAP+ = 0.0GAP- = 0.0BETA = 1.2ALPHA = 0.8LOOP = 1

There is no strength degradation applied in this example.

29

Degrading Bi-linear Rule

IHYST = 10 Degrading Bi-linear Hysteresis. [Otani 1981].

This is similar to the Bi-linear rule except that the stiffness degrades with increasing inelastic deformation.

Degrading Bi-linear rule.

ALFA


30

Clough Degrading Stiffness Hysteresis

IHYST = 11 CLOUGH Degrading Hysteresis. [Otani 1981] - No further data is required.

This rule was the first degrading stiffness rules to represent reinforced concrete members. The rule is thesame as the modified TAKEDA rule with the parameters ALFA and BETA both equal to 0.0.

31

Q-HYST Degrading Stiffness Hysteresis

IHYST = 12 Q-HYST Degrading Stiffness Hysteresis. [Saiidi 1979].

This rule is the same as the Modified Takeda rule with the parameter BETA set to 0.0 and unloading as perEmori and Schnobrich.

Q-HYST Degrading rule.

ALFA


Note: This rule is not available for the Variable Flexibility and 4-Hinge Beam Members.

32

Muto Degrading Tri-linear Hysteresis

IHYST = 13 MUTO Degrading Tri-linear Hysteresis. [Muto 1973].

After cracking the model is an Origin-Centered rule. After yield is reached the model become a Bi-linearhysteresis with the equivalent elastic stiffness equal to the secant stiffness to the yield point.

Muto Degrading Tri-linear rule.

ALFA FCR(i)+ FCR(i)-

ALFA Bi-linear factor (cracking to yield) FFCR(i)+ Cracking moment or force at i ( > 0.0) FFCR(i)- Cracking moment or force at i ( < 0.0) F


actions and which action they refer to.2. Concrete and Steel Beam-column sections require symmetry in moments and therefore

FCR(i)- = - FCR(i)+ etc.

33

Fukada Degrading Tri-linear Hysteresis

IHYST = 14 FUKADA Degrading Tri-linear Hysteresis. [Fukada 1969].

Fukada Degrading Tri-linear rule.

ALFA BETA FCR(i)+ FCR(i)-

ALFA Bi-linear factor (cracking to yield) FBETA Unloading Stiffness factor (see Takeda ALFA) FFCR(i)+ Cracking moment or force at i ( > 0.0) FFCR(i)- Cracking moment or force at i ( < 0.0) F


actions and which action they refer to.2. Concrete and Steel Beam-column sections require symmetry in moments and thus

FCR(i)- = - FCR(i)+ etc.

34

Bi-linear Elastic Rule

IHYST = 15 Bi-linear Elastic Hysteresis. - No further data is required.

This rule is similar to the Bi-linear hysteresis except that the rule unloads elastically down the same path whichmeans that no hysteretic energy is dissipated..

35

Non-linear Elastic Rule (URM)

IHYST = 16 Non-linear Elastic Hysteresis - No further data is required.

This non-linear elastic model represents the non-linear behaviour of face-loaded masonry wall units.No hysteretic energy is dissipated.

36

Degrading Elastic Rule

IHYST = 17 Degrading Elastic Rule. - No further data is required.

The degradation of the elastic stiffness is proportional to the amount of equivalent ductility. This equivalentductility is equal to the displacement divided by the nominal yield deformation.

37

Ring-Spring Hysteresis

IHYST = 18 Ring-Spring Hysteresis. [Hill 1994]

This device can be used as a seismic energy dissipation device. The default model operates in the compressiveforce - compressive displacement quadrant of the force-displacement plot.

Ring-Spring

RSTEEP RLOWER DXINIT KTYPE KLOOP

RSTEEP Unloading Steep Stiffness factor (usually greater than 1.0) FRLOWER Unloading Lower Stiffness factor (usually less than the Bi-linear factor) FDXINIT Initial Displacement FKTYPE = 0 ; Uni-directional, = 1 ; Bi-directional IKLOOP = 0 ; New Definition, = 1 ; Original Definition. I

Note:1. This rule is normally only available for the Spring Members. In this case do not supply yield data as the

yield point is defined by DXINIT, see below.2. The rule may be used for the flexural components of the Giberson one-component beam option of the

FRAME members when it would normally be expected to be used in the bi-directional mode. It may alsobe used for the axial component of the Giberson beam members provided the beam has no flexuralstiffness i.e. EI is zero, representing a truss-like action. In both of these cases the appropriate yieldmoments or yield forces must be provided with dummy non-zero values (the actual yield values arecomputed internally by the hysteresis rule but non-zero yield forces or moments are required in order thatthe member is treated as non-linear).

3. When initial pre-stress (FRAME members) or pre-load (SPRING members) forces are applied to the Uni-directional Ring-spring (KTYPE = 0) they must be compressive (i.e. negative) forces.

38

Hertzian Contact Spring

IHYST = 19 Hertzian Contact Spring Hysteresis Rule. [Davis 1992]

The Hertzian contact spring is useful for modelling the contact between impacting structures. It really modelscontact between spheres but this seems to be used in wider applications. It is only available for the SPRINGmembers and the CONTACT members.

Hertzian Contact Spring

MPP MPN PFP PFN GAP+ GAP-

MPP Stiffness Multiplier for Positive Displacement FMPN Stiffness Multiplier for Negative Displacement FPFP Power factor for Positive Displacement FPFN Power factor for Negative Displacement FGAP+ Initial slackness in Positive direction ($ 0.0) FGAP- Initial slackness in Negative direction (# 0.0) F

39

Mehran Keshavarian Hysteresis

IHYST = 20 MEHRAN KESHAVARZIAN Degrading and Pinching Hysteresis. [Keshavarzian 1984]

Mehran Keshavarian Degrading and Pinching rule.

ALFA

ALFA Unloading stiffness (0.0 # ALFA # 0.5) (see Takeda) F

Note: This rule is not available for the Variable Flexibility and 4-Hinge Beam Members.

40

Widodo Foundation Compliance

IHYST = 21 WIDODO Foundation Compliance Model.[Widodo 1995]

These non-linear elastic rules are designed to model foundation compliance springs including the modelling ofa wall footing that can suffer partial or tip uplift. This is only appropriate to SPRING members, see section 12..

Widodo Foundation Compliance.

A(i) P(i) Q(i)

A(i) Multiplier for i th Component FP(i) Power Factor for First part of i th Component FQ(i) Power Factor for Second Part of i th Component F

Notes:1. The i refers to the different actions on the member, see the member data descriptions for the number

of actions and which action they refer to.2. This rule is not available for the Variable Flexibility Beam members.

41

Li Xinrong Reinforced Concrete Column Hysteresis

IHYST = 22 Li XINRONG Reinforced Concrete Column Hysteresis. [Li Xinrong 1994]

This rule is only available for the Reinforced Concrete column option for the FRAME members, see section 11.The degrading rule modifies the stiffness of the member to allow for the effects due to variation of the axial forceacting in the column.

Li Xinrong Degrading Reinforced Concrete Column.

FPC RHO PB U ALFA BETA PINCH

FPC Concrete Compressive Strength f'c ( < 0.0) FRHO Percentage Longitudinal Steel content FPB Yield Moment - Axial Force Diagram Balance Axial Force FU Unloading Coefficient (0.7 to 1.0) (Li Xinrong used 0.9) FALFA Factor for unloading (0.5 to 1.0) (Li Xinrong used 0.9) FBETA Factor used in relocation of unloading point (0.8) FPINCH Pinching Factor (0.7 to 0.9) F

42

IHYST = 23 BOUC Hysteresis Rule. [Wen 1976]

This very general parametric hysteresis rule gives a smooth transition of the change of stiffness as thedeformation of the member changes. It has been used to represent lead-rubber bridge bearings or energydissipators [Bessasson 1992] and has been used for the analysis of inelastic buildings subjected to randomvibration [Baber 1981].

Bouc Degrading Stiffness.

A1 A2 A3 A4 A5 N D3 D4 D5 MODE INIT

A1 Loop Fatness parameter ( 0.1 to 0.9) FA2 Loop Pinching parameter (-0.9 to 0.9) FA3 Stiffness parameter (usually 1.0) FA4 Degradation parameter (usually 1.0) FA5 Strength parameter (usually 1.0) FN Power Factor, Controls Abruptness (1 to 3, usually 1) ID3 Strength Degradation parameter (0.0 to 0.1) (0.0 no degradation) FD4 Loop Size Degradation (0.0 to 0.2) (0.0 no degradation) FD5 Stiffness Degradation (0.0 to 0.2) (0.0 no degradation) FMODE = 0 Constantinou Version

= 1 Baber and Wen VersionINIT = 0 Normal

= 1 Bi-linear until first unloading after yielding

Note: This rule is not available for the Beam-Column Members

Bouc Hysteresis Versions

Baber and Wen

Constantinou

where and are the displacement velocity, is the elastic stiffness, is the bi-linear factor and is the yielddisplacement. is the yield force and is the change in displacement. Q is the force in the spring and F isthe current stiffness factor. The tangent stiffness is . and are the Bouc hysteresis controlparameters, is the power factor.

43

Bouc Hysteresis Rule

The Bouc rule is controller by the parameter , which in RUAUMOKO is initially 0.0 and is integrated step-by-stepas in the above equations. The rule is such that at the static analysis which means that the initialstiffness is the bi-linear stiffness and the force in the member is proportional to the bi-linear stiffness and thedisplacement. To over come some of these effects an option is to force the rule to be bi-linear until reversal afterthe first yield. A result is that there is a marked reduction in member force at the change of rule. further work isbeing done to fully understand the implications of the use of this hysteresis.

44

Steel Brace Member Hysteresis

IHYST = 24 REMENNIKOV Steel Brace Member Hysteresis.

Represents the out-of-plane buckling of a steel brace member.

REMENNIKOV Steel Brace rule.

Iminor Sminor k ALFA BETA THETA0 E1 E2 E3 E4 N SHAPE

Iminor Second Moment of Area about Minor axis FSminor Plastic Section Modulus about Minor axis Fk Effective Length Parameter (Leff = kL) FALFA Strain Hardening Alpha (1.0 # " # 1.5) FBETA Beta factor ($ > 1.0) recommended range 1.2 to 1.4 FTHETA0 Initial out-of-straightness (length units) FE1 Effective modulus e1 (>0.0) FE2 Effective modulus e2 (>0.0) FE3 Effective modulus e3 (>0.0) FE4 Effective modulus e4 FN = 0; ALFA above used for strain hardening effects. I

= 1; Built-in strain hardening rule and ALFA is reset to 1.0SHAPE = 1; Flanged section such as an I section. I

= 2; Circular hollow section= 3; RHS or SHS section

Notes:1. This hysteresis is available only for the Giberson One-component beam and the Steel beam-column

options of the FRAME member type. (see Section 11a)2. The member only permits this hysteresis in the axial component. The member is assumed to be bi-linear

in flexure (provided the yield moments are non-zero in sections 11e or 11g).3. The beam or beam-column cross-section area and the axial yield forces in section 11e or the yield

interaction forces and moments in section 11g must be supplied. 4. It is recommended that Iteration on Residuals, say MAXIT = 3 and FTEST = 0.001, be used with this rule

(see section 5).5. It is recommended that a small time step be used so that the transitions within the rule may be followed.

45

Def

initi

on o

f Diff

eren

t Zon

es

46

Idealization Curves for Tangent Modulus History

Tangent Modulus – Axial Force Relationship

Analytical Axial Force – Plastic Hinge Rotation Curve

47

Takeda with Slip Hysteresis

IHYST = 25 TAKEDA with SLIP Hysteresis. [Kabeyasawa 1983]

This rule allows slip when the deformation reloads in the member strong direction.

TAKEDA with SLIP rule.

ALFA BETA1 BETA2 FC(i) RC(i)

ALFA Unloading Degradation parameter (see Takeda ALFA) (0.0 # ALFA # 1.0) FBETA1 Slipping stiffness parameter FBETA2 Re-loading stiffness parameter FFC(i) Cracking Force for Component i ( > 0.0) FRC(i) Cracking Displacement for Component i ( > 0.0) F


of actions and which action they refer to.2. The initial elastic stiffness supplied with the section properties is the secant stiffness passing through the

origin and the yield points on the member hysteresis curve.3. The yield points in the negative direction for component i is at ( -FC(i), -RC(i) )4. Slip only occurs when re-loading towards the stronger direction.

48

The following example show the use of the Takeda with Slip hysteresis loop to model the behaviour of a pre-1970reinforced concrete beam which is reinforced with plain round bar reinforcement [Liu, 2001]. The loops show theobserved experimental loop and the matching loop from the program HYSTERES using the loop parametersprovided below.

Section Property parametersK0 = 10.4 kN/mmR = 0.05YP+ = +93.4 kNYP- = -61.4 kN

IHYST=25 Stiffness Degradation parameters (see previous page)ALFA = 0.2BETA1 = 1.2BETA2 = 1.5FC = 26.9 kNRC = -0.65 mm

Strength Degradation parametersILOS = 1DUCT1 = 3DUCT2 = 8RDUCT= 0.3DUCT3 = 10

49

Bounding-Surface Hysteresis

IHYST = 26 AL-BERMANI Bounding-surface Hysteresis. [Zhu, 1995]

This rule allows for the Bauschinger effects in steel members by using a bounding surface rather than the moreoften used but more complicated Ramberg-Osgood functions.

Bounding Surface rule.

ALFA BETA

ALFA Positive ALFA (0.0<ALFA<0.9) FBETA Negative BETA (0.0<BETA<0.9) F

Notes:1. The bi-linear factor p must be greater then 0.001. (see section 11c or section 12a)

This limitation on p should prevent mathematical difficulties with the logarithmic and exponentialfunctions.

2 The use of this rule in Concrete and Steel Beam column members will require symmetry in the actionsat each end, i.e. ALFA = BETA etc.

50

Peak Oriented Hysteresis

IHYST = 27 PEAK Oriented Hysteresis. - No further data is required.

This rule is similar to the Origin Centered rule except that on unloading the force-displacement relationship movesalong a line to the maximum force-displacement point in the opposite direction. If yield has not occurred in thatdirection the opposite yield point is used as the target.

51

Matsushima Degrading Hysteresis

IHYST = 28 MATSUSHIMA Strength Reduction Hysteresis. [Matsushima 1969]

This rule represents the behaviour of short reinforced concrete columns failing in shear. The rule uses basicallya bi-linear hysteresis but that the elastic stiffness and strength degrade every time unloading takes place fromthe post-yield part of the bi-linear force displacement curve.

Matsushima rule.

A B

A Stiffness Multiplier A (0.0 < A < 1.0) FB Strength Multiplier B (0.0 < B < 1.0) F

Notes:1. A and B are raised to then power N where N is the number of times the system unloads from the bi-linear

force-displacement hysteresis back-bone.

52

KATO Shear Hysteresis

IHYST = 29 KATO Degrading Shear Model. [Kato 1983]

Represents the behaviour of a reinforced concrete member failing in shear. A tri-linear skeleton curve with afalling bi-linear part is used.

Kato Shear rule.

PTRI ALFA BETA GAMMA FU(i)+ FU(i)-

PTRI Tri-linear Factor (must be less than or equal to zero) FALFA Unloading Degrading Factor (0 < ALFA < 1) (see Takeda) FBETA Slip Stiffness Factor (0 # BETA < 1) FGAMMA Slip Length Factor (0 # GAMMA < 1) FFU(i)+ Positive FU at component i (>0.0) FFU(i)- Negative FU at component i (<0.0) F


of actions and which action they refer to.2. The bi-linear factor p must be less than 0.0 and less than the tri-linear factor PTRI. (see section 11c or

section 12a)3. The actions FU should less than the appropriate yield actions FY.4. The use of this rule in Concrete members will require symmetry in the actions at each end, i.e. FU(i)+

= -FU(i)- etc.5. For reinforced concrete members failing in shear the recommended values are ALFA = 0.4, BETA = 0.6

and GAMMA = 0.95.6. For reinforced concrete members flexure dominated members the recommended values are ALFA = 0.2,

BETA = 0.0 and GAMMA = 0.0.

53

Elastomeric Spring Damper

IHYST = 30 Elastomeric Spring Damper Hysteresis. [Pekcan 1995]

Represents a double-acting elastomeric spring which has resistance due to both displacement and velocity. Thestiffness properties are basically bi-linear elastic.

Elastomeric Spring Damper rule.

C DMAX ALFA

C Damper Constant ($0.0) FDMAX Maximum Damper Stroke ($0.0) FALFA Velocity Exponent (>0.0) F

Notes:1. The force FD in the elastomeric damper is given by

where the d is the displacement of the spring and where K0 is the initial stiffness of the device and is thelongitudinal spring stiffness of the member. The stiffness rK0 is the stiffness after the prestress Fy isovercome where r is the bi-linear factor for the spring member. The prestress force Fy is taken as thepositive longitudinal yield force of the member and if the prestress is zero the spring stiffness is takenas constant equal to rK0.

2. If DMAX is zero then the ratio of d to dmax is taken as 1.0. This has the effect of taking the exponent $in the reference paper as zero.

3. The exponent ALFA was taken as 0.2 in the reference.

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Composite Section Hysteresis

IHYST = 31 Composite Section. - Modified SINA Hysteresis.

This rule allows for the modelling of composite concrete-steel beams or concrete T beams where the behaviouris different in the positive and negative flexural actions.

Composite Section rule.

BETA FCR(i) FCC(i)

BETA Stiffness Factor Cracking to Yield in Negative direction (ALFA < 1.0) FFCR(i) Cracking Force in Negative direction at component i (FRC(i) < 0.0) FFCC(i) Cracking Closing Force at component i (FCC(i) < 0.0) F


of actions and which action they refer to.2. The post cracking stiffness factor BETA must be greater than the bi-linear factor r (see member

properties sections)

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Different Positive-Negative Stiffness Hysteresis

IHYST = 32 Different Positive and Negative Stiffness. Modified Bi-linear Hysteresis.

This rule allows for different stiffnesses in the positive and negative directions. The basic hysteresis rule is amodification of the degrading Bi-linear rule.

Different Positive and Negative Stiffness rule.

ALFA BETA

ALFA Negative stiffness factor of the positive stiffness (ALFA > 0.1) FBETA Unloading Degrading Factor, see TAKEDA ALFA (0.0 < BETA < 0.9) F

56

IHYST = 33 Masonry Strut Hysteresis (Crisafulli 1997).

This rule allows for the modelling of masonry panels in framed structures. If the strut model is used with the springmembers then only the longitudinal stiffness is specified for the strut member and two struts are required to modeleach panel, one strut across each diagonal of the panel. The masonry strut hysteresis is also used for theMasonry Panel Element where four struts represent the panel together with a shear spring..

Masonry Strut Hysteresis rule.

Stress-strain relationship

FC FT UC UUL UCL EMO GUN ARE

FC Compressive strength (stress units) (FC < 0.0) FFT Tensile strength (stress units) (FT > 0.0) FUC Strain at FC (UC < 0.0) FUUL Ultimate strain (UUL < 0.0) (UUL # 1.5 UC) FUCL Closing strain FEMO Initial masonry modulus (EMO $ 2 FC/UC) FGUN Stiffness unloading factor (GUN $ 1.0) FARE Strain reloading factor (ARE > 0.0) F

Strut data

AREA1 AREA2 R1 R2 IENV

AREA1 Initial strut cross-sectional area (AREA1 > 0.0) FAREA2 Final strut cross-sectional area (AREA2 # AREA1) FR1 Displacement at 1 (R1 < 0.0) FR2 Displacement at 2 (R2 # R1) FIENV = 0 ; Sargin stress-strain envelope descending branch I

= 1 ; Parabolic stress-strain envelope descending branch

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Masonry Strut Strength Envelope

Masonry Strut Hysteresis

58

Notes:FC The compressive strength f'

m2 is the main parameter controlling the resistance of the strut. It must benoted that FC does not represent the standard compressive stress of masonry but should be adoptedtaking into account the inclination of the compressive principal stresses and the mode of failure expectedin the masonry panel. See Crisafulli 1997.

FT Tensile strength f't represents the tensile strength of the masonry or the bond strength of the panel-frameinterface, whichever is smallest. The consideration of the tensile strength has been introduced in themodel in order to gain generality. However, results obtained from different examples indicate that thetensile strength, which is generally much smaller than the compressive strength, has no significantinfluence on the overall response. Therefore, in the absence of more detailed information, the tensilestrength can be assumed to be zero.

UC The strain at maximum stress g'm usually varies between -0.002 and -0.005 and its main effect on theoverall response of the infilled frame is the modification of the secant stiffness of the ascending branchof the stress-strain curve.

UUL The ultimate strain gu is used to control the descending branch of the stress-strain relationship. Whena large value is adopted for, example gu = 20 g'm , a smooth decrease of the compressive stress isobtained.

UCL The closing strain gcl defines the limit strain at which the cracks partially close and compressive stressescan be developed. Values of the closing strain ranging between 0 and 0.003 lead to results which agreeadequately with experimental data. If a large negative value is adopted, for example gcl = gu , this effectis not considered in the analysis.

EMO The elastic modulus Emo represents the initial slope of the stress-strain curve and its value can exhibita large variation. Various expressions have been proposed for the evaluation of the elastic modulus ofmasonry. It is worth noting, however, that these expressions usually define the secant modulus at astress level between 1/3 and 2/3 of the maximum compressive stress. In order to obtain an adequateascending branch of the strength envelope it is assumed that Emo $ 2 f'm2 / g'm .

GUN The unloading stiffness factor (un controls the slope of the unloading branch. It is assumed to be greaterthan or equal to 1.0 and usually ranges from 1.5 to 2.5.

ARE The reloading strain factor "re defines the point where the reloading curves reach the strength envelope.The calibration of the hysteretic model for the axial behaviour of masonry showed that good results areobtained using values ranging between 0.2 and 0.4. However, higher values, for example 1.5, arerequired to model adequately the cyclic response of the infilled frames. This is because other sourcesof nonlinear behaviour, such as sliding shear, need to be indirectly considered in the response of themasonry struts.

Four parameters are required to represent the cross-sectional area of the masonry strut. These are the initial areaAms1 = AREA1 and final area Ams2 = AREA2 and the axial displacements at which the cross-sectional areachanges, )R1 = R1 and )R2 = R2. In a simplified model, it can be assumed that AREA1 and AREA2 are thesame using a low value of the strut area to avoid an excessive increase in the axial strength. In a more refinedanalysis, a higher value of the initial area can be adopted, whereas the final area can be reduced by about 10%to 30%. The displacement R1 and R2 can be estimated as g'm dm/5 and g'm dm (where dm is the length of themasonry strut) respectively, at least until more precise information becomes available. Several empiricalexpressions, which are described in section 6.2.1.3 of the reference, have been proposed for the evaluation ofthe equivalent width of the masonry strut, whose value normally ranges from 0.1 to 0.25 of the diagonal lengthof the infill panel.

IENV The descending branch of the stress-strain curve is usually modelled with a parabola instead of the curveassociated with Sargin's equation in order to obtain a better control of the response of the strut after themaximum stress has been reached.

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Hyperbolic Hysteresis

IHYST = 34 Hyperbolic Hysteresis (no further data required)(Konduor and Zelansko (1963))(also Duncan and Chang (1970))

This rule has been popular in representing the shear stress–shear strain relationships in soils subjected toearthquake excitation.

.

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Degrading Bi-linear With Gap Hysteresis

IHYST = 35 Degrading Bilinear with Gap Hysteresis

This hysteresis was initially developed to model a strain-hardening behaviour which changed with increasingcycle number. The members were used in parallel with a member having a more conventional hystereticbehaviour such as Bi-linear or Ramberg-Osgood. The total member force was taken as the sum of the twonumber forces.

Degrading Bi-linear with Gap

GAP+ GAP– PUN

GAP+ Initial gap in positive direction ($ 0.0) FGAP– Initial gap in negative direction (# 0.0) FPUN Unloading stiffness factor ($ 1.0) F

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Bi-linear with Differing Positive and Negative Stiffness Hysteresis

IHYST = 36 Bi-linear with Different +/– stiffness hysteresis

The rule is to represent actions which exhibit different stiffnesses under positive or negative forces or moments.This may be typical of reinforced concrete T sections for example.

Bi-linear with +/– stiffness

ALFA BETA GAMMA IOP

ALFA Positive stiffness is ALFA * nominal stiffness ALFA $ 0.1 FBETA Negative stiffness is BETA * nominal stiffness BETA $ 0.1 FGAMMA Unloading degradation factor F

see Takeda (IHYST=4) ALFA 0.5 $ GAMMA $ 0.0 IOP = 0 ; Bi-linear factor is the same in both directions I

= 1 ; Positive bi-linear factor = ALFA * bi-linear factorNegative bi-linear factor = BETA * bi-linear factor

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Non-linear Elastic Power Rule

IHYST = 37 Non-linear Elastic Power Rule

This rule is similar to the Bi-linear Elastic Hysteresis, IHYST = 15 except that it avoids the problems with thesudden change of stiffness on unloading encountered due to the lack of energy dissipation in these non-linearelastic hysteresis rules.

Non-linear Elastic Power Rule

PFP(i) PFN(i)

PFP(I) Power factor in positive direction for component i (0.01 # PFP # 3.0) FPFN(i) Power factor in negative direction for component i (0.01 # PFN # 3.0) F


of actions and which action they refer to. 1. Normally PFP and PFN are less than 1.0

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Revised Origin-Centred Bi-linear Hysteresis

IHYST = 38 Revised Origin Centred Bi-linear Hysteresis (No further data is required)

On unloading the path is back to the origin. In reloading the path follows the previous unloading path on that sideof the origin.

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Dodd-Restrepo Steel Hysteresis Rule

IHYST = 39 Dodd-Restrepo Steel Hysteresis Rule

This hysteresis rule is designed to allow for the Bauschinger effects in the steel hysteresis.

Dodd-Restrepo Steel Rule

ESH Esu Fsu OmegaF

ESH Deformation (curvature) at initiation of strain hardening FEsu Deformation (curvature) at peak load FFsu Force (moment) at peak load FOmegaF Bauschinger Effect Factor (0.6 < OmegaF < 1.3) F

(Default value = 1.0)

Reference:

Dodd, L.L. and Restrepo-Posada, J.I. Model for Predicting Cyclic Behaviour of Reinforcing Steel. J. StructuralEngineering, ASCE, Vol. 121, No. 3, Mar. 1995, pp 433–445.

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Plot of Displacement History

Plot of Computed and Experimental Force Histories

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IHYST = 40. Bounded Ramberg-Osgood Hysteresis. No extra data required.

This loop is similar to that for IHYST = 3 except that bounds have been applied to the forces so that off-sets tothe forces do not occur during small cycles of displacement.

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IHYST = 41. Pyke modification to the Ramberg-Osgood Hysteresis. No extra data required.

This loop is similar to that for IHYST = 3 except that the small cycle behaviour has been modified to prevent off-sets on the force in these small cycles. These loops were initially used to model the behaviour of soils.The smallloops indicate a greater rate of change of force with increasing displacement i.e. a greater curvature in the plots.

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IHYST = 42. HERA - SHJ (Sliding Hinge Joint) Hysteresis.

This loop developed by the Heavy Engineering Research Association (New Zealand) is to represent thebehaviour of a sliding moment connection between steel beams with a concrete slab above them and connectedto at the joints to steel columns.

HERA-SHJ Hysteresis Rule

Cspp Cspn Ru Tdp Tdn Ispr

Cspp Positive Moment Intercept ( > 0.0 ) FCspn Negative Moment Intercept ( < 0.0 ) FRu Unloading stiffness factor ( > 0.0 ) FTdp Positive Design Theta ( > 0.0 ) FTdn Negative Design Theta ( < 0.0 ) FIspr = 0; Without Belleville Springs I

= 1; With Belleville Springs

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IHYST = 43 Resettable Actuator Hysteresis. No extra data required.

This hysteresis is to represent the behaviour of a semi-active damper member [Hunt, 2003]. The force isproportional to the displacement until a saturation force is attained, Fy+ or Fy- (the yield forces for themember) when the system appears to show a perfectly plastic response. On any reversal of displacement theforce is automatically reset to zero and the origin is moved to the existing displacement and the system willthen behave as an elastic member until either saturation is achieved or the displacement again changes sign.

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IHYST = 44 Pampanin Reinforced Concrete Beam-Column Joint Hysteresis.

Pampanin Reinforced Concrete Beam-Column Joint rule.

IOP AlfaS1 AlfaS2 AlfaU1 AlfaU2 DeltaF Beta

IOP =1; Option 1 - Reloading Power Factor I=2; Option 2 - Reloading Slip Factor

AlfaS1 Slip Stiffness Power Factor As1 ( 1.5 # As1 # 3.0) FAlfaS2 Option 1- Reloading Power Factor As2 ( 0.5 # As2 # 1.0) F

Option 2- Reloading Slip Factor Xi ( 1.0 # Xi # 1.5)AlfaU1 Initial Unloading Power Factor Au1 (-1.0 # Au1 # 0.0) FAlfaU2 Final Unloading Power Factor Au2 ( 0.3 # Au2 # 1.0) FDeltaF Unloading Force Factor (%) Df (-1.0 # Au1 # 0.0) FBeta Reloading Factor Beta (-1.0 # Beta # 0.0) F

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IHYST = 45 Degrading Stiffness RAMBERG-OSGOOD Hysteresis.

Degrading Stiffness Ramberg-Osgood rule.

IOP ALFA BETA GAMMA RESID

IOP =1; Original Ramberg-Osgood hysteresis (see IHYST= 3) I=2; Limited Ramberg-Osgood hysteresis (see IHYST=40)=3; “Pyke” Ramberg-Osgood hysteresis (see IHYST=41)

ALFA % stiffness degradation per cycle (0.0 # ALFA # 10) FBETA Ductility where stiffness starts to degrade with ductility (BETA $ 1.0 or = 0.0) F

If BETA=0.0 then there is NO degradation with ductility.GAMMA Ductility where stiffness stops degrading with ductility (GAMMA > BETA) FRESID Residual Stiffness when degrading with Ductility (RESID $ 0.50) F

Note: The bi-linear factor in the section data is used as the Ramberg-Osgood factor r and must be greaterthan or equal to 1.0

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IHYST = 46 DEAN SAUNDERS Reinforced Concrete Column Hysteresis.

This hysteresis is to represent the behaviour of Older Reinforced Concrete Columns where plain roundreinforcement is used.

DEAN SAUNDERS Reinforced Concrete Column rule.

PHIY+ PHIY- MTH+ MTH- ALFA BETA IOP

PHIY+ Positive Yield Deformation. Must be greater than (Yield Action)/Stiffness. FPHIY- Negative Yield Deformation. Must be less than (Yield Action)/Stiffness. FMTH+ Positive Threshold Action. Must be less than Positive Yield Action. FMTH- Negative Threshold Action. Must be greater than Negative Yield Action. FALFA Unloading stiffness degradation factor (0.0 # ALFA # 0.5) FBETA Reloading Factor (BETA $ 1.0) FIOP =0; Threshold actions reduce with strength degradation. I

=1; Threshold actions remain constant when yield actions degrade.

Notes: 1. There is a Bezier curve fitted between the point (MTH+,(MTH+)/STIFF) and (YP,PHIY+) withthe initial slope STIFF and the final slope r*STIFF.

2. On unloading the rule is origin centered when the action is less than MTH+. When the actionis greater than MTH+ the unloading stiffness degrades with the factor ALFA as observed inthe Dergading Bi-Linear Hysteresis (IHYST = 10).

3. The behaviour in the negative Action-Deformation quadrant is identical to that in the positiveAction-Deformation quadrant.

4. The parameter BETA only comes into action if the deformation in the other quadrant hasexceeded the yield deformation.

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IHYST = 47 Multi-Linear Elastic Hysteresis.

Multi-Linear Elastic rule.

N F1 D1 F2 D2 F3 D3

N Number of segments beyond Bi-linear (1 # N # 3) IF1 Fraction of stiffness in first segment beyond Bi-linear FD1 Multiplier on Yield Displacement where F1 applies (D1 $ 1.05) FF2 Fraction of stiffness in second segment beyond Bi-linear FD2 Multiplier on Yield Displacement where F2 applies (D2 $ 1.05*D1) FF3 Fraction of stiffness in third segment beyond Bi-linear FD3 Multiplier on Yield Displacement where F3 applies (D3 $ 1.05*D2) F

Note: The F1, F2 and F3 factors should not be less than 0.0 for single degree of freedom systems.

Multi-Linear Elastic Hysteresis

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IHYST = 48 Kinematic/Isotropic Strain Hardening Bi-Linear Hysteresis.

Kinematic/Isotropic Strain Hardening Bi-Linear rule.

ALFA BETA

ALFA Stiffness Degrading Factor (See IHYST=10) (0.0 # ALFA # 0.5) FBETA Isotropic Hardening Factor (0.0 # BETA # 1.0) F

If BETA=0.0 then there is NO Isotropic Strain Hardening.If BETA=1.0 then there is Full Isotropic Strain Hardening.

Note: The bi-linear factor ‘r’ in the section data must be greater than 0.0 if Kinematic or Isotropic strainhardening is to occur

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IHYST = 49 Kinematic/Isotropic Strain Hardening RAMBERG-OSGOOD Hysteresis.

Kinematic/Isotropic Strain Hardening Ramberg-Osgood rule.

ALFA BETA IOP

ALFA Ramberg-Osgood multiplier (0.0 # ALFA) FIf ALFA=0.0 then ALFA is taken as 1.0 (Default value)

BETA Isotropic Hardening Factor (0.0 # BETA # 1.0) FIf BETA=0.0 then there is NO Isotropic Strain Hardening.If BETA=1.0 then there is Full Isotropic Strain Hardening.

IOP =1; Original Ramberg-Osgood hysteresis (see IHYST= 3) I=2; Limited Ramberg-Osgood hysteresis (see IHYST=40)=3; “Pyke” Ramberg-Osgood hysteresis (see IHYST=41)

Note: The bi-linear factor in the properties section data is used as the Ramberg-Osgood factor r and mustbe greater than or equal to 1.0

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IHYST = 50 Flag-Shaped Bi-Linear Hysteresis.

Flag-shaped Bi-Linear rule.

BETA1 BETA2 ... BETAi (i = 1 to N)

BETA1 Flag Height Action 1 (0.0 # BETA1 # 1.0) FBETA2 Flag Height Action 2 (0.0 # BETA2 # 1.0) FBETAi Flag Height Action i (0.0 # BETAi # 1.0) F

Note: If BETA=0.0 then the loop is Bi-linear elastic.If BETA=1.0 then the loop on unloading returns to the originN is the number of actions requiring data for the member. See Spring or Frame member data.

Flag-Shaped Bi-linear Hysteresis

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MEMORANDA

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MEMORANDA

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MEMORANDA

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