Ruaumoko Appendices

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Ruaumoko Appendices

Research May 2015

DOI: 10.13140/RG.2.1.4493.7127

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Athol Carr

University of Canterbury

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ction Book

Ruaumoko Manual

Volume 5:Appendices

Author:

Athol J. Carr

Civil Engineering


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Department of Civil Engineering COMPUTER PROGRAM LIBRARY

Program name:

RUAUMOKO

Program type:

In-elastic Time-H istory Analysis

Program code:

ANSI Fortran77

Author:

Athol J C arr

Date:

November 27, 2008

APPENDICES

for programs

RUAUMOKO2D,RUAUMOKO3D, HYSTERES& INSPECT

-

APPENDIX A - STRENGTH DEGRADATION

-

APPENDIX B - STIFFNESS DEGRADATIONHysteresis Loop data

Copyright \Athol J. Carr, University of Canterbury, 1981-2007. All Rights reserved.


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APPENDIX A

DEGRADING STRENGTHparameters (Only if ILOS> 0)

DUCT1 DUCT2 RDUCT DUCT3 RCYC

DUCT1 Ductility at which degradation begins ( > 1.0) F

DUCT2 Ductility at which degradation stops ( > DUCT1) F

RDUCT Residual Strength as a fraction of the Initial Yield Strength F

DUCT3 Ductility at 0.01 initial strength ( blank or > DUCT2) F

RCYC % 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 of

RDUCTuntil the ductility reaches DUCT3when the strength suddenly reduces to 1% of the

original strength.

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

cycles.

ILOS= 7 As for ILOS= 6 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 of

RDUCTuntil the ductility reaches DUCT3when the strength suddenly reduces to 1% of theoriginal strength.

2. If Strength Loss is based on cycle number rather than the ductility then DUCT1is the cycle number that

the strength starts to reduce and DUCT2is the cycle number at which the strength reaches the residua l

value. It must be noted that the cycle number is computed as the number of times the hysteresis rule

leaves the post-yield back-boneor skeleton curve divided by 2 and this might be greater than the

number of cycles of hysteresis particularly if there has been a one sided ratchet-like behaviour of the

hysteresis. 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 the

user.

3. If a number is prov ided for the variable DUCT3above then the strength decreases linearly from

RDUCTtimes the initial strength at DUCT2to 0.01 of the initial strength at ductility (cycle number)

DUCT3. If this number is omitted then the strength remains constant after DUCT2is reached.

4. See Appendix B for information on which Hysteresis rules are able to accept strength degradation.

5. If ILOSis greater than 0 then as the strength is reduced the stiffness is reduced to match. This means

that the yield displacement, rotation or curvature rema ins constant as the strength decreases m aking

the definition of member ductility consistent. If the hysteresis loop being used has other strength

parameters such as a cracking force or m oment then these are also reduced proportionally to the yield

strength. If this is not done then some of the hysteresis loops may be impossible to follow where the

yield strength would becom e less than the cracking strength.

6. If ILOSis supplied as a negative number, i.e. -5, the strength degrada tion rule would follow that for

ILOS=5 but the stiffness would not be reduced and other hysteresis rule actions would also not be

reduced. 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 the

strength decreases. Care would also be necessary insetting the levels of strength degradation to

ensure that the hysteresis loop does not becom e 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 stiffness

remains constant the yield displacement reduces and therefore for a given member deformation the apparent

ductility increases. This has shown up in that the residual strength, or the 1% strength, is reached at much

smaller displacements, or curvatures, than the user had expected. The program has now been modified

such that as the yield forces, or moments, degrade the stiffness also degrades. This means that the yield

displacements remain constant and the definitions of ductilities remain more consistant. As some hysteresis

rules 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 to

a smaller level than say the cracking moment leading to confusion within the hysteresis rule, such force

quantities are now also degraded as the yield strength degrades. This is more likely to be realistic than the

earlier operation of the strength degradation in that for most member sections the yield point is defined by the

extreme fibre yield strain and given the section properties the yield strain, or curvature, is more likely to

remain constant than is the yield force or moment. There are still some difficulties when there are different

degradations in each direction, ILOS =1, 4 or 5 as the stiffness will vary depending whether the member

displacement is positive or negative.


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APPENDIX B

STIFFNESS DEGRADATIONparameters

Hysteresis Rules for Inelastic Member Behaviour

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

0 = E lastic (default)

1 = Elasto-plastic 2 = Bi-linear

3 = Ram berg-Osgood

4 = Modif ied Takeda Degrading Stif fness

5 = B i- linear w ith S lackness

6 = Kivell Degrading Stiffness

7 = Origin Centered Bi- linear Hysteresis

8 = SINA Degrading Stiffness

9 = Stewart Degrading Stiffness with Slackness

10 = Bi-linear Degrading Stiffness

11 = Clough Degrading Stiffness

12 = Q-HYST Degrading Stiffness

13 = Muto Tri-linear Degrading Stiffness

14 = Fukada T ri-linear D egrading Stiffness15 = Bi-linear Elastic

16 = Non-linear E lastic (Un-Rein forced Masonry)

17 = Degrading Elastic

18 = Ring-Spring Isolator or Damper

19 = Hertzian Contact Non-linear Spring

20 = M ehran Keshavarzian's Degrading Stiffness

21 = W idodo Foundation Compliance

22 = Li X inrong Reinforced Concrete Column Degrading Stif fness

23 = Bouc Degrading Stiffness

24 = Remennikov Out-of-plane Buckling Steel Brace

25 = Takeda with Slip Degrading Stiffness

26 = Al-Berm ani Bounding Surface Hysteresis

27 = Peak Oriented Hysteresis28 = Matsushima Strength Decay model

29 = Kato Shear model

30 = Elastomeric Damper Spring

31 = Com posite Section, m odified SINA model

32 = Different Stiffness in Positive and Negative directions. Modif ied Bi- linear rule

33 = Masonry Strut Hysteresis

34 = Hyperbolic Hysteresis

35 = D egrading Bi-linear with Gap Hysteresis

36 = Bi- linear with Dif fering Posit ive and Negative Sti ffness Hysteresis

37 = N on-linear Elastic Power Rule Hysteresis

38 = Revised Origin Centred Hysteresis

39 = Dodd-Restrepo Steel Hysteresis

40 = Bounded Ramberg-Osgood Hys teresis41 = M odified (Pyke) Ram berg-O sgood Hyste resis

42 = HERA-SHJ Steel Hinge unit.

43 = Resetting Origin Loop

44 = Pampanin Rein forced Concrete H inge hysteresis

45 = Degrading S tiffness Ramberg-Osgood Hyste resis

46 = D ean Saunders Reinforced Concrete Colum n

47 = Multi-linear Elastic

48 = Iso tropic/K inematic Stra in Harden ing Bi-L inear

49 = Isotropic /K inematic Strain-Hardening Ramberg-Osgood

50 = Flag-shaped Bi-linear Hysteresis

51 = Two-Four Hysteretic damper

52 = Schoettler-Res trepo Reinforced Concrete Hys teresis

53 = Rajesh Dhakal Steel Hysteresis

54 = Brian peng Concrete Hysteresis

55 = Air-column Damper

56 = Modified SINA hysteresis


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57 = Revised TAKEDA hysteresis

58 = Shape mem ory Alloy Flag-shaped hysteresis

59 = Ram berg-Osgood with Alpha hysteresis

60 = IBARRA with pinching hysteresis

61 = IBARRA Peak Oriented hysteresis

62 = IBARRA Bi-linear hysteresis

63 = Bi-linear Elastic with G ap hysteresis


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Use of Hysteresis Rules for Frame members in RUAUMO KO-2Dand RU AUMOK O-3D

IHYSTHysteresis

Rule

1cpt

beam

R-C

col.

Steel

col.

Gen

col.

2cpt

beam

VFlex

beam

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 No34 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 Pyke 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


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Use of Hysteresis Rules for Frame members in RUAUMO KO-2Dand RU AUMOK O-3D

IHYSTHysteresis

Rule

1cpt

beam

R-C

col.

Steel

col.

Gen

col.

2cpt

beam

VFlex

beam

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

51 Two-Four Hystertic damper No No No No No No

52 Schoettler-Restrepo Yes No No No Yes No

53 Rajesh Dhakal Steel No No No No No No

54 Brian Peng Concrete No No No No No No

55 Semi-active Air-damper No No No No No No

56 Modified SINA Yes Yes Yes Yes Yes Yes

57 Revised TAKEDA hysteresis Yes Yes Yes Yes Yes Yes

58 Shape Memory Alloy Yes Yes Yes Yes No No

59 Ramberg-Osgood with Alpha Yes Yes Yes Yes Yes Yes

60 IBARRA Pinching Yes Yes Yes Yes Yes Yes

61 IBARRA Peak-oriented Yes Yes Yes Yes Yes Yes

62 IBARRA Bi-linear Yes Yes Yes Yes Yes Yes

63 Bi-linear Elastic with Gap Yes Yes Yes Yes No No


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Use of Hysteresis Rules for Spring members in RUAUMOK O-2D

IHYST Hysteresis Rule ITYPE = 1,3,4,5,6,7

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 Pyke Ramberg-Osgood Yes

42 HERA-SHJ Yes

43 Resetting Origin Yes


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IHYST Hysteresis Rule ITYPE = 1,3 or 4

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

51 Two-Four Hysteretic Damper Yes

52 Schoettler-Restrepo Yes

53 Rajesh Dhakal Steel Yes

54 Brian Peng Concrete Yes

55 Semi-active Air-damper Yes

56 Modified SINA Yes

57 Revised TAKEDA Hysteresis Yes

58 Shape Memory Alloy Yes

59 Ramberg-Osgood with Alpha Yes

60 IBARRA Pinching Yes

61 IBARRA Peak-oriented Yes

62 IBARRA Bi-linear Yes

63 Bi-linear Elastic with Gap Yes


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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


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44 Pampanin Yes




48 Isotropic Strain Hard. Bi-lineaqr Yes

49 Isotropic Strain Hard. Ramberg Yes


51 Two-Four Hysteretic Damper Yes

52 Schoettler-Restrepo Yes

53 Rajesh Dhakal Steel Yes

54 Brian Peng Concrete Yes

55 Semi-active Air-damper Yes



58 Shape Memory Alloy Yes







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


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


51 Two-Four Hysteretic Damper No

52 Schoettler-Restrepo No

53 Rajesh Dhakal Steel No

54 Brian Peng Concrete No

55 Semi-active Air-damper No



58 Shape Memory Alloy No







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Use of Strength Degradation and Damage Indices in RUAUMOKO -2D and RUAUMO KO-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 Pyke Ramberg-Osgood Yes Yes

42 HERA-SHJ Yes No

43 Resetting Origin No No


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

51 Two-Four Hysteretic Damper No No

52 Schoettler-Restrepo No No

53 Rajesh Dhakal Steel No No

54 Brian Peng Concrete No No

55 Semi-active Air-damper No No

56 Modified SINA Yes Yes

57 Revised TAKEDA Hysteresis Yes Yes

58 Shape Memory Alloy Yes No

59 Ramberg-Osgood with Alpha Yes Yes

60 IBARRA Pinching No Yes

61 IBARRA Peak-oriented No Yes

62 IBARRA Bi-linear No Yes

63 Bi-linear Elastic with Gap No Yes


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Notes on notation for hysteresis rules:

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

Fis the force or moment in the member.

dis the deformation or curvature in the member.

0K is the initial elastic stiffness, i.e. the EI of a flexural beam or beam column, the AE/Lfor the axial

stiffness of a beam or beam column, or the stiffness K of a spring member.

yF is the yield force or moment.

ris the bi-linear factor or Ram berg-Osgood factor.

y y y 0 is the ductility where = d / d where, in general, the yield displacementd = F / K

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 mem ber then an error message is

printed 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 the

small-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 Degradation

on the computed Damage Indices is uncertain and a warning is printed after reading the member

properties.

If Strength Reduction or Dam age Indices are not allowed for the specified Hysteresis Rule and they are

specified in the input data, the data is read and then the control param eters ILOSand/or IDAMGare

reset to zero. W arnings of these re-settings are printed in the output.

No*. The Bouc and Matsushim a 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 then

the SINA hysteresis is used for the transverse (local y) direction.

For the Ruaumoko (2D) version the Frame m ember ITYPE=7, the four hinge beam has the allowable

hysteresis table that follow the same rules as that for the variable flexibility beam.


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Linear Elastic Hysteresis

DEGRADING STIFFNESS parameters

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


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Elasto-Plastic Hysteresis

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

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


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Bi-Linear Hysteresis

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


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Ramberg-Osgood H ysteresis

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

Note: The bi-l inear factor in the section data is used as the Ramberg-Osgood factor rand must be

greater than or equal to 1.0


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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 som e sma ll 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 the

loops from the maximum and minimum displacements. In the year 2000 the Ramberg-Osgood loop reverted

to its original definition and the bounded version was moved to IHYST= 40.


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Modified Takeda Hysteresis

IHYST= 4 Modified TAKEDA Hysteresis [Otani 1974].

Modified Takedarule.

ALFABETA NF KKK

ALFA Unloading stiffness (0.0 ALFA 0.5) F

BETA Reloading stiffness (0.0 BETA 0.6) F

NF Reloading stiffness power factor (NF 1) I

KKK =1; Unloading as in DRAIN-2D I

=2; Unloading as by Emori and Schnobrich

Note: Increasing ALFAdecreases the unloading stiffness and increasing BETAincreases the reloading

stiffness. The power factor NFis usually taken as 1.0


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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 one

direction may stretch the members leading to slackness in the bracing system. The model allows for either

yield in compression, in say a cross-braced system, or for a simple elastic buckling in compression which

would be more appropriate in a single brace member.

Bi-linear with Slacknessrule.

GAP+ GAP- IMODE RCOMP C EPS0 ILOG

GAP+ In itia l s lackness , pos itive direction. ( > 0.0) F

GAP- In itia l s lackness , negative d irec tion ( < 0.0) F

IMODE = 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 rin Compression F

C Strain-Rate Constant (if 0.0 Strain-rate effects are ignored) F

EPS0 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-colum n sections require GAP+= -GAP-.

2 If no value is prescribed fo r RCOMP, i.e. there are less than four items on the line or RCOMPis the

word DEFAULTor Dthen 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 mem bers should be used for the different actions. The

default bi-linear factor is that for the force components.

4 If the stra in ra te constant C is non zero then the positive and negative yield forces are m ultiplied by the

factor

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


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Kivell Degrading Hysteresis

HYST = 6 KIVELL Degrading Stiffness [Kivell 1981].

The pinching m odel of Kivell was designed to represent the behaviour of the nails in steel nail-plates

connecting timber members together at the joints. The assumed cubic unloading-reloading curve is

represented by three straight lines.

Kivell Degrading rule.

ALFA

ALFA Unloading stiffness (0.0 ALFA0.4) F


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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.


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SINA D egrading Tri-linear Hysteresis

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

SINADegrading Tri-linearrule.

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

ALFA Bi-linear factor (positive cracking to yield) F

BETA Bi-linear factor (negative cracking to yield) F

FCR(i)+ Cracking mom ent or force at i ( > 0.0) F

FCR(i)- Cracking mom ent or force at i ( < 0.0) F

FCC(i) Crack closing mom ent 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


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Wayne S tewart Degrading Hysteresis

IHYST= 9 W ayne Stewart Degrading Stiffness Hysteresis. [Stewart 1984].

This very general rule was initially developed by Wayne Stewart for the representation of timber framed

structural walls sheathed in plywood nailed to the framework. The model allows for initial slackness as well as

subsequent degradation of the stiffness as the nails enlarged the holes and withdrew themselves from the

framework.

Stewart Degrading with slacknessrule.

FU FI PT RI PUNL GAP+ GAP- BETA ALPHA LOOP

FU Ultimate force or mom ent ( > 0.0) F

FI Intercept force or mom ent ( > 0.0) F

PTRI Tri-linear factor beyond ultimate force or mom ent F

PUNL Unloading stiffness factor ( > 1.0) F

GAP+ Initial slackness, positive axis ( > 0.0) F

GAP- Initial slackness, negative axis ( < 0.0) F

BETA Beta or Softening factor ( 1.0) F

ALPHA Reloading or Pinch power factor ( 1.0) F

LOOP =0 Loop as defined I

=1 Modified loop

Notes: Concrete and Steel Beam-column sections require GAP+= -GAP- and that all other

components 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 mod ification allows the use of strength degradation. In the original model strength degradation

affects only the cracking moments Fy and not Fu . Also the PTRI(read as part of this data line) andr

(read as part of the member section data) are interchanged.


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Operation of Wayne Stew art Hysteresis rule

Note: Vos = Fi etc.


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

FU = 1.5 times yield force or mom ent

FI = 0.25 times yield force or mom ent

PTRI = 0.0

PUNL = 1.45

BETA = 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

the program HYSTERES using the following parameters

Section Stiffness properties

K0 = 51.1 kN/mm

R = 0.001

FY + = +58.4 kN

FY - = -58.4 kN

IHYST=9 Stiffness Degradation parameters (see preceding pages)

FRC (i.e.FU) = 27.6 kNFI = 6.0 kN

PTRI = 0.14

PUNL = 1.1

GAP+ = 0.0

GAP- = 0.0

BETA = 1.2

ALPHA = 0.8

LOOP = 1

There is no strength degradation applied in this example.


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Degrading B i-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



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Clough D egrading 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 the

same as the modified TAKEDA rule with the parameters ALFAand BETA both equal to 0.0.


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Q-HYST Degrading Stiffness Hysteresis

IHYST= 12 Q-HYST Degrading St if fness Hysteresis . [Saiidi 1979].

This rule is the same as the Modified Takeda rule with the parameter BETAset to 0.0 and unloading as per

Emori and Schnobrich.

Q-HYST Degrading rule.

ALFA


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


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Muto Degrading Tri-linear Hysteresis

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

After cracking the model is an Origin-Centered rule. After yie ld is reached the model become a B i-linear

hysteresis with the equivalent elastic stiffness equal to the secant stiffness to the yield point.

MutoDegrading Tri-linear rule.

ALFA FCR(i)+ FCR(i)-

ALFA Bi-linear factor (cracking to yield) F

FCR(i)+ Cracking 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


2. Concrete and Steel Beam-column sections require symmetry in moments and therefore

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


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Fukada Degrading Tri-linear Hysteresis

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

FukadaDegrading Tri-linearrule.

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

ALFA Bi-linear factor (cracking to yield) F

BETA Unloading Stiffness factor (see Takeda ALFA) F

FCR(i)+ Cracking mom ent or force at i ( > 0.0) F


Notes:

1. Thei refers to the different actions on the member, see the member data descriptions for the number of


2. Concrete and Steel Beam-column sections require symmetry in moments and thus

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


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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 which

means that no hysteretic energy is dissipated..


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Non-linear Elastic Rule (UR M)

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

This non-linear elastic model represen ts the non-linear behaviour of face-loaded m asonry wall units.

No hysteretic energy is dissipated.


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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 eq uivalent

ductility is equal to the displacem ent divided by the nom inal yield deformation.


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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 compressive

force - 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) F

RLOWER Unloading Lower Stiffness factor (usually less than the Bi-linear factor) F

DXINIT Initial Displacement F

KTYPE = 0 ; Uni-directional, = 1 ; Bi-directional I

KLOOP = 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 m embers 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 flexural

stiffness i.e. EI is zero, representing a truss-like action. In both of these cases the ap propriate yield

moments or yield forces must be provided with dummy non-zero values (the actual yield values are

computed internally by the hysteresis rule but non-zero yield forces or m oments are required in order that

the member is treated as non-linear).

3. When init ial 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.


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Hertzian Contact Spring

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

The Hertzian contact spring is useful for mode lling the contact between impacting structures. It really models

contact between spheres but this seems to be used in wider applications. It is only available for the SPRING

members and the CONTACT members.

Hertzian Contact Spring

MPP MPN PFP PFN GAP+ GAP-

MPP Stiffness Multiplier for Positive Displacement F

MPN Stiffness Multiplier for Negative Displacement F

PFP Power factor for Positive Displacement F

PFN Power factor for Negative Displacement F

GAP+ Initial slackness in Positive direction (0.0) F

GAP- Initial slackness in Negative direction (0.0) F


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Mehran K eshavarian Hysteresis

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

Mehran Keshavarian Degrading and Pinching rule.

ALFA

ALFA Unloading stiffness (0.0 ALFA0.5) (see Takeda) F

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


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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 of

a wall footing that can suffer partial or tip uplift. This is only appropriate to SPRING m embers, see section 12..

Widodo Foundation Compliance.

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

A(i) Multiplier for ith Component F

P(i) Power Factor for First part of ith Component F

Q(i) Power Factor for Second Part of ith 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 mem bers.


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Li Xinrong Reinforced Concrete Co lumn 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 m embers, see section 11.

The degrading rule modifies the stiffness of the mem ber to allow for the effects due to variation of the axial force

acting in the column.

Li Xinrong Degrading Reinforced Concrete Column.

FPC RHO PB U ALFA BETA PINCH

FPC Concrete Compressive Strength f'c ( < 0.0) F

RHO Percentage Longitudinal Steel content F

PB Yield Moment - Axial Force Diagram Balance Axial Force F

U Unloading Coefficient (0.7 to 1.0) (Li Xinrong used 0.9) F

ALFA Factor for unloading (0.5 to 1.0) (Li Xinrong used 0.9) F

BETA Factor used in relocation of unloading point (0.8) F

PINCH Pinching Factor (0.7 to 0.9) F


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IHYST= 23 BOUC Hyste resis Ru le . [Wen 1976 ]

This very general parametric hysteresis rule gives a smooth transition of the change of stiffness as the

deformation of the member changes. It has been used to represent lead-rubbe r bridge bearings or energy

dissipators [Bessasson 1992] and has been used for the analysis of inelastic buildings subjected to random

vibration [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) F

A2 Loop Pinching parameter (-0.9 to 0.9) F

A3 Stiffness parameter (usually 1.0) F

A4 Degradation parameter (usually 1.0) F

A5 Strength parameter (usually 1.0) F

N Power Factor, Controls Abruptness (1 to 3, usually 1) I

D3 Strength Degradation parameter (0.0 to 0.1) (0.0 no degradation) F

D4 Loop Size Degradation (0.0 to 0.2) (0.0 no degradation) F

D5 Stiffness Degradation (0.0 to 0.2) (0.0 no degradation) FMODE = 0 Constantinou Version

= 1 Baber and W en Version

INIT = 0 Normal

= 1 B i-linear un til 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 yield

displacement. is the yield force and is the change in displacement. Q is the force in the spring and Fis

the current stiffness factor. The tangent stiffness is . and are the Bouc hysteresis control

parameters, is the power factor.


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Bouc Hysteresis Rule

The Bouc rule is controller by the parameter , which in RUAUMOKO is initially 0.0 and is integrated step-by-step

as in the above equations. The rule is such that at the static analysis which means that the initial

stiffness is the bi-linear stiffness and the force in the member is proportional to the bi-linear stiffness and the

displacement. To over come som e of these effects an option is to force the rule to be bi-linear until reversal after

the first yield. A result is that there is a marked reduction in mem ber force at the change of rule. further work is

being done to fully understand the implications of the use of this hysteresis.


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Steel Brace Mem ber Hysteresis

IHYST= 24 REMENNIKOV Steel Brace Member Hysteresis.

Represents the out-of-plane buckling of a steel brace member.

REMENNIKOV Steel Bracerule.

Iminor Sminor k ALFA BETA THETA0 E1 E2 E3 E4 N SHAPE

Iminor Second Moment of Area about Minor axis F

Sminor Plastic Section Modulus about Minor axis F

effk Effective Length Parameter (L = kL ) F

ALFA Strain Hardening Alpha (1.0 1.5) F

BETA Beta factor (> 1.0) recommended range 1.2 to 1.4 F

THETA0 Initial out-of-straightness (length units) F

E1 Effective modulus e1 (>0.0) F



E4 Effective modulus e4 F

N = 0; ALFAabove used for strain harden ing effects. I

= 1; Built-in strain hardening rule and ALFAis reset to 1.0

SHAPE = 1; Flanged section such as an Isection. 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 mom ents 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 Res iduals , 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.


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Definition of Di


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Idealization Curves for Tang ent Modulus History

Tangent M odulus Axial Force Relationship

Analytical Axial Force Plastic Hinge Rotation Curve


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Takeda w ith 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 SLIPrule.

ALFA BETA1 BETA2 FC(i) RC(i)

ALFA Unloading Degradation parameter (see Takeda ALFA) (0.0 ALFA1.0) F

BETA1 Slipping stiffness parameter F

BETA2 Re-loading stiffness parameter F

FC(i) Cracking Force for Component i ( > 0 .0 ) F

RC(i) Cracking Displacement for Component i ( > 0.0) F

Notes:



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 negat ive direction for component iis at (-FC(i),-RC(i))

4. Slip only occurs when re-loading towards the stronger direction.


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The following exam ple show the use of the Takeda with Slip hysteresis loop to model the behaviour of a pre-1970

reinforced concrete beam which is reinforced with plain round bar reinforcement [Liu, 2001]. The loops show the

observed experimental loop and the m atching loop from the program HYSTERES using the loop parameters

provided below.

Section Property parameters

K0 = 10.4 kN/mm

R = 0.05

YP + = +93.4 kN

YP - = -61.4 kN

IHYST=25 Stiffness Degradation parameters (see previous page)

ALFA = 0.2

BETA1 = 1.2

BETA2 = 1.5

FC = 26.9 kN

RC = -0.65 mm

Strength Degradation parameters

ILOS = 1

DUCT1= 3

DUCT2 = 8

RDUCT= 0.3

DUCT3 = 10


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Bounding-Surface H ysteresis

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 more

often used but more complicated Ramberg-Osgood functions.

Bounding Surfacerule.

ALFA BETA

ALFA Positive ALFA (0.0


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Peak O riented H ysteresis

IHYST= 27 PEAK Oriented Hysteresis. - No further data is required.

This rule is similar to the Origin Centered rule except that on unload ing the force-displacement relationship moves

along a line to the maximum force-displacement point in the opposite direction. If yield has not occurred in that

direction the opposite yield point is used as the targe t.


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Matsushima D egrading Hysteresis

IHYST= 28 MATSU SHIMA Strength Reduction Hysteresis. [Matsushima 1969]

This rule represents the behaviour of short reinforced concrete columns failing in shear. The rule uses basically

a bi-linear hysteresis but that the elastic stiffness and strength degrade every time unloading takes p lace from

the post-yield part of the bi-linear force displacement curve.

Matsushimarule.

A B

A S tif fness Multip lier A (0.0 < A < 1.0) F

B Streng th Mu ltip lier B (0 .0 < B < 1.0) F

Notes:

1. A and B are raised to then power N where Nis the number of times the system unloads from the bi-linear

force-displacement hysteresis back-bone.


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KATO Sh ear Hysteresis

IHYST= 29 KATO Degrading Shear Model. [Kato 1983]

Represen ts the behaviour of a reinforced concrete member failing in shear. A tri-linear skeleton curve with a

falling bi-linear part is used.

Kato Shearrule.

PTRI ALFA BETA GAMMA FU(i)+ FU(i)-

PTRI T ri-linear Factor (m ust be less than or equal to zero) F

ALFA Unloading Degrading Factor (0 < ALFA< 1) (see Takeda) F

BETA Slip Stiffness Factor (0 BETA< 1) F

GAMMA Slip Length Factor (0 GAMMA< 1) F

FU(i)+ Positive FU at component i (>0.0) F

FU(i)- Negative FU at component i (


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Elastomeric Spring Damper

IHYST= 30 Elastomeric Spring Damper Hysteresis. [Pekcan 1995]

Represen ts a double-acting elastomeric spring which has resistance due to both displacement and velocity. The

stiffness properties a re basically bi-linear elastic.

Elastomeric Spring Damper rule.

C DMAX ALFA

C Damper Constant (0.0) F

DMAX Maximum Damper Stroke (0.0) F

ALFA Velocity Exponent (>0.0) F

Notes:

D1. The force F in the elastomeric damper is given by

0where the dis the displacement of the spring and where K is the initial stiffness of the device and is the

0 ylongitudinal spring stiffness of the member. The stiffness rK is the stiffness after the prestress F is

yovercome where ris the bi-linear factor for the spring member. The prestress force F is taken as the

positive longitudinal yield force of the mem ber and if the pres tress is zero the spring stiffness is taken

0as constant equal to rK .

max2. If DMAXis zero then the ratio of dto d is taken as 1.0. This has the effect of taking the exponent

in the reference paper as zero.

3. The exponent ALFAwas taken as 0.2 in the reference .


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Composite S ection 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 behaviour

is different in the positive and nega tive flexural actions.

Composite Sectionrule.

BETA FCR(i) FCC(i)

BETA Stiffness Factor Cracking to Yield in Negative direction (ALFA< 1.0) F

FCR(i) Cracking Force in Negative direction at component i (FRC(i)< 0.0) F

FCC(i) Cracking Closing Force at component i (FCC(i)< 0.0) F

Notes:



2. T he po st 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 a llows for different stiffnesses in the positive and negative directions. The basic hysteresis rule is a

modification of the degrading B i-linear rule.

Different Positive and Negative Stiffnessrule.

ALFA BETA

ALFA Negative stiffness factor of the positive stiffness (ALFA > 0.1) F

BETA Unloading Degrading Factor, see TAKEDA ALFA (0.0 < BETA< 0.9) F


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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

spring mem bers then only the longitudinal stiffness is specified for the strut mem ber and two struts are required

to model each panel, one strut across each diagonal of the panel. The masonry strut hysteresis is also used for

the Masonry Panel Element where four struts represent the panel together with a shear spring..

Masonry Strut Hysteresisrule.

Stress-strain relationship

FC FT UC UUL UCL EMO GUN ARE

FC Compressive strength (stress units) (FC < 0.0) F

FT Tensile strength (stress units) (FT > 0.0) F

UC Strain at FC (UC< 0.0) F

UUL Ultimate strain (UUL < 0.0) (UU L1.5 UC ) F

UCL Closing strain F

EM O Initial masonry modulus (EM O2 FC /UC) F

GUN Stiffness unloading factor (GU N 1.0) F

ARE Strain reloading factor (ARE> 0.0) F

Strut data

AREA1 AREA2 R1 R2 IENV

AREA1 Initial strut cross-sectional area (AREA1> 0.0) F

AREA2 Final strut cross-sectional area (AREA2AREA1) F

R1 Displacement at 1 (R1 < 0.0) F

R2 Displacement at 2 (R2 R1) F

IENV = 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


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Notes:

mFC The com pressive strength f is the main parameter controlling the resistance of the strut. It must be'

noted that FC does not represent the standard compressive stress of masonry but should be adopted

taking into account the inclination of the compressive principal stresses and the mode of failure expected

in the masonry panel. See Crisafulli 1997.

tFT Tensile strength f' represents the tensile strength of the masonry or the bond strength of the pane l-frame

interface, whichever is smallest. The consideration of the tensile strength has been introduced in the

model 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 significant

influence on the overall response. Therefore, in the absence of more detailed information, the tensile

strength can be assumed to be zero.

mUC The strain at maximum stress ' usually varies between -0.002 and -0.005 and its main effect on the

overall response of the infilled frame is the modification of the secant stiffness of the ascending branch

of the stress-strain curve.

uUU L The ultimate strain is used to control the descending branch of the stress-strain relationship. When

u ma large value is adopted for, example =20 ' , a smooth decrease of the compressive stress is

obtained.

clUCL The closing strain 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 agree

cl uadequately with experimental data. If a large negative value is adopted, for example = , this effect

is not considered in the analysis.

moEM O The elastic modulus E represents the initial slope of the stress-strain curve and its value can exhibit

a large variation. Various expressions have been proposed for the evaluation of the elastic modulus of

masonry. It is worth noting, however, that these expressions usua lly define the secant modulus at a

stress level between 1/3 and 2/3 of the maximum compressive stress. In order to obtain an adequate

mo m mascending branch of the strength envelope it is assumed that E 2 f' / ' .

unGUN The unloading stiffness factor controls the slope of the unloading branch. It is assumed to be greater

than or equal to 1.0 and usually ranges from 1.5 to 2.5.

reARE The reloading strain factor 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 are

obtained using values ranging between 0.2 and 0.4. However, higher values, for example 1.5, are

required to mode l adequately the cyclic response of the infilled frames. This is because other sources

of nonlinear behaviour, such as sliding shear, need to be indirectly considered in the response of the

masonry struts.

Four param eters are required to represent the cross-sectional area of the masonry strut. These are the initial area

ms1 ms2A = AREA1 and final area A = AREA2 and the axial displacements at which the cross-sectional area

R1 R2changes, = R1 and = R2 . In a simplified model, it can be assumed that AREA1 and AREA2are the

same using a low value of the strut area to avoid an excessive increase in the axial strength. In a more refined

analysis, a higher value of the initial area can be adopted, whereas the final area can be reduced by about 10%

m m m m mto 30%. The displacement R1 and R2 can be estimated as' d /5 and ' d (where d is the length of the

masonry strut) respectively, at least until more precise information becom es available. Several empirical

expressions, which are described in section 6.2.1.3 of the reference, have been proposed for the evaluation of

the equivalent width of the masonry strut, whose value normally ranges from 0.1 to 0.25 of the diagonal length

of the infill panel.

IENV The descending branch of the stress-strain curve is usually modelled with a parabola instead of the curve

associated with Sargin's equation in order to obtain a better con trol of the response of the strut after the

maximum 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 stressshear strain relationships in soils subjected to

earthquake excitation.

.


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Degrading Bi-linear With Gap Hysteresis

IHYST = 35 Degrading Bi linear with Gap Hysteresis

This hysteresis was initially developed to m odel a strain-harden ing behaviour wh ich changed with increasing cycle

number. The members were used in parallel with a member having a more conventional hysteretic behaviour

such as Bi-linear or Ramberg-Osgood. The total mem ber force was taken as the sum of the two number forces.

Degrading Bi-linear with Gap

GAP+ GAP PUN

GAP+ Initial gap in positive direction (0.0) F

GAP Initial gap in negative direction (0.0) F

PU N 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 BET A GAM MA IOP

ALFA Posit ive st if fness is ALFA * nominal st if fness ALFA 0.1 F

BETA Negative stiffness is BETA * nominal stiffness BETA 0.1 F

GAMMA 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 factor

Negative bi-linear factor = BETA * bi-linear factor


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Non-linear Elastic Pow er 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 the

sudden change of stiffness on unloading encountered due to the lack of energy dissipation in these non-linear

elastic 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) F

PFN(i) Power factor in negative direction for component i (0.01 PFN 3.0) F

Notes:



1. Normally PFP and PFNare less than 1.0


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Revised Origin-Centred Bi-linear H ysteresis

IHYST = 38 Revised Origin Centred Bi-linear Hysteresis (No further data is required)

On unload ing the path is back to the origin. In reloading the path follows the previous unloading path on that side

of the origin.


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Dodd-Restrepo Steel Hysteresis Rule

IHYST = 39 Dodd-Res trepo Steel Hys teresis Rule

This hysteresis rule is designed to a llow for the Bauschinger effec ts in the steel hysteresis.

Dodd-Restrepo Steel Rule

ESH Esu Fsu OmegaF

ES H Deformation (curvature) at initiation of strain hardening F

Esu Deformation (curvature) at peak load F

Fsu Force (moment) at peak load F

OmegaF 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. Structural

Engineering, ASCE, Vol. 121, No. 3, Mar. 1995, pp 433445.


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Plot of D isplacement 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 sim ilar to that for IHYST= 3 except that bounds have been applied to the forces so that off-sets to

the 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 mod ified to prevent off-

sets on the force in these sma ll cycles. These loops were initially used to model the behaviour of soils.The sm all

loops 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 the

behaviour of a sliding moment connection between steel beam s with a concrete slab above them and connected

to at the joints to steel columns.

HERA-SHJ Hysteresis Rule

Cspp Cspn Ru Tdp Tdn Ispr

Cspp Positive Mom ent Intercept ( > 0.0 ) F

Cspn Negative Mom ent Intercept ( < 0.0 ) F

Ru Unloading stiffness factor ( > 0.0 ) F

Tdp Positive Design Theta ( > 0.0 ) F

Tdn Negative Design Theta ( < 0.0 ) F

Ispr = 0; Withou t Belleville Springs I

= 1; With Be lleville 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 is

proportional to the displacement until a saturation force is attained, Fy+or Fy- (the yield forces for the

member) when the system appears to show a perfectly plastic response. On any reversal of displacement the

force is automatically reset to zero and the origin is moved to the ex isting displacement and the system will

then 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 Jointrule.

IOP AlfaS1 AlfaS2 AlfaU1 AlfaU2 DeltaF Beta

IOP =1; Option 1 - Reload ing Power Facto r I

=2; Option 2 - Reload ing S lip Factor

AlfaS1 Slip Stiffness Power Factor As1 ( 1.5 As1 3.0) F

AlfaS2 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) F

AlfaU2 Final Unloading Power Factor Au2 ( 0.3 Au2 1.0) F

DeltaF Unloading Force Factor (%) Df ( 20 DeltaF 50) F

Beta Reloading Factor Beta (-1.0 Beta 0.0) F

Pampanin Hysteresis IOP=0


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Pampanin Hysteresis IOP=1


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IHYST = 45 Degrading St if fness RAMBERG-OSGOOD Hysteresis .

Degrading Stiffness Ramberg-Osgoodrule.

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) F

BETA 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) F

RESID 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 rand m ust be greater

than or equal to 1.0


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IHYST= 46 DEAN SAUNDERS Reinforced Concrete Column Hysteres is .

This hysteresis is to represent the behaviour of Older Reinforced Concrete Columns where plain round

reinforcement is used.

DEAN SAUN DERS Reinforced Concrete Column rule.

DY+ DY- Funl+ Funl- ALFA BETA IOP

DY+ Positive Yield Deformation. Must be greater than (Yield Action)/Stiffness. F

DY- Negative Yield Deformation. Must be less than (Yield Action)/Stiffness. F

Funl+ Positive Threshold Action. Must be less than Positive Yield Action. F

Funl- Negative Threshold Action. Must be greater than Negative Yield Action. F

ALFA Unloading stiffness degradation factor (0.0 ALFA 0.5) F

BETA Reloading Factor (BETA 1.0) F

IOP =0; Threshold actions reduce with strength degradation. I

=1; Threshold actions remain constant when yield actions degrade.

Notes : 1. There is a 4 po int Bezier curve fitted between the point (Funl+,(Funl+)/STIFF ) and (YP,DY+)

with the initial slope STIFFand the final sloper*STIFF.

2. On unloading the rule is origin centered when the action is less than Funl+. When the action

is greater than Funl+the unloading stiffness Ku degrades with the factor ALFAas observed

in the Degrading Bi-Linear Hysteresis (IHYST= 10).

3. The behaviour in the negative Action-Deformation quadrant is identical to that in the posit ive

Action-Deformation quadrant.

4. The parameter BETAonly comes into action if the deformation in the other quadrant has

exceeded the yield deformation.

Dean Saunders H ysteresis Rule


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Example of Dean Saunders Hysteresis

This example show the behaviourwhen strength degradation is also applied. It compares experimental results

with computational results.

In this example

Fy+ =289 kNm Fy- =-250kNm Funl =65kNm,

Ko =46.3 kNm/mm y+ =11.35mm y- =-11.35mm

=0.01 =1.25 r =0.01

Iop =1

W ith the exception of strength degradation, which is progressive in the model, the results agree qu ite well for the

overall response of the observed hysteresis. The current limitation for the proposed hysteresis rule is that strength

degradation as ca lculated in Ruaumoko is computed outside the hysteresis rule. This results in the reloading lineconverging to the previously stored force and maximum displacement coordinate before degrading down the

ductility degradation slope. To eliminate this limitation the rule will need to include a local strength degradation

feature that degrades the reload ing line based on cycle number and starts from the threshold capacity.

Reference: Saunders, D.B. Seismic Performance of Pre 1970's Non-Ductile Reinforced Concrete Waffle

Slab Frame Structures Constructed with Plain Round Reinforcing Steel. Ph.D Thesis,

Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand. 2004,

p184+appendices.


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IHYST = 47 Multi-L inear E lastic Hys teresis .

Multi-Linear Elasticrule.

N F1 D1 F2 D2 F3 D3

N Number of segments beyond Bi-linear (1 N 3) I

F1 Fraction of stiffness in first segment beyond Bi-linear F

D1 Multiplier on Yield Displacement where F1 applies (D1 1.05) F

F2 Fraction of stiffness in second segment beyond Bi-linear F

D2 Multiplier on Yield Displacement where F2 applies (D2 1.05*D1) F

F3 Fraction of stiffness in third segment beyond Bi-linear F

D3 Multiplier on Yield Displacement whereF3applies (D3 1.05*D2) F

Note: TheF1, 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-Linearrule.

ALFA BETA

ALFA Stiffness Degrading Factor (See IHYST=10) (0.0 ALFA 0.5) F

BETA 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 strain

hardening is to occur


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IHYST= 49 Kinematic/Isotropic Strain Hardening RAMBERG-OSGOOD Hysteresis.

Kinematic/Isotropic Strain Hardening Ramberg-Osgoodrule.

ALFA BETA IOP

ALFA Ramberg-Osgood multiplier (0.0 ALFA) F

If ALFA=0.0 then ALFAis taken as 1.0 (Default value)

BETA 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.

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 rand must

be greater than or equa l to 1.0


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IHYST= 50 Flag-Shaped B i-Linear Hys teresis .

Flag-shaped Bi-Linearrule.

BETA1 BETA2 ... B ETAi (i = 1 to N)

BETA1 Flag Height Action 1 (0.0 BETA1 1.0) F

BETA2 Flag Height Action 2 (0.0 BETA2 1.0) F

BETAi 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 origin

Nis the number of actions requiring data for the mem ber. See Spring or Frame member data.

Flag-Shaped Bi-linear Hysteresis


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IHYST= 51 Two-Four Hyste re tic Damper

Two-Four Hysteretic Damper rule.

BETAi DELTAi (i = 1 to N)

BETA Initial Sticking Force1 (0.0 BETA) F

DELTA Change Time from linear to sticking force, Seconds F

DELTA=0 implies instantaneous change

Two-Four H ysteresis


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IHYST= 52 SCHOETTLER-RESTREPO Reinforced Concrete Column Hysteresis. (2 l ines of data)

This hysteresis is to represent the behaviour of Reinforced Concrete Beams

SCHOETTLER-RESTREPO Reinforced Concrete Beam rule. Line 1

Kneg Rneg Fcr+ Fcr- Rho+ Rho- Dult+ Dult- IOP

Kneg Ratio of negative (compressive) stiffness to positive stiffness. (Kneg> 0.0) F

Rneg Bi-linear Factor in negative direction. (Rneg> 0.0) F

Fcr+ Ratio of positive Cracking Strength to Yield strength. (Fcr+ < 1.0) F

Fcr- Ratio of negative Cracking Strength to Yield strength. (Fcr- < 1.0) F

Rho+ Secant Stiffness Factor to Positive Yield. (Rho+ < 1.0) F

Rho- Secant Stiffness Factor to Negative Yield. (Rho- < 1.0) F

Dult+ Ultimate deformation factor. Positive direction. (Dult+ > 1.0) F

Dult- Ultimate deformation factor. Negative direction. (Dult- > 1.0) F

IOP =0; For use as reinforce concrete member I=1; For use as a concrete strut

Notes: 1. The posit ive s tif fness is that prov ided in the sect ion propert ies.

2. The positive bi- linear factor is that provided in the section properties.

3. The cracking strengths are taken as fractions of the positive and negative yield strengths

provided under yield forces and moments in the section properties.

4. The Rho *Stiffness is the secant stiffness to the yield point.

5. The ultimate deformations are input as a mult iplier of the respective yield displacement

and must be greater than 1.0..

6. Pinchmust be g reater than 0.0, if 0.0 is supplied then Pinch is reset to 1.0

SCHOETTLER-RESTREPO Reinforced Concrete Beam rule.Line 2

Alpha Beta Pinch Kappa+ Kappa- Fresid Dfactor

Alpha Unloading stiffness factor (0.0 < Alpha < 0.9) F

Beta Reloading stiffness factor . (0.0 < Beta < 5.0) F

Pinch Pinching factor (0.0


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Figure 1: Backbone Curve

Figure 2: Uncracked Yielded States


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Figure 3: Cracked Yielded States

Figure 4: Yielded Yielded States


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Figure 5: Yielded Yielded States with pinching


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IHYST= 53 DH AK AL Steel Hysteresis.

This hysteresis is to represent the behaviour of Reinforcing Steel

DHAKAL Reinforcing Steel rule. Line 1

IHARD IBCKL FYAV eHARD1 FU eU FHARD2 eHARD2 RATIO EBLKT

IHARD =1; Parabolic from initial hardening stiffness (Mander et.al. 1984) I

=2: Parabolic from intermediate point (Rodriguez et al 1999)

=3; Bilinear f rom intermediate point (Dhakal 2002)

IBCKL =1; Buckling included (Dhakal and Maekawa 2001) I

=0; Buckling is neglected (Tension envelope is used for compression)

FYAV Average Tensile Yie ld Strength, Mult ipl ier on Yield Strength (Default= 1.0) F

eHARD1 Strain at the start of strain hardening, Multiplier of Yield Strain (Default= 10.0) F

FU Ultim ate tensile strength Multiplier of Yield Strength (Default= 1.5) F

eU Strain at the u ltimate point, Multiplier of Yield Strain F

(Default = 1 0.0*eHARD1)

FHARD2 Stress at intermediate point in hardening zone, Multiplier of Yield action F

(Default= FY+0.75(FU-FY))

or if (IHARD= 1) the 2nd Strain Hardening Stiffness Factor ESH2

eHARD2 Strain at intermediate point in hardening zone, Ratio of Yield Strain F

(Default = eHARD1+0.5(eU-eHARD1))

RATIO Buckling length to bar diameter ratio (Used if IBCKL=1) F

EBLKT Buckling len gth (if 0.0 tak en as elem ent len gth) (Used if IBCKL=1) F

Dhakal Reinforcing Steel Hysteresis Loop


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IBCKL = 0

Dhakal Reinforcing Steel Hysteresis Loop


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IHYST= 54 BRIAN PENG Concrete Hys teresis .

This hysteresis is to represent the behaviour of Concrete

BRIAN PENG Concrete rule. Line 1

TLIMIT CLIMIT BETA Fbo L TFACTOR CFACTOR eTT

TLIMIT Limit to calculateeT L (Strain at start of contact stress effect) (Default = 0.0025) F

CLIMIT Limit to calculate eC L (Strain at end of stress contact effect) (Default = 0.005)F

BETA Strain Rate factor (Static = 1.5 to 2.0; Dynamic = 1.0) (Default = 2.0) F

Fbo Residual Compressive Bond Strength (Default = 0.2) F

(Default = -0.2*FT where FT is tensile strength)

L Length factor ( = 1.0 for stress-strain) (Default =1.0) F

TFACTOR Factor for eTL (multiplying factor to magn ify eT L) (Default =1.0) F

CFACTOR Factor for eCL (multiplying factor to magn ify eC L) (Default =1.0) F

eTT Tensile Concrete Strain for Contact Stress Effect (Default =Ft/KC) F

Brian Peng Con crete Hysteresis Loop


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Effect of varying Tlimit and Climit

Effect of varying Beta


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Effect of Varying Fbo

Effect of varying Tfactor and Cfactor


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IHYST= 55 Resettable Air-Cylinder Semi-Active Damper.

This hysteresis is to represent the behaviour of a sem i-active resettable control device.

Resettable Air-cylinder Semi-Active Damper. data

IOPT AREA COEFF GAMM A FreeD+ FreeD- Fstiff Friction+ Friction-

IOPT = 1: 1-2-3-4 quadrant action (see figures below) I

= 2; 2-4 quadrant action (see figures below)


= 4; 1-2-3-4 quadrant action (see figures below, also see IHYST = 43)

= 5; 2-4 quadrant action (see figures below, also see IHYST= 51)


AREA Area of pis ton F

COEFF Gas Coefficient (i.e. Atmospheric constant for air = 100000 N/m ) F2

GAMMA Power Factor (i.e. Air = 1.4) (Default =1.4) F

FreeD+ Free Length Positive direction F

FreeD- Free Length Negative direction F

Fstiff Fric tion St if fness factor ( times nominal member s ti ffness) (Default =20.0) F

Friction+ Friction limit force Positive direction F

Friction- Friction limit force Negative direction F

Notes : For IOPT = 1, 2 or 3 the behaviour of the rese ttable device follows an isentropic compressible gas law

where

Pressure*Volum e = Constantgamma

i.e.

For IOPT = 4, 5 or 6

Where Kois the members nom inal stiffness (see section properties data).

For IOPT = 2 or 5 Force= 0.0 if the displacement and the velocity have the same signs.

resetFor IOPT = 3 or 6 Force = 0.0 if the displacement and the velocity have opposing signs. d is set to

zero

In all cases, on reversal of direction of displacement the force is set to zero and the displacement resets.

If both friction force limits are equal to zero then Fstiff is set to zero and there is no friction.

If Fstiffis less than or equal to zero then there is no friction The friction follows the standard Elasto-

plastichystersis rule (see IHYST=1).

The yield actions (forces or moments) specified for the loop are taken as limiting actions for the loop.

This means that the force (mom ent) cannot be greater thanYPor less thanYN . These must be supplied

as non-zero values if the loop is to operate.

For IOPT = 1, 2 or 3 the displacement cannot be greater or equal to FreeD+ or be less than or equal

FreeD-. If these values are reached or exceeded the analysis will terminate with an error message.

For IOPT = 4, 5, or 6 there are no displacement limits.


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Resettable Air-cylinder Semi-active (1-4) Device Loop

Behaviour with air only, no friction


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IHYST = 56 Modified SINA Degrading Tri-linear Hysteresis. [Saiidi 1979].

Modified SINADegrading Tri-linearrule. One line for each action requiring data.

ALFA BETA GAMMA DELTA PHI FCRP FCRN FCCP FCCN IOP PMAX PMIN

ALFA Bi-linear factor (positive cracking to yield) (0.2 ALFA 0.9) F

BETA Bi-linear factor (negative cracking to yield) (0.2 BETA 0.9) F

GAMMA Unloading power factor (0.0 GAMMA 0.5) F

DELTA Pinching Factor (0.0 DELTA 0.8) F

PHI Ratio o f Compression to Tens ile Stiffness (0 .1 PH I 10.0) F

If PHI = 0.0 then PHI reset to 1.0

FCRP Cracking action as ratio of Positive Yield (0.3 FCRP 0.9) F

FCRN Cracking action as ra tio o f Nega tive Yie ld (0 .3 FCRN 0.9) F

FCCP Crack closing action as ratio of Positive Yield (0.1 FCCP 0.7) F

FCCN Crack closing action as ratio of Negative Yield (0.1 FCCN 0.7) F

IOP =0; Cracking and yield deformations set at static analysis I

=1; Cracking and yield deformations set at first cracking

=2; Cracking and yield deformations set at first yield or when axial force falls

outside range of PMINto PMAX

PMAX Maximum (Most tensile) axial force to set deformation limits. F

PMIN Minimum (Most compressive) axial force to set deformation limits. F

Notes:

1. One complete line is required for each non-l inear action, i.e. 2 lines for Frame members in Ruaumoko2d

and 4 lines for Frame members in Ru

Ruaumoko Appendices

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