Click the Hystersis title to see a graphic of the loop (note a few are large files +35Kb).
Stiffness Degradation (for Frame, Spring and Foundation Members)
The following is the choice of Hysteresis Rules available in Ruaumoko, Ruaumoko3D,
Hysteres and Inspect:
0. Linear Elastic behaviour: The default model. No hysteretic behaviour occurs
Elasto-Plastic hysteresis: The simplest hysterestic model with no stiffness shown after yield occurs.
Bi-linear hysteresis: A simple extension of the elasto-plastic loop where there is some stiffness exhibited after yield.
RAMBERG-OSGOOD hysteresis: This is the original model of the Ramberg-Osgood loop but tends to exhibit un-realistic forces if the loop reverses again if the relationship has not moved very far from the back-bone curve. See hysteresis loops 40 and 41.
TAKEDA Bi-linear Degrading Stiffness: This is used to model plastic hinges in reinforced concrete beams.
Bi-linear with Slackness: This loop was initially designed to represent the behaviour of steel cross-braces in framed structures. As the steel yields the slackness in the braces increases.
KIVELL Degrading Stiffness: This loop was initially used for nail-plate connections in timber frames.
Origin Centered Degrading Stiffness: A simple degrading stiffness model which exhibits a very small amount of energy dissipation in each cycle of oscillation.
SINA Degrading Stiffness: This is used to model plastic hinges in reinforced concrete beams.
STEWART Degrading Stiffness: This loop was initially used for modeling nailed panels to timber frames but has been very successfully applied to reinforced concrete columns which use plain round reinforcement bars.
Degrading Bi-linear Stiffness: This is used to model plastic hinges in reinforced concrete beams.
CLOUGH Degrading Stiffness: This is used to model plastic hinges in reinforced concrete beams. This was the first degrading stiffness hysteresis.
Q-HYST Degrading Stiffness: This is used to model plastic hinges in reinforced concrete beams.
MUTO Tri-linear Degrading Stiffness: This is used to model plastic hinges in reinforced concrete beams.
FUKADA Tri-linear Degrading Stiffness: This is used to model plastic hinges in reinforced concrete beams.
Bi-linear Elastic: A simple non-linear elastic rule without any energy dissipation.
Non-linear Elastic (initially used for Un-Reinforced Masonry panels): A simple non-linear elastic rule without any energy dissipation.
Degrading Elastic: A simple degrading stiffness model without any energy dissipation.
Ring-Spring model: This has a flag-shaped hysteresis loop. This loop was developed to represent the behaviour of ring-spring energy dissipators.
HERTZIAN Contact Spring: This loop represents the behaviour of an elastic contact on a rigid surface.
MEHRAN Degrading Stiffness: This is used to model plastic hinges in reinforced concrete beams.
WIDODO Foundation Compliance Model: Used to represent the non-linear rotational compliance spring under structural walls on a compliant foundation.
LI-XINRONG Reinforced Concrete Column hysteresis: This loop represents the effects of variations in axial force on the behaviour of plastic hinges in columns.
BOUC-WEN hysteresis: A very general hysteresis, much used in random vibration studies as it is amenable for use in analytical solutions.
REMENNIKOV Steel Brace model: This loop is designed to model the lateral buckling of steel brace members.
TAKEDA with Slip (Otani): A loop designed to represent reinforced concrete beams exhibiting bond slip at the beam ends.
AL-BERMANI Bounding-Surface model (Zhu): A simple loop used to represent steel behaviour.
Peak Oriented hysteresis: A simple hysteresis loop developed in Japan.
MATSUSHIMA Degrading Stiffness: A simple degrading stiffness and strength model.
KATO Degrading Shear model: The hysteresis was developed to represent the behavoiur of shear in reinforced concrete members.
Elastomeric Damper model: A loop to represent the behaviour of elastomeric dampers.
Composite Section SINA Degrading Stiffness: An extension of the SINA hysteresis to represent composite section behaviour.
Different +/- Stiffness Bi-linear Stiffness: A bi-linear hysteresis with different stiffnesses in the positive and negative displacement directions.
Masonry Strut hysteresis (Crisafulli): This loop was initially developed for masonry panels but is also applicable to concrete.
Hyperbolic hysteresis: An hysteresis rule initially used in geotechnical engineering but having a smooth force-displacement relationship.
Degrading Bi-linear hysteresis with Gap: This is an extension of the Bi-linear with Slackness hysteresis loop to allow for progressive stiffness degradation.
Bi-Linear +/- Stiffness: A bi-linear hysteresis with different stiffnesses in the positive and negative displacement directions.
Non-linear Elastic Power Rule: This loop provides a non-linear elastic rule without the ringing effects associated with a sudden increase in stiffness seen in the bi-linear elastic hysteresis with no energy dissipation to damp out the high frequency oscillation.
Revised Origin Centered Degrading Stiffness: This loop is a modification of the original Origin Centered hysteresis in that the stiffness in each quadrant is independent of the other.
Dodd-Restrepo Steel hysteresis model: This loop represents well the Bauschinger effects seen in cyclic behavoiur of steel.
Ramberg-Osgood hysteresis (this is a bounded model, used since 1984). A modified loop without the forces exceeding realistic values on small cycle reloading.
Ramberg-Osgood hysteresis (this uses the "Pyke" range to bound forces): A modified loop initially used in geotechnical engineering to represent a soil behaviour without the forces exceeding realistic values on small cycle reloading.
HERA-SHJ Steel Beam sliding-joint model (under development with HERA(NZ)): The loop represents a sliding beam-column hinge connection
Re-settable Actuator
(semi-active damper) hysteresis: This loop is to represent the
behaviour of a semi-active control device. Strength Degradation:
Many of the hysteresis rules allow for degradation of the strength of the
members. The Yield Forces or Yield Moments may degrade as a function of
the member ductility or the number of cycles of inelastic action. This is
independent of the stiffness degradation associated with a hysteresis rule
itself. There are, however, some hysteresis rules that have their own built-in
degradation of strength.