Function
 Add, modify or delete inelastic hinge properties.
 Inelastic hinges are applied to inelastic time history analysis only.
 The Spring Type hinge defined in General Link Properties can be used for pushover analysis if the inelastic hinge properties are assigned to the hinge.
Call
From the main menu, select [Properties] tab > [Inelastic Properties] group > [Inelastic Hinge] > [Inelastic Hinge Properties]
Input
Define Inelastic Hinge Properties dialog box
 Click Add to add Inelastic Hinge Properties.
 To modify previously defined Inelastic Hinge Properties, select a property name, click the Modify/Show button and change the input.
 To delete previously defined Inelastic Hinge Properties, select a property name and click the Delete button.
 To copy previously defined Inelastic Hinge Properties, select a property name and click the Copy button.
 CSV Import : Import inelastic hinge properties saved in a CSV file.
 CSV Export : Export inelastic hinge properties to a CSV file. Only the inelastic hinge properties defined as User Type will be available for output. Only the inelastic hinge properties defined as Yield Strength (Surface) Calculation MethodUser Type and Interaction TypeNone will be available for output.
 Close : Close Inelastic Hinge Property dialog box.
Name
Enter the name representing the inelastic hinge properties.
Description
Enter a brief description for inelastic hinge properties being defined.
Yield Strength(Surface) Calculation Method
User Input : User directly defines inelastic hinge properties.
Autocalculation : Inelastic hinge properties are automatically calculated using the selected material, section, and member information.
Type
Define the form of the inelastic hinge, which is provided in four types.
BeamColumn
MomentRotation (MTheta) : It concentrates the inelastic behavior represented by rotational and translational springs at each end and the center. And the remaining parts are assumed to behave elastically. Inelastic hysteresis behaviors are defined by skeleton curves, which are empirical hysteresis models. The axial component is represented by a spring at the center and two translational components are represented by springs at each end defined by forcedisplacement relationships. The two flexural components, My and Mz, are represented by springs defined by the relationship between moment and angle of rotation at either I or J or at both ends.
MomentCurvature (MPhi Distributed) : Unlike lumped hinges, it assumes inelastic behavior throughout the member. The plastic hinge locations in the length direction of a member assigned by the user are defined as the integration points. The flexibility matrix of a section, which represents the distribution of internal forces, is calculated through the integration points. The number of integration points can be 1 and between 3 and 20. If the number of integration points is 2, the moment at the free end of a cantilever beam does not come to exactly zero due to the inherited characteristic of the integration method. Therefore, two integration points are not permitted. Inelastic hysteresis behavior can be defined by 2 models, empirical Skeleton and Fiber. The hinge behaviors can be expressed by force  deformation relationships in each axis direction, and the hinge hysteresis behavior of the flexural components can be expressed by the relationships of moment and angle of rotation. Inelastic behaviors can be defined for 3 axis components and 2 flexural (My & Mz) components.
General Link
Unlike Lumped and Distributed hinges, which are influenced by the inelastic properties of materials and members, the inelastic plastic hinge properties for the corresponding linear properties of each component of Property Type defined in General Link Properties are defined. The elastic stiffness of each component is defined by effective stiffness and acts as the initial stiffness in inelastic analysis. The inelastic hysteresis behavior of a spring is defined by a skeleton model. The inelastic properties of a spring can be defined for all 3 translational and 3 rotational directions. LRB and HDR type vibration isolator hysteresis models can be defined only by using Spring Type.
In order to assign inelastic hinge properties to the Spring Type general link element that is defined in Boundary > Link > General Link > General Link Property, for pushover analysis, the Type must be set to "Spring"
Truss
The axial component is represented by a spring at the center defined by the forcedisplacement relationship. The inelastic hysteresis behavior of a spring is defined by a skeleton model.
Hinge Type
Define the hysteresis behavior model of an inelastic hinge.
Skeleton : It is an empirical hysteresis model, which assumes that the property of each directional component is independent of one another. Each component is defined as a uniaxial hinge hysteresis model. Such independently acting hinges are 3 translational and 3 rotational hinges.
In the case where the inelastic hinge property is assigned to a Spring Type general link element for pushover analysis, the hysteresis model is automatically set to Skeleton.
Fiber : Fiber model is used to define multiaxis hinge hysteresis model. In the fiber model, a beam section is divided into fibers, which undergo axial deformations only. By using the fiber model, the user can trace a more accurate momentcurvature relationship compared to using a hysteresis model of the member. The momentcurvature relationship is based on the stressstrain relationship of the fiber material and an assumed strain distribution on the section. Moreover, this model considers translation of neutral axis due to axial force.
Interaction Type
For Column members, the type of considering interaction between axial force and moment is selected.
None : Interaction between axial force and moments is not considered.
In the case where the inelastic hinge property is assigned to a Spring Type general link element for pushover analysis, the interaction between axial force and moment is automatically set to None.
PM in Strength Calculation : PM interaction in time history analysis is reflected by calculating the flexural yield strength of a hinge considering the effect of axial force. In this method, the interaction between biaxial bending moments is ignored. The axial force is assumed to act with each directional bending moment independently when the hinge status is evaluated at each time step. Recalculation of bending moment yield strength reflecting axial force is carried out in a loading condition, which satisfies the following three conditions:
1) It must be the first among the sequential time history load cases, which will be consecutively analyzed.
2) Inelastic static analysis must be carried out.
3) Displacement control must be used.
The elements are inelastic beam elements assigned with hinge properties to which PM interaction is applied. The initial axial and bending moment at this time are determined by the combination of linear elastic analysis results of all the static loads contained in Time Varying Static Load. The factors used in the combination are defined by the Scale Factors specified in Time Varying Static Load.
PMM in Status Determination : This method uses a multiaxis hinge hysteresis model in inelastic time history analysis. Interaction between axial force and biaxial moments is realized by applying the plasticity theory. The interaction is considered at each time step through evaluating the status of inelastic hinges using the 3dimensional yield surface. MIDAS/Civil supports the kinematic hardening type.
Parametric PM (MultiCurve) : The flexural behavior of the beam element is described by bending moment vs. curvature relationship. This relationship is input in the form of multilinear functions. The moment vs. curvature relationship is a function of the axial force. Note that the axial force is positive when the element is in compression and negative when in tension. The flexural behavior of the beam element is defined by two bending vs. curvature relationships, one for each principal plane of inertia. Interaction between the two bending moments (M_{y} and M_{z}) are not taken into account.
For Lumped and Distributed Types, the Fy and Fz components cannot consider interaction with axial force and moments.
Material
Type : Select a material type for the inelastic hinge properties to be applied. 5 types are provided  Steel, Reinforced Concrete, Steel Reinforced Concrete composite section (filled), Steel Reinforced Concrete composite section (encased) and User Defined. Depending on the type of selected material, the method of defining the yield stress of each element is evaluated differently.
Steel : The first yielding is defined if the maximum flexural stress of a section reaches the yield stress. The 2nd yielding is defined if the flexural stress of the entire section reaches the yield stress.
RC : The first yielding is defined if the maximum flexural stress of a section reaches the cracking stress of concrete. The second yielding is defined if the stress block of concrete reaches the ultimate strength or the rebars yield.
SRC(filled) : Concrete filled steel  same as the steel section calculation codes.
SRC(encased) : Concrete encased steel  same as the concrete section calculation codes.
User Defined : Properties are calculated using the material properties defined by the user.
Code
A design code is selected, which is used for obtaining yield strength and cracking strength coefficient of concrete for RC and SRC (encased) types only. ACI and AIJ are provided. Cracking strength coefficient used in ACI is 7.5 in lbin unit, and in AIJ it is 1.8 in kgfcm unit.
Name
Select a Material Name for which the inelastic hinge will be applied.
Member
Type : Select a member type for which the inelastic hinge will be applied from Beam, Column and Brace.
Element Position : Select a position of the Member Type for applying the inelastic hinge. I, M and J represent iend, middle (center) and jend respectively, which are selected only for the RC Beam member type. This is intended to extract reinforcing data from the selected position of RC Beam members.
Section
Name : Select a section name for which the inelastic hinge will be applied.
Component Properties
Inelastic hinge properties by each component of section strength are entered.
Component : Select the components of sectional strength for which properties will be entered. The Spring Type permits properties in all directional components, whereas Lumped and Distributed types permit all but the Mx component.
Hinge Location : Select the locations of lumped inelastic hinges. Axial component is fixed to the center of a member. Iend, jend or both ends can be selected for the bending moment components.
Num. of Section : Enter the number of integration points for inelastic hinges of the distributed type. Up to 20 sections are permitted, and moment  curvature relationships are calculated at all the sections corresponding to the points.
Hysteresis Model : Select a hysteresis model for an inelastic hinge.
Properties : Enter the properties of inelastic hinges for each component.
Fiber Name : If a distributed hinge of the fiber type is selected, select a fiber element name.
Yield Surface Properties : If "PM in Strength Calculation" or "PMM in Status Determination" is selected in Interaction Type, enter the related data for PM interaction curve and 3D yield surface.
Hysteresis Model
Kinematic Hardening hysteresis model
Kinematic Hardening hysteresis mode
Response points at the initial loading move along a trilinear skeleton curve. The unloading stiffness is identical to the elastic stiffness. It shows the tendency of strength increase with the increase in loading. This is used to model the Bauschinger effect of metallic materials. Accordingly, it is cautioned that energy dissipation may be overestimated for concrete. Due to the characteristic of the model, only the positive (+) and negative () symmetry is permitted for the strength reduction ratios after yielding.
Originoriented type hysteresis model
Originoriented type hysteresis model
Response points at the initial loading move along a trilinear skeleton curve. Response points at unloading move toward the origin and again move along the skeleton curve after reaching the opposite skeleton curve.
Peakoriented type hysteresis model
Peakoriented type hysteresis model
Response points at the initial loading move along a trilinear skeleton curve. Response points at unloading move toward the point of maximum displacement on the opposite side. If the first yielding has not occurred on the opposite side, the response points move toward the first yielding point on the skeleton curve.
Clough type hysteresis model
Clough type hysteresis model
Response points at the initial loading move along a bilinear skeleton curve. Unloading stiffness is obtained from the elastic stiffness reduced by the equation below. As the deformation progresses after yielding, unloading stiffness reduces gradually.
where,
K_{R} : unloading stiffness
K_{0} : elastic stiffness
D_{y} : yield displacement in the zone where unloading begins
D_{m} : maximum displacement in the zone where unloading begins (In the zone where yielding has not occurred, replace it with the yield displacement)
β : constant for determining unloading stiffness
If the sign of loading changes in the process of unloading, response points move toward the point of maximum displacement in the zone of progressing direction. If yielding has not occurred in this zone, the response points move toward the yield point on the skeleton curve. If unloading becomes loading without changing the loading sign, the response points move along the unloading path. If the loading continually increases, loading continues on the skeleton curve again.
Degrading Trilinear type hysteresis model
Initial unloading state prior to yielding in the uncracked zone (for small displacement)
Initial unloading state (for large displacement) and
inner loop prior to yielding in the uncracked zone
where,
K_{R1} : first unloading stiffness
K_{R2} : second unloading stiffness
K_{0} : elastic stiffness
K_{C} : first yield stiffness in the zone where the loading point is oriented due to unloading
K_{1} : the slope between the origin and the second yield point in the zone where the loading point is oriented due to unloading
b : stiffness reduction ratio. If unloading occurs between the first and second yield points on the skeleton curve, it is fixed to 1.0.
F_{M+} , F_{M} : maximum load at each positive (+) and negative (? sides
D_{M+} , D_{M} : maximum deformation at each positive (+) and negative (? sides
Response points at the initial loading move along a trilinear skeleton curve. The unloading stiffness is determined by the location of the unloading point on the skeleton curve and whether or not the first yielding has occurred in the opposite side zone.
If unloading occurs between the first and second yield points on the skeleton curve, loaddeformation coordinates progress toward the first yield point on the skeleton curve on the opposite side. If the loading sign changes in the process, the coordinates progress toward the maximum deformation point on the skeleton curve in the zone of the progressing direction. If yielding has not occurred in this zone, the coordinates progress toward the first yield point. If the skeleton curve is encountered in the process of progressing, the coordinates progress along the skeleton curve.
If unloading takes place in the zone beyond the second yield point on the skeleton curve, the loaddeformation coordinates progress following the next unloading stiffness.
Original Takeda type hysteresis model
Unloading state prior to yielding in the uncracked zone (for small displacement)
Unloading state prior to yielding in the uncracked zone (for large displacement)
Response points at the initial loading move along a trilinear skeleton curve.
When the current displacement or deformation, D, exceeds D1 for the first time or the point of maximum deformation up until now
1. The point moves along the trilinear skeleton curve.
2. If unloading occurs from the straight line toward the opposite direction, the point moves toward the first yield point on the opposite side.
3. If the maximum displacement on the opposite side is in the elastic zone, the range of this elastic zone extends to the first yield point on the opposite side.
4. If the maximum deformation on the opposite side exceeds D1, the displacement in this elastic zone is defined up to the point of restoring force becoming 0. If it passes beyond the 0 point, it moves toward the maximum deformation point on the opposite side. The stiffness at unloading from the straight line directed toward this maximum deformation uses the stiffness of unloading from the maximum deformation point on the opposite side.
When the current displacement or deformation, D, exceeds D2 for the first time or the point of maximum deformation up until now
1. The point moves along the trilinear skeleton curve.
2. If unloading occurs from this straight line toward the opposite direction, the point moves from the unloading point along the straight line of the stiffness obtained from the equation below.
where,
K_{un2} : unloading stiffness of the outer loop
P1 : first yield loading in the zone opposite to the unloading point
P2 : second yield loading in the zone to which the unloading point belongs
D1 : first yield displacement in the zone opposite to the unloading point
D2 : second yield displacement in the zone to which the unloading point belongs
D_{max} : maximum deformation in the zone to which the unloading point belongs
β : constant for determining unloading stiffness of the outer loop
3. If the maximum deformation point on the opposite side does not exceed D1, the range of the slope Kun2 extends up to P1 on the opposite side. If it goes beyond this P1, it directs toward the D2 point. If unloading occurs from the straight line directed toward the D2 point, it moves along the straight line of the slope Kb. If the restoring force exceeds 0, it directs toward the maximum deformation point. If unloading occurs from the straight line directed toward the maximum deformation point, it moves along the slope Kun2. If the restoring force goes beyond 0, it directs toward the maximum deformation point on the opposite side.
4. If the loading sign changes in the process of unloading and while reloading takes place, unloading may occur before reaching the target point on the skeleton curve. Loops are formed in the process, which are all referred to as inner loops. The unloading stiffness within the inner loops is determined by the equation below.
where,
K_{RI} : unloading stiffness of inner loop
K_{un2} : unloading stiffness of outer loop in the zone to which the start point of unloading belongs
γ : reduction factor for unloading stiffness of inner loop
5. If the maximum deformation on the opposite side exceeds D1, the range of the slope Kun2 extends up to the point of restoring force becoming 0, and if it goes beyond 0, it directs toward the maximum deformation point. If unloading takes place from the straight line directed toward this maximum deformation point, D at this point becomes the maximum deformation point of the inner loop. And it moves along the slope Kun2 and directs toward the maximum deformation point if the restoring force exceed the 0 point. Even in the case where unloading takes place from the straight line directed toward this maximum deformation point, D becomes the maximum deformation point of the inner loop and moves along Kun2. If the restoring force goes beyond the 0 point, it directs toward the maximum deformation point.
Takeda Tetra Linear type hysteresis model
Takeda Tetra Linear type hysteresis model
Response points at the initial loading move along a tetralinear skeleton curve.
If the current displacement or deformation, D, does not exceed D3, the hysteresis rules are identical to the Original Taketa hysteresis.
If the current displacement or deformation, D, exceeds D3, response points move along the slope K4. For unloading, response points move by the same rules as the Original Taketa hysteresis.
The Takeda tetralinear hysteresis model can be applied to beam element and General Link of Spring Type of Lumped Type and Distributed Type.
Modified Takeda type hysteresis model
Response points at the initial loading move along a trilinear skeleton curve.
If the current displacement or deformation, D, exceeds D2 for the first time or the maximum deformation point up until now, response points move along the trilinear skeleton curve. If unloading takes place from this straight line toward the opposite direction, the points move along the slope Kun2 until the point of the restoring force becoming 0. If the restoring force goes beyond the 0 point, the points move toward the maximum deformation point on the opposite side.
where,
K_{un2} : unloading stiffness of outer loop
K_{0} : elastic stiffness
D1 : first yield displacement in the zone of unloading point
D_{max} : maximum deformation in the zone to which the unloading point belongs
β : constant for determining unloading stiffness of the outer loop
Even in the case where unloading takes place from the straight line directed toward the maximum deformation point from the point of the 0 restoring force, the points move along the slope Kun2 until the points reach the 0 restoring force. After the point of 0 restoring force is passed, the points move toward the maximum deformation point on the opposite side.
The Modified Takeda type hysteresis model can be applied to beam element and General Link of Spring Type of Lumped Type and Distributed Type.
Modified Takeda Tetra Linear type hysteresis model
Modified Takeda Tetra Linear type hysteresis model
Response points at the initial loading move along a tetralinear skeleton curve.
If the current displacement or deformation, D, does not exceed D3, the hysteresis rules are identical to the Modified Taketa hysteresis.
If the current displacement or deformation, D, exceeds D3, response points move along the slope K4. For unloading, response points move by the same rules as the Modified Taketa hysteresis.
The Modified Takeda Tetralinear type hysteresis model can be applied to beam element and General Link of Spring Type of Lumped Type and Distributed Type.
Normal Bilinear type hysteresis model
Normal Bilinear type hysteresis model
Response points at the initial loading move along a bilinear skeleton curve. The unloading stiffness is identical to the elastic stiffness. The Normal Bilinear type hysteresis model can be applied to beam element and General Link of Spring Type of Lumped Type and Distributed Type.
Elastic Bilinear type hysteresis model
Elastic Bilinear type hysteresis model
Regardless of loading and unloading, response points always move along a bilinear skeleton curve without any pattern of curved loops. The Elastic Bilinear type hysteresis model can be applied to beam element and General Link of Spring Type of Lumped Type and Distributed Type.
Elastic Trilinear type hysteresis model
Elastic Trilinear type hysteresis model
Regardless of loading and unloading, response points always move along a trilinear skeleton curve without any pattern of curved loops. The Elastic Trilinear Type hysteresis model can be applied to beam element and General Link of Spring Type of Lumped Type and Distributed Type
Elastic Tetralinear type hysteresis model
Elastic Tetralinear type hysteresis model
Regardless of loading and unloading, response points always move along a tetralinear skeleton curve without any pattern of curved loops. The Elastic Tetralinear Type hysteresis model can be applied to beam element and General Link of Spring Type of Lumped Type and Distributed Type.
LRB Isolator Bilinear type hysteresis model
LRB Isolator Bilinear Type hysteresis model
The initial stiffness is calculated by the strain used specifically for calculating the initial stiffness. Movement on a bilinear skeleton curve is the hysteresis rule provided that the strain does not exceed Rmin.
Q_{d50} : yield property
K_{p50} : yield strength
H ： layer thickness
ALF : yield stiffness ratio (1/6.5)
R_{min} : strain used specifically for calculating initial stiffness
K_{E50} : initial spring coefficient（spring coefficient at 50% deformation of the LRB device）
LRB Isolator Bilinear type hysteresis model can be applied to General Link of Spring Type only.
LRB Isolator Trilinear type hysteresis model
LRB Isolator Trilinear type hysteresis model
H : layer thickness
Area : contact area
R_{min} : initial shear strain (Default 0.01)
SW : bearing type
1 : HDR－G12 (default)
2 : HDR－G10
3 : LRB－G12
4 : LRB－G10
5 : RB－G12
6 : RB－G10
7 : HDR－G8
8 : HDR－S－G12
LRB Isolator Trilinear type hysteresis model can be applied to General Link of Spring Type only.
High Damping Rubber Isolator type hysteresis model
High Damping Rubber Isolator type hysteresis model
H : layer thickness
Area : contact area
R_{min} : initial shear strain (Default 0.01)
SW : bearing type
1 : KL301（default）
2 : KL401
3 : KL302
4 : KL501
5 : UHDG6
6 : HDG8
7 : TOYO
8 : G=8 kgf/㎠
9 : G=10 kgf/㎠
10 : G=12 kgf/㎠
Gs: coefficient multiplied to shear elastic modulus (default : 1.0)
Hs: coefficient multiplied to equivalent damping (default : 1.0)
Us: coefficient multiplied to yield loading property coefficient (default : 1.0)
HDR Damping Rubber Isolator Type hysteresis model can be applied to General Link of Spring Type only.
Slip Bilinear Type hysteresis model
Slip Bilinear Type hysteresis model
At initial loading, response points move along the bilinear skeleton curve.
When unloading when D1 < D, the following rules are followed, depending on whether the opposite side surrenders.
1) Displacement before the opposite side experiences yield: It is lowered by a gradient of elasticity to point A, where the resilience becomes zero, and moves on the strain axis (X axis) from point A to point B inversion.
2) Displacement after the opposite side experiences yield: It is lowered by a gradient of elasticity to point A, where the restoring force is zero, and moves on the strain axis (X axis) from point A to point C inversion.
Once response points go beyond point B, the member is reloaded along the slope of elastic stiffness until the response points reach the skeleton curve. Then the member is unloaded with the slope of elastic stiffness until the restoring force becomes 0. From a reversal point, the response points move along the Displacement Axis (Xaxis). This process is repeated.
In the Slip Bilinear type hysteresis model, an initial Gap can be set.
Slip Bilinear/Tension Type hysteresis model
At initial loading, response points move along the bilinear skeleton curve.
When D1 < D, the member is unloaded along the slope of elastic stiffness up to point A ?a point where the restoring force is 0, and then the response points move along the Xaxis.
When reloading, the response points move along the Displacement Axis (Xaxis) up to point A. Once response points go beyond point A, reloading continues along the slope of elastic stiffness until the response points reach the skeleton curve.
In the Slip Bilinear/Tension type hysteresis model, only a (+) initial Gap can be set.
In the Slip Bilinear/Compression type hysteresis model, only a () initial Gap can be set.
Slip Bilinear/Compression Type hysteresis model
When the initial Gap is entered in the Slip Bilinear type hysteresis model, plastic ratio (D/D1) is calculated by the equation .
Slip Trilinear Type hysteresis model
Slip Trilinear Type hysteresis model
At initial loading, the response points move along the trilinear skeleton curve.
When D1 < D, the member is unloaded along the slope of elastic stiffness up to point A ?a point where the restoring force is 0. Once the response points reach a reversal point A during unloading, they move along the Xaxis up to point B.
Once response points go beyond point B, the member is reloaded along the slope of elastic stiffness until the response points reach the skeleton curve. Then the member is unloaded with the slope of elastic stiffness until the restoring force becomes 0. From a reversal point, the response points move along the Displacement Axis (Xaxis). This process is repeated.
In the Slip Trilinear type hysteresis model, an initial Gap can be set.
Slip Trilinear/Tension Type hysteresis model
At initial loading, response points move along the trilinear skeleton curve.
When D1 < D, the member is unloaded along the slope of elastic stiffness up to point A ?a point where the restoring force is 0, and then the response points move along the Xaxis.
When reloading, response points move along the Displacement Axis (Xaxis) up to point A. Once the response points go beyond point A, reloading continues along the slope of elastic stiffness until the response points reach the skeleton curve.
In the Slip Trilinear/Tension type hysteresis model, only a (+) initial Gap can be set.
In the Slip Trilinear/Compression type hysteresis model, only a () initial Gap can be set.
Slip Trilinear/Compression Type hysteresis model
When the initial Gap() is entered in the Slip Trilinear type hysteresis model, plastic ratio (D/D1, D/D2) is calculated by the equation .
MultiLinear Plastic Kinematic Type hysteresis model
(1) Overview of Hysteresis
MultiLinear Plastic Kinematic Type Hysteresis is defined on multilinear skeleton curves based on the kinematic hardening rules. The curve can be symmetrically or unsymmetrically defined. The types of corresponding elements include lumped hinge, distributed hinge, spring and truss elements.
(2) Definition of Skeleton Curve
ForceDisplacement Curve
The skeleton curve is defined by the forcedisplacement relationship defined by the user. The following restrictions apply to defining the forcedisplacement curve:
ForceDisplacement Curve has no limitation on the number of data.
 At least one data point must be defined on both the positive and negative sides, and the numbers of data on the positive and negative sides must be identical.
 The initial value must be set to (0,0).
 No identical values can be used for Displacements, and the forcedisplacement data are arranged in reference to the displacements.
 The signs of force and displacement must be the same at all times.
 A negative slope is not permitted in ForceDisplacement Curve. As such, the forces must gradually increase on the positive side and decrease on the negative side. No fluctuation is permitted.
(3) Rules for Hysteresis of MultiLinear Plastic Kinematic Type
1. In the case of , the hysteresis curve for MultiLinear Plastic Kinematic Type follows the conventional kinematic hardening rules.
2. In the case of , when the force is unloaded on the skeleton curve, the unloading takes place backward at a slope of K0 by the magnitude of P1(+) or P1() (Rule:1). It is then directed towards the point of unloading by the magnitude of the first
yielding displacement, D1() or D1(+), on the opposite side until the restoring force becomes 0 (Rule:2). Once the restoring force exceeds 0, the kinematic hardening rules apply.
MultiLinear Plastic Takeda Type hysteresis model
(1) Overview of Hysteresis
MultiLinear Plastic Takeda Type Hysteresis is a multilinear stiffness degradation model. The curve can be symmetrically or unsymmetrically defined. The types of corresponding elements include lumped hinge, distributed hinge, spring and truss elements.
MultiLinear Plastic Takeda Hysteresis Model
(2) Definition of Skeleton Curve
ForceDisplacement Curve
The skeleton curve is defined by the forcedisplacement relationship defined by the user. The following restrictions apply to defining the forcedisplacement curve:
 ForceDisplacement Curve has no limitation on the number of data.
 At least one data point must be defined on both the positive and negative sides, and the numbers of data on the positive and negative sides must be identical.
 The initial value must be set to (0,0).
 No identical values can be used for Displacements, and the forcedisplacement data are arranged in reference to the displacements.
 The signs of force and displacement must be the same at all times.
 A negative slope is not permitted in ForceDisplacement Curve. As such, the forces must gradually increase on the positive side and decrease on the negative side. No fluctuation is permitted.
Unloading Stiffness Parameter, β
The stiffness at unloading on the (+) and () sides is computed as follows. When β=0 , the unloading stiffness becomes the same as the elastic stiffness.
where, D1(+), D1() : Yielding displacements on (+) & () sides
D1max(+), D1max(): Maximum displacements on (+) & () sides (Replace with the yielding displacement when yielding has not occurred.)
β: Unloading stiffness parameter (0≤ β ≤1)
(3) Rules for Hysteresis of MultiLinear Elastic Type
1. In the case of │Dmax│<D1, the curve becomes linear elastic, which retains the elastic slope, K0, passing though the origin.
2. When D first exceeds D1(+) or exceeds the maximum D up to the present, the curve follows the skeleton curve.
3. When the force is unloaded at the state, D1(+) < D or D<D1(), the curve follows the unloading stiffness at a slope of Kr(+) or Kr().
4. D moves towards the Dmax on the opposite side when the sign of the force changes in the process of unloading. If the opposite side has not yielded, the yielding point becomes the maximum displacement.
MultiLinear Plastic Pivot Type hysteresis model
(1) Overview of Hysteresis
MultiLinear Plastic Pivot Type Hysteresis (Pivot Hysteresis hereafter) is a multilinear stiffness degradation model proposed by R. K. Dowell, F. Seible & E. L. Wilson(1998). Pivot Hysteresis uses multiple pivot points to control the nonlinear relationship of stressstrain or momentrotation of reinforced concrete members. Thus, this model can accurately depict the stiffness degradation and the pinching effect when unloading takes place.
The curve can be symmetrically or unsymmetrically defined. The types of corresponding elements include lumped hinge, distributed hinge, spring and truss elements.
(2) Definition of Skeleton Curve
ForceDisplacement Curve
The skeleton curve is defined by the forcedisplacement relationship defined by the user. The following restrictions apply to defining the forcedisplacement curve:
 ForceDisplacement Curve has no limitation on the number of data.
 At least one data point must be defined on both the positive and negative sides, and the numbers of data on the positive and negative sides must be identical.
 The initial value must be set to (0,0).
 No identical values can be used for Displacements, and the forcedisplacement data are arranged in reference to the displacements.
 The signs of force and displacement must be the same at all times.
 A negative slope is not permitted in ForceDisplacement Curve except for the final value. As such, the forces must gradually increase on the positive side and decrease on the negative side except for the last points on the curve. No fluctuation is permitted.
Primary Pivot Point
The Primary Pivot Points, P1 and P3 represent the points towards which the unloading curves are oriented in the Q1 and Q3 zones. The Primary Pivot Points, P1 and P3 control the degradation of the unloading stiffness caused by the change in deformation or displacement. P1 and P3 are located along the extended lines of the initial stiffness on the (+) and () sides, which are defined by the yield strengths, Fy(+) and Fy() and Scale Factors, α1 and α2.
α1 : Scale Factor used to define the pivot point, P1 when unloading from the Q1 side (α1 ≥1)
α2 : Scale Factor used to define the pivot point, P3 when unloading from the Q3 side (α2≥1)
The locations of the Primary Pivot Points, P1 and P3 move to P1* and P3* after yielding respectively, whenever the maximum displacement point is renewed by the Initial Stiffness Softening Factor, η. However, when η=0, the locations of the Primary Pivot Points, P1 and P3 remain unchanged.
Primary Pivot Point
Pinching Pivot Point
The Pinching Pivot Points, PP2 and PP4 represent the points towards which the unloading curves are oriented in the Q1 and Q3 zones after the restoring force exceeds 0. PP2 and PP4 are located on the skeleton curve in the elastic zone on the (+) and () sides, which are defined by the yield strengths of the initial stiffness, Fy(+) and Fy() and Scale Factors, β1 and β2.
β1 : Scale Factor used to define the pivot point, PP2 when loading on the Q2 side (0< ≤1)
β2 : Scale Factor used to define the pivot point, PP4 when loading on the Q4 side (0< ≤1)
The locations of the Pinching Pivot Points, PP2 and PP4 after yielding will move to PP2*and PP4* respectively, whenever the maximum displacement point is renewed by the Initial Stiffness Softening Factor, η. However, when η =0, the Pinching Pivot Points, PP2 and PP4 remain unchanged.
Pinching Pivot Point
Initial Stiffness Softening Factor : η
η is an initial stiffness softening factor used to control the initial stiffness degradation after yielding. After yielding, the Primary Pivot Points, P1 and P3 are relocated to P1*and P3*, which are located on the lines extended from the maximum displacement points on the (+) and () sides respectively. P1*and P3* are defined by Fy(+) and Fy(), Scale Factors, and , and the initial stiffness softening factor, η.
In addition, the Pinching Pivot Points,PP2 and PP4 move to PP2* and PP4* respectively. PP2* (or PP4*) is defined by the intersection point of the straight line passing through P1* and the origin (or P3* and the origin) and the straight line connecting PP2 (or PP4) to the maximum displacement point on () side (or (+) side).
Renewal of Scale Factors, β1 and β2
The Pinching Pivot Point Scale Factors, β1 and β2 are renewed after yielding under the conditions below.
Initial Stiffness Softening Factor
Renewal of Scale Factors, β1 and β2
(3) Rules for Hysteresis of MultiLinear Plastic Pivot Type
1. In the case of │Dmax│<D1, the curve becomes linear elastic, which retains the elastic slope, Ko passing the origin. (Rule: 0)
2. i) The curve follows the skeleton curve when the displacement exceeds for the first time. (Rule: 1)
ii) When unloading takes place on this straight line, the curve is directed towards P1 or P3. (Rule: 2)
iii) In the case of reloading before the restoring force reaches 0, the curve continues to follow the same unloading straight line. (Rule: 3) If it reaches the skeleton curve, it follows along the skeleton curve. (Rule: 4)
iv) When the restoring force exceeds 0, the curve is directed towards PP2 or PP4. (Rule: 5)
v) When PP2 or PP4 is exceeded and yielding has not occurred, the curve moves along the straight line of the elastic slope. (Rule: 6) When yielding takes place due to large deformation, the curve moves along the skeleton curve. (Rule: 7)
3. i) When unloading takes place on the skeleton curve after both sides have yielded, the curve moves towards P1 or P3.
(Rule: 8) However, it is directed towards the renewed P1* or P3* if η is not equal to 0.
ii) If the restoring force exceeds 0, the curve is directed towards PP2 or PP4. However, it is directed towards the renewed PP2*or PP4* if η is not equal to 0. (Rule: 9)
iii) If unloading takes place before reaching PP2 or PP4, the curve moves along the straight line passing through the unloading point and P4 (or P2). (Rule:10) If reloading takes place before the restoring force reaches back to 0, the curve moves back towards P3 (or P1). (Rule: 11)
iv) If the restoring force exceeds 0, the curve moves along the line connecting the point of zero restoring force to P3 (or P1). (Rule: 12) When the curve intersects with a line connecting PP2 (or PP4) and (or ), it is directed towards (or ). (Rule: 13)
PM MultiCurve Type
PM MultiCurve Type allows for bilinear and multilinear plasticity. Strain hardening can be isotropic, kinematic or mixed. The momentcurvature relationship can either be symmetric or nonsymmetric with respect to the sign of the curvature. Whether it is symmetric or nonsymmetric, entire momentcurvature curve should be entered. The first data point corresponds to negative rupture and the last data point corresponds to positive rupture. One data point – the zero point – must be at the origin. A different number of data points can be used for the positive and negative sections of the curve.
Bending moment and curvature relationship can depend on the axial force and the dependence can be different in tension and in compression. The input for the bending momentcurvature curve consists of bending momentcurvature curves for different levels of axial force. Note that the number of axial forces must be two at least.
To obtain the bending momentcurvature curve for a level of axial force not input, interpolation is used. This interpolation is performed, not on the bending momentcurvature curves, but on the bending momentplastic curvature curves; the bending momentplastic curvature curves are automatically calculated from the bending momentcurvature curves.
The momentcurvature relationship can either be symmetric or nonsymmetric. Whether it is symmetric or nonsymmetric, entire momentcurvature curve should be entered.
Strain hardening can be isotropic, kinematic or mixed.
Each moment component will follow 1D vonmises model.
Under the specific axial force, the yield moment can be defined as the followings.
When the Spring Type general link element is defined as inelastic hinge for pushover analysis, all the hysteresis models provided by midas Civil can be used.
Directional Hinge Properties dialog
Type
Select whether or not the skeleton curve is symmetrical. Nonsymmetry of the curve can be applied to Yield Strength, Stiffness Reduction Ratio and Hinge Status. However, Kinematic Hardening Model does not permit nonsymmetry of Stiffness Reduction Ratio due to its characteristics.
Yield Properties
Define Yield Properties.
Input Method
User Input : User defines the Yield Properties.
Auto Caculation : The Yield Proerties are automatically calculated.
Input Type
Yield Properties
StrengthStiffness Reduction Ratio : Yield Properties are defined by specifying StrengthStiffness Reduction Ratio.
StrengthYield Displacement : Yield Properties are defined by specifying StrengthYield Displacement.
Yield Strength
Yield strength is specified. It is user defined based on material and section properties. The user specifies positive (+) values regardless of tension (t) or compression (c). The program treats compression as negative () internally.
P1 : P1 represents the first yield strength. If the Material Type is Steel or SRC (filled), the first yield represents the state in which the maximum bending stress of the section reaches the yield stress. If the Material Type is RC or SRC (encased), the first yield represents the state in which the maximum bending stress of the section reaches the cracking stress of concrete.
P2 : P2 represents the second yield strength. If the Material Type is Steel or SRC (filled), the second yield represents the state in which the bending stress of the entire section reaches the yield stress. If the Material Type is RC or SRC (encased), the second yield represents the state in which the stress in the concrete section reaches the ultimate strength or the stress in reinforcing steel reaches the yield strength. In case of bending, the concrete stress is based on a rectangular stress block.
P3 : P3 represents the third yield strength.
Stiffness Reduction Ratio
Enter the stiffness reduction ratios of a sloped skeleton curve when Strength  Stiffness Reduction Ratio is selected for Input Type.
α1 : Ratio of stiffness immediately after the first yielding divided by the initial stiffness
α2 : Ratio of stiffness immediately after the second yielding divided by the initial stiffness, which is defined when the skeleton curve is of Trilinear or Tetralinear type.
α3 : Ratio of stiffness immediately after the third yielding divided by the initial stiffness, which is defined when the skeleton curve is of Tetralinear type.
Yield Displacement
Enter the yield displacement of a sloped skeleton curve when Strength  Yield Displacement is selected for Input Type.
D1 : first yield displacement component or deformation
D2 : second yield displacement component or deformation, which is defined when the skeleton curve is of Trilinear or Tetralinear type.
D3 : third yield displacement component or deformation, which is defined when the skeleton curve is of Tetralinear type.
Deformation Indexes
Data required for calculating the indexes, which represent the level of deformation of an inelastic hinge
Ductility Factor : Select a basis of calculating ductility. Depending on the selection by the user, ductility factor is calculated by dividing the current deformation by the first yield deformation or the second yield deformation
Hinge Status : Enter the reference ductility, which classifies the state of a hinge in 5 different levels. In case of a nonsymmetric hinge, the hinge status level at each time step is determined by the larger of the positive (+) and negative () levels. Level1 (0.5) signifies the elastic status and Level2 (1) signifies the yield status. Level3 (2), Level4 (4) and Level5 (8) represent the level of ductility of each member. In analysis results, the status is presented in blue, green, yellowish light green, orange, and red colors.
Initial Stiffness
The initial stiffness used in inelastic analysis is either selected or entered by the user.
Select the initial stiffness used in the inelastic analysis or enter it yourself.
6EI/L , 3EI/L, 2EI/L: Provided that the inelastic hinge is of a lumped type for the bending moment component, the initial stiffness is selected on the basis of the longitudinal distribution of bending moment. This cannot be selected in case of Distributed Type and Spring Type.
6EI/L: when end values of linearly distributed bending moment are identical in magnitude but in opposite directions
3EI/L: when one end is 0
2EI/L: when the magnitudes and signs of end values are identical
User: the user directly enters the initial stiffness if the Input Type is Strength  Stiffness Reduction Ratio.
Elastic Stiffness: elastic stiffness of a member is used as the initial stiffness for inelastic analysis.
Skeleton Curve: when Strength  Yield Displacement is selected for the Input Type, the ratio of the user specified yield strength and yield displacement is used as the initial stiffness.
Unloading Stiffness Parameter
Exponent in Unloading Stiffness Calculation : This is an option used to determine the unloading stiffness of the outer loop used in the Clough and Takeda type models among hysteresis models of skeleton curves. This is used to reflect the effect of reduction in stiffness, which occurs as the deformation progresses after yielding. The unloading stiffness is determined by the elastic stiffness reduced by the yield displacement and maximum displacement in the zone where unloading begins and the exponent entered here.
Inner Loap Unloading Stiffness Reduction Factor : This is used to determine the unloading stiffness of the inner loop. The inner loop is formed when unloading occurs before reaching the target point on the skeleton curve while reloading after the loading sign changes in the process of unloading. The unloading stiffness of the inner loop is calculated by multiplying the unloading stiffness of the outer loop by the reduction ratio for the unloading stiffness of the inner loop.
Yield Surface Properties dialog
PM Interaction Curves
Enter the PM interaction curve data required to calculate 3dimensional yield surfaces. All strength values must be entered with positive sign. Sign convention for plotting PM curve is positive for compression and negative for tension.
Type of Input : Two input methods, user defined and autocalculation based on material and section type, are supported to define the variables below. If some items are autocalculated and the remainder is to be user defined, Autocalculation should be performed first, and then necessary items can be modified after converting to User Input.
Crack Strengths : The following three items are required only if the Material Type is of RC or SRC (encased). All the numerical values are entered as positive.
NC0(t) : Cracking strength due to pure tension force
MC0y : Cracking strength of a section subject to moment about yaxis without the presence of axial force
MC0z : Cracking strength of a section subject to moment about zaxis without the presence of axial force
The following 12 items are required irrespective of the Material Type. But for RC and SRC (encased) sections, approximate NC(t), NC(c), NCBy, NCBz, MCy,max and MCz,max are either entered or autocalculated on the basis of NC0(t), MC0y and MC0z. All the numerical values are entered as positive.
Strengths for the 1st PM Interaction Curves
NC(t): First yield strength subject to pure tension force
NC(c): First yield strength subject to pure compression force
NCBy: Axial force at the time of balanced failure in the first yield interaction curve for the yaxis moment of the section
NCBz: Axial force at the time of balanced failure in the first yield interaction curve for the zaxis moment of the section
MCy,max: Maximum bending yield strength in the first yield interaction curve for the yaxis moment of the section
MCz,max: Maximum bending yield strength in the first yield interaction curve for the zaxis moment of the section
Strengths for the 1nd PM Interaction Curves
NY(t): Second yield strength subject to pure tension force
NY(c): Second yield strength subject to pure compression force
NYBy: Axial force at the time of balanced failure in the second stage yield interaction curve for the yaxis moment of the section
NYBz: Axial force at the time of balanced failure in the second yield interaction curve for the zaxis moment of the section
MYy,max: Maximum bending yield strength in the second yield interaction curve for the yaxis moment of the section
MYz,max: Maximum bending yield strength in the second yield interaction curve for the zaxis moment of the section
Shape of the 1st and 2nd PM Interaction Curves
Input the PM interaction curve shapes. The shape of an interaction curve is defined by coordinates of 11 points among which the furthermost extreme coordinates for tension, compression and flexure are fixed to 0 or 1. Only the remaining 8 points are thus entered. If Material Type is RC or SRC (encased), the interaction curve for the first yield is of a linear shape and as such input is unnecessary. In calculating or displaying the axial component of the coordinates, the sign convention is (+) for compression and () for tension
Approximation of Yield Surface Shape
On the basis of PM interaction curve, the parameters for 3dimensional yield surface are either user defined or autocalculated. If some items are autocalculated and the remainder is to be user defined, Autocalculation should be performed first, and then necessary items can be modified after converting to User Input. In case of Alpha, only user defined entry is possible. The value of each parameter is used in the equation of yield surface displayed in the dialog box.
Beta y, Beta z, Gamma : Being the exponential powers of PMy or PMz interactions, different values can be entered for the first and second yields. For Beta y and Beta z on the other hand, two separate values representing the ranges of larger and smaller axial forces relative to the axial force at the time of balanced failure can be entered. Alpha: Exponential powers of MyMz interactions for the first and second yields.
Alpha : Exponent for MyMz interaction for 1st and 2nd yielding
Interaction Curves and Approximated Yield Surfaces
The PM interaction curves entered by the user or calculated by material and section properties and the 3dimensional yield surfaces composed from them are displayed. The yield surfaces are displayed by showing the outlines of projection on the reference plane. Through this can we then check how well the PM interaction curves and the yield surfaces coincide.
Plot : Select an interaction curve or yield surface to be displayed. PMy, PMz or MyMz can be selected.
Only the inelastic hinge properties defined by the Yield Strength (Surface) Calculation MethodUser Type, Interaction TypeNone can be output.
CSV Export
CSV Export & Description
Column No. 
Item 
Input 
Description 

1 
Inelastic Hinge Properties Name 


2 
Type 
L, D, S,T 
L : Lumped D : Distributed S : Spring T : Truss 
3 
Component 
1 ~ 6 
1 : Fx 2 : Fy 3 : Fz 4 : Mx 5 : My 6 : Mz 
4 
Num. of Section 
1, 3 ~ 20 
Enter only if you selected the distribution type for the BeamColumn. 
5 
Hysteresis Model 
KH, OO, PO, C, DT, TT, MT, MTT, NB, EB, E, ET 
KH : Kinematic Hardening OO : Origin Oriented PO : Peak Oriented C : Clough DT : Degrading Trilinear TT : Takeda Tetralinear MT : Modified Takeda MTT : Modified Takeda Tetra NB : Nomal Bilinear EB : Elastic Bilinear E : Elastic Trilinear ET : Elastic Tetralinear 
6 
Type 
0, 1 
0 : Symetric 1 : Asymmetric 
7 
Initial Stiffness 
6, 3, 2, U, E, S 
6 : 6EI/L 3 : 3EI/L 2 : 2EI/L U : User E : Elastic S : Skeleton 
8 
Initial Stiffness, K 

If you enter "U", User Type in column 7, enter the initial stiffness directly. 
9 
Yield Properties  Input Type 
R, D 
R : Strength  Stiffness Reduction Ratio D : Strength  Yield Displacement 
10 
Unit  Force 


11 
Unit  Length 


Enter columns 12 ~ 29 differently depending on the input type of Yield Properties.
Column No. 

when Strength  Stiffness Reduction Ratio is selected 
when Strength  Yield Displacement is selected 

12 
(+) 
P1 : primary yield strength 
P1 : primary yield strength 
13 
α1 : Ratio of stiffness of primary yield gradient divided by initial stiffness 
D1 : Primary yield displacement or strain component 

14 
P2 : secondary yield strength 
P2 : secondary yield strength 

15 
α2 : Ratio of stiffness of secondary yield gradient divided by initial stiffness 
D2 : Secondary yield displacement or deformation components 

16 
P3 : Third yield strength 
P3 : Third yield strength 

17 
α3 : Ratio of stiffness of third yield gradient divided by initial stiffness 
D3 : Third yield displacement or strain component 

18 
 
P4 : Fourth yield strength 

19 
 
D4 : 4th yield displacement or strain component 

20 

P1 : primary yield strength 
P1 : primary yield strength 
21 

α1 : Ratio of the stiffness of the first yield gradient divided by the initial stiffness 
D1 : Primary yield displacement or strain 
22 

P2 : Secondary yield strength 
P2 : Secondary yield strength 
23 

α2 : Ratio of the stiffness of the second yield gradient divided by the initial stiffness 
D2 : Secondary yield displacement or deformation components 
24 
() 
P3 : 3rd yield strength 
P3 : 3rd yield strength 
25 

α3 : Ratio of the stiffness of the third yield gradient divided by the initial stiffness 
D3 : Third yield displacement or strain component 
26 

 
P4 : Fourth yield strength 
27 

 
D4 : Fourwindow yield displacement or deformation component 
28 

β : Exponent in Unloading Stiffness Calculation 
β : Exponent in Unloading Stiffness Calculation 
29 

α : Inner Loap Unloading Stiffness Reduction Factor 
α : Inner Loap Unloading Stiffness Reduction Factor 