## Function

- You can input, modify, or delete the properties of a general link element. The general link element is used to model various components such as dampers, interface elements, compression or tension-only members, inelastic hinges, and ground springs. The general link element can have linear or nonlinear properties by utilizing the characteristics of a spring.

Procedure |
Menu |
---|---|

1. Define material properties |
[Properties] tab > [Material Properties] group > [Material Properties] |

2. Define section properties |
[Properties] tab > [Section Properties] group > [Section Properties] |

3. Create elements |
[Node/Element] tab > [General] group > [Create] > [Create Element] |

4. Define general link properties - Linear properties - Nonlinear properties |
[Boundary] tab > [Links] group > [General Link] > [General Link Properites] |

5. Assign general link |
[Boundary] tab > [Links] group > [General Link] > [General Link] |

6. Define boundary conditions |
[Boundary] tab |

7. Enter the static loads |
[Load] Tab > [Type : Static Loads] > [Static Loads] group > [Self Weight] [Load] Tab > [Type : Static Loads] > [Pressure Loads] group > [Assigh Floor Loads] > [Assigh Floor Load] |

8. Enter masses |
[Project] tab > [Settings] group > [Structure Type] [Load] Tab > [Type : Static Loads] > [Masses] group > [Masses] |

9. Enter the time history loads 1) Generate time history load for vertical (gravity) loads - Define Time History Load Case 2) Generate time history load for seismic loads - Define Time History Load Case |
[Load] tab > [Type : Dynamic Loads] > [Time History Analysis Data] group > [Load Cases] |

10. Enter Eigenvalue Analysis Control (Ritz Vector) |
[Analysis] tab > [Analysis Control] group > [Eigenvalue] |

11. Perform analysis |
[Analysis] tab > [Perform] group > [Perform Analysis] |

12. Check analysis results - Displacement / Velocity / Acceleration |
[Results] tab > [Type : Time Hisroty Analysis] > [T.H Results] > [Disp/Vel/Accel] |

## Call

From the main menu, select **[Boundary] tab > [Links] group > [General Link] > [General Link Properties]**

## Input

Define General Link Properties dialog box

**Add**

To enter or add new properties of general link elements.

**Modify**

To modify the properties of general link elements already defined.

**Delete**

To delete the properties of general link elements already defined.

Add/Modify General Link Properties dialog box

### Name

Enter the name for which the properties of general link elements will be defined.

### Application Type

Select the type of general link element. The types applied to analysis are largely classified into Element Type and Force Type.

**Element Type** : The Element Type general link element directly reflects the nonlinear behavior of the element by renewing the element stiffness matrix in the process of analysis.

**Force Type** : The Force Type general link element does not renew the element stiffness matrix. And rather, it reflects the nonlinear behavior indirectly by converting the member force calculated on the basis of the nonlinear properties into an external force.

### Property Type

A specific link element is selected for an Application Type. The Element Type general link element provides 3 types; Spring, Linear Dashpot and Spring and Linear Dashpot. The Force Type general link element provides 6 types; Viscoelastic Damper and Hysteretic System used to represent damping devices, Lead Rubber Bearing Isolator and Friction Pendulum System Isolator used to represent base isolators, compression-only Gap element and tension-only Hook element.

Among the Element Type General Link Elements, Spring Type (6 degrees of freedom - Dx, Dy, Dz, Rx, Ry & Rz) can be reflected in Pushover analysis. Also linear and inelastic analyses can be performed if the linear and inelastic hinge properties are assigned to the General Link Element. Inelastic hinge properties can be defined in Model > Property > Inelastic Hinge Property.

### Description

Enter a brief description for the properties.

### Self Weight

Enter the total weight of the nonlinear link element. The entered self-weight is equally divided and distributed to both ends of the element and converted into Static Load or Mass.

### Use Mass

The user may specify additional mass for the general link element.

Self-weight of a General Link should be entered in Total Weight under Self Weight. Entered Total Weight will be applied to the direction assigned from Load>Self Weight for static analysis, and will be converted into nodal masses for dynamic analysis. In addition, check on Use Mass and input Total Mass to use specific mass separately from the nodal masses converted from Total Weight. However, if "Do not Covert" is selected from Model>Structure Type> Conversion of Structure Self-weight into Masses, nodal masses converted from Total Weight and Total Mass will not be reflected in the analysis.

### Linear Properties

Specify whether or not the individual springs of the 6 degrees of freedom of the general link element exist, and enter the corresponding effective stiffness.

Stiffness and Damping are entered for the Element Type, and Effective Stiffness and Effective Damping are entered for the Force Type general link element.

The stiffness or effective stiffness of a general link element is used for linear static and dynamic analyses. If modal superposition and direct integration methods are used in a linear time history analysis, the effective damping applies only when "Group Damping" is selected for the structure. The Element Type general link element in a nonlinear time history analysis reflects the initial element stiffness based on the entered stiffness.

And if it relates to inelastic hinge properties, the stiffness is renewed in the analysis.

The Force Type general link element, on the other hand, retains the element stiffness based on the effective stiffness. Even if nonlinear properties are defined, the stiffness matrix remains unchanged. Especially, the effective stiffness in a boundary nonlinear time history analysis using the Force Type general link element represents imaginary stiffness to avoid rigid action in the algorithm. If the effective stiffness value is very large in nonlinear analysis, non-convergence may occur in the process of repetitive analyses, and as such an appropriate value should be entered. It is common practice to specify the initial stiffness of damping and isolator devices.

**DOF** : Check in the box to specify whether or not the springs of the 6 deformation degrees of freedom exist.

**Dx, Dy, Dz** : Translational deformation degrees of freedom in the x, y & z directions of the Element Coordinate System

**Rx, Ry, Rz** : Rotational deformation degrees of freedom about the x, y & z axes of the Element Coordinate System

**Coupled** : Enter 6x6 coupled matrix for linear stiffness and damping.

### Nonlinear Spring Properties

Check in the box to specify nonlinear spring properties for the 6 springs of the nonlinear link element by entering the parameters defining the nonlinear properties.

At this point, those springs that can be defined with nonlinear properties are limited to the degrees of freedom, which already have Linear Spring Properties. That is, the limitation applies to the degrees of freedom for which the DOF check boxes of Linear Spring Property are already checked in.

**DOF** : Check in the box to specify whether or not the nonlinear properties of the corresponding degrees of freedom exist.

**Nonlinear Properties** : Checking in the box prompts the dialog box. Enter the parameters defining the properties of the corresponding nonlinear springs.

### Shear Spring Location

Check in the box to specify the locations of the shear springs.

The locations are defined by the ratios of relative distances from the starting node N1 to the total length. Dy and Dz represent the shear springs in the ECS y and z - axes respectively.

If the locations of the shear springs are specified, the end moments differ due to the shear forces (Difference in moments = shear force x member length). Conversely, if the locations of the shear springs are unspecified, the end moments are always equal without being affected by the shear forces.

**Entry of parameters pertaining to nonlinear properties of individual springs**

Enter the parameters defining the nonlinear properties of individual springs for 6 types of nonlinear link elements.

**Viscoelastic Damper**

**Viscoelastic Damper**

The Viscoelastic Damper consists of linear springs and (non)linear viscous dampers connected in parallel for each of the six degrees of freedom, along with springs connecting them to the nodes. In Civil2006, three types of Viscoelastic Damper models are provided:

**1. Damper Type= Maxwell Model**

The Maxwell Model, depicted in the figure below, is a model where linear springs and viscous dampers are connected in series. It is used for the analysis of Fluid Viscoelastic Devices.

The force-deformation relationship of the Maxwell Model is expressed as follows:

**Damping (C _{d})** : Damping coefficient of viscoelastic damper

**Reference Velocity (V _{0})** : Value to make velocity term dimensionless

In general, 1.0 will be entered, but it depends on the change in the length units.

**Damping Exponent (s)** : Exponent defining the nonlinear viscosity damping property of the viscoelastic damper (Viscosity damping force acts in the opposite direction to the deformation rate and is proportional to the absolute value of the deformation rate to the power of s).

Viscosity damper can be modeled as either a linear viscosity damper ( s=1), which is proportional to the deformation rate, or a nonlinear viscosity damper (0.0<s<1.0), which is proportional to the deformation rate to the power of s. In general, Damping Exponent is 0.35~1.00.

**Bracing Stiffness (k _{b})** : Stiffness of the connection member (Selecting Rigid Bracing to ignore the stiffness effect of the connection member or inputting a user-defined value)

**2. Damper Type= Kelvin(Voigt) Model**

Kelvin Model consists of a linear spring and a viscosity damper connected in parallel, as shown in the figure below, and is used for Solid Viscoelastic Device analysis.

Force-displacement relationship of Kelvin Model is given as below. Since the right side is all known terms, the force acting in viscoelastic damper can be obtained from the equation.

**Damper Stiffness (k _{d})** : Stiffness of viscoelastic damper

**Damping (C _{d})** : Damping coefficient of viscoelastic damper

**Reference Velocity (V _{0})** : Value to make velocity term dimensionless

In general, 1.0 will be entered, but it depends on the change in the length units.

**Damping Exponent (s)** : Exponent defining the nonlinear viscosity damping property of the viscoelastic damper (Viscosity damping force acts in the opposite direction to the deformation rate and is proportional to the absolute value of the deformation rate to the power of s).

Viscosity damper can be modeled as either a linear viscosity damper (s=1.0), which is proportional to the deformation rate,or a nonlinear viscosity damper(0.0<s<1.0)which is proportional to the deformation rate to the power of s. In general, Damping Exponent is 0.35~1.00.

**3. Damper Type= Damper Brace Assembly Model**

Damper Brace Assembly Model is a Kelvin Model connected by a spring, as shown in the figure below, and is used for analyzing the bracing as a vibration control device.

Force-displacement relationship of Damper Brace Assembly Model is given as below. Since the right side is all known terms, the force acting in viscoelastic damper can be obtained from the equation.

**Damper Stiffness (k _{d})** : Stiffness of viscoelastic damper

**Damping (C _{d})** : Damping coefficient of viscoelastic damper

**Reference Velocity (V _{0})** : Value to make velocity term dimensionless

In general, 1.0 will be entered, but it depends on the change in the length units.

**Damping Exponent (s)** : Exponent defining the nonlinear viscosity damping property of the viscoelastic damper (Viscosity damping force acts in the opposite direction to the deformation rate and is proportional to the absolute value of the deformation rate to the power of s).

Viscosity damper can be modeled as either a linear viscosity damper (s=1.0), which is proportional to the deformation rate, or a nonlinear viscosity damper (0.0<s<1.0), which is proportional to the deformation rate to the power of s. In general, Damping Exponent is 0.35~1.00.

**Bracing Stiffness (k _{b})** : Stiffness of connecting member (specify the value)

**Gap**

**Gap**

Gap springs exhibit stiffness when the relative displacement of N2 point with respect to N1 point, in each degree of freedom, is a negative value greater than the initial gap within the spring. Additionally, an additional parallel linear viscous damping coefficient can be input for the Gap spring.

**Stiffness (k)** : Stiffness of the Gap spring

**Open (o)** : Initial gap within the Gap spring

Gap Type Nonlinear Spring dialog box

**Hook**

**Hook**

For the Hook spring, stiffness is manifested when the relative displacement of N2 point with respect to N1 point, in each degree of freedom, is a positive value greater than the initial gap within the spring. Additionally, an additional parallel linear viscous damping coefficient can be input for the Hook spring.

**Stiffness (k)** : Stiffness of hook spring

**Open (o)** : Initial slippage distance within the hook spring

Hook Type Nonlinear Spring dialog box

**Hysteretic System**

**Hysteretic System**

Hysteretic system consists of 6 independent springs having the properties of Uniaxial Plasticity. In addition, a linear viscosity damping coefficient can be entered in parallel with each Hysteretic System spring.

**Stiffness (k)** : Initial elastic spring stiffness before yielding

**Yield Strength (F _{y})** : Yield strength of spring

**Post Yield Stiffness Ratio (r)** : Ratio of post-yield stiffness to elastic stiffness prior to yielding

**Yielding Exponent (s)** : Parameter determining the shape of Force-Deformation curve near the yield strength transition region (Larger values lead close to the Bi-linear shape.)

**Hysteretic Loop Parameter (α)** : Parameter determining the shape of hysteretic curve

**Hysteretic Loop Parameter (β)** : Parameter determining the shape of hysteretic curve

Hysteretic System Type Nonlinear Spring dialog box

**Lead Rubber Bearing Isolator**

**Lead Rubber Bearing Isolator**

Lead Rubber Bearing Isolator retains the properties of coupled Biaxial Plasticity for the 2 shear deformations and the properties of independent linear elastic springs for the remaining 4 deformations. In addition, a linear viscosity damping coefficient can be entered in parallel with the spring of each degree of freedom.

**Shear deformation springs (Dy, Dz)**

**Stiffness (k)** : Initial elastic spring stiffness before yielding

**Yield Strength (F _{y})** : Yield strength of spring

**Post Yield Stiffness Ratio (r)** : Ratio of post-yield stiffness to elastic stiffness prior to yielding

**Hysteretic Loop Parameter (α)** : Parameter determining the shape of hysteretic curve

**Hysteretic Loop Parameter (β)** : Parameter determining the shape of hysteretic curve

Shear Spring in Lead Rubber Bearing Isolator dialog box

**Axial deformation and 3 rotational deformation springs (Dx, Rx, Ry, Rz) **

**Stiffness (k)** : Stiffness of the spring

Axial or Rotational Spring in Lead Rubber Bearing Isolator dialog box

**Friction pendulum System Isolator**

**Friction pendulum System Isolator**

Friction Pendulum System Isolator retains the properties of coupled Biaxial Plasticity for the 2 shear deformations, the nonlinear property of the Gap behavior for the axial deformation and the properties of independent linear elastic springs for the remaining 3 rotational deformations. The Force-Deformation relationship of the axial spring of the friction pendulum system type isolator is identical to that of Gap with the initial gap of 0. In addition, a linear viscosity damping coefficient can be entered in parallel with the spring of each degree of freedom.

**Axial deformation spring (Dx)**

**Stiffness (k)** : Stiffness of spring

Gap Type Axial Spring in Friction Pendulum System Isolator dialog box

**Shear deformation springs (Dy, Dz)**

**Stiffness (k)** : Initial shear stiffness prior to sliding

**Friction Coefficient, Slow (μs)** : Friction coefficient for slow deformation velocity

**Friction Coefficient, Fast (μf)** : Friction coefficient for fast deformation velocity

**Rate Parameter (r)** : Rate of the change of friction coefficient with respect to the deformation velocity

**Radius of Sliding Surface (R)** : Radius of the sliding surface curvature

**Hysteretic Loop Parameter (α)** : Parameter determining the shape of hysteretic curve of shear spring

**Hysteretic Loop Parameter (β)** : Parameter determining the shape of hysteretic curve of shear spring

Shear Spring in Friction Pendulum System Isolator dialog box

**Rotational deformation springs (Rx, Ry, Rz)**

**Stiffness (k)** : Stiffness of spring

Rotational Spring in Friction Pendulum System Isolator dialog box

**Triple Friction Pendulum System Isolator**

**Triple Friction Pendulum System Isolator**

The Triple Friction Pendulum Isolator (TFPI) exhibits multiple changes in stiffness and strength with increasing amplitude of displacement. It is known that the TFPI offers better seismic performance, lower bearing costs, and lower construction costs as compared to conventional seismic isolation technology. The properties of each of the bearing’s three pendulums are chosen to become sequentially active at different earthquake strengths. As the ground motions become stronger, the bearing displacements increase. At greater displacements, the effective pendulum length and effective damping increase, resulting in lower seismic forces and bearing displacements. TFPI is symmetric in the local xy- plane. Only input of Dy properties component is activated. Dz properties will be the same as Dy properties.

The parameter defining the axial deformation spring is as follows:

**Stiffness (k)** : Stiffness of spring

The parameters defining the shear deformation springs are as follows:

**Stiffness (k)** : Initial shear stiffness prior to sliding

Frictional Coefficient, Slow (μs): Friction coefficient for slow deformation velocity

Frictional Coefficient, Fast (μs): Friction coefficient for fast deformation velocity

**Required Condition** :

μ (Outer Top) > μ (Outer Bottom) > μ (Inner Bottom) = μ (Inner Top)

**Rate Parameter (r)** : Rate of the change of friction coefficient with respect to the deformation velocity

**Radius of Sliding Surface (R)** : Radius of the sliding surface curvature

Stop Distance: Parameter determining the shape of hysteretic curve of shear spring

**Required Condition** :

d (Inner Bottom) > [μ (Outer Bottom) - μ (Inner Bottom)] x R (Inner Bottom)

d (Inner Top) > [μ (Outer Top) – μ (Inner Top)] x R (Inner Top)

The parameters defining the 3 rotational deformation springs are as follows:

**Stiffness (k)** : Stiffness of spring