bridge insight the complete guide to link elements

VOL. 01

LINK ELEMENTSTHE COMPLETE GUIDE TO

BRIDGE INSIGHT

midas Bridge

The CompleteGuide toLink Elements

01. What are Link Elements?

CONTENTS

2

02. Differences Between Link Elements

4

03. Link Application Examples

6

04. Common Mistakes inModeling Link Elements

10

The Complete Guide to Link Elements BRIDGE INSIGHT The Complete Guide to Link Elements BRIDGE INSIGHT

What are LinkElements?

-Link elements are a means to define rules of force transfer between 2 distinct nodes in a finite element model without modeling the structural member (like beams, plates, etc.). These links are generally used when specific details about the connection stiffness or behavior are known, but the links themselves aren’t the main focus of the analysis. A few of the links available in midas Civil are:

01

01-1.Elastic Link

An elastic link connects nodes for which the stiffness is defined by the user for all 6 Degrees of

Freedom (DOF) for force transfer. The x-axis of the elastic link is along the direction of the two

connecting nodes. Five different types of elastic links are available in midas Civil, as listed

below.

01-1-1. Elastic link - GeneralThe engineer must provide a finite number as stiffness for force/moment transfer in all six DOF

between two nodes for such links. An elastic link - general can be used when defining a bridge

bearing for linear analysis.

01-1-2. Elastic link - RigidAs the name suggests, this connection is quite rigid, and the engineer doesn’t need to provide

the individual stiffness in all directions as required for an elastic link of type general. The

software automatically assigns a stiffness of about 105 x stiffness of the stiffest member in the

model for DOF of this link, which essentially makes the link rigid for all practical purposes. This

stiffness is capped at 2.1 x 1012 kN/m for translation and 3.5 x 1011 kN-m/rad in rotation to avoid

any instability in the structural matrix. Such link type can be used to transfer force rigidly

between members to connect the pier cap and pier element.

01-1-3. Elastic link - Compression OnlyThis type of link is used to connect two nodes in situations when only the compressive force is

to be transferred between the nodes. The engineer provides the stiffness of the link to be

considered when transferring this compressive force. The direction of force transfer is always

from node no. 2 to node no. 1. Ideally, this type of link is used when uplift is expected in the

structure due to acting loads, like in the case of incrementally launched bridges.

Figure 1. Elastic link

01-2.Rigid Links

01-3.General Links

A rigid link is a connection between two nodes, where one

node, the master node, dictates how the other node, i.e., the

slave node, would behave. The two nodes are connected to

act as a rigid body. The master node shows which degrees of

freedom are restrained. The six 1's at the master node location

represent a degree of freedom. From the first to the last digit,

these represent DX, DY, DZ, RX, RY & RZ, respectively. The

number "1" implies that a particular DOF is restrained, and "0"

implies that a particular DOF is free. The "111111" indicate that

all degrees of freedom are restrained. Such links are used in

situations where the structure is theoretically expected to

behave as a rigid body, like connecting the bottom of the pier

with the top of the piles.

A general link is a non-linear connection between the two nodes used in boundary non-linear

analysis. This non-linearity is only considered in dynamic analysis, while these behave as linear

for static analysis. The engineer must define the linear as well as non-linear behavior. Linear

stiffness is a finite stiffness value as provided by the engineer for all DOF.

The non-linear definition can be done for multiple behaviors like viscoelastic dampers, lead

rubber isolator, etc., based on the actual expected non-linear behavior. The stiffness definition

for linear and non-linear behavior are independent of one another.

01-1-4. Elastic link - Tension OnlyThis link connects two nodes in situations when only tensile force is to be transferred between

the nodes. The stiffness of the link considered when transferring this tensile force is provided

by the engineer. The direction of force transfer is always from node no. 1 to node no. 2.

Ideally, such a link is used when a tensile brace is used to resist lateral forces.

01-1-5. Elastic link - Multi-linearThis type of link is used when the stiffness of the link itself is subject to change depending on

the acting loads in a linear analysis. To define this behavior, the engineer must provide the

force-deformation function and the DOF for which this function is valid. Such links can be

used to define the soil behavior under lateral loading.

Figure 2. Rigid link

2 3


Differences BetweenLink Elements

-

02

02-1.Rigid Link vs.Elastic Link- Rigid

For all practical purposes, both these links could be the same. However, theoretically, these are

very different, and each has its pros & cons.

02-1-1.Elastic link - rigid establishes a connection between two nodes simultaneously, while a rigid link

can connect one master node with multiple slave nodes. Hence, it is much easier to use rigid

links when a rigid behavior is defined in multiple nodes at once. Rigid type elastic links can

also be used, but it could be quite inconvenient depending on the number of nodes to be

connected.

02-1-2.In the case of a rigid link, the DOF of the master node governs the behavior of the slave node.

When a support is provided to a node, the DOF is constrained by the support condition.

Therefore, if a support condition is provided at the slave node location, there would be two

governing DOF conditions for the same node, leading to errors. In such a situation, where a

support condition is provided at the slave node location, only an elastic link of general type

should be used.

02-1-3.Forces in an elastic link are obtained in tabular format. However, the force output for rigid links

is not available.

Figure 3. Proper way to model a connection from girder to the support location using links

Figure 4. Behaviour of Elastic Link (Type: General) in different types of analysis Figure 5. Behaviour of General Link in different types of analysis

02-2.General Link vs.Elastic Link- Rigid

02-2-1.Elastic link - general will always have linear behavior, no matter the analysis type. However, a

general link will have non-linear behavior in non-linear time history analysis and linear in all

other analysis types.

02-3.General Link vs.Elastic Link- Multi-linear

02-3-1.Multi-linear behavior is considered in static analysis in an elastic link of type multi-linear, while

the behavior is linear for a general link.

02-3-2.Superposition of load cases should not be done when using elastic link of type multi-linear

since for each load case, the stiffness is considered from the origin (0,0) of load vs. displace-

ment input. The change in actual stiffness of the link due to the superposition of loads will not

be considered. However, the load superposition could be done in the case of a general link

since the behavior is linear.

4 5

Differences BetweenLink Elements

-

02

02-1.Rigid Link vs.Elastic Link- Rigid

For all practical purposes, both these links could be the same. However, theoretically, these are

very different, and each has its pros & cons.

02-1-1.Elastic link - rigid establishes a connection between two nodes simultaneously, while a rigid link

can connect one master node with multiple slave nodes. Hence, it is much easier to use rigid

links when a rigid behavior is defined in multiple nodes at once. Rigid type elastic links can

also be used, but it could be quite inconvenient depending on the number of nodes to be

connected.

02-1-2.In the case of a rigid link, the DOF of the master node governs the behavior of the slave node.

When a support is provided to a node, the DOF is constrained by the support condition.

Therefore, if a support condition is provided at the slave node location, there would be two

governing DOF conditions for the same node, leading to errors. In such a situation, where a

support condition is provided at the slave node location, only an elastic link of general type

should be used.

02-1-3.Forces in an elastic link are obtained in tabular format. However, the force output for rigid links

is not available.

4 5

Figure 6. Behaviour of Elastic Link (Type: Multi-linear) in different types of analysis


Case 2.

Connecting pier to foundation plate elements

Some engineers prefer to model the pile cap as plate elements to consider the flexibility in pile

cap and thus obtain realistic forces. It is necessary to model the pile cap as thick plates with a

drilling degree of freedom in such cases. This is necessary because there can be asymmetric

longitudinal forces acting on the pier cap, which may cause rotation in the pier. However, many

engineers tend to miss this rule. Let us consider an example for comparison as below. The pile

cap has been modeled as thick plate elements without a drilling degree of freedom.

From the examples, it can be noted that vertical reactions from all the methods are the same.

However, the horizontal reactions are quite different. Practically, we do not expect a horizontal

reaction in the transverse direction at these locations. These are 0 in methods 1 & 2. Again,

these are quite negligible for method 3. However, these are quite huge for method 4. It can

also be noted that the longitudinal reaction is quite low in the case of method 4. It is always

recommended to model the bearing elastic links and provide the fixed boundary condition

below the bearing location if the entire substructure isn't modeled. Method 1 is recommended

for just modeling the substructure to reduce time and obtain practical results.

Link ApplicationExamples

-

03

Case 1.

Box girder superstructure up to the bottom of bearing

To model such a structure, we need to use a combination of rigid links & elastic links. This

process can be done in many ways. Four different methods are shown below, and the results

are compared.

6 7

Figure 7. Methods for modeling connection at diaphragm location for a box girder bridge Figure 8. Pier and pile cap connection with the applied load (kN)

Fz = 1992.6 kN

Fx = 1286.3 kN

Fy = 0.0 kN

Fz = 1992.6 kN

Fx = 1285.9 kN

Fy = 0.0 kN

Fz = 1992.6 kN

Fx = 1285.0 kN

Fy = 5.8 kN

Fz = 1992.6 kN

Fx = 32.8 kN

Fy = 1758.1 kN

(a) Method 1: Inclined rigid link + elastic link – general for bearings

(b) Method 2: Horizontal rigid link + vertical elastic link –rigid + elastic link – general for bearings

(c) Method 3: Inclined elastic link – rigid + elastic link – general for bearings

(d) Method 4: Inclined elastic link – rigid only (No elastic links for bearings)

Case 3.

Modeling a pylon with a continuous cable for an extradosed bridge

The cable is only anchored on deck at both ends and passes through the pylon. This method is

performed to reduce the bending moment in the pylon and mainly introduce axial forces in it.

The global analysis of such a model is important for force transfer in the structure and not the

exact forces in the saddle itself. For that, a separate Finite Element (FE) modeling is

performed. To replicate the force transfer of such saddle in the structure, both elastic and rigid

links need to be used. For the rigid links, DY and DZ are restrained. Elastic links of general type

are modeled with 108kN/m stiffness in DX direction.


The only difference between the two is that in one case, the nodes within the pier's perimeter

have been connected to the pier node via a rigid link, as indicated by the red circle. This

method is applied because the connection between the pier and pier cap is essentially a joint

supposed to behave as a rigid body.

As it could be noted, the deformations are extremely high for the structure in which the pier

isn’t connected to the pile cap elements via the rigid link. This is mainly because the pier

elements are undergoing rotational deformations as the pile cap is not effectively restraining it.

This is incorrect behaviour.

8 9

Figure 9. Total deformation under applied loading

Figure 10. Asymmetrically loaded extradosed bridge with continuous cable anchored only in deck

(a) Geometry of the structure

(d) Asymmetric loading and symmetric but symmetric axial forces in the cable on either side of pylon

(b) Elastic links directly connecting cable nodes,by passing the pylon node

(c) Rigid link with pylon node as master nodeand cable nodes as slave nodes

Most common mistakes happen when construction stages are introduced in the model.

04-1.

Activating the connected nodes without activating the link

Common Mistakes inModeling Link Elements

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04

10


11

Figure 11. Vertical displacement in pylon due to self-weight

Activating links without activating the required nodes

To activate any boundary condition (link), it is necessary to activate the node(s) to which that

boundary condition is assigned. If any of the nodes is not activated at the time of relevant

boundary group activation in the construction stage, then the boundary will not be assigned.

04-2.

Incorrect modeling with rigid link links

In such a situation, the DOF at the slave nodes are released automatically, and the structure

usually ends up being unstable. It is advised to use Elastic Link (Type: Rigid) for such

situations.

04-3.

Figure 12. Necessary nodes to be activated before activating the link in construction stage

Figure 13. Incorrect connection modelling with 2 rigid links

(a) Structural activation withoutnode connectivity

(b) Incorrect deformed shape and forcedistribution in subsequent stages

(c) Correct deformation after activatingrigid links connecting the free nodes with pylon

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bridge insight the complete guide to link elements

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