C6. Connections - links – assembly

C.6.1 Releasing the bars/springs/degrees of freedom

In all models, the default connection between two beam elements is perfectly fixed. However, it is necessary to be able to release degrees of freedom on some connection nodes between elements (beam-column, sliding plate). Each software have different functionalities to do so.

It is important to rely on the software's manual and to check, with simple load cases and with static or modal deformations, that the behavior of the connection coincides with what is expected.

Care must be taken into maintaining the stability at each node such that not all the bars arriving at a node are released in rotation or displacement.

C.6.2 Mesh continuity

Sometimes the number of elements on either side of the connection line (or surface) is not the same. Thus, there is a risk that only the common nodes (in green) are considered a connection. (figure below).

Bad connection between finite elements of the same type and DOF

More commonly, a transition zone can be created using elements containing the same DOF per node with suitable geometries (figure below).

The meshing of the transition zone

C.6.3 Connecting different types of elements

Using elements of different nature in the same model introduces complexity and one should always question the necessity of mixing the elements. This complexity arises at the connection between elements of different natures. They can be beam/shell, shell/solid, or beam/solid connections.

Particular attention will be paid to the possible connection of different types of structural elements: element with 6 degrees of freedom (UX, UY, UZ, ROTX, ROTY, ROTZ) / element with 3 degrees of freedom (UX, UY, UZ). This type of connection can cause the appearance of instabilities or unexpected joints.

Several software packages compensate for these difficulties with specific elements capable of handling these links and degrees of freedom problems. This should be checked and the relevance of the local behavior of the model should be verified.

C.6.4 Connection between a bar and a plate

There are three cases:

either the beam and plate elements are in the same plane,

or the beam is a rib of the plate,

or the beam and the plate are perpendicular.

C.6.4.1 Coplanar Beam and Plate

For a bar element connected to two plate elements, the transfer of moments should be ensured by means of additional elements, or by the introduction of stress equations linking the degrees of freedom.

In the illustrations below, in case 1, there may not be an accurate transfer of moments and nothing forces the bar to remain perpendicular to the plate (intrinsically the shell nodes cannot block axis moments perpendicular to the plane of the FEs). Case 2 consists of imposing an equation that links the displacements of the plate edge with the bar. This is a reliable method, but it is not proposed by all software. Cases 3 and 4 consist of adding rigid bars to reproduce the displacement dependence between nodes. Special attention must be paid to the definition of the rigidity of these bars, which can be a source of instability in the software.

Connection of elements of different nature - Moment transfer

C.6.4.2 Connection between a bar and an out-of-plane plate

The case where the beam acts as a stiffener associated with the slab as in the case of ribbed slabs is discussed in detail in C.8 Composite sections (beam/slab).

C.6.4.3 Connection of a bar perpendicular to a plate

The last case is that of the column-plate connection. The big difficulty, in addition to the transmission of bending from the bar to the plate, is the transmission of torsion from the bar to the plate. By default, the plate does not have a rotational DOF around the axis perpendicular to its plane, so it cannot take up the torsional moment brought by the column. Therefore, it is necessary to find the right kinematic connection conditions. To ensure that the bending and torsional forces of the bar are taken up by the plate, it is necessary to have rigid connections at the junction (in red on the diagrams below).

Modeling of the bar-plate connection (deck supported by a column, seen from below)

Example of the column (1D element) embedded in a plate and subjected to torsion.

Illustration of the consideration of the different number of degrees of freedom between elements of different nature.

The model simulates a 20 cm thick concrete plate on which a concrete column of 1 m diameter is "embedded", simply by connecting the lower end of the column to a node of the plate:

The horizontal translations are fixed at the corners of the plate to block this torsion. The torque introduced is 10 MN.m.

The results are as follows:

Unfortunately, the numerical computations converge, but ... several aspects of the results can and should attract the attention of the modeler:

the value of the rotation, both at the head and at the foot of the posts (54.2 radians!)

the presence of Mz moments in the corners while the supports are released in Rz

the sum of the reactions is not zero

finally, the value of the reactions Fx and Fy seems low (order of magnitude to be found: 10000 kN.m/7 m (lever arm)/4 points = 360 kN).

It is enough to create an embedment using (fictitious) bars at the foot of the column, in the slab ...

... to obtain accurate overall results. (The local efforts at the foot of the column are of course disturbed by these fictive bars).

C.6.5 Plate/solid and beam/solid connections

In the case of plate-solid connections, it is necessary to establish a connection to recover the embedding moment. As in C.6.4, you can either create a connecting plate on the surface of the solid (on one or both sides) or extend the shell inside the solid.

Modeling the shell-solid connection

The same reasoning is applied in the case of a Beam-Solid connection.

C.6.6 Stiffness Values / Stiffness Deviations / "Rigid elements".

Many software offer "rigid beam" or "rigid link" elements.

This type of element is sometimes a kinematic dependency (mathematical relation) between two elements and sometimes a fictitious bar whose stiffness is very high.

However, the presence in the global matrix of the system of elements with large differences in stiffness can cause problems of convergence. See the final example on matrix calculation presented in paragraph A.1.

These instabilities or numerical errors do not necessarily appear with an error message.

In most cases, it is advisable to use elements whose stiffness is defined by the user and to test the influence of this stiffness on the global behavior.

C.6.7 Linking different types of elements: Structural Zoom - Examples

Insertion of plate finite elements in a global model

To understand the specific behavior of a particular area of a structure modeled using 1D elements, and to avoid having to manage a model that is too heavy, it may be necessary to insert plate elements instead of the initial bar elements. The connection between these two parts of different nature is made by means of links or rigid bars in "cobwebs".

Examples of connections of a model composed of beam elements with parts modeled in plates:

Structural zoom

One may also wish to model only a part of the structure with plate elements and impose at the boundaries of this part the displacements or the efforts at the nodes resulting from the global beam model (principle of structural zoom). These displacements or efforts are then transmitted to the plate elements by rigid links made of beam-type elements. These areas of connections between beams and plates must be modeled far enough from the area to be studied to ensure that the efforts introduced by the rigid connections are correctly diffused to the studied zone.

For example, as part of the analysis of a connection zone between two RWB (Reconstituted Welded Beams), the zone was modeled in plate and shell elements (see figure below). At the ends of the RWB modeled over a certain length, torsors are introduced through rigid connections, with the structure being supported at the level of the lower plate. The view below shows that these rigid links are located sufficiently far (about 2 m) from the area to be studied. It should be noted that the plate is sufficiently rigid so that no rigid links need to be created.

The following example represents the structure of the girder of the extremity of a relatively wide bridge. The two support reactions are introduced (on the right) under this girder, which is considered perfectly embedded in the deck (on the left). They come from a global beam/plate model. The self-weight and dead loads on the girder itself are modeled, if necessary. This approach simplifies data entry, as it requires only a few support reactions rather than the complex torsors to be obtained at the interface with the deck due to the nature of the global model.

The global model with simplified modeling of a girder in an extremity.

A detailed local model of the abutment box