Post-processing of connection loads

VII.4.4.2 Post-processing of connection loads

For the post-processing of connection loads, the first step of the calculations is always to estimate for each connection the axial force, the shear force, the torsional moment and the bending moment. Afterwards the criterion for the connection is calculated (sliding, gapping, insert, rivet...). More precisely, one calculates the critical connection (node or element) and the associated reserve factor.

VII.4.4.2.1 Calculation of the different components of connection loads

One explains here how the components of loading (axial and shear forces, torsional and bending moments) are first calculated for the different connections before the calculation of reserve factors for a selected criterion.

The parameters used for the calculation of these connection load components are always the first 6 parameters of the connection criterion function:

1.: The name of the load case for which the calculation is done.
2.: The name of a first Group (group1) corresponding generally to a part of the structure to which the connections are connected (sandwich panel, shell, metallic fitting...).
3.: The name of second Group (group2) of finite element entities corresponding generally to the modeling of the connections (For example RBE2 elements, CBAR or CBUSH elements...).
4.: A String corresponding to the type of operations done to build the different components of connection loads. This String determines which Results are first read from Result files, and how they are manipulated afterwards. More information about this parameter is given below.
5.: An integer or String value corresponding to the coordinate system in which the force and moment vectors are to be expressed before extracting the different force and moment components.
6.: A vector of three real values corresponding to the axis of the connection in the coordinate system given by the previous argument. The direction of this vector must be defined in such a way that a positive axial force corresponds to a tension in connection. For example, when internal forces are extracted from Grid Point Forces results, this is achieved by defining the vector pointing from grp2 to grp1 (to the direction of the group containing the elements from which Grid Point Forces are extracted.)

Presently, the available extraction methods for the load components, given by the fourth argument above are the following:

“GPFINT” if loads are obtained using Grid Point Forces, Internal Forces and Moments.
“GPFMPC” if loads are obtained using Grid Point Forces, MPC Forces and Moments.
“GPFSPC” if loads are obtained using Grid Point Forces, SPC Forces and Moments.
“MPCFRC” if loads are obtained from MPC Forces and Moments.
“SPCFRC” if loads are obtained from SPC Forces and Moments.
“BMFRC” is loads are obtained from Beam Forces and Moments. (This may correspond to forces of several elements like CBAR, CBEAM, CBUSH or CFAST.)

When the option “BMFRC” is adopted, the loads are extracted on the “beam-type” elements modeling the connections (CBUSH elements for example). This means that the only the second Group argument (third argument of the function) matters. The first Group argument is not considered. In all other cases, Group operations are done to obtain a list of nodes which is the intersection of the two Group arguments provided. More precisely, the Group “targetGrp” is build as follows:

    If extractionMethod = "BMFRC" Then
        Set targetGrp = grp2
    Else
        Set nodeGrp1 = db.getNodesAssociatedToRbes(grp1)
        Set tmpGrp1 = db.getNodesAssociatedToElements(grp1)
        nodeGrp1.importEntitiesByType "Node", tmpGrp1

        Set nodeGrp2 = db.getNodesAssociatedToRbes(grp2)
        Set tmpGrp2 = db.getNodesAssociatedToElements(grp2)
        nodeGrp2.importEntitiesByType "Node", tmpGrp2

        Set tmpGrp3 = nodeGrp1.opMul(nodeGrp2)
        Set tmpGrp2 = db.getElementsAssociatedToNodes(tmpGrp3)
        Set tmpGrp1 = grp1.opMul(tmpGrp2)
        Set targetGrp = tmpGrp1.opAdd(tmpGrp3)
    End If

Depending on the type of extraction, and on specific aspects of the problem, the correspondence between grp1 and grp2 on one side and the connections or assembled part may differ. For example:

When MPC or SPC forces and moments are post-processed. The choice of grp1 and grp2 is indifferent as loads are extracted on the intersection nodes only.
When one processes Grid Point Forces internal forces and moments, the definition of grp1 and grp2 may matter. Consider the example represented in Figure VII.4.1 in which Part 2 is a sandwich panel modeled with shell elements. Then,
- If one calculates inserts margins of safety, loads should be extracted on elements of sandwich panel at connection nodes because the inserts of sandwich panels are loaded by connections of Groups “ConnectGrp2” and “ConnectGrp3”. This means the grp1 should correspond to Part 2 and grp2 to either “ConnectGrp2” and “ConnectGrp3”.
- On the other hand, if one calculates sliding between Part 1 and Part 2, only the loads transmitted by elements of Group “ConnectGrp2” must be recovered. Then grp1 should correspond to Group “ConnectGrp2” and grp2 to Part2. Of course, this will work only if the connections are modeled with elements (CBUSH, CBAR,...) and not MPCs or rigid body elements (RBEs).
In many cases, grp1 and grp2 can be switched without consequences on the results. Then it is generally less expensive to select grp1 corresponding to the Group containing the connections.
Note however that when grp1 and grp2 are switched, the vector defining axial direction should be reversed too!

Figure VII.4.1: Example of assembly of different layers with a single connection.

All the operations are managed by subroutine “getConnectionLoads” of “ExtractionCriteria” VBA module. This subroutine is called by each of the connection post-processing function. This is why the six parameters (eight values) of these connection post-processing functions are always the same.

VII.4.4.2.2 “getSlidingRF” function

This function calculates reserve factors for the sliding criterion with the following expression:

RF = \frac{C_{f} * P_{min}}{FoS * (C_{f} * \max (F_{axial}, 0) + F_{shear})},

in which $C_{f}$ is the friction coefficient between assembled elements and $P_{min}$ is an estimate of the minimum possible pretension of the bolt. Parameters specific to this function are:

The factor of safety “FoS”. (Parameter 7 of the function.)
The minimum estimated pretension of a connection “Pmin”. (Parameter 8 of the function.)
The friction coefficient “Cf”. (Parameter 9 of the function.)
Two optional parameters containing the name of the GMSH file in which the envelope of inverse reserve factors is saved, and the name of the Result by which it is referred to in the GMSH file.

The function returns an Array of one line and four columns containing:

The ID of the finite element entity to which minimum reserve factor corresponds. This is the ID of an element for “BMFRC” extraction and a node ID otherwise.
The corresponding axial force.
The corresponding shear force.
The minimum reserve factor.

VII.4.4.2.3 “getGappingRF” function

This function calculates reserve factors for the gapping criterion with the following expression:

RF = \frac{P_{min}}{FoS * (\max (F_{axial}, 0) + M_{bending} ∕ R)},

in which $R$ is a parameter that allows to take into account the prying effect related to the bending moment in the connection and $P_{min}$ is an estimate of the minimum possible pretension of the bolt. Parameters specific to this function are:

The factor of safety “FoS”. (Parameter 7 of the function.)
The minimum estimated pretension of a connection “Pmin”. (Parameter 8 of the function.)
The friction coefficient “Radius”. (Parameter 9 of the function.)
Two optional parameters containing the name of the GMSH file in which the envelope of inverse reserve factors is saved, and the name of the Result by which it is referred to in the GMSH file.

The function returns an Array of one line and four columns containing:

The ID of the finite element entity to which minimum reserve factor corresponds. This is the ID of an element for “BMFRC” extraction and a node ID otherwise.
The corresponding axial force.
The corresponding bending moment.
The minimum reserve factor.

VII.4.4.2.4 “getInsertRF” function

This function calculates reserve factors for the insert criterion with the following expression:

RF = \frac{1}{FoS \sqrt{{(\frac{F_{axial}}{PSS})}^{2} + {(\frac{F_{shear}}{QSS})}^{2}}},

In which “PSS” is the axial allowable of the insert and “QSS” is its shear allowable. Parameters specific to this function are:

The factor of safety “FoS”. (Parameter 7 of the function.)
The insert axial allowable “PSS”. (Parameter 8 of the function.)
The insert shear allowable “QSS”. (Parameter 9 of the function.)
Two optional parameters containing the name of the GMSH file in which the envelope of inverse reserve factors is saved, and the name of the Result by which it is referred to in the GMSH file.

The function returns an Array of one line and four columns containing:

The ID of the finite element entity to which minimum reserve factor corresponds. This is the ID of an element for “BMFRC” extraction and a node ID otherwise.
The corresponding axial force.
The corresponding shear force.
The minimum reserve factor.

VII.4.4.2.5 “getShearBearingRF” function

This function calculates reserve factors for the shear-bearing failure mode with the following expression:

RF = \frac{ShrAll}{FoS * F_{shear}},

in which $ShrAll$ is the shear bearing allowable. Parameters specific to this function are:

The factor of safety “FoS”. (Parameter 7 of the function.)
The shear-bearing allowable “ShrAll”. (Parameter 8 of the function.)
Two optional parameters containing the name of the GMSH file in which the envelope of inverse reserve factors is saved, and the name of the Result by which it is referred to in the GMSH file.

The function returns an Array of one line and three columns containing:

The ID of the finite element entity to which minimum reserve factor corresponds. This is the ID of an element for “BMFRC” extraction and a node ID otherwise.
The corresponding shear force.
The minimum reserve factor.

VII.4.4.2.6 “getPullThroughRF” function

This function calculates reserve factors for the pull-through failure mode with the following expression:

RF = \frac{PullAll}{FoS * max (F_{axial}, PullAll * 1 0^{- 9})},

in which $PullAll$ is the pull-through tensile allowable. Parameters specific to this function are:

The factor of safety “FoS”. (Parameter 7 of the function.)
The pull-through allowable “PullAll”. (Parameter 8 of the function.)
Two optional parameters containing the name of the GMSH file in which the envelope of inverse reserve factors is saved, and the name of the Result by which it is referred to in the GMSH file.

The function returns an Array of one line and three columns containing:

The ID of the finite element entity to which minimum reserve factor corresponds. This is the ID of an element for “BMFRC” extraction and a node ID otherwise.
The corresponding axial force.
The minimum reserve factor.

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