Connection rigidity

The consideration of rigidity values of connection details is often questioned in practice. The following contribution should familiarize the support structure designer with rigidity values so that the effects can be better estimated. 

Modelling 
In the verification of support structures, the designer must compare the modelling of the structure with the design and consider connection rigidity if necessary. This can be assessed both with translation and also rotational rigidities. In wood construction, the translation rigidities can be determined using the kser values set out in EN 1995-1-1 [1]. The rotational rigidity of a connection with pin-shaped connectors is determined as follows [1+2]. For system connectors, the product specific rigidity values are found in the respective European technical assessments. For SHERPA connectors, this is the ETA-12/0067 [2] (see Tab. 1).

If you consider a connection between a main and secondary connection, this can be simplified using two rotation springs. These are on the one hand the rotation spring rigidity of the system connector and on the other the system rigidity that results from the rigidity of the support structure (see Fig. 1). For the determination of the overall rigidity of the connection (kφ,ser), the individual rotation springs can be summarized by a serial connection. Thus the connection rigidity (kφ,ser) results as follows: equation [3]. It is evident (see equation 3) that the lower rigidity of both rotation springs is crucial to the overall rigidity and thus for the connection torque.

The system rigidity reflects the rotation capacity of the support structure at the connection point of the system connector. If one is looking at a fork shaped edge support, the system rigidity of the support structure varies along the longitudinal direction of the support. In the area of the fork bearing, the system rigidity is higher than in the middle of the support. The determination of system rigidity at the connection point of a support structure can only be done using a model of the entire structure. The connection torque to be set can be estimated through the modelling of a bilateral, symmetrical torsion spring mounted single span girder using the torsion module (see. Tab. 1) on the flexible fixed supports. The connection torques can be determined as follows depending on the ratio of the rigidities (αEI) for a uniformly distributed load: equation [4].




Verification
Through the torsion module (k2,φ,ser), the torque bearing capacity as well as the transverse bearing capacity are important for the measurement of the system connector. Because these types of connectors were designed to transfer transverse forces, the load of the connection torque to be set is considered by a reduction of the transverse bearing capacity (see equation 5). Borderline eccentricity eborder thus describes the connection eccentricity from which the contact pressure of the top oblique screw on the secondary support is in balance with the horizontal force through the eccentricity torque [3]. If the borderline eccentricity is exceeded, contact is lost between the connector and the timber component and the torque screws are subjected to tension. Figure 3 shows the reduction factor αR2,k of the characteristic load capacity in the direction of insertion (R2,k) for the consideration of the torque strain.

Conclusion
The present article shows that it is expedient to consider the connection rigidity of a connection. In conventional connections, this may be done using the polar inertia torque and the associated slip module following [1]. For system connectors, the rigidity of the elected connection is found in the respective European technical assessments. If one takes the rigidities of the connection into consideration, usually multiple iteration steps are necessary during the measurement. This has the background that the designed connector or the selection of a connector implies rotational rigidity. This is in balance with the connection torque to be set. In order to achieve an economical solution, multiple calculation steps are necessary.


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