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000787
Dipl.-Ing. (FH) Gerhard Rehm
2021-03-29

Considering Elastic Slip Modulus of Timber Connection

For a timber connection as shown in Figure 01, you can take into account the torsional spring rigidity (spring stiffness for rotation) of the connections. You can determine it by means of the slip modulus of the fastener and the polar moment of inertia of the connection.

Flexibility of Timber Connection
Flexibility of Timber Connection

Polar Moment of Inertia

The connection's polar moment of inertia shown in Figure 01 results in:

Ip = ∑xi2i=1n + ∑yi2i=1n

Ip

Polares Trägheitsmoment ohne Anteil der Verbindungsmittelflächen

xi

Abstand vom Schwerpunkt der Verbindungsmittelgruppe zum Verbindungsmittel in x-Richtung

yi

Abstand vom Schwerpunkt der Verbindungsmittelgruppe zum Verbindungsmittel in y-Richtung
Polar Moment of Inertia

Ip = 752 + 752 + 2252 +2252 = 112,500 mm2

Modulus of Displacement Determination for the Serviceability Limit State

The modulus of displacement for the serviceability limit state can be calculated according to [1], Table 7.1. For bolts with a diameter of 20 mm in C24 softwood, the modulus per shear plane is calculated as follows:

Kser = ρm1.5 · d23

Kser

Verschiebungsmodul pro Scherfuge

ρm

Mittelwert der Rohdichte in kg/m³

d

Durchmesser des Verbindungsmittel
Modulus of Displacement per Shear Plane

Kser = 4201.5 ⋅ 20/23 = 7,485 N/mm = 7,485 kN/m

This results in two shear planes for an internal steel plate. In addition, the modulus of displacement should be multiplied by a factor of 2.0 for steel plate-timber connections according to [1], Chapter 7.1 (3). You can determine the modulus of displacement for the bolt as follows:

Kser= 2 ⋅ 2 ⋅ 7,485 kN/m = 29,940 kN/m

Modulus of Displacement Determination for the Ultimate Limit State

According to [1], the modulus of displacement of a connection in the ultimate limit state, Ku, has to be assumed as follows:

Ku = 23 · Kser

Ku

Anfangsverschiebungsmodul 

Kser

Verschiebungsmodul eines Verbindungsmittels
Initial Modulus of Displacement

Ku = 2/3 ⋅ 29,940 kN/m = 19,960 kN/m

[2] and [3] require considering the design value of the modulus of displacement of a connection.

Kd = KuγM

Kd

Bemessungswert des Verschiebungsmoduls

Ku

Anfangsverschiebungsmodul 

γM

Teilsicherheitsbeiwert für Verbindungen gemäß [1] Tabelle 2.3
Design Value of Modulus of Displacement

Kd = 19,960 kN/m / 1.3 = 15,354 kN/m

Torsional Spring Stiffness Determination

For the ultimate limit state design, you have to use the design value of the slip modulus for calculation and the mean value for the serviceability limit state design; thereby you obtain two torsional spring rigidities.

Cφ,SLS = Kser · Ip

Cφ,SLS

Drehfedersteifigkeit für den Grenzzustand der Gebrauchstauglichkeit

Kser

Verschiebungsmodul eines Verbindungsmittels

Ip

Polares Trägheitsmoment ohne Anteil der Verbindungsmittelflächen
Torsional Spring Stiffness for Serviceability Limit State

Cφ,SLS = 29,940 N/mm ⋅ 112,500 mm2 = 3,368 kNm/rad

Cφ,ULS = Kd · Ip

Cφ,ULS

Drehfedersteifigkeit für den Grenzzustand der Tragfähigkeit

Kd

Bemessungswert des Verschiebungsmoduls

Ip

Polares Trägheitsmoment ohne Anteil der Verbindungsmittelflächen
Rotational Spring Stiffness for Ultimate Limit State

Cφ,ULS= 15,354 N/mm ⋅ 112,500 mm2= 1,727 kNm/rad

To take both rigidities into account, activate the "Modify Stiffness" sub-tab (select the corresponding check box in the Calculation Parameters sub-tab of the Load Combinations tab in the Edit Load Combinations and Calculations dialog box). As in this example, this allows you to multiply the torsional spring rigidity for all SLS combinations by Cφ,ULS / Cφ,SLS. The value of Cφ,SLS is entered in the support or hinge conditions. Thus, you can calculate with a torsional spring rigidity of 1.727 kNm/rad in all ULS combinations and with 3.368 kNm/rad in all SLS combinations. This approach is also shown in the video.

In this example, the elastic foundation rotation is considered to be infinite and is not taken into account.

Torsional Spring Stiffness Determination Utilizing RF-/JOINTS Timber - Steel to the Timber Add-on Module

When calculating the connection with RF-/JOINTS Timber - Steel to Timber, the results of the torsional spring stiffnesses are also displayed (see Figure 02). In RSTAB, you have to transfer them manually to the support or hinge conditions. In RFEM, this can be done automatically. The connections are automatically created in RFEM and the stiffness is adopted accordingly. The video shows the procedure.

Rotational Spring Stiffness in RF-/JOINTS Timber - Steel to Timber
Rotational Spring Stiffness in RF-/JOINTS Timber - Steel to Timber

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KB 000787 | Considering Elastic Slip Modulus of Timber Connection
Author

Mr. Rehm is responsible for developing products for timber structures, and he provides technical support for customers.

Links
References
  1. Austrian Standards. (2015). Eurocode 5: Design of Timber Structures – Part 1-1: General – Common Rules and Rules for Buildings; DIN EN 1995-1-1:2010-12. Berlin: Beuth Verlag GmbH.
  2. DIN. (2013). National Annex – Eurocode 5: Design of Timber Structures – Part 1-1: General – Common Rules and Rules for Buildings, DIN EN 1995-1-1/NA:2013-08. Berlin: Beuth Verlag GmbH.
  3. Austrian Standards. (2015). Eurocode 5: Design of Timber Structures – Part 1-1: General – Common Rules and Rules for Buildings. Consolidated Version with national specifications, national comments and national supplements for the implementation of OENORM EN 1995-1-1; ÖNORM B 1995-1-1:2015-06-15.
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Frequently Asked Questions (FAQ)
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