# Considering Elastic Slip Modulus of Timber Connection

## Technical Article on the Topic Structural Analysis Using Dlubal Software

### Technical Article

For a timber connection, as shown in Figure, 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.

#### Polar Moment of Inertia

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

Polar moment of inertia

$$Ip = ∑xi2i=1n + ∑yi2i=1n$$

 Ip Polar moment of inertia without component of fastener surfaces xi Distance from the centroid of the fastener group to the fastener in the x-direction yi Distance from the centroid of the fastener group to the fastener in the y-direction

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 softwood C24, this results in per shear plane as follows:

Modulus of Displacement per Shear Plane

$$Kser = ρm1.5 · d23$$

 Kser Modulus of displacement per shear plane ρm Mean value of the density in kg/m³ d Diameter of the fastener

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 the factor 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

#### Mmodulus 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:

Initial modulus of displacement

$$Ku = 23 · Kser$$

 KU Initial modulus of displacement Kser Displacement modulus of a fastener

Ku = 2/3 ⋅ 29,940 kN/m = 19,960 kN/m

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

Design value of the modulus of displacement

$$Kd = KuγM$$

 Kd Design value of the modulus of displacement KU Initial modulus of displacement γM Partial safety factor for connections according to [1] Table 2.3

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

#### Torsional Spring Stiffness Determination

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

Torsional spring stiffness for the serviceability limit state

$$Cφ,SLS = Kser · Ip$$

 Cφ, SLS Torsional spring stiffness for the serviceability limit state Kser Displacement modulus of a fastener Ip Polar moment of inertia without component of fastener surfaces

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

Torsional spring stiffness for the ultimate limit state

$$Cφ,ULS = Kd · Ip$$

 Cφ, ULS Torsional spring stiffness for the ultimate limit state Kd Design value of the modulus of displacement Ip Polar moment of inertia without component of fastener surfaces

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

To take into account both rigidities, activate the ‘Modify Stiffness’ subtab (select the corresponding check box in the Calculation Parameters subtab 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,SLS / Cφ,ULS. 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.

#### Ttorsional Spring Stiffness Determination Utilizing the RF-/JOINTS Timber - Steel to 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 trandfer 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.

#### Dipl.-Ing. (FH) Gerhard Rehm

Product Engineering & Customer Support

Mr. Rehm is responsible for the development of products for timber structures, and provides technical support for customers.

#### Reference

 [1] Eurocode 5: Design of timber structures - Part 1-1: General - Common rules and rules for buildings; EN 1995-1-1:2010-12 [2] 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 [3] 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

Write Comment...

Write Comment...

• Views 1542x
• Updated 04/30/2021

Do you have questions or need advice?
Contact our free e-mail, chat, or forum support or find various suggested solutions and useful tips on our FAQ page.

RFEM | Basics

Online Training 07/13/2021 9:00 AM - 1:00 PM CEST

Eurocode 2 | Concrete structures according to DIN EN 1992-1-1

Online Training 07/29/2021 8:30 AM - 12:30 PM CEST

RFEM | Structural dynamics and earthquake design according to EC 8

Online Training 08/11/2021 8:30 AM - 12:30 PM CEST

RFEM for Students | USA

Online Training 08/11/2021 1:00 PM - 4:00 PM EDT

Eurocode 3 | Steel structures according to DIN EN 1993-1-1

Online Training 08/25/2021 8:30 AM - 12:30 PM CEST

Eurocode 5 | Timber structures according to DIN EN 1995-1-1

Online Training 09/23/2021 8:30 AM - 12:30 PM CEST

Glass Design with Dlubal Software

Webinar 06/08/2021 2:00 PM - 2:45 PM CEST

Blast Time History Analysis in RFEM

Webinar 05/13/2021 2:00 PM - 3:00 PM EDT

Timber Beam and Surface Structures | Part 2: Design

Webinar 05/11/2021 2:00 PM - 3:00 PM CEST

Plate and Shell Buckling Utilizing Dlubal Software

Webinar 03/30/2021 2:00 PM - 2:45 PM CEST

Webinar 03/10/2021 2:00 PM - 3:00 PM EDT

The Most Common User Errors With RFEM and RSTAB

Webinar 02/04/2021 2:00 PM - 3:00 PM BST

Webinar 01/19/2021 2:00 PM - 3:00 PM EDT

Dlubal Info Day Online | December 15, 2020

Webinar 12/15/2020 9:00 AM - 4:00 PM BST

FEA Troubleshooting and Optimization in RFEM

Webinar 11/11/2020 2:00 PM - 3:00 PM EDT

Soil-Structure Interaction in RFEM

Webinar 10/27/2020 2:00 PM - 2:45 PM BST

NBC 2015 Modal Response Spectrum Analysis in RFEM

Webinar 09/30/2020 2:00 PM - 3:00 PM EDT

Documenting Results in the RFEM Printout Report

Webinar 08/25/2020 2:00 PM - 2:45 PM CEST

Webinar 08/20/2020 2:00 PM - 3:00 PM EDT

How to Be More Productive Using RFEM

Webinar 07/07/2020 3:00 PM - 4:00 PM CEST

Introduction to Solid Modeling in RFEM

Webinar 06/30/2020 2:00 PM - 3:00 PM EDT

Modeling with Solids in RFEM

Webinar 06/09/2020 3:00 PM - 3:45 PM CEST

Length 3:32 min

Length 2:50:30 min

Length 1:01 min

Length 1:03 min

Length 1:02 min

Length 0:40 min

Length 52:33 min

Length 1:06:58 min

Length 2:37 min

Length 1:03 min

Length 1:20 min

Length 0:39 min

Length 0:59 min

Length 0:42 min

Length 0:36 min

Length 1:15 min

Length 1:22 min

Length 0:27 min

}