## Moment Behaviour In Timber Connections Rigid Model Behaviour

Validation of the strength of a connection required to transfer a moment in a structure is undertaken in two stages. There is the analysis of the structure to determine the stress resultants the connection will be subjected to and this is followed by the design procedure to demonstrate that the connection is strong enough to resist these forces.

Unless a structure is statically determinate, depending on whether connections behave in a rigid or a semi-rigid manner, the force distribution in a structure in which connections are designed to transfer moment will differ. When the connections are rigid in behaviour the structure will be at its stiffest and when they are semi-rigid the stiffness will be reduced and the stress resultant distribution around the structure will change.

The elastic analysis of indeterminate timber structures fitted with connections that exhibit rigid behaviour can readily be undertaken using traditional methods or by common software applications. The connections are considered to be rigid and the stiffness properties of the members will be determined as defined in 2.3.4.2. Where the connections in the structure are semi-rigid in behaviour, the analysis procedure has to be modified, as discussed in 12.6.

12.5.1 Assumptions in the connection design procedure

When designing a timber connection subjected to moment, because the members of the connection are generally stiff in comparison with the stiffness behaviour of the connection fasteners, to simplify the analysis it is normal practice to assume that the members behave as rigid elements. This is a reasonable assumption provided that there is no significant bending of the members over the length of the connection and should be achieved by ensuring that the bending stresses in the connection members are relatively small.

All movement is taken to be due to displacement at the fastener position, and in the rigid model approach, the following assumptions are made:

(a) The position of the centre of rotation of the fasteners in the connection remains fixed. When a connection is subjected to a moment as well as lateral loading, the forces induced in the fasteners will depend on whether or not the centre of rotation of the connection is fixed or changes as the loading increases. In timber connections, the centre of rotation will normally change as the loading is applied. However, because of the relatively high rigidity of the fastener configurations normally used in structural connections, the change in position will generally be small and in the rigid model approach the assumption is made that the centre of rotation is fixed. On this basis, the centre of rotation is taken to be the centroid of the fastener group. Where the fasteners are all the same size, which is normal practice in a timber connection and has been assumed for the design procedures in this chapter, the centre of rotation will be the geometric centre of the group.

(b) From the assumption in (a), when lateral shear forces act on a connection, each fastener will take an equal share of the force. Hence, if the shear force per shear plane in the connection is Hd and there are n fasteners per shear plane, the lateral force taken by each fastener in the shear plane, Fh>d, will be:

(c) Adopting the conservative approximation that all fasteners in the connection will have the same linear load-stiffness behaviour, for a rigid connection condition

Fastener im

Fastener

Fastener im

Fastener

Fastener group position after rotation of connection under the action of a moment

C, centroid of the fastener group

Fig. 12.1. The rotational behaviour of fasteners in a connection.

C, centroid of the fastener group

Fastener group position after rotation of connection under the action of a moment

Fig. 12.1. The rotational behaviour of fasteners in a connection.

the forces in the fasteners can be derived using either a rigid model approach or by assuming that there will be a small rotation between the adjacent connection members. The same result will be obtained from either approach and the latter method has been used in the analysis.

Although the above assumption means that the strength of the connection will be independent of the fastener stiffness, the ultimate limit states (ULS) slip modulus will be taken to apply in the development of the solution.

Assuming a small rotation of the member in the connection when loaded by the action of a moment, the fasteners will rotate about the centre of rotation and transfer load by embedding stresses to the other members in the connection.

The further the fastener is from the centre of rotation, C, the greater will be the associated displacement and the maximum displacement will occur at the fastener furthest from the centroid, as shown in Figure 12.1. When the connection is subjected to a rotation, ft, fastener, imax, at the greatest distance from the centre of rotation, rmax, will have the largest displacement, 5max, and the displacement of any intermediate fastener i at a distance ri from the centroid will be:

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