## The Analysis Of Structures With Semirigid Connections

If the connections in a statically indeterminate structure exhibit semi-rigid rather than fully fixed rotational behaviour, there will be a reduction in the stiffness of the structure leading to smaller moments at connections, an increase in member span moments and an increase in those displacements that are affected by the moment distribution in the structure. By taking the effect of semi-rigidity into account, in the analysis process a more realistic assessment of the moment distribution and displacement behaviour of the structure will be obtained.

EC5 allows the structural model in an analysis to take into account the effects of deformations of connections having adequate ductility and by using the slip properties of the fastener types given in EC5 a methodology can be developed to accommodate semi-rigid behaviour.

For semi-rigid rotational behaviour, the moment in the shear plane of a connection, M, can be related to the relative rotation between the adjacent connection members by the following relationship,

where k is the secant rotational stiffness, and will be referred to as the rotational stiffness of the connection. The rotational stiffness of a rigid, pinned or semi-rigid connection is shown in Figure 12.11.

With a rigid connection, irrespective of the value of the moment, the relative rotation of the connection members will be zero and the M — relationship will be a vertical line acting through the origin as shown in Figure 12.11b. The rotational stiffness for this condition will be infinity. For a pinned connection, no moment can develop and the M — relationship will be a horizontal line acting through the origin. The rotational stiffness for this condition will be zero. All conditions between these extremes will constitute semi-rigid rotational behaviour.

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