Modelling of semi-rigid connections in Multiframe is performed using Member end springs.  Each member end spring is modelled as an individual item within the structural model. Furthermore each end spring is associated with only a single member and then only with one end of the member. This distinction is important as an end spring should not be considered to be properties of a member. Whenever a spring is specified at an end of a member a new end spring is added to the model.

To add Member or edit end springs to a member

§    Select the member or members to be modified

§    Choose Member End Springs from the Frame menu

For each component of the member end forces that you which to make semi rigid

§    Click on the tab corresponding to the component

§    Click on End 1 and/or the End 2 check boxes to specify the ends of the member which are to be modelled using end springs.

And for each end

§    Select the model used to determine the spring stiffness

§    Specify the value of the parameter(s) used by the selected model

§    Click on the OK button

Three linear models are available for modelling the stiffness of the end springs. Each model defines a different method for specifying the stiffness of the spring. The models are as follows

1) Spring Stiffness (Sc) – The stiffness of the end spring is specified directly.

2) Rigidity Index (r) – The linear model of Lightfoot and LeMessurier (1974). This model computes the spring stiffness is direct proportion to the member stiffness according to the relationship.

                             Sc = r * 4EI/L

The value of r ranges from zero for a pinned or free connected to infinity for a rigid connection.

3) Fixity Factor (n) – Another linear model for spring stiffness was suggested by Romstad and Subramanian (1970) and Yu and Shanmugam (1986).  The model uses the fixity factor (n) to define the spring stiffness using the following relationship

                             Sc = n/(1-n) * 4EI/L

The value o the fixity factor ranges from 0.0 to 1.0 where a value of 0.0 represents a pinned or free connection and value of 1.0 a rigid connection.

The last two methods were derived for modelling moment connections. However they have been generalised within Multiframe such that a similar scaling of the diagonal terms in the stiffness matrix is performed for shear, axial and torsional components of the end spring.

The properties of member end springs can be edited via the End Springs table in the Data Window.  Member End Springs can be added and deleted via the Member Ends table in the Data Window.  An end spring can be added by simply entering a number in the End Spring column, if this number is greater than the number of end springs in the model, then a new end spring is added using the default properties. If the number is that of an existing end spring then a new end spring is added using the properties of the existing spring.  In both cases the number entered by the user will change to reflect he number of the new spring. An end spring is deleted from a member by simply setting the number of the end spring to zero.