# Semi-Rigid Member Connections

## Introduction

You may optionally specify semi-rigid behavior for strong bending (Rz) and/or weak bending (Ry). The other degrees of freedom (Dx, Dy, Dz, Rx) are always controlled by member end releases so will be either fully rigid or fully released.

Many typical steel connections are really not completely rigid or completely
free (or pinned), but are semi-rigid to some degree. These include the
single web angle, double web angle, top and seat angles with double web angles,
end plate, T-stub, and header plate connections. The semi-rigid connection
feature of
*VisualAnalysis* allows these connections to be modeled with their various
moment-theta curve shapes (rigidities).

This feature can have serious **performance**
implications as you analyze. The analysis requires inverting a
nonsymmetrical 12x12 matrix *for each connection*.

## Using Semi-Rigid Connections

*VisualAnalysis* has three different ways for modeling a semi-rigid
connection: constant rigidity connections, bilinear rigidity connections, and
three parameter power models.

The constant rigidity model only takes the connection rigidity value, Ri (linear moment rotation curve). The bilinear moment rotation curve model takes two rigidity values and a moment value. The moment value is used to specify when the second rigidity value kicks in. Lastly, the three parameter power model is essentially a modified exponential model. This model takes three parameters; n, Ri, and Mu. The parameter n is the shape factor or power index. The larger the value of n, the steeper the curve and the closer it "fits" the two tangents. Ri is the initial stiffness of the connection. Mu represents the maximum moment and determines where the horizontal asymptote is that the curve will come up to.

Three parameter power model curve.

### How do I specify a semi-rigid end?

To specify a semi-rigid connection, select a member and open the Semi-Rigid characteristics located under the Modify tab. The options allow for a node and direction to apply rigidity changes by one of the three models described above to be selected. Semi-rigid behavior can be assigned to each node of a member, the rz direction in a plane frame, and the ry and rz directions in a space frame.

### How do I know what rigidity value to use for my connection?

This can be somewhat difficult to determine. There are a number of texts that address semi-rigid behavior. For example, Stability Design of Semi-Rigid Frames by Chen, et al. gives formulas and tables for specific connections and their associated rigidity values. See the reference section for more information about semi-rigid connections.

### Could this be used to model a plastic hinge?

Yes, both the bilinear rigidity and three parameter power models facilitate a "limit" moment value. This could be specified as the plastic moment allowing for an approximate model of hinging behavior. Note that members would have to be split and/or tweaked further to account for hinge behavior not occurring at the column connections. So while it works, it would still be a manually iterative analysis to determine hinge locations and split and insert them. And the locations would be different for each load case or combination! So it is not a very practical plastic-analysis for any non-trivial frame or set of load cases.

### Nonlinear Analysis - Potential Limitations

The rigidity model selected for semi-rigid behavior of the connection will designate whether a linear or a nonlinear analysis is performed. What does this mean? This can affect two things; mode shapes and 2nd order results.

The constant rigidity model uses a linear analysis and everything is
essentially as usual. The bilinear rigidity and the three parameter power
model both require a nonlinear analysis. This is done automatically behind
the scenes but you do need to know a little about its happenings. It is
generally true in *
VisualAnalysis* that mode shapes, and first or second order results cannot be
obtained when a nonlinear analysis is performed. This is also true for
these two semi-rigid connection models.

## Reporting Semi-Rigid Connections

Member Semi-Rigid Connections is the only report item available. For each specified semi-rigid connection this report specifies:

- The member and node it is applied to - this is just the member and node name respectively.
- The Semi-Rigid connection model type - this can be constant stiffness, bilinear stiffness, or the 3 parameter power model.
- The direction - this is the degree of freedom specified as semi-rigid.
- Stiffness 1 - this is the stiffness for the constant rigidity model, the first stiffness for the bilinear model, and the initial rigidity for the 3 parameter power model.
- Stiffness 2 - this is the second stiffness for the bilinear model and is not used in the other two models.
- Moment - For the bilinear model, this is the transition moment, for the 3 parameter power model this is the ultimate moment.
- Power - This displays the shape factor for the 3 parameter power model. For either of the other two models it will display -NA-.

## References

Stability Design of Semi-Rigid Frames by W.F. Chen, Yoshiaki Goto, and J.Y. Richard Liew. John Wiley & Sons, Inc. Copyright 1996 ISBN 0-471-07670-8.

Modeling of Connections in the Analyses of Thin-Walled Space Frames by H. Shakourzadeh, Y.Q. Guo, and J.L. Batoz. Computers and Structures 71, 423-433, Copyright 1999.