Mz Mechanisms for steel columns supported by mat/ piled mat slabs
Background
When a steel column is supported by a direct (green) support there are no mechanism issues in the solver. However, when there is no direct support and the column is instead supported by a slab (e.g. a foundation mat), after analysis the solver status issues warnings for mechanisms in the Mz direction.
Answer
This occurs due to the nodes of the 2D elements of the slab mesh not being fixed in the drilling degree of freedom (DDOF) - which is rotation about the Z axis.
Thus the nodes within a mat foundation slab solver model - including those at the bottom of columns supported by the slab - are all torsionally released (Mz direction). However, the default for a direct support is fixed in the Mz direction.
Columns with such mechanisms will have pin-end beams framing into them.
Beams with pinned ends framing into columns do not provide rotational stiffness to the column. Therefore, a mechanism occurs since there is nothing preventing the column from spinning about its own longitudinal axis. So a column supported by a mat foundation connected to beams with pinned ends will typically display equilibrium warnings in the solver status window (see below)
This type of local mechanism is discussed in the article (Guide to resolving mechanisms) in the Related Articles section at the bottom of this page. However, these mechanisms can be difficult to track down since there is currently no method of displaying purely rotational displacement of nodes when viewing deflections in the Results View.
Note that this issue does not occur with concrete columns as their connection to the slab mesh in the solver model is different from those of other material columns.
The slab is meshed around the concrete column section perimeter and connected to the central 1D analysis element of the column by ‘rigid arms’ (shown with pink-colored lines in the solver model). For Columns of other materials, such as steel, the central analysis element is connected directly to a slab mesh node. See the picture below showing this.
Resolution
To resolve this issue, rotational fixity (about the Z axis) must be provided to such columns in some manner. It is up to the engineer to decide on and use a method of doing this appropriate to their model/ situation following their design intent. However, we can recommend a couple of methods as outlined below.
- Use dummy 'spoke' members1 to effectively embed the column bases in the Slab 2D element mesh as illustrated below; note that while the length and orientation of these members are not crucial2, their end releases (both ends) should be set to fully fixed. To model a pinned column connection to the slab, the bottom of the column can be pinned (about the major and/ or minor axis)
1These dummy ‘spokes’ can be modeled using beams of a general material (so they are not designed) or analysis elements with sensible arbitrary section properties (please refer to the analysis element properties article in the Related article section)
2A sensible approach for the length/extent of the members can be to represent the nature of the connection (in reality) between the column and the slab. If this is a base plate connection, for example, the ‘spoke’ members would be within the extent of the base plate.
- Sit the steel column (fully fixed bottom) on a short concrete column (fully fixed top and bottom) - a sort of 'plinth'. In this case, the concrete column slab mesh cut out + rigid arms will ensure Mz fixity, as explained above.