Any static loading on a structure, when combined with the structure support reactions (considered as additional loads), is a self-equilibrium loading. In such a loading the total loads upon the structure are in force and moment equilibrium. However, the equilibrium loads still produce moments and forces in the structure.
In certain cases, it is desirable to analyze a self-equilibrium loading upon a floor system while ignoring the effects of the floor system supports. We call this type of analysis a self-equilibrium analysis.
The most common use of self-equilibrium analyses is to ensure that a load path in Concept is consistent with a load path in a lateral analysis performed by a separate program.
If a lateral analysis of a building (perhaps using RAM Frame) is performed, and that analysis considers the slab to be part of the lateral load path, the slab (including the slab-column connections) needs to be designed to resist the forces and moments determined in the lateral analysis. This design can be performed using a self-equilibrium analysis. The forces/reactions from all of the supports (above and below the slab) onto the slab are considered as loads to the slab.
The result of this self-equilibrium analysis is a slab load path that is fully consistent with the lateral analysis of the entire building. The distribution of forces (and the displacements) within the slab may not match those in the building lateral analysis, but the distribution of slab forces in Concept is almost always more accurate than those predicted in the full building analysis.
There is no limit to the type or quantity of loads that can be applied in a self-equilibrium loading. However, the loads applied must be nearly in self-equilibrium. If the loads are out of equilibrium Concept will apply restraints to the slab to ensure that equilibrium can be maintained. The restraint reactions can be viewed in the Calc Log.
Note: See Chapter 14, “Importing a Database from the RAM Structural System” for information on how to automatically import self-equilibrium lateral loads.
Note: Mat/Raft foundations are typically not well suited for self-equilibrium analyses as the soil reactions are not known before the analysis.
If you use self-equilibrium loadings, Concept creates an internal floating stiffness matrix in addition to the regular stiffness matrix. The floating stiffness matrix considers the slab, but not the supports above or below the slab. Concept also adds some minimal supports to the matrix to make it stable.
The minimal supports that Concept adds to the floating stiffness matrix are located at real support locations, but not at every real support location. Typically, Concept adds three supports to provide full stability, but not to provide any restraint.
Note: Concept gives a warning if there are not at least two support locations where minimal supports can be added. The motivation for adding the minimal supports at the same location as real supports is that these locations are likely to be locations where self-equilibrium loads are applied, so any reactions at these locations can typically be considered as “corrections” to the self-equilibrium loads.
Punching checks consider the loads applied at the punching check location in their reaction calculations. Punching checks are the only “support” that have reactions from self-equilibrium analyses.
Concept reports all displacements for self-equilibrium loadings as zero. Self-equilibrium loadings have no effect on the displacements calculated for load combinations or rule sets.
Pattern loading can be used in a self-equilibrium analysis, but it should almost never be used. When used, all patterns should contain a self-equilibrium set of loads.
Perhaps the best way to understand Lateral SE could be this simple example:
Consider the structure with two elevated floors shown in the Figure below. Each level is 3m high and the structure is 10m wide.
Assume the following:
The forces on the top level slab (including column reactions) are:
Fx0 = 100kNFx1 = -50kN Fx2 = -50kNFz1 = -15kN Fz2 = 15kNMy1 = 75kN-m My2 = 75kN-m
These forces are in equilibrium and are applied directly to the slab in a lateral SE loading. Pay special attention to the Fz reactions. Many users absent mindedly neglect the Fz forces (column axial forces) when transferring Lateral SE forces manually, but they are very significant to the total equilibrium.
Concept then calculates the correct forces in the slab, design strips and punching checks.
For the intermediate level there are more forces to consider (all of these are from the frame analysis). The forces that the columns apply to the slab are:
Fx3 = 50kN Fx4 = -50kNFx5 = 50kN Fx6 = -50kNFz3 = 15kN Fz4 = -45kNFz5 = -15kN Fz6 = 45kNMy3 = 75kN-m My4 = 75kN-mMy5 = 75kN-m My6 = 75kN-m
These forces are in equilibrium and are applied directly to the slab in a lateral SE loading. Since the “3” and “4” forces occur at the same location, they can be added together and applied as a single load (same for “5” and “6”).
Note: There is one simplification - if you do not care about diaphragm forces, then you can ignore all the Fx and Fy forces. This assumes that the Fx and Fy forces act at the center of your slab and that the centroid elevation of your slab is constant. When these two assumptions are not true, the effects of these forces are typically still not large, but you may need to use some judgment before you ignore them.
Note: Ram Structural System lateral loads will generally be exported to Ram Concept in a self-equilibrium state, but user defined lateral nodal loads, especially those that include vertical (z direction) forces will not be in equilibrium and as such, those should only be processed as Normal analysis loads in Ram Concept.