One-way and two-way load decomposition

Tekla Structural Designer
2021
Tekla Structural Designer

One-way and two-way load decomposition

Apart from when slabs are set to be meshed in the analysis, any panel loads applied to slab panels and roof panels have to be decomposed on to supporting members prior to analysis.

Potential load decomposition methods

In traditional hand calculations a "tributary area" (sometimes called "yield line") loading approach would have been adopted to determine the decomposed loads, but this has limitations when dealing with complex geometry such as:

  • Slabs not supported on all edges
  • Complex panel shapes
  • Panels with openings

Also the "tributary area" approach can only approximately handle point, line, and patch loads (by converting them to area loads).

Because of these limitations the "tributary area" method is not used in Tekla Structural Designer - instead a method referred to as FE decomposition is applied instead. This is based on finite element analysis.

FE decomposition model

The FE decomposition model can be demonstrated using the following two-way slab on beams example.

2_way_load_decomposition_example.png

For this type of structure:

  • A separate FE decomposition model is created for every floor (or sloped plane).
  • Beam column and wall nodes in each FE decomposition model (shown selected in pink below) are all rigidly supported.
2_way_load_decomposition_solver_model_new.png

• Each FE decomposition model is analysed and the reactions at the rigidly supported nodes are turned back into VDLs along beams and walls, and point loads on columns.

2_way_load_decomposed_loads.png

A common question

So if the slabs have to be meshed for the FE decomposition during pre-analysis, why not do away with decomposition entirely and just mesh the slabs when performing 3D analysis of the entire model instead?

Because this gives results that you don't like....

In the first run of the model below the slabs are left unmeshed, this requires the loads on the two-way slabs to be FE decomposed prior to analysis. The bending moments from the resulting 3D Analysis are as shown, (max hogging -198, max sagging 165):

A_common_question_1.png

The above results can be compared against a second run of the model in which the 2-way slabs are set to be meshed in the 3D analysis. FE decomposition is no longer required and the bending moments from the resulting 3D Analysis are as shown, (max hogging -89, max sagging 82)

A_common_question_2.png

In this second run, because the slabs are included in the 3D analysis model, some of the load is being transferred directly to the supporting columns and walls via the slabs themselves. While this is not wrong, it goes against the engineer's expectation - which would be to design the beams on the basis that they transfer all the load to the supporting members.

Controlling decomposition via the 'Mesh 2-way slabs in 3D Analysis' property

As stated in the previous section, the engineer's expectation would be to design the beams on the basis that they transfer all the load to the supporting members. This is achieved in Tekla Structural Designer because (by default), two-way slab are not meshed in the 3D analysis and grillage chasedown solver models.

Note however that by switching on the Mesh 2-way slabs in 3D Analysis level property the engineer can allow some of the load to be transferred directly to the supporting columns and walls via the slabs.

Solver model under consideration
Decomposition method specified in slab properties 3D Analysis and Grillage chasedown models FE chasedown model
Two-way

Mesh 2-way slabs in 3D Analysis level property not selected (default):

  • load decomposition performed (2-way)
Note: Beams designed on the basis that they transfer all the load to the supporting members.
  • load decomposition not performed
Mesh 2-way slabs in 3D Analysis level property selected:
  • load decomposition not performed
Note: Beams designed on the basis that 2-way slabs transfer some of the load to the supporting members.
One-way
  • load decomposition performed (1-way)
  • load decomposition performed (1-way)

Decomposition rules for the different types of panel and overlapping panels

The way in which Tekla Structural Designer decomposes panel loads depends on how the slabs/panels are modeled and how they are spanning.

Slab/Panel type Decomposition
One-way spanning slab item

Panel loads applied to the slab are 1-way decomposed directly on to supporting members/two-way spanning slab edges before performing 3D analysis.

The rotation angle of the slab item determines the decomposition direction.
Note: Any openings in 1 way slabs are ignored and thus have no impact on load decomposition.
Roof panel

Panel loads applied to the roof panel are 1-way decomposed directly on to supporting members/two-way spanning slab edges before performing 3D analysis.

The rotation angle of the roof panel determines the decomposition direction.

Two-way spanning slab item
  • At those levels where the Mesh 2-way Slabs in 3D Analysis option is selected, load decomposition is not required.

  • At other levels, any loads applied to two-way slabs are automatically 2-way decomposed back to supporting members during the 3D pre-analysis stage, immediately prior to the 3D analysis stage.

Note: Where openings have been defined, any portion of a panel load that lies within the opening will not be decomposed.
Roof panel overlapping a one-way spanning slab item

Panel loads are 1-way decomposed directly on to supporting members/two-way spanning slab edges before performing 3D analysis.

The rotation angle of the slab item (and not the roof panel) determines the decomposition direction.

Note: Any openings in 1 way slabs are ignored and thus have no impact on load decomposition.
Roof panel overlapping a two-way spanning slab item
  • If there are no openings in the slab, decomposition is as per Two-way spanning slab item type described above.
  • Where openings exist, any panel load applied inside the opening is first one-way decomposed in the direction defined by the rotation angle of the roof panel on to the two-way slab at the edge of the opening. It is then further decomposed back to supporting members as per Two-way spanning slab item type described above.
    Note: This does not apply when the panel load is an area load that has been applied to the slab item (as opposed to the roof panel), or a level load, or a slab load. In each of these instances the load will automatically be boxed out around the opening.
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