To represent this phenomenon, the above image presents a graphical representation of bending moments in the form of charts created in the FEM mesh nodes. The mesh was densified over one of the columns, twice compared to the global grid. The critical sections require increased density of the discretization, and this leads to an intensification of force concentration.
In addition, classical FEM analysis underestimates the rigidity of the column – slab connection. In fact, the slab rests on a column of specific dimensions and does not physically experience such bending as in the case of a point support. This results in that case of flat-slabs, the bending moment transmitted from the slab to the columns can be significantly underestimated.
Literature offers many solutions to this phenomenon. Usually, thickening the slab near the columns provides an increase of stiffness and shear strength, and also increases the perimeter of the critical section. De facto, it increases the support zone beyond the area of one FEM node with the simultaneous omission of these thickened panels in the analysis, which leads to the interpretation of forces from the edge of the column. However, this is a very labour-intensive method; in addition, it is very sensitive to any changes in the design.
GRAITEC Advance Design smooths the results over the column area by automatically generating rigid constraints, which simulates the high rigidity of the column’s connection with the slab.
Bending moment distribution above the inner column – modified colour scale
Using the built-in tool of Advance Design - "Dynamic Contouring”, the maximum values of the bending moments within the cross-section of the column are excluded. The moment for reinforcement design really oscillates around 300 kNm.
Moments in the area of the column using the Dynamic Contour tool of Advance Design
For later comparison, the bending moment diagrams for the corresponding direction on the columns are presented (envelope). The model was prepared as a separate story – columns are fixed at their ends, but on the top TZ is released. In the current situation, the column supports the slab with one node, which leads to underestimation of stiffness.
The envelope of bending moments on a column with respect to the direction of the bending moments in the shell
Advance Design deals automatically with all issues related to the point support of slabs by columns or by nodal supports.
This feature uses a rigid node connection, connecting the main column node with the adjacent FEM mesh nodes. The area in which the mesh nodes will be connected is controlled by the thickness of the slab. For linear elements, such as columns, nodes are connected at a distance from the edge of the column. Thanks to this, we can generate connections practically on the edge of the column. What is very important, this tool automatically adapts the FEM mesh, although originally the nodes on the edge of the column did not exist, they are automatically generated during meshing.
The column can have any ratio of dimensions - the mesh will be generated correctly in every case, because it is not defined by radius but by the sections of a column.
Automatic generation of FEM mesh nodes at the column edge
In addition, these nodes are connected by rigid connections - this operation is also automatic. They guarantee reduction of moments in the column area and additional stiffening of this connection.
Automatic node connections in Advance Design
Diagrams and maps of bending moments
As you can see on the bending moments diagram, forces in the column area are practically zeroed - they are not significant from the point of reinforcement design. The moment at the edge of the column is greater than the one in the original model.
It can be concluded that manual reading of the moment from the edge of the column in the case of support with one FEM node leads to an underestimation of bending moments above the support in the slab - and thus also in the column.
Underestimating bending moments in the slab can lead to redistributions or cracking, however underestimating the moments in the column can have catastrophic consequences. As you can see, the moments in the column almost doubled.
Moments in the column
In conclusion, FEM modelling of building structures poses many difficulties for engineers. Depending on the structure, there will be different issues that require certain steps to analytically simulate what is happening in reality as closely as possible. Designers have often underestimated this effect or used all kinds of simplifications, mainly due to the time-consuming nature of known solutions. The Advance Design tools allow us to solve these issues automatically.
Bibliography:
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