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Design of Flat Slab structures

How to address design particularities of flat slab structures using Graitec Advance Design

 

Flat slabs

Flat slabs are more and more used nowadays, given their structural, architectural and MEP benefits. Of course, this comes with a list of design particularities - negligible in typical framing structures (such as punching shear) - that the structural engineer must address in order to achieve safeness and performance.

Some of the main benefits of using flat-slabs:

  •    Reduced manual labour for concrete formwork
  •    Reduced quantities of formwork
  •    Smooth interior surface that serves architects and also mechanical engineers

 

Calculation model in Advance Design

Maps of bending moments in a slab in Advance Design

Structural analysis

Modelling a flat-slab structure using FEM software is simple at first glance. However, one of the particularities that comes first when designing the slab is the concentration of internal forces in the slab directly above the column and taking into account the local strength of the slab at the column head. This is mainly due to the method of creating an analytical model with the finite element method.

This is due to the way the linear finite elements (columns) are connected to the surface finite elements (in the slab) through one node.

Nodes of the FEM model in connection with a column with a plate (default mesh, the column node is marked in red)         Map of bending moments in the form of graphs based on the FEM mesh of Advance Design

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:

  1. Włodzimierz Starosolski - Reinforced concrete structures according to PN-B-03264: 2002 and Eurocode 2 - Volume II, edition 11, 2008
  2. Włodzimierz Starosolski - Selected problems of computer modelling of engineering structures, 2003
  3. EN 1992-1-1 Eurocode 2 - Design of concrete structures, part 1-1: General rules and provisions for buildings

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