Tuesday, February 12, 2013

Modeling of Slab Column joint

In structural engineering, the Flat Slab is identified as a slab which is supported generally without beams by columns with or without column heads. However, I have understood that Flat Slab designs are not quite popular in Sri Lanka, may be owing to its complexity in design, detail and construction. But things what I am going to discuss here are equally important in any other column slab design problem such as pile cap etc.

Generally the slab can be analyzed by dividing it in to longitudinal and transverse frames consisting of columns and strips of slab. This is identified as Equivalent Frame method and frames are analyzed by moment distribution. However these manual methods are things for the past. More sophisticated and user friendly Finite Element Methods (FEM) and software are widely used to solve the problem.

Plate mesh and the columns : STADD Pro

3D view of the Model

However it can be seen  in FEM that the support moments in slab column joint are sometimes unacceptable  owing to its unrealistic high values. The anomaly is varying as accordance with span, column sizes and slab thicknesses.

Longitudinal Bending Moment Diagram

Transverse Bending Moment Diagram

However , most FE software offers  'peak smoothing' techniques to addresst this problems.

In General, the number of elements used in a FEM model can greatly affect the accuracy of the solution. As the number of elements, or the fineness of the mesh, is increased, the accuracy of the model increases as well. However in this particular Slab Column problem finer mesh would deteriorate the quality of the results more.

Deflection pattern : scale is adjusted

The solution for this problem  lies on the  realistic modeling of boundary conditions  of the slab.

In this regard, I usually  adopt two methods;

  1.) As the first method, Slab may modeled as a plate/shell element while column may modeled as a three dimensional solid object.  By doing so, we get closer to the real world scenario of the slab column joint. However analysis of this model may be time consuming and required higher degree of computer resources.

2.) In the second method, the flat plate is modeled as a plane of finite elements, and columns are simplified to “pin” or “fixed” supports applied at the elevation of the plane of the slab. Sometimes these supports are modeled as springs with a finite elastic stiffness to improve the behavior of the model.

In this method it is essential to connect nodes rigidly which lies within the area of the column section to the end of the frame member. This technique is otherwise referred to as a master-slave technique, where the end of the frame member column is the master joint, and the joints in the slab within the column area are slaves.

This technique offers an advantage over the use of three dimensional solids with respect to computational efficiency  and  Analyzing time of the model.

I hope this will help you in FEM modeling.


  1. This is interesting Yasela. Have you tried applying your technique to pile caps? I've found in the past that the assumption of a rigid foundation to manually analyse pile groups can give rise to unrealistically high pile axial forces as the distance from the centroid of the group increases.
    As I understand the true distribution of pile forces tends to be more uniform, due to the flexibility of the pile cap.
    My efforts to model pile groups using SAP2000 were not successful, for reasons you have stated here. Even when the slab's stiffness is increased by several orders, I found that the effect of the pile on the slab moment reduces very quickly when moving away from the pile.
    I will try your method when I get the chance.

  2. Thanks Asanka ,

    Yea I have applied these techniques in Pile cap modeling and I have found that it works well. As my understanding, we assume that foundation is rigid in comparison to the soil and that the pressure distribution is linear. For smaller spans this particular assumption is satisfactory. However generally I choose adequate thickness for pile cap, so that it behave rigidly, as well as it withstand against the punching shear failure owing to high axial forces of piles. For laterally loaded pile groups in bridges simply I use Tomlinson equations ( W/n+Wex/(x1+x2….+xn)) and I have found no contradictions of it compared to FEM results.

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