# Post-tensioned concrete slab

The design example proposed in this technical article is related to a small five floor parking house. The floor structure made from C35/45 is directly subject to the load by transport. The columns are rectangular with dimensions BxH =0.55x0.55m. The slab thickness is 290mm. The axial distances between the columns are 9,0m for both directions.

Fig.: Model of the 4th floor

Several combinations are defined in this example. One group is for the ultimate limit state (ULS_short, ULS_long) and the second group is for the serviceability limit state (characteristic, frequent, quasi-permanent). The load factors are automatically taken into account for each combination in the background. When the prestressing is modelled as real tendon then short term losses are calculated automatically. It means that only the reduction for long term losses (estimation 15%) is applied for this case.

## Design of prestressing

For the design of prestressing force it is supposed that prestressing tendons are designed in column as well as span areas. One half of the tendons in each direction is uniformly distributed in the span and one half is concentrated around the columns. This seems to be the optimum solution with respect to both design and economy. The acting of the prestressing on the structure is considered as follows.

Source: VSL: http://www.vsl.net/Portals/0/vsl_techreports/PT_Slabs.pdf

## Real tendon on the 2D member directly

Definition of the prestressing in the post-tensioned 2D member is done using standard tool Post-tensioned internal tendon. Till version SCIA Esa PT 2007.1 post-tensioning in a 2D member had to be defined on a fictive rib which was defined on the slab. This solution was bit complicated and not so user friendly. That’s why the concept of the “hanging nodes” has been implemented. Hanging nodes is a term used in the finite element method describing the interpretation of an element on the mesh. The mesh of the tendon and attached elements (1D beam or 2D) is independent. The tendons are modelled as a 1D member with eccentricity if hanging nodes are not used. When the hanging nodes are used then the stiffness of the tendon is added to the closest mesh element according to the type of projection.

Fig.: Tendon defined in 2D members

This functionality enables the user to attach internal post-tensioned tendons directly to 2D slab and shell elements. No dummy beam 1D (rib) is necessary. The mesh of the internal post-tensioned tendon and attached 2D elements can be independent.

For tendons allocated on 1D members (beams) it is possible to project the tendon perpendicularly on beam or proportionally. For tendons allocated on 2D members (slabs) only perpendicular projection is possible.

Fig.: The 4th floor after definition of all tendons

## Results

The internal forces can be evaluated as basic magnitudes in the Results and in Concrete too are the same for both cases, but the differences are in the Elementary design magnitudes. There are several differences between those internal forces. The short overview of differences is summarized in the following table.

Results

Concrete

Method for calculation of Design magnitudes

ENV method [6]

NEDIM (Baumann theory) [5]

Design magnitudes in the direction of the local axis (X, Y) of the slab YES

NO

Design magnitudes in the direction of the reinforcement NO

YES

Taking into account torsional moment mxy YES

YES

Shear effect (6.2.3(7)) NO

YES

Fig.: Typical distribution of bending moments myD- in the slab

Fig.: Detail of the internal column within nonprestressed reinforcement

One floor of the parking house has been modelled and checked in this tutorial. We introduced two possibilities how to defined prestressing in the slab (equivalent load, real tendon). Each option has some advantages and disadvantages. The general overview is in the following table.

Real tendon

Preparation and definition of the prestressing Difficult Simple
Short-term losses NO YES
Long-term losses NO NO
Internal forces from prestressing in design YES

YES

Area of prestressing in design NO (free bars are used)

NO (free bars duplicate geometry of the tendons)

Design ULS(ULS+SLS) YES YES
Check of allowable concrete stresses NO NO
Check prestressed capacity or response NO NO
Check of prestressing reinforcement NO

YES (partly)

Check of punching with respect to prestressing YES

YES

Code dependent deflection (CDD) YES NO
Is module post-tensioning needed? NO YES

The solution for a post-tensioned slab is not 100% comfortable and it doesn’t bring complete solution but with the help of the tutorial you will be able to perform the design of such a kind of structure including checking.

Lukáš Dlouhý

09/02/2013