Posttensioned 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.
Loads and combinations of loads
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, quasipermanent). 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.
Real tendon on the 2D member directly
Definition of the prestressing in the posttensioned 2D member is done using standard tool Posttensioned internal tendon. Till version SCIA Esa PT 2007.1 posttensioning 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.
This functionality enables the user to attach internal posttensioned tendons directly to 2D slab and shell elements. No dummy beam 1D (rib) is necessary. The mesh of the internal posttensioned 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.
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 
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.
Item  Equivalent load 
Real tendon 

Preparation and definition of the prestressing  Difficult  Simple 
Shortterm losses  NO  YES 
Longterm 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 posttensioning needed?  NO  YES 
The solution for a posttensioned 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