Prestressed Concrete Design in RFEM

Technical Article

Efficient design of prestressed structural components requires a few additional steps that go beyond the standard reinforced concrete design, from modeling tendons, to the calculation of equivalent loads, to the cross‑section resistance design. Therefore, it is important that the software for prestressed concrete design is structured and the navigation is possible in the program. RFEM with two add‑on modules RF‑TENDON and RF‑TENDON Design fulfills these requirements and allows engineers to carry out the complete design of prestressed beams, frames, plates, buildings and bridges according to EN 1992‑1‑1 with National Annexes and SIA 262.

Modeling Structure

Structural modeling is the first step of the prestressed component design. In RFEM, you can simply and quickly enter beams, frames and plates, or model complex buildings and bridges. RFEM 5 includes the environment typical for CAD software so the program handling is intuitive.

For modeling frame and truss structures, there is a wide range of typified member cross‑sections available in the program. Special cross‑sections can be defined in SHAPE‑THIN and used for the finite element analysis in RFEM.

The input of loads is facilitated by the implemented load generators, such as for snow load determination. A load combination is created automatically according to the selected standard. It is also possible to manually define load situations, for example in the case of specific construction states. The photorealistic visualization of the model in 3D rendering always provides an immediate input control.

Figure 01 - RFEM Model of Residential Building with Prestressed Concrete Ceiling

Tendon Geometry

The definition of the 3D tendon geometry with respect to the shape of the structure can be very time‑consuming and difficult, especially in the case of spatially curved structural components. By projecting these components into the XY and XZ plane, the spatial problem can be simplified to 2D geometry. In this case, the beam is displayed directly in the XY and XZ planes, and the definition of the tendon geometry is thus greatly simplified.

Another possible difficulty could be the definition of a tendon shape in a slender prestressed beam. The problem may be caused by the fact that the beams are usually very long and flat. When displaying the entire beam, the cross‑section height is very small and it is very difficult to recognize the tendon distribution in detail. In this case, there is an option in RF‑TENDON to vertically and horizontally scale the prestressed concrete beam. Thus, you can display the height of a slender beam larger so the tendon shape is better recognizable.

Figure 02 - Oversized Projection of Prestressed Concrete Beam

The tendon geometry can be generated automatically using the standard shape of the tendon. The program generates the tendon geometry with regard to the existing supports. If necessary, it is possible to adjust the position of the tendon subsequently.

The program creates the 3D geometry of a tendon by merging both projections in the XY and XZ planes. From both projections of the curved beam, the 3D tendon diagram is generated. In this way, you can quickly and easily obtain the tendon geometry of the curved prestressed concrete beam. For straight prestressed concrete beams, it is not necessary to work in two projections.

Effects of Prestress

The equivalent loads, which correspond to the prestress effects, are automatically determined as the resulting forces with regard to the eccentricity and the directional change of the tendon. These equivalent loads can be displayed graphically. It is also possible to graphically compare the equivalent loads from the prestress with the external load from the constant and variable load. In this way, the prestress effect can be easily recognized in the design in RF‑TENDON.

The prestress effect on the design is controlled by the intensity of the prestress forces. According to Prof. Tung‑Yen Lin, the quasi-permanent component of the external load should be compensated by the equivalent load from prestress. This “Load Balancing Method” can thus be used for the preliminary design of tendons. Both the external loads and the equivalent loads from the preload can be graphically displayed in RF‑TENDON.

Figure 03 - Result Graphic of Equivalent Loads from Prestress

The stress in the tendon and the equivalent loads from prestress are calculated with regard to the tendon losses. Anchor slippage and friction losses are determined by direct integration of the strain along the tendon length. The calculation method fully considers all angular changes of the 3D tendon geometry. The stress losses due to the elastic concrete strain are determined using the ideal cross‑section properties. The long‑term losses are calculated according to the design standard, taking into account the strain losses due to the creep and shrinkage of the concrete subjected to permanent loads and the stress losses in the prestressing steel due to the relaxation under tension. When determining the creep effect, the load history is considered.

Structural Analysis

Prestress effects automatically apply to the structure and the structural analysis using the finite element method can be performed. The prestress effects are calculated with regard to the primary and secondary effects. The internal forces of design strips of the prestressed plate can be integrated into the internal forces of a virtual result member and subsequently used for the cross‑section design. The internal forces, including the prestress effects, are calculated in RFEM and exported to RF‑TENDON Design.

Design of Prestressed Cross-Sections

The final step in the design of prestressed components is to verify the prestressed concrete cross‑section. For this, the RF‑TENDON Design add‑on module is used. In this program, the design according to Eurocode 2 and SIA 262 is available. Nationally determined parameters and methods can be considered in accordance with eight National Annexes, including DIN EN 1992‑1‑1/NA and ÖNORM EN 1992‑1‑1.

Each cross‑section shape and reinforcement layout can be checked by calculating the 3D stress distribution in the cross‑section. Furthermore, the predefined reinforcement templates are available for typical cross‑section shapes. The position of the tendons and ducts in the cross‑section are automatically taken from the 3D tendon geometry.

RF-TENDON Design checks whether the cross-section meets SIA or Eurocode 2 standard requirements for both the ultimate and the serviceability limit state design, including the requirements for bridges of EN 1992‑2. Moreover, RF‑TENDON Design can consider the interactions of all internal forces such as axial forces, bending moments, shear, and torsion. The serviceability limit state values are checked during the design of stresses, crack widths, decompression and deflection.

Providing the possibility of an extended analysis with the stress‑strain response of the cross‑sections, stiffness calculation, and the possibility to display the moment-curvature diagram, RFEM is a powerful software for structural analysis according to Eurocode and SIA. Due to the modern graphical user interface, clear information about the design status, the option to quickly get brief results, or to carry out detailed design as well as the system with warnings and recommendations, the program is extremely user‑friendly and universal.

Figure 04 - Stress-Strain Reaction of Beam in ULS

Conclusion

All necessary steps to perform the prestress design in RFEM 5 can be called by the user. RF‑TENDON is an effective, easy-to-understand and user-friendly program for the design of prestressed beams and frame structures as well as plate and complex structures. On the other hand, the program offers a simple and intuitive input, which allows you to perform quick preliminary designs very efficiently. RF‑TENDON and RF‑TENDON Design provide the complete solution and support the user when performing the prestress design and dealing with Eurocode 2.

Reference

[1]  Navrátil, J. (2014). Prestressed Concrete Structures (2nd ed.). Ostrava: Technical University of Ostrava, Faculty of Civil Engineering.

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RFEM Main Program
RFEM 5.xx

Main Program

Structural engineering software for finite element analysis (FEA) of planar and spatial structural systems consisting of plates, walls, shells, members (beams), solids and contact elements

Price of First License
3,540.00 USD
RFEM Concrete Structures
RF-TENDON 5.xx

Add-on Module

Tendon definition in prestressed concrete members

Price of First License
2,060.00 USD
RFEM Concrete Structures
RF-TENDON Design 5.xx

Add-on Module

Prestressed concrete design according to Eurocode 2

Price of First License
1,610.00 USD