General Method for Stability Analysis According to EN 1992-1-1

General Method for Stability Analysis According to DIN EN 1992-1-1 in RFEM 6

Theoretical Background

The General Method according to 5.8.6 has the following further requirements with regard to the analysis and design.

Geometric Nonlinearity – Second-Order Analysis

According to Section 5.8.6(1), geometric nonlinearities must be taken into account. The determination of internal forces is carried out accordingly on the deformed system according to the second-order analysis, taking imperfections into account.

Physical Nonlinearity – Material

The general rules for nonlinear methods according to 5.7 still apply. In Sec. 5.7(1), "an adequate non-linear behavior for materials is assumed". According to 5.7(4)P, the use of material characteristics that represent the stiffness in a realistic way, but take into account the uncertainties of failure, shall be used when using nonlinear analysis.

Thus, it is necessary to use the appropriate stress-strain diagrams for concrete and reinforcing steel.

• Creep deformation

Das Kriechen ist dabei zu berücksichtigen und darf mithilfe einer modifizierten Spannungs-Dehnungs-Linie nach 5.8.6 (3) angesetzt werden. For this, the strain values of the concrete are multiplied by the factor (1 + ϕ_ef), where ϕ_ef is the effective creep ratio according to 5.8.4. The procedure is shown in the following image as an example.

Distortion of Stress-Strain Curve in Reinforced Concrete

• Tension stiffening

The effect of the concrete between the cracks (tension stiffening) may be taken into account. For this, select an appropriate method, either by means of a suitable concrete characteristic line for the tension area (1 in the image below) or by means of a modified reinforcing steel characteristic line (2 in the image below).

Considering Tension Stiffening Effect in RFEM

Safety Concept

• Internal forces and deformations

According to EN 1992-1-1, Section 5.8.6 (NDP 5.8.6(3)), the internal forces and deformations may be determined by using average material properties (f_cm, f_ctm, …).

• Cross-section design in ULS

However, it is necessary to perform the design of the ultimate load capacity in the governing sections using the design values (f_cd, f_yd, …) of the material properties.

Subject of Analysis

Modeling of the column to be analyzed is based on the Evaluation Example 0033-D-DBV-AK from [1] and Example 10 from [2]. It is located on the edge of a three-span frame structure consisting of four cantilevered columns and three single beams with a hinged connection.

For the design, the column is modeled as a single column. It is subjected to the vertical force of the precast girder, as well as snow and wind.

System Sketch | Center of Single Column

Nonlinear Stability Analysis in RFEM 6

Based on the general principles, the nonlinear analysis and the ultimate limit state design are now carried out for the example mentioned above.

The Concrete Design and Nonlinear Material Behavior add-on are required.

Materials

First, class C30/37 concrete and class B500S(B) reinforcing steel are imported from the Material Library.

Concrete

For the "Concrete" material type, the "Anisotropic | Damage” nonlinear material model is very well suited for the design according to the general method.

Stress-Strain Diagram
In the "Anisotropic | Damage” tab of the material model, you can select various types of diagram definitions in the “General” category, including “ULS P+T | Design values acc. to 5.8.6". For this option, the safety factors that result from the standard selected in the Base Data for the concrete design are also specified below.

In the lower part of the dialog box, in the "Strengths" category, you can control the course of the diagram for the compression area and tension area using the strength parameters.

Für die nichtlineare Analyse der Stütze wird der Druckbereich mit dem Diagrammtyp „Parabel“ (nach 3.1.5) sowie der Druckfestigkeit f_cm und der Zugbereich mit f_ctm abgebildet.

The "Stress-Strain Diagram" tab shows the resulting diagram on which the nonlinear analysis is based.

The following image shows the input dialog box for concrete of the “Anisotropic | Damage” material type.

Material Model Anisotropic | Damage - Image 1/4: Assigning Material Model

Creep
You can activate creep in the "Time-Dependent Properties of Concrete" tab.

Reinforcing Steel

For the “Reinforcing Steel” material type, select the appropriate nonlinear material model “Isotropic | Plastic”.

Stress-Strain Diagram
You can also set the diagram type for the reinforcing steel in the specific tab. In this example, the default setting is used.

The following image includes the input dialog box for reinforcing steel of the “Isotropic | Plastic” material type.

Material Model Assignment for Reinforcing Steel: Isotropic | Plastic (Members)

Structural System and Loading

The modeled structural system and its loading correspond to the specifications from [1] and are summarized in the following image.

Image 1/2: Structural System

Cross-Section – Advanced Time-Dependent Properties
Wenn im Materialdialog das Kriechen aktiviert ist, dann steht im Dialog für die Querschnittsdefinition die Option „Erweiterte zeitabhängige Kennwerte des Betons“ zur Verfügung.

The creep parameters used in this example are shown in the image below.

Advanced Creep Properties | Concrete Cross-Section Analysis

Member – Design Properties
The design properties for the column are activated in the member dialog box. The reinforcement is defined according to the reference solution [1] and summarized in the following image.

Reinforcement Layout for Column

Imperfections

The imperfections are determined according to the specifications of Eurocode 2. In the example to be analyzed, the inclination ("initial sway") is θ_i = 1/315.

Member Imperfection According to EN 1992-1-1

Mesh Settings

In the settings for the FE mesh generation in the Mesh Settings dialog box, the option for the member divisions should be active for the nonlinear analysis of concrete members, as highlighted in the following image.

Nonlinear Analysis | Settings of Reinforced Concrete Members

Analysis

The nonlinear analysis according to the General Method in compliance with EC 2, 5.8.6, applies the settings as highlighted in the image below.

Nonlinear Analysis | Concrete Imperfection

1 – Analysis Type for Linear Creep

In this example, the creep is modeled linearly using a modified stress-strain diagram (see the Creep Deformation section). For this, set the analysis type to "Static Analysis | Creep & Shrinkage (Linear)”.

2 – Creep Loading Times

The loading times for creep are defined in the "Times" section.

3 – Second-Order Analysis

The required second-order analysis for load combinations is already preset by default in the static analysis settings.

4 – Considering Imperfection

It is necessary to activate the imperfection to be considered for the corresponding combinations. You can assign it in the imperfection case, in the combination wizard, or in the load combination. Further information can be found in the technical article "Considering Member Imperfections" and in Chapter Imperfection Cases of the RFEM 6 online manual.

5 – Activating Reinforcement in Structure Modification

Damit die Bewehrungssteifigkeit bereits in der Finite-Elemente-Analyse berücksichtigt werden kann, ist es erforderlich, die Stabbewehrung mithilfe einer Strukturmodifikation für Stahlbeton zu aktivieren, wie nachfolgend dargestellt.

Structure Modification | Reinforcement Effect

Settings for Concrete Design

For concrete design, the relevant design situation, the objects to be designed, and their ultimate configurations are assigned.

Further information on entering data for concrete design can be found in Chapter Concrete Design Settings of the introductory example for concrete design.

ULS Concrete Design Situations

The results of the material and physical nonlinear analysis are directly transferred to the concrete design.

The settings for the concrete design can be found in detail in the RFEM file, which is available to download below this article.

Calculation and Results

Once you start the calculation, the nonlinear analysis is carried out, followed by the concrete design. Finally, the results are provided for the evaluation.

Structural Analysis

The following images show the results of the nonlinear analysis according to the General Method in compliance with EC 2, 5.8.6.

The design moment distribution and the deformations are as follows.

Nonlinear Analysis Results | Creep Behavior

The next image shows the deformation diagram depending on the load factor in the calculation diagram for the governing combination CO101, considering creep. For comparison, the deformations of CO102 without the creep component are also displayed.

Nonlinear Result Analysis | Calculation Diagram

Concrete Design

The concrete design checks for the ultimate limit state, including the stability analysis according to the General Method in compliance with EC 2, 5.8.6, have been carried out.

The next image shows an extract from the design results.

Concrete Design Results | ULS Analysis

Conclusion

In this technical article, the design according to the General Design Method of Eurocode 2, 5.8.6 was performed using an example of a reinforced concrete column.

In summary, the procedure can be divided into the following steps.

• Definition of the material with appropriate material models, stress-strain diagrams, and creep activation
• Creating the cross-section and defining creep parameters
• Modeling the structural system, including design properties
• Definition of loading with imperfections
• Check of the mesh settings
• Nonlinear analysis settings
  • Analysis type (here: "Static Analysis | Creep & Shrinkage (Linear)")
  • Second-order analysis
  • Loading times for creep
  • Activating reinforcement
• Running the analysis and design
• Result evaluation