The CSA S16:19 Stability Effects in Elastic Analysis method in Annex O.2 is an alternative option to the Simplified Stability Analysis Method in Clause 8.4.3. This article will describe the requirements of Annex O.2 and application in RFEM 6.
This article describes how a flat slab of a residential building is modeled in RFEM 6 and designed according to Eurocode 2. The plate is 24 cm thick and is supported by 45/45/300 cm columns at distances of 6.75 m in both the X and Y directions (Image 1). The columns are modeled as elastic nodal supports by determining the spring stiffness based on the boundary conditions (Image 2). C35/45 concrete and B 500 S (A) reinforcing steel are selected as the materials for the design.
A member's boundary conditions decisively influence the elastic critical moment for lateral-torsional buckling Mcr. The program uses a planar model with four degrees of freedom for its determination. The corresponding coefficients kz and kw can be defined individually for standard-compliant cross-sections. This allows you to describe the degrees of freedom available at both member ends due to the support conditions.
An elastic foundation can be applied to a member. Thus, the influence of the soil is usually included in the modeling. Member elastic foundations can only be defined for the "Beam" member type.
Structure stability is not a new phenomenon when referring to steel design. The Canadian steel design standard CSA S16 and the most recent 2019 release are no exception. Detailed stability requirements can be addressed with either the Simplified Stability Analysis Method in Clause 8.4.3 or, new to the 2019 standard, the Stability Effects in Elastic Analysis method provided in Annex O.
For a timber connection as shown in Figure 01, you can take into account the torsional spring rigidity (spring stiffness for rotation) of the connections. You can determine it by means of the slip modulus of the fastener and the polar moment of inertia of the connection.
You can use the elastic support option to avoid singularities due to a fixed nodal support in RFEM. This can be defined directly in the dialog box of the nodal support as a column in Z. It is necessary to take into account the geometry of the column, the material, and the support conditions. Here, we want to look at the option of modeling the column as a surface foundation.
Often, it happens that stress peaks occur on a nodal support that is attached to a surface. You can avoid such singularities by modeling the nodal support as a column.
With the orthotropic elastic-plastic material model, you can calculate solids with plastic material properties in RFEM 5 and evaluate them according to the Tsai‑Wu failure criterion. The Tsai-Wu criterion is named for Stephen W. Tsai and Edward M. Wu, who published it in 1971 for plane stress states.
The elastic‑plastic material model in RFEM 5 allows you to calculate surfaces and solids with plastic material properties and to carry out a stress evaluation. This material model is based on the classic von Mises plasticity.
An elastic foundation can be applied to a member. The foundation is used to include the influence of soil in the modeling. Member elastic foundations can only be defined for the "Beam" member type.
With the nonlinear elastic material model in RFEM 5, you can calculate and carry out a stress analysis of surfaces and solids with nonlinear material properties.
In the "Material Model - Isotropic Nonlinear Elastic" window, you can select the yield laws according to the von Mises, Tresca, Drucker-Prager, and Mohr-Coulomb yield rules. This makes it possible to describe the elasto-plastic material behavior. The yield function depends on the principal stresses or the invariants of a stress tensor. The criteria apply to 2D and 3D material models.
The previous article, titled Lateral-Torsional Buckling in Timber Construction | Examples 1, explains the practical application for determining the critical bending moment Mcrit or the critical bending stress σcrit for a bending beam's lateral buckling using simple examples. In this article, the critical bending moment is determined by considering an elastic foundation resulting from a stiffening bracing.
The elastic deformations of a structural component due to a load are based on Hooke's law, which describes a linear stress-strain relation. They are reversible: After the relief, the component returns to its original shape. However, plastic deformations lead to irreversible deformations. The plastic strains are usually considerably larger than the elastic deformations. For plastic stresses of ductile materials such as steel, yielding effects occur where the increase in deformation is accompanied by hardening. They lead to permanent deformations - and in extreme cases to the destruction of the structural component.
When designing a steel cross-section according to Eurocode 3, it is important to assign the cross-section to one of the four cross-section classes. Classes 1 and 2 allow for a plastic design; classes 3 and 4 are only for elastic design. In addition to the resistance of the cross-section, the structural component's sufficient stability has to be analyzed.
The following article describes designing a two-span beam subjected to bending by means of the RF-/STEEL EC3 add-on module according to EN 1993-1-1. The global stability failure will be excluded due to sufficient stabilizing measures.
RFEM and RSTAB offer different options to model bored piles. One option is to display bored piles as single-valued supports or hinged columns. Another option is realistic modeling while taking the soil into account by means of applying a member elastic foundation. The two following examples will describe it in detail. However, pile base resistance, skin friction, and soil layers are not considered in this technical article.
When designing steel columns or steel beams, it is usually necessary to carry out cross-section design and stability analysis. While the cross-section design can usually be performed without giving further details, the stability analysis requires further user-defined entries. To a certain extent, the member is cut out of the structure; therefore, the support conditions have to be specified. This is particularly important when determining the ideal elastic critical moment Mcr. Furthermore, it is necessary to define the correct effective lengths Lcr. These are required for the internal calculation of slenderness ratios.
One of my earlier articles described the Isotropic Nonlinear Elastic material model. However, many materials do not have purely symmetrical nonlinear material behavior. In this regard, the yield laws according to von Mises, Drucker-Prager and Mohr-Coulomb mentioned in this previous article are also limited to the yield surface in the principal stress space.
A previous article presented different variants of surface elastic foundations in addition to the traditional subgrade reaction modulus method. The following article describes another method for surface foundation. This method considers the adjacent ground areas by means of a foundation overlap. In this case, foundation parameters refer to the continuing works by Pasternak and Barwaschow.
Basically, you can design the structural components made of cross-laminated timber in the RF-LAMINATE add-on module. Since the design is a pure elastic stress analysis, it is necessary to additionally consider the stability issues (flexural buckling and lateral-torsional buckling).
For the serviceability limit state design according to Section 6.6 of Eurocode EN 1997‑1, settlement has to be calculated for spread foundations. RF-/FOUNDATION Pro allows you to perform the settlement calculation for a single foundation. For this, you can chose between an elastic and a solid foundation. By defining a soil profile, it is possible to consider several soil layers under the foundation base. The results of the settlement, foundation tilting, and vertical soil contact stress distribution are displayed graphically and in tables to provide a quick and clear overview of the calculation performed. In addition to the design of the foundation settlement in RF-/FOUNDATION Pro, the structural analysis determines the representative spring constants for the support and can be exported to the structural model of RFEM or RSTAB.
A foundation is usually created in RFEM using the subgrade reaction modulus method. The reason for this is the relatively easy and straightforward manageability. Also, no iterative calculations are necessary and the computing time is relatively short. The subgrade reaction means that, for example, a foundation plate is loaded flat elastically.
SHAPE‑THIN cross‑section properties software determines the effective section properties of thin‑walled cross‑sections according to Eurocode 3 and Eurocode 9. Alternatively, the program allows plastic design of general cross‑sections according to the Simplex Method. In this process, plastic cross-section reserves are iteratively calculated for elastically determined internal forces. The following example describes the effective cross-section properties in the notching area of a rolled I-section. Afterwards, the results are compared with the plastic analysis.
Prior to the analysis of steel cross‑sections, the cross‑sections are classified according to EN 1993‑1‑1, Sec. 5.5, with respect to their resistance and rotation capacity. Thus, the individual cross-section parts are analyzed and assigned to Classes 1 to 4. The cross-section classes are determined subsequently and usually assigned to the highest class of the cross-section parts. If plastic resistance is to be applied to further design of cross-sections of Class 1 and Class 2, you can analyze the elastic resistance of cross-sections as of Class 3. In the case of cross-sections of Class 4, local buckling occurs even before reaching the elastic moment. In order to take this effect into account, you can use effective widths. This article describes the calculation of the effective cross-section properties in more detail.
The following article describes the design of a single-span beam subjected to bending and compression, which is performed according to EN 1993‑1‑1 in the RF-/STEEL EC3 add-on module. Since the beam is modeled with a tapered cross-section and thus it is not a uniform structural component, the design must be performed either according to General Method in compliance with Sect. 6.3.4 of EN 1993‑1‑1, or according to the second-order analysis. Both options will be explained and compared, and for the calculation according to the second-order analysis, there is an additional design format using Partial Internal Forces Method (PIFM) available. Therefore, the design is divided into three steps: design according to Sect. 6.3.4 of EN 1993‑1‑1 (General Method), design according to the second‑order analysis, elastic (warping torsion analysis), design according to the second‑order analysis, plastic (warping torsion analysis and Partial Internal Forces Method).
In RFEM 5.06 and RSTAB 8.06, the nodal support type "Elastic Support via Column in Z…" has been extended so you can use an individual cross‑section as a column cross‑section; for example, HEA from the cross‑section library. The column's cross-section is used to calculate the elastic support.
In the following example, the stability analysis of a steel frame can be performed according to the General Method in compliance with EN 1993‑1‑1, Sect. 6.3.4 in the RF‑/STEEL EC3 add-on module. The first of my three posts shows the determination of the critical load factor for design loads required by the design concept, which reaches the elastic critical buckling load with deformations from the main framework plane.
If a model should contain members with elastic foundations, the contact forces and moments are displayed in numerical form in the result windows. The graphical display of results is specified by the "Members" entry in the Results Navigator.