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  • Answer

    Due to the nonlinear calculation, especially the definition of slippage is a challenge for the equation solver. The following hints can help you to avoid possible instabilities.

    Load Increments
    When considering nonlinearities, it is often difficult to find the equilibrium. You can avoid instabilities by applying the loading in several steps (see Figure 01). For example, if two load steps are specified, half of the load is applied in the first step. The iterations are performed until the equilibrium is found. Then, in the second step, the complete load is applied to the already deformed system and the iterations are performed again until the state of equilibrium is reached. Please keep in mind that the load increments have an unfavorable effect on the computing time. Therefore, 1 (that is, no incrementally increasing load) is preset in the text box. Furthermore, it is possible to specify how many load steps should be applied for each load case and load combination (see Figure 02). The global settings are then ignored.

    Definition of Slippage
    Generally, slippage (for example, in a connection) is defined by means of the "Partial Activity" nonlinearity (see Figure 03). It can be used to define the hinge displacement from which the forces should be transferred. As you can see in the diagram, the stop, that is the stiffness that acts according to the corresponding release displacement, is considered as rigid (vertical branch, see the red arrows). However, under certain circumstances, this may lead to numerical problems in the calculation. To avoid this, the stiffness that acts according to the release displacement should be slightly reduced. You can achieve this by defining a very stiff spring (see Figure 04).

    In addition to the very stiff stop, numerical problems may occur within the slippage. In this case, a small stiffness has to be considered for the effect of the slippage in order to increase the horizontal branch a little bit. The stiffness should be selected so small that it has no decisive effect (see Figure 05). This situation is possible by using the "Diagram"nonlinearity.

    Arrangement of Member Hinges
    When arranging the hinges, you should ensure that they are not defined in the same direction on both member ends. Thus, there is a state in which the member is not sufficiently supported and the system already fails in the first iterations. In such a case, the slippage on one side of the member only should be defined and the size of the slippage adjusted accordingly (see Figure 06).

  • Answer

    This feature is intended to detect the modeling errors in a structure that may lead to instability. Using this method, it is possible to calculate such systems and to graphically determine the instability cause.

    This feature is not suitable for the following problems:
    • Calculation aborts due to overloading (stability problems)
    • Determination of buckling curves and buckling modes
    If the system is stable and the stability problems only occur during the calculation according to the second-order analysis, this function sets all results to 0.

    A detailed description of solving the instability problems is included in FAQ 2257.
  • Answer

    There can be various reasons for the calculation abort due to an unstable structural system. On the one hand, it can indicate a "real" instability due to overloading the structural system, but on the other hand, the modeling inaccuracies may also be responsible for this error message. In the following, you can find a possible procedure of how to find the instability cause.

    1. Check of Modeling

    First, you should check if the modeling of the structural system is correct. It is recommended to use the model check tools provided by RFEM/RSTAB (Tools → Model Check). For example, these options allow you to find identical nodes and overlapping members, so you can delete them, if necessary.

    Furthermore, you can calculate the structure subjected to pure dead load in a load case according to the linear static analysis, for example. If results are displayed subsequently, the structure regarding the modeling is stable. If this is not the case, the most common causes are listed below (see also the video "Model Check" under "Downloads"):

    • Incorrect definition of supports / lack of supports
      This can lead to instabilities as the structure is not supported in all directions. Therefore, the support conditions must be in equilibrium with the structural system as well as with the external boundary conditions. Statically overdetermined or kinematic systems also lead to calculation aborts due to a lack of boundary conditions.

      Figure 02 - Kinematic System - Single-Span Beam Without Rigid Support

    • Torsion of members about their own axis
      If members rotate about their own axis, that is, a member is not supported about its own axis, it can lead to instabilities. This is often caused by the settings of member hinges. Thus, it may happen that there are the torsional releases entered at both the start node and the end node. However, you should pay attention to the warning that appears when starting the calculation.

      Figure 03 - Entering Torsional Releases on Start and End Nodes

    • Missing connection of members
      Especially in the case of large and complex models, it may quickly happen that some members are not connected to each other, and thus they "float in the air." Also, if you forget about crossing members that should intersect with each other, it can lead to instabilities as well. A solution provides the model check of "Crossing Unconnected Members," which searches for the members that cross each other, but do not have a common node at the intersection point.

      Figure 04 - Result of Model Check for Crossing Members

    • No common node
      The nodes rest apparently at the same location, but on closer inspection, they deviate slightly from each other. This is often caused by CAD imports, and you can correct it by using the model check.

      Figure 05 - Result of Model Check for Identical Nodes

    • Formation of hinge chain
      Too many member end hinges on a node can cause a hinge chain that leads to a calculation abort. For each node, only n-1 hinges with the same degree of freedom relative to the global coordinate system may be defined, where "n" is the number of connected members. The same applies to line releases.

      Figure 06 - Kinematic System due to Hinge Chain

    2. Check of Stiffening

    If the stiffening is missing, it may also lead to the calculation aborts due to instabilities. Therefore, you should always check whether the structure is stiffened sufficiently in all directions.

    3. Numerical Problems

    An example of this is shown in Figure 08. It is a hinged frame that is stiffened by tension members. Because of the column contractions due to vertical loads, the tension members receive small compressive forces in the first calculation step. They are removed from the structure (since only tension can be absorbed). In the second calculation step, the model without these tension members is unstable. There are several ways to solve this problem. You can apply a prestress (member load) to the tension members in order to "eliminate" the small compressive forces, assign small stiffness to the members, or remove the members one by one in the calculation (see Figure 08).

    4. Detecting Causes of Instability

    • Automatic model check with graphical result display
      The RF-STABILITY (RFEM) add-on module can help you to obtain the graphical display of the instability cause. Select the "Calculate eigenvector for unstable model…" (see Figure 09), it is possible to calculate the unstable structure. The eigenvalue analysis is performed on the basis of the structural data so that the instability of the affected structural component is displayed graphically as a result.

      Figure 09 - Graphical Display of Instability

    • Critical load problem
      If load cases or load combinations are calculated according to the geometrically linear analysis, and the calculation is only aborted as of the second-order analysis, there is a stability problem (critical load factor less than 1.00). The critical load factor indicated which coefficient must be used to multiply the load so that the model subjected to a specific load becomes unstable (for example, buckling). Therefore: The critical load factor of less than 1.00 means that the system is unstable. Only the positive critical load factor greater than 1.00 allows for the statement that the loading due to the specified axial forces multiplied by this factor leads to the buckling failure of a stable structure. In order to find the "weak point," the following approach is recommended, which requires the RF‑STABILITY (RFEM) or RSBUCK (RSTAB) add-on module (see also the video "Critical Load Problem" under "Downloads").

      First, it is necessary to reduce the load of the affected load combination until the load combination becomes stable. The load factor in the calculation parameters of the load combination can help. This also corresponds to the manual determination of the critical load factor if the RF-STABILITY or RSBUCK add-on module is not available. In the case of pure linear structural elements, it may already be sufficient to calculate the load combination according to the geometrically linear analysis and select this directly in the add-on module. Then, the buckling curve or shape can be calculated and displayed graphically on the basis of this load combination in the corresponding add-on module. The graphical result display allows you to find the "weak point" in the structure and then optimize it specifically. By default, the RF-STABILITY or RSBUCK add-on modules only determine global mode shapes. In order to also determine the local mode shapes, it is necessary to activate the member division (RF‑STABILITY), or to increase the division for trusses to "2" at least (RSBUCK).

      Figure 10 - Activating Division for Members in RF-STABILITY

      Figure 11 - Member Division in RSBUCK

  • Answer

    It is quite likely that the high deformations are caused by the consideration of shrinkage and the horizontal storage in the model.

    The shrinkage is taken into account internally on the load side as elongation, in which connection a failure due to the prevention of shrinkage is also possible. If the shrinkage is prevented by a non-displaceable horizontal bearing, forces are created which can lead to failure of the concrete and thus to a significant increase in deformation or even instability of the model.

    In this context, it is important that when using the nonlinear deformation calculation, the boundary conditions of the model are mapped as realistically as possible.

  • Answer

    Basically, you should pay attention to the following points:

    Entering Model

    The structure in RF‑STAGES and RFEM may differ due to the definition in RF‑STAGES. Therefore, the structure in RF-STAGES may be different than in RFEM. In order to find the instability at a certain construction stage, it is necessary to model the structure in this construction stage in RFEM and take it into account separately. In this context, it should also be noted that the entries are not synchronized between RFEM and RF-STAGES. For example, a member end hinge removed in RFEM is not automatically removed in the RF-STAGES model.

    Method of Analysis

    RF-STAGES calculates permanent load cases according to the large deformation analysis. As a result of this analysis, instabilities may occur which are not present in a load case when calculating according to the linear static analysis (critical load problems), for example.

    Special Structural Elements

    Some of the structural elements available in RFEM are not supported in RF‑STAGES. These structural elements can also cause the instability in certain cases. The following structural elements are not fully supported in RF‑STAGES:

    • Line hinges
    • Member elastic foundations
    • Sets of members
    • Intersections
    • Nodal releases
    • Line releases
    • Surface releases
    • Nodal constraints
  • Answer

    In the first iteration step, all members are considered. Before the next step, the program determines which members cannot resist the determined compressive forces due to their definition, for example tension members with negative axial forces. Then, the tension member with the greatest compressive force is removed from the stiffness matrix. Thus, the next iteration step follows.

    Next, the member definitions are compared to the determined axial forces. For the next iteration step, the tension member subjected to the highest actions is removed from the stiffness matrix. This procedure is continued until no member is subject to the internal forces that it cannot resist.

    In this way, you can often achieve a better convergence behaviour for the system because of redistributing effects. This calculation option requires more time because the program must run through a larger number of iterations. Furthermore, you have to make sure that a sufficient number of possible iterations is set (see the 'Settings' dialog box section in Figure).

    For this method, it might also happen that the initially failed member is reinserted, because it is subjected to tension forces due to possible redistribution effects.

  • Answer

    The member end rests geometrically exactly on the pipe surface, but the automatic integration of structural elements is only possible for plane surfaces. Since the end point of the member was not integrated into the pipe surface, no common FE node is created. For RFEM, the member has no connection to the pipe, thus resulting in a termination of the calculation.

    You can manually integrate the member end node into the pipe surface: double-click the pipe surface to open the 'Edit Surface' dialog box. In the 'Integrated' tab, you can integrate the node as long as the 'Automatic object detection' option is deactivated (Figure 01).

    Due to the integration, the member is connected to the pipe surface. A common FE node is created and the calculation is performed successfully (Figure 02).

  • Answer

    The calculation can be terminated due to an unstable structural system for various reasons. There can be a 'real' instability due to overloading the system, but the instability effects may also be caused by failing members.

    In the calulcation parameters, you can deactivate the nonlinearity 'Members due to member type' (see Figure 01). If the calculation is then possible without the error message, the problem is probably caused by failing members.

    Figure 01 - Deactivating Nonlinearities

    The complete failure of the tension members can be prevented using the option 'Failing Members to Be Removed Individually During Successive Iterations' in the dialog box Global Calculation Parameters (see Figure 02). This should help in most cases. The number of possible iterations should be specified sufficiently large.

    Figure 02 - Removing Failing Members Individually

    An alternative method is to apply a prestress to the tension members to prevent the failure of them.

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