1. Introduction #
In the AXISVM program, an important parameter for the stability analysis of steel and timber design elements is the buckling length. The buckling length depends on the support and restraint conditions of the structural element. Currently, the program allows the direct input of the buckling length, the buckling factor (restraint factor) and an automatic calculation option for steel design elements.
2. Problem statement #
For a complex structure, where it is not obvious what to use, there may be difficulties to get these values. For example, as in the case of bridge-like structure below, the buckling length/factor of the marked chord member must be determined. The cross-section of the design member is HEB180 and the length is 13.60 m. The aim is to determine Ky, which describes the displacement of the out of plane buckling of the lattice structure.
To solve this problem, Buckling length based on buckling shape, available in X8, helps to determine the buckling length/ buckling factor obtained from the result of Buckling analysis directly from the buckling shape.
3. Application of the method #
To use this function, it is necessary to have result of the Buckling analysis (Buckling tab). It is recommended to choose load cases and load combinations, that are relevant for the design member to get the critical cases.
On the left side of the pop-up window there is a tree with load cases and load combinations for which the calculation has been carried out in the buckling analysis. The elements of the tree can be optionally switch on and off. In the middle there is a summary table and on the right there is a model window to display the displacements of the selected buckling shape.
The last column of the table is the Selection, here you can select the relevant shape. The program calculates so-called sensitivity factors to help in the selection. Each sensitivity factor is listed below in the order of the columns founded in the table:
Directional sensitivity factor: Sdir
→ It shows the fraction of the strain energy of the design member that is due to buckling about the certain axis. For pure buckling about the certain axis, the value is 100%. A reduced value indicates the presence of buckling in the opposite plane or flexural torsional buckling. In the latter case, the displacement in the plane under investigation may also belong to a lateral torsional buckling.
Structural sensitivity factor: Sstruct
→ It shows the fraction of the total strain energy of the whole structure that is due to the buckling of the design member about the certain axis. For local buckling of the design member, the value is 100%. A reduced value indicates that the loss of stability is not or not only due to the selected design member.
- Buckling mode shape sensitivity factor: Smode
→ The ratio of the strain energy of the design member in the certain buckling shape to the sum of the strain energy for the calculated buckling shapes with positive eigenvalue. A high value indicates the buckling shapes in which the deformation of the design member about the certain buckling axis is significant. This value is the best indication of which buckling shapes are recommended to investigate.
The recommended aspects of the selection of the critical buckling shape: A high value for the Smode shows which buckling shapes are recommended to take into consideration. From these shapes probably the shape with smallest eigenvalue is the corresponding. A reduced value of Sdir or Sstruct indicates that the buckling shape is not local. For the selection, the buckling shapes always have to be checked visually.
In the Problem statement the critical load combination is the 11th for the marked design member. Among several other load combinations, the buckling analysis was also performed for this case. The results for the 11th load combination are shown in the following table.
Based on the Smode sensitivity factor, the two highest values are given by 2nd and 4th buckling shape. Considering the displacement diagram, the 2nd is a global buckling shape and shape 4th is local. The shape is recommended to select, because of the slightly higher value of Ky and the associated lower load factor. Thus Ky = 0.308 is determined. As mentioned earlier, visual checking of the displacements is essential in the selection.
Design with AXISVM, users already had the option to manually or in tabular form to determine the buckling lengths based on eigenvalues. Our new feature, available in version X8 makes it easier, reduces the possibility of errors and gives you more control over the buckling parameters during the design.
