Friday, 25 September 2015


Guidance for the application of imperfections in ConSteel 9 

Part 1

This guidance on the imperfections is scheduled to be a series, what would cover the use of the imperfection functions in ConSteel, background theory of imperfections by the Eurocode (1993-1-1), and practical uses of imperfection functions in ConSteel.
This first part of the series will show the types of the imperfection types of the Eurocode, and how to use these implemented imperfection functions in ConSteel.

Basically, EC 3 defines 3 methods for the stability checks of individual members and global structures:
a, Slenderness and reduction factor based method (1993-1-1 part 6.3)
b, Imperfection method (1993-1-1 part 5.3)
c, Imperfection and slenderness/reduction factor based method (1993-1-1 part 5.2.2 b) )

Eurocode defines two types of imperfections, local and global types. Local imperfections are applied on individual members, while global type of imperfections are applied on the whole structure. 

Application of imperfections in ConSteel
Local imperfections:

Initial bow can be defined on the property bar, as a member attribute of the selected bar member at the Bow imperfection cells. It is a half sinus wave with a set amplitude, based on the length of the member. Independent from the loadings, and from support system.It can be defined in the direction of Z and Y axes of the bar members local coordinate system.  Direction of the bow imperfection can be changed in the positive and negative directions of the axes with a minus (-) sign.

After defining an initial bow on the model, it will automatically taken into account during the analysis, since it is a model attribute. No further settings are required.

Relative initial bow of members for flexural buckling is defined as a local imperfection by Eurocode 3, part 5.3.2 (b). The design value of the amplitude eo/L is based on the buckling curves, according to the table 6.1 of EN3. These buckling curves are determined from test results which were performed on fork-pinned columns.

Global types of imperfections

Global types of imperfections can be taken into account during the analysis, by choosing them from the Global imperfection Dropdown menu on the analysis parameters dialog.

Initial sway defines a sway on the whole model. Usually this effect is negligible in certain types of structures. It is used in the case of those frames, which are sensitive to buckling in a sway mode.  The formula for the calculation of φ is given in ConSteel. More types of initial sway imperfections can be defined in different directions, with different extents. It can be chosen later, at the analysis parameters tab that which one should be used for the analysis of the structure.
On the finite element model, we can get a feedback about the applied initial sway imperfection, as the picture below shows. If it is checked at the analysis parameters tab, further calculations will be applied on this modified finite element model.

Initial sway is defined in part 5.3.2 (a) of EN 1993-1-1. Value of initial sway is depending on the height of the applicable columns, height of the structure, and number of the columns in a row. It should be applied in all relevant horizontal directions, but need only to be considered in one direction at a time.

Notional load or the equivalent horizontal force. It can be taken into consideration in any load cases, and load combinations with the checkboxes. ConSteel checks (on finite element level), if there are vertical loads in the loadcases/combinations on columns. Vertical loads will be multiplied with the multiplication factor, and it will be placed as a horizontal force in the desired direction, what can be chosen automatically, or it can be given manually. In case of automatic choice of direction, ConSteel checks all of the directions, and the vertical loads will be placed in the dominant one.

Method of equivalent horizontal forces is defined in EC1993-1-1 chapter 5.3.2 (5)B, (7).

Application of eigenshapes can cover local and global imperfections too, depending on the applied buckling shape.
The method of the eigenshape application is the following. After a buckling analysis, we will get the buckling shapes of the model, what we can use to modify the finite element model, and use them as imperfections. Next time, if we take into account the imperfection during the analysis of the model, it will be performed on this modified finite element model. Steps of defining imperfection using the function:

  1. Click "Apply eigenshape as imperfection" after buckling analysis is performed. The dropdown menu can be reached with a right click on the bar member.
  2. On the next dialog, Type of the amplitude can be selected (mm or multiplication factor). In case of chosing "mm" option, the amplitude will be defined where the maximum deformation of the finite element points are. In case of choosing the multiplication factor, a multiplicator has to be given by the buckling values of the model. (It is important, that these buckling values has no physical content, they are normalized, in order to be able to display). Value of the amplitude can be defined manually, OR by clicking the three dots button, what will lead to step 3
  3. On the amplitude of eigenshape dialog, there is two options of defining the amplitude, based on different parts of the standard. The first (upper blue box on the picture below) is based on the equivalent initial bow imperfection (Table 5.1), and the second is based on the elastic critical buckling shape (lower blue box on the picture below).
  4. On the global imperfections dialog, further options are available. Values of amplitudes can be still modified here, manually. Different amplitudes can be defined for different buckling eigenvalues. It can be decided here, that which of them should be taken into account.

Used chapters of the standard:
Equivalent initial bow imperfection 1993-1-1 5.3.2 (3) b)
Equivalent imperfection based on the elastic critical buckling shape 1993-1-1 5.3.2 (11)


For further information about structural imperfections, please check out our webinar about this topic:
Application of structural imperfections in the design to Eurocode 3