Steel Design
General
The following design considers EC2 (standard) and the National Annex (NA) for Denmark, Finland, Germany, Hungary, Norway, Sweden and United Kingdom.
With the steel module arbitrary structures in space can be designed with regard to a 1th order or a 2nd order analysis.
In the Code Check all checks prescribed in the codes depending on section type, section class and acting section forces are displayed
Limitations
Torsion
Only uniform torsion (St Venant torsion) is considered in the present version. For thin walled open sections the effect of warping torsion (Vlasov torsion) could be important and must then be considered separately.
Crushing of the web
Crushing of an un-stiffened web due to a concentrated force is not checked in the present version.
Global analysis
General
The design can be performed using either:
- 1th order analysis, using the initial geometry of the structure or,
- 2nd order analysis, taking into account the influence of the deformation of the structure.
Choice between a 1th order or a 2nd order analysis
For structures not sensitive to buckling in a sway mode a 1th order analysis is sufficient. The design for member stability should then be performed with non- sway buckling lengths.
In many cases it is easy to decide if a structure is sway or non-sway but in other cases it could be more difficult.
One way to estimate if the non-sway condition is fulfilled is described in EC3 part 1-1 with the following criterion:
αcr = Fcr / FEd > 10 => Non-sway
where:
αcr is the critical parameter meaning the factor by which the design loading would have to be increased to cause elastic instability in a global mode,
FEd is the design loading on the structure,
Fcr is the elastic critical buckling load for global instability mode based on initial elastic stiffness.
An imperfection calculation in FEM-Design will display the critical parameters for the number of buckling shapes required by the user as shown below.
Critical parameter αcr displayed for the three first buckling shapes with regard to load combination L1.
As all critical parameters are > 10 a 1th order analysis and a design with non- sway buckling lengths would be sufficient in this case.
If the criterion above is not fulfilled 2nd order effects must be considered but a 1th order analysis could still be used in most cases. This could be done either by amplifying the 1th order moments or by using sway-mode buckling lengths. In FEM-Design the latter method should be used.
A full 2nd order analysis can be used for steel design in all cases.
Structural stability
The calculations with regard to instability will be performed in different ways depending on the type of analysis.
1th order theory
For a 1th order design the following apply:
Both the flexural, lateral torsional and torsional buckling are calculated depending on the slenderness with respect to reduction factors specified in the appropriate code. The reduced slenderness for flexural and torsional buckling may be computed as:
λ = [A fy / Ncr]1/2
The critical normal force for flexural buckling Ncr will in this case be calculated using appropriate buckling lengths defined by the user in both directions for all members. The critical normal force Ncr for torsional buckling will be calculated according to support conditions defined by the user for all members. The reduced slenderness for lateral torsional buckling may be computed as:
λLT = [W fy / Mcr]1/2
The critical moment Mcr will be calculated as buckling of the compressed flange with regard to a buckling length defined by the user.
Imperfections
Initial bow imperfections may be neglected as these effects are included in the formulas for buckling resistance of the members.
For sway mode structures initial sway imperfections has to be considered. This could be done by changing the geometry before calculation or by defining systems of equivalent horizontal forces as described below
2nd order theory
A 2nd order calculation produces the critical normal force Ncr for flexural buckling and a corresponding stability check is not required. The critical normal force Ncr for torsional buckling or the critical moment Mcr are not calculated since a basic finite element only contains the second order effects of the axial force and the effect of warping is neglected. The effect of the lateral torsional and torsional buckling will then have to be calculated as for 1th order above.
Imperfections
For all structures initial local bow imperfections should be considered.
As the flexural buckling design is based on the 2nd order effects of the bending moments it is vital that there is a moment distribution in all members. By considering local bow imperfections this is ensured also for hinged members without lateral load.
For sway mode structures also initial sway imperfections has to be considered. This could be done in the conventional way by changing the geometry before calculation or by defining systems of equivalent horizontal forces as described in the section below.
In FEM-Design both initial bow imperfections and initial sway imperfections are considered automatically by using an alternative method presented in EC3 1-1 as described below in the section below. The user has to connect each load combination to one of the calculated buckling shapes and the program will then calculate imperfections with regard to this shape. It is up to the user to decide how many buckling shapes that has to be considered and to which load combinations these shapes should be connected to receive an adequate result. No design based on a 2nd order analysis for compressed members can be performed without considering imperfection for one of the available buckling shapes. Some examples describing this process are presented in the manual Useful examples.
Imperfections for global analysis of frames
The following imperfections should be taken into account:
- Global imperfections for the structure as a whole.
- Local imperfections for individual members.
The assumed shape of global imperfections and local imperfections may be derived from the elastic buckling mode of a structure in the plane of buckling considered.
Both in and out of plane buckling including torsional buckling with symmetric and asymmetric buckling shapes should be taken into account in the most unfavorable direction and form.
For frames sensitive to buckling in a sway mode the effect of imperfections should be allowed for in frame analysis by means of an equivalent imperfection in the form of an initial sway imperfection and individual bow imperfections of members.
Conventional method
Global initial sway imperfections
This effect could be considered in two ways.
- By changing the frame geometry before analysis with the slope as shown below. The slope φ will be calculated according to the relevant code.
- By defining a system of equivalent horizontal forces as shown below:
Where, in multi-storey beam and column building frames, equivalent forces are used they should be applied at each floor and roof level.
These initial sway imperfections should apply in all relevant horizontal directions, but need only be considered in one direction at a time.
The possible torsional effects on a structure caused by anti-symmetric sways at the two opposite faces, should also be considered
- Relative initial local bow imperfections of members for flexural buckling
Equivalent horizontal forces introduced for each member as shown below could consider this effect.
The value eo considering initial bow as well as residual stresses is calculated according to the relevant code.
Alternative method
As an alternative to the methods described above for calculating imperfections the shape of the
elastic critical buckling mode ηcr of the structure may be applied as a unique global and local imperfection according to EC3 1-1. This method is used in FEM-Design when a 2nd order analysis together with imperfection for one of the available buckling shapes is chosen.
The amplitude of this imperfection may be determined from:
