The Direct Analysis Method
AISC developed the Direct Analysis Method (DAM) as a solution to meeting stability analysis and design requirements in a modern way that is most suitable for implementation in analysis and design software. This method is not limited in its application, applies to all buildings when designing to US codes, and is the most general and accurate approach provided. The requirements for the DAM include:
 Secondorder analysis: A secondorder analysis which considers both PΔ and Pδ effects is required.
 Initial imperfections: The effects of initial imperfections of the structure geometry are considered by applying notional loads, which are lateral loads proportional to the gravity loads applied at each framing level.
 Inelasticity: The axial and flexural stiffnesses of members that contribute to the stability of the structure are required to be reduced. This is to account for the effects of residual stresses that lead to inelastic softening before the members reach their design strength.
 Effective Length Factor: Setting K to be 1.0 can be allowed because the effects for which it was meant to compensate (initial imperfections and inelasticity) have already been accounted for in the method.
DAM implementation in Tekla Structural Designer
Tekla Structural Designer implements the Direct Analysis Method fully, using a rigorous secondorder analysis. The following table describes how the AISC requirements have been implemented.
AISC Required effect to be considered  Tekla Structural Designer implementation 

Flexural, shear, and axial deformations  A general 3D analysis is performed which considers all required deformations. 
All component and connection deformation that contribute to the lateral displacement of the structure  All moment connections are assumed to be fully restrained. As is typical of most analysis programs, it is rationalized that these deformations do not contribute significantly to the stability of the structure and are therefore not directly included in the analysis. 
Secondorder effects (both PΔ and Pδ) 
The Chen and Lui rigorous secondorder analysis is implemented. The twocycle iterative method automates a twopass analysis procedure during which nodal displacements are used to determine ‘stress stiffening’ in structural elements. The resulting matrix accommodates the PΔ and Pδ effects as well as accounting for ‘stress stiffness’. See also: What are the "2nd Order" Analysis options listed on the Analyze Ribbon in TSD? Are they the same as "PDelta" analysis? 
Geometric imperfections  Notional loads are calculated and applied wherever there's a column stack or wall panel division based on the gravity load for each appropriate load combination. 
Member stiffness reductions due to residual stresses  All relevant members have reduced axial and flexural stiffnesses, the default for this being 0.8. The option to take t_{b} = 1.0 and increase the notional load factor is exercised. 
Choice of analysis type

Firstorder analysis
This option is not suitable for final design of steel members. A standard linear elastic static analysis is included within Tekla Structural Designer to assist the user with steel structures that prove to be unstable and fail to complete secondorder analysis.
The results from the firstorder analysis can be utilized to "predesign" all members, after which you are more likely to have sections that will be sufficient for secondorder analysis to solve.
The firstorder analysis is also used to determine both building drifts and member deflections in order to determine structure stability, seismic drift and serviceability design. The stability coefficient (Δ_{2}/Δ_{1}) is based on an approximate calculation of the secondorder deflections of the structures based on the firstorder analysis results.

Secondorder Analysis
This option is suitable for use in the Direct Analysis Method. Secondorder analysis is performed using a two step iterative method incorporating a geometric stress stiffness matrix. An initial linear static analysis is performed, the stiffness matrix is updated to account for forces derived from initial displacements and finally a second linear static analysis is performed using the modified stiffness matrix.
This secondorder analysis accurately determines both:
 PΔ (Pbig delta) effects resulting from loads acting on the global deformation of the entire structure or a part of the structure
 Pδ (Plittle delta) effects resulting from the line of action of the axial force in a member acting at an eccentricity due the deformed shape of the member.
The forces resulting from this analysis are utilized in the member design.
Also during the design process firstorder analysis is used to determine both building drift and member deflections in order to determine structure stability, seismic drift and serviceability design.
The stability coefficient (Δ_{2}/Δ_{1}) is based on a combination of results from both the second and firstorder analyses.
Note: There is potential for buckling to occur during 2nd order analysis. See the following article for more details: What is 2nd Order Buckling Analysis? How and when would I use it?
Analysis model adjustments
Certain adjustments should be made to the structural model in order to prepare it for analysis – these are controllable by the user.
 For both first and secondorder analysis
 concrete member section properties should be set as cracked, and suitable Modification Factors should be applied via Analysis Settings, (see ACI 31805 10.11.1)
 For secondorder analysis
 2005 AISC Specification 7.3 (3) & (4) requires that for those
members whose stiffness is considered to contribute to the lateral
stability of the structure, a reduced flexural stiffness (EI) and a
reduced axial stiffness (EA) must be used in the analysis. In Tekla Structural Designer, a reduction factor of 0.8 (default) is automatically applied to the
stiffness (EI and EA) of all steel members. You are able to review this
default stiffness factor and adjust it if you require via Design Settings >
Analysis. Note: The above factor is applied in addition to any Modification Factors specified for steel members in Analysis Settings.
 2005 AISC Specification 7.3 (3) & (4) requires that for those
members whose stiffness is considered to contribute to the lateral
stability of the structure, a reduced flexural stiffness (EI) and a
reduced axial stiffness (EA) must be used in the analysis. In Tekla Structural Designer, a reduction factor of 0.8 (default) is automatically applied to the
stiffness (EI and EA) of all steel members. You are able to review this
default stiffness factor and adjust it if you require via Design Settings >
Analysis.
Additionally, in order to adhere to the Direct Analysis Method, certain extra enhancements are made to the analysis model:
 For both first and secondorder analysis
 All load combinations require a minimum lateral load at each level of the structure of
0.2% (2005 AISC Specification 7.3 (2)). In addition, Tekla Structural Designer assumes τ_{b} = 1.0, so an additional 0.1% is required
(2005 AISC Specification 7.3 (3)).
It is the user's responsibility to include notional loads in combinations using the combinations wizard. for these Tekla Structural Designer automatically calculates the additional notional load to be 0.3% of the gravity component in each combination. (Although the user is provided with an option in Model Settings to override this with their own percentage values if they require.)
Hence in combinations that have notional loads included by the user, Tekla Structural Designer automatically calculates the additional notional load to be 0.3% of the gravity component in each combination. (Although the user is provided with an option in Model Settings to override this with their own percentage values if they require.)
 All load combinations require a minimum lateral load at each level of the structure of
0.2% (2005 AISC Specification 7.3 (2)). In addition, Tekla Structural Designer assumes τ_{b} = 1.0, so an additional 0.1% is required
(2005 AISC Specification 7.3 (3)).
 For secondorder analysis
 For designs using ASD, prior to secondorder analysis all loads are automatically factored up by 1.6 and before design, all design forces are reduced by a factor of 1.6 as required by 2005 AISC Specification 7.3 (1).
Suggested workflow
When applying the Direct Analysis Method the following approach is recommended. This helps to avoid spending unproductive time on analysis issues and a potentially overly conservative design:
 Never just construct a model (or import one e.g. from Revit) and attempt design using secondorder analysis straight away (by setting Design > Settings > Analysis > Secondorder).
 Always conduct a full Firstorder analysis and design for both gravity and
lateral combination to size members for these by setting Design > Settings
> Analysis > Firstorder. This should ensure that:

There are no mechanisms  troubleshoot and remove any mechanisms that come to light at this stage by following this article Guide to resolving Mechanisms.

Section sizes are sensible and adequate for Firstorder design forces. They will then usually be adequate for secondorder analysis without buckling (though not always). See this article for more about this; I have analysis Warnings and/ or Errors about buckling. Why is this happening and what do I do about it?

 It is a good idea to assess displacements and Drift check results after this initial design also as these can highlight parts of the structure that are poorly braced or not well connected to the lateral force resisting system (LFRS). However bear in mind that these are not final results  secondorder analysis may lead to increased section sizes which will moderate drift results.
 Only when all members are passing at this stage, and overall displacements and drift results appear reasonable, should you proceed to secondorder analysis and design. Set Design > Settings > Analysis > Secondorder and first perform a “check” design, by turning off autodesign for all members then running a Design (Static) command, and assess the results of this.
 Members that now fail at this stage are most likely to be members in the LFRS
since secondorder magnification effects will tend to be largest in these. If
there are only a few failing members, consider skipping to step 6. Otherwise,
set ONLY the failing members to autodesign on, then run a full model design
(Design (Static)).

When this is complete, assess the efficiency of the section sizes assigned to the autodesigned members by examining their utilization ratios (URs) (tip  Design review filters can help with this). If the UR’s are low, it may be that presize sections (which are assigned to all autodesign members for the first analysis run) are causing excessive secondorder magnification of design forces leading to inefficient section selection.

Though it is rare, buckling issues may occur during the secondorder analysis if the presize sections are inadequate. The "Prevent out of plane instability" setting can be used to mitigate this in some circumstances as described in this support article.

 If there are only a few members failing the secondorder checkdesign  or if
excessive secondorder magnification or buckling of presize sections is
occurring  we recommend conducting a 'manual' iterative secondorder analysis
and design as follows:
 After setting secondorder analysis for design and running a “check” design as described in step 4) above, add any failing members to a sub structure and set them to autodesign on.
 Run a design of this substructure ONLY from the Structure tree
context menu as shown in the picture below. Note that when this is complete
by default this will set autodesign off for the members in it (but check
that this is the case).
 Run a “check” design of the entire structure  this updates the global analysis results for the new sections which may produce a change in member forces so some members may now fail again.

Set any failing members (ONLY) back to autodesign, update the sub structure if necessary, then design it once more.
 Iterate steps c) and d) until all members are passing.

This "manual" iterative approach avoids the potential for presize sections to fail analysis due to buckling or cause excessive secondorder amplification leading to a suboptimal design solution.

Note however that you may still need to manually size members to satisfy Drift checks or, for members of a SFRS, to pass specific seismic design checks (members are not autosized for these).
