# How are sway deflections calculated?

Sway deflections are calculated using a 'special' combination. The term ‘special’ is used to denote that the combination considered by analysis for this purpose is different to the static combinations. It is different in the following ways:

- The ‘special’ combination is derived for each static combination in which NHF/EHFs are included and is specific to each combination
- It considers
**only the gravity loads**in the combination, not lateral loads- For more about this point, see the article
__How are EHFs used in Tekla Structural Designer and what for?__

- For more about this point, see the article
- It consists of the required % of the
gravity loads in the combination__factored__. So it includes only lateral loads. It does not contain any vertical loads at all.__applied laterally__- Though codes and design guides usually talk about a total NHF/EHF
load, Tekla Structural Designer actually calculates and applies them in a more sophisticated manner by determining the amount of gravity load arriving at each column/ wall in each level.*level*- This is done by first calculating the differential in axial load above/ below the level for each column/ wall for all levels for each combination with NHF/EHF’s applied to give the total (factored) gravity load arriving at each column/ wall in each level.
- This method automatically considers the actual distribution of gravity load in levels and accounts for such things as transfer beams and slabs.
- Note that exactly the same method is used to calculate the weight distribution for seismic loads (for the Seismic Weight combination) - because this is exactly the same thing. In essence Gravity load = weight.

- The required % of this load (e.g. 0.5% for sway for the BS and Eurocodes) is then calculated and applied
at each column/ wall for all levels__laterally__ - You can view the applied lateral NHF/EHF loads in the Results view (see pictures below). Tekla Structural Designer has this feature to view them so that you can understand the nature and application of NHL/EHF loads and hence the origin of the sway deflections. The same logic applies to the similar feature Tekla Structural Designer has to look at the seismic loads in the Results View.

- This is done by first calculating the differential in axial load above/ below the level for each column/ wall for all levels for each combination with NHF/EHF’s applied to give the total (factored) gravity load arriving at each column/ wall in each level.

- Though codes and design guides usually talk about a total NHF/EHF
- The sway deflections - both those displayed in the Results View > Drift > Sway deflections and in the sway checks - are derived from the solution of this 'special' combination of lateral (only) loads.
- The ‘special’ combinations are formed and solved internally (using 1st order linear analysis). They are NOT listed specifically in combinations for results viewing and we do not have access to all results for them elsewhere, since only the deflections from them are of interest. The deflection results are viewable via the Results View > Drift > Sway... results and sway check tabular results and details.

**I notice that the lateral deflections for a static combination with NHF/EHFs are different to the sway deflections for this combination - why?**

From the above answer, we should understand that the sway deflections are the result of** lateral loads only**.

However lateral deflection - sway - can also result from vertical-only loading. Such deflections are of course included in the deflections of the static combinations which include vertical loads. We can verify this by looking at the deflections of gravity combinations (those without any lateral load in).

Unless the geometry, distribution of stiffness and loading of a building is perfectly symmetrical, some sway from gravity (vertical) loads only will always occur and it can be considerable. Hence, for most practical building structures, the lateral deflections of static combinations will always be somewhat different to the sway results, potentially significantly so.

The entire point of sway checks is to assess the lateral flexibility of the building - and hence its susceptibility to 2nd order effects - by the application and solution of a set of lateral loads NOT vertical loads as well. Hence importantly we calculate, apply and solve internally the ** lateral only** EHF/NHF loads for each combination.

See the pictures below illustrating this:

- Comparison of static combination deflections for a
combination without EHFs and the same combination including these. These are then compared with the Sway deflections for the combination with EHFs. Note that:__GRAVITY__- There are lateral deflections for the
combination__GRAVITY__ - When these are subtracted from those of the combination WITH EHFs the resulting values are the same as those of the Drift > Sway results.
- Note however that this is NOT how the Drift > Sway results are actually calculated - they are calculated as described above.

- There are lateral deflections for the
- We can view the applied EHFs via the Results View > EHF ribbon button as shown below. It is the solution of these that produces the sway deflection results.
- We can verify this by creating and analyzing a load case with these loads applied manually as nodal loads as shown below.
- Note that for the Eurocode, the graphical EHF values shown are only the same as those used in the sway check when 0.5% is also used for Global Imperfections EHFs