Sway sensitivity is automatically determined in **ProtaStructure** when the design code is set to EC2 and ACI.

For other codes as discussed below, an assessment of sway sensitivity can also be made, however it should be noted this is based on analytical results and the recommendations of the ACI code.

Whenever sway sensitivity is assessed automatically you are advised to be aware of the limitations that apply.

These can be viewed by clicking the *‘Limitations’* button on the **Building Analysis **menu > **Reports** > next to **Slenderness Calculation** / **Sway Classification Report**.

The **Lateral Drift & Bracing** can be assessed via the Settings Center > Project Settings.

In both the BS8110 & CP65 code, there are no provisions for assessing sway sensitivity by analytical methods.

Therefore, when using BS8110 or CP65, we recommend you check the option for **"****User Defined Bracing for Columns and**** ****Walls" **and then apply the condition (braced or unbraced) that you deem appropriate for the building.

If you do not check this option, ProtaStructure will make an assessment of sway sensitivity based on analytical results and the recommendations of the** ACI **code.

This assessment is lateral deflection dependent. ACI code gives guidance on appropriate adjustments to section/material properties to be used in the building analysis for the purposes of this assessment. Such adjustments will increase the deflection value used in the checks. ACI code method is discussed in detail in sections below.

- A mixture of two different code of practices used in a single project is not ideal or sound from engineering perspective. Further, it may be explicitly forbidden by country specific practice or authorities.
- This can result in different classifications for different storeys, which is not a condition that is recognized by BS8110.
- ACI classification may result in many columns being classified as slender. Hence, additional slenderness moment may result in unexpectedly high number of column design failures or significantly higher steel than conventional BS8110 method.

For more information about direction of braced and unbraced for wall, you may refer to Wall Braced Direction.

** Global P-Delta Effects — **it is an inherent assumption in the above that walls provide sufficient lateral stiffness that global sway of the building is small and hence "Big" P-delta effects can be ignored in braced structures. For un-braced structures, there is no clear statement on whether or not global P-Delta is also considered ignorable or is simply considered to be adequately catered for in the amplification of design moments noted below.

** Slenderness Classification — **this is based on the effective length.

- In braced structures effective lengths are < 1 and
- in un-braced structures effective lengths are > 1.

It is considerably more likely that a member gets classified as slender when it has been classified as un-braced.

Short (Non-Slender) Members will see no amplification of moment at all, even if they are un-braced.

Slender Members (Members susceptible to P-Delta effects) :

**Braced-Slender Elements**- additional moments are calculated based on effective length and are considered to be a maximum at around mid-height. These moments are not added to the highest end moment so this may or may not end up being a critical design condition. This additional moment is clearly intended to cater for "little" P-delta effects (strut buckling)**UnBraced-Slender Elements**- additional moments are calculated based on effective length (which is longer and hence additional moments will be greater), and are considered to be a maximum at the member ends. The additional moment is added to the highest end moment so this will always end up being a critical design condition.

It is assumed that this amplification of the critical design condition is intended to cater for both big and little P-delta effects.

The advantage of the above procedure is that moment amplification in each column is related only to the classification and slenderness of that column.

When the design code is set to BS8110, CP65 or HK-2004; if you uncheck ** “User Defined Bracing for Columns and Walls”**, a facility is made available for assessing the susceptibility of individual storeys to P-Delta effects. This uses the ACI method of classification during the building analysis.

** Bracing Classification — **using the ACI approach each storey level within a building is classified as sway or non-sway. The code also provides a method allowing analytical assessment of this classification based on deflections arising from a linear analysis of the structure.

** Global P-Delta Effects — **when a storey is classified as

- A second order analysis (which would inevitably affect all members in the structure)
- Approximate moment magnification methods; cl.10.13.2 appears to indicate that this moment amplification only needs to be applied to the slender members at each floor level (similar to BS8110) is this logical? Or should this amplify the sway moments in all columns and walls on a level by level basis?

** Slenderness Classification — **this is based on the effective length. At

Short (Non-Slender) Members will see no amplification of moment at all even if they are at "Sway" levels.

Slender Members (Members susceptible to P-Delta effects) :

- Slender Elements at Non-Sway Levels - additional moments are calculated based on effective length and are considered to be a maximum at around mid height. These moments are not added to the highest end moment so this may or may not end up being a critical design condition.

In essence the approach here is identical to that used for braced slender members in BS8110.

- Elements at Sway Levels - as noted above the end moments of all members may be amplified to account for Global P-Delta effects. If a member at such a level is classified as slender, the calculation of the magnified moment is not based on the effective length of each individual member, moment magnifiers are based either on the stability index for the floor (cl.10.13.4.2) or an assessment of the average buckling capacity of all members at the floor (cl.10.13.4.3 - similar to the optional method in BS8110).

The additional moment is added to the highest end moment so this will always end up being a critical design condition. Additional check (cl.10.13.5) - having amplified the end moments there is a requirement to check that intermediate slenderness effects (using effective length = 1.0L) are not more critical

While the method of moment amplification is different for slender members at sway levels, the general principles of moment amplification are the same in BS8110 and ACI and the terms used for classification are interchangeable:

• BS8110 Braced = ACI Non-Sway

• BS8110 Un-Braced = ACI Sway

The ACI has the advantage that the classification is not a matter of engineering judgement and also that it introduces the flexibility to mix both braced and un-braced classifications within one structure.

The ACI amplifications are applied only to lateral load cases - this does not address the fact that sway will occur as a result of vertical loads applied to any unsymmetrical structure and hence ignores the possibility that significant P-delta effects could accrue due to this aspect of sway. However, for the majority of "building" type structures this simplification/assumption is likely to be acceptable.

There does seem to be a question mark relating to the ACI approach for slender columns. If the sway moment amplification is made using the stability index then should the column be taken into design as a braced column using an effective length = 1.0 (because the unbraced (global P-Delta) aspect of slenderness has already been allowed for?). This seems much less conservative than the suggested implementation procedure for EC2 discussed below.

In EC2 similar terminologies are used but the meanings are different:

- Cl 5.8.1 - Introduces concept of braced and bracing members.
- Cl 5.8.2 - Second Order Effects - this clause distinguishes between global effects (applying to the whole structure) and isolated member effects (slenderness).

** Bracing Classification — **Bracing members are the members which are assumed to provide the lateral stability of the structure. Columns and walls that are not “bracing members” are classified as “braced”. Unfortunately there is an element of engineering discretion involved in this classification which will be discussed later.

** Global P-Delta Effects — **there is some guidance on determining if these effects can be ignored (For the purposes of this discussion we will classify structures in which global P-Delta effects cannot be ignored as "sway sensitive"). Cl 5.8.3.3 (1) gives a simple equation that is only applicable in limited circumstances and is actually also difficult to apply. Initial calculations using this equation have suggested that it would be too conservative resulting in too many structures being classified as sway sensitive.

Annex H provides slightly more general guidance. In order to automate the Annex H classification in ProtaStructure, the approach has been modified to become similar in principal to the ACI classification method. It is noted that a single classification gets applied to the entire sway resisting structure (the bracing members). If it is determined that global P-Delta effects cannot be ignored (the structure is sway sensitive) then the approach becomes a user driven procedure, in which the sway loads are amplified in accordance with Annex H. This is a relatively simple procedure applied as follows:

1. View the sway sensitivity report to obtain the suggested load amplification factors.

2. Apply this amplification to the existing load combination factors.

3. Re-analyze using the option to over-ride further sway sensitivity assessment and design the structure as if it is not sway sensitive (because the global P-Delta effects are now catered for).

Tests have indicated that the sway sensitivity assessment procedure described above results in a non-sway classification for the vast majority of structures .

Although the classification applies to the bracing members, it is impossible to isolate these when analyzing the structure, so P-delta forces (introduced by load amplification or P-delta analysis) will accrue in all members (braced or bracing, short or slender).

** Slenderness Classification — **this is based on the effective length. For braced members effective lengths are < 1 and for bracing members effective lengths are > 1. It is considerably more likely that a member gets classified as slender when it has been classified as a bracing member.

Short (Non-Slender) Members:

- As noted above, if these members exist in a sway sensitive frame then there may have been some amplification of the design forces introduced during the general analysis procedure.
- no other amplification of moments is then applied.

Slender Members (Members susceptible to P-Delta effects) :

- Slender Braced Members - additional moments are calculated based on effective length and are considered to be a maximum at around mid height. These moments are not added to the highest end moment so this may or may not end up being a critical design condition

In essence the approach here is identical to that used for braced slender members in BS8110 and ACI.

- Slender Bracing Members - as in BS8110 - additional moments are calculated based on effective length (which is longer and hence additional moments will be greater). Un-like BS8110 the additional moment does not have to be added to the highest end moment (because the end moment is already amplified if the structure is sway sensitive). In EC2 additional moments in slender members are introduced in the same way regardless of whether or not the member exists in a sway sensitive frame.

In summary - it seems EC2 maintains a distinction between global P-delta effects and local slenderness effects which potentially results in a 2 stage amplification of moments. Once the sway sensitivity is assessed the global P-Delta effects are introduced in the analysis results as necessary. For the local slenderness effects the general principles of moment amplification in EC2 are very similar to those applied in BS8110:

- EC2 Braced = BS8110 Braced
- EC2 Bracing = BS8110 Un-Braced (but we would expect that the EC2 amplification might be lower since the BS8110 amplification at this point mixes both global and local effects whilst in EC2 any global effects would already have been introduced).

EC2 requires the user to distinguish between the braced and the bracing members of a structure. This can be specified on the Lateral Drift tab of Building Parameters.

This setting has nothing to do with assessing sway sensitivity which is dealt with separately.

The purpose is to identify Bracing Members in each Global Direction (The member types that contribute to lateral stability of the building). The default setting is as shown above, (columns considered to be braced; walls considered to be braced about their minor axis, but to provide bracing to the structure about their major axis).

Most of the guidance surrounding EC2 suggests/assumes that most buildings will be classified as non-sway. Essentially the expectation is that the assumption made in BS8110 design, that any building stabilised by shear/ core walls is non-sway, will prove to be correct.

Whether this proves to be true is somewhat irrelevant, the fact is that sway sensitivity classification has to be made and the Eurocode provides three options for doing this:

- Use cl 5.8.3.3 (eq 5.18)
- Use guidance from
**Annex H** - Do a P-Delta analysis and check that the change in results is less than 10% (cl 5.8.2), if true than you can revert to linear elastic analysis.

If the structure is classified as sway sensitive then there are two options for dealing with this:

- Annex H - Application of increased horizontal forces.
- Do a P-Delta Analysis by checking the option
in the Load Combination Editor**"Apply P-Delta Analysis"**

Please refer the Scope & Limitation of ProtaStructure P-Delta Analysis : Load Combination > P-Delta Analysis

In fact there is a third option which might be applied when an engineer discovers a building is sway-sensitive - they may find a way to add more shear walls and change the classification!

Initially the P-delta option may seem attractive but it must be recognized that EC2 is very clear on the fact that realistic member properties accounting for creep and cracking must be used and the calculation of these properties becomes a unique procedure for every member.

For sway sensitive structure, the** Annex H** guidance has been adopted for ProtaStructure.

A model is constructed as shown above with two 3m wall panels providing stability in each direction.

Floor to floor ht= 3.0 m

Wall Length / Width= 3m / 0.2m

Concrete Grade= C30/37

G= 7 kN/m2 (total including walls)

Q= 2.5 kN/m2

Beams are provided for load collection only - they are pinned at both ends in order that lateral loads are focused in the shear walls.

The notes with eq H.8 indicate that cl 5.8.7.2 should be referred to - the stiffness of the members used in the analysis leading to the classification must be adjusted and Cl 5.8.7.2 is referred to for the adjustment.

Cl 5.8.7.2 gives a procedure for calculation of Nominal Stiffness of compression members. Rigorous use of this clause would require iteration since the adjusted properties are member specific (load and reinforcement and even direction dependent).

Simplified alternatives are given, the simplest of which still involves the use of theta-ef (the "Effective Creep Ratio") which remains a member specific calculation.

Referring to eq 5.26, if we assume theta-ef is around 1.5 then the suggested approximate stiffness adjustment can be calculated:

• Kc = 0.3 / (1 + 0.5*theta-ef) = approx 0.175

For the beams adjustments must be made to allow for creep and cracking - assume:

- I-cracked = 0.5 I-conc
- (eqn5.27) Ecd-eff = Ecd / (1 + theta-ef) = Ecd / 2.5
- Therefore total adjustment to EI = 0.5/2.5 = 0.2.

Overall it seems that initial adjustments might be as low as 0.15 to 0.2 EI for all members. To put this in perspective consider the slightly more concise advice given in the ACI. ACI suggests reducing stiffness (EI) to a factor of 0.35 (or 0.7 if the members can be shown to be uncracked). It is also noted that the 0.35 factor should be further reduced if sustained lateral loads are applied, it seems logical that notional loads should be regarded as sustained lateral loads. Therefore, a 0.2 adjustment factor may prove to be a little over conservative, but it is not wildly different to the ACI advice.

Consider also that ACI classifies a building as sway sensitive when Q > 5% while EC2 allows this to increase to 10% - therefore, if the EC2 adjustment factor is around 0.175 compared to ACI factor of 0.35, then the classifications of the buildings would be almost identical.

In **Effective Material and Section Stiffness Factors**, the Bending Stiffness of all members are adjusted to 0.35 before analysis as discussed above.

The report shows the structure is classified as sway-sensitive at all but the lowest floor level.

In the ACI only 5% second order effects are assumed to be ignorable. Q is the measure of this and at this point it is interesting to note that although Q is only marginally smaller than 0.05 at the lowest level, it becomes quite significantly greater at the top level.

In fact, if we reduce this to a 4 storey building then the report below shows that the structure is still classified as sway-sensitive at the upper levels.

As shown above, P-Delta effects can be proportionally higher at upper levels.

For ACI code, Sway Classification Report is named as "Slenderness Calculation Report"

Based on the discussion in __Model Analysis Properties__, In **Effective Material and Section Stiffness Factors**, the Bending Stiffness of all members are adjusted to 0.17. Note that although we are using 0.17, you may decide on a higher or lower value based on your engineering judgement.

The report shows that the 5 storey structure is classified as sway-sensitive at all floor levels.

In EC2 10% second order effects are assumed to be ignorable. Q is the measure of this and so the actual check is that if Q > 0.1 then the classification is sway-sensitive. For the figures above we can see this is true at all levels.

It is noted that although Q is only marginally greater than 0.1 at the lowest level, it becomes quite significantly greater at the top level.In fact, if we reduce this to a 4 storey building then the report below shows that although Q becomes less that 0.1 at the lowest level, the structure is still classified as sway-sensitive at the upper levels.

Although the reduced section properties together with the increased ignorable P-Delta amplification limit means that the threshold for sway-sensitive/non-sway classification is very similar for the two codes, the amplification factors that apply to buildings that are classed sway sensitive are bigger (double) for EC2.

EC2 does not seem to recognise the concept that a building can have different sway sensitivity at different levels, a single classification and amplification factor is applied to the whole building. This requirement is catered for in the report by including an extra line for ‘All‘ storeys. In the above 4 storey example the Q value calculated for “All” storeys is 0.1497 (therefore sway sensitive).

Total deflection = 5.99mm

Total Axial Load (F-V.Ed)= 30349

Total Shear Load (F-H.Ed)= 101.2

Total height = 12m

Q = 1.5 (30349 * 0.00599) / (101.2 *12) = 0.1497 > 0.1 (therefore sway sensitive).

Provided the model is classified as non-sway no further adjustments are required - the member design is performed using the existing load combinations and factors.

If (as in this case) the model is classified as sway-sensitive, the second-order effects must be accounted for in the design. As previously stated, the code provides two options for achieving this:

• Annex H - Application of increased horizontal force (automatically adopted in ProtaStructure)

• Do a P-Delta Analysis (option available in ProtaStructure).

In ProtaStructure the former approach is adopted - when the model is classified as sway-sensitive a load amplification factor is automatically applied to the existing design load combinations.

The option to perform P-Delta Analysis is also available in the **Load Combination Editor **

The amplification factor, Delta-s, is calculated from the Q value for “All” storeys as follows:

Delta-s = FH,Ed / FH,0Ed = 1 / (1-Q)

In the original 5 storey example Q = 0.271. Hence the amplification factor displayed on the Horizontal Drift Classification Report is

1/(1-0.271) = **1.372**.

It is possible to over-ride this value if required and enter an amplification factor based on your own engineering judgement. To do this, re-display the Building Parameters, then from the Lateral Drift tab check the box to apply the ‘User-defined’ Sway Amplification Coefficient. You can then over-ride the automatically calculated value in one or both directions.

If you have applied user-defined sway amplification coefficients, it is not necessary to re-analyse the building before the members are designed.

With reference to : __Load Combination > P-Delta Analysis__ , ProtaStructure P-delta analysis takes into account **P-Small Delta **only, not the **P-Big Delta**.

Besides, it does not provide any information on the level of actual load vs P-Critical (Buckling limit).

To be on the safe side, we recommend you do not ignore addition slenderness moment / moment magnification. At the very least, it gives users valuable information on how slender and how heavily loaded the columns are. Hence, by default, these are not ignored even if P-delta Analysis is performed.

In the end, it's entirely up the the engineer's decision. If you want to disregard slenderness / magnification moment, you can manually overwrite the auto-calculated values by:

- In the individual
*Column Reinforcement (Interactive) Design*dialog, go to "**Slenderness**" tab. - For British & EuroCode :
- Check "
**Edited**" next to**Effective Length Factors** - Change / decrease the factors manually (usually 1.0 or less will result in zero additional slenderness moment)
- Click "
**Interactive Design**" to update the final design forces & automatically re-design the column - Go to
tab again & check to ensure the manually edited values are retained.**Slenderness**

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