Important questions about RSA

[WR1]

I am involved in project where I urgently need to have good answers to following questions related to response spectrum analysis for my clear understanding and to assert to client that my approach is right.

I am not designing shear walls under RSA load cases but only for static cases. Scale factor between static and dynamic is 3 in X and 2 in Y so the dynamic forces are lot lesser than the static ones. Also I am not amplifying torsion in RSA. And combining orthogonal effects with SRSS approach and not by combinations.

 

1. Do we need to amplify accidental torsion according to Table M of UBC-97 regardless of seismic zone? In ASCE you need to do it only for SDC C and above.

 

2. If RSA is done using ETABS (shifting of mass 5%, then determining acceleration at each node, then multiplying tributary mass to get torsional force), then do we still need to amplify RSA eccentricity by Ax (Amplified torsion)? In my understanding you need to only amplify static seismic cases.

 

3. According to FEMA, UBC-97 and Wilson, there are 2 methods of orthogonal effects. 100% X+30% Y or SRSS. That means I can define a scale factor in U1 and U2 both in the same spectrum load case and select SRSS, instead of defining U1 and U2 (2 separate cases) and then combining them in load combinations. FEMA and Wilson (2004) prefer to use SRSS (100%X and 100% Y to have same strength against earthquake in all directions).

 

4. Do I need to consider U3 in RSA for vertical direction equal to 2/3 of horizontal or i can ignore it? It is already considered equal to 0.5CaI (UBC-97) or 0.2Sds (ASCE) in static load cases by the way.

 

5. Do we design shear walls on RSA? Because would'nt it be too conservative (unrealistic) to design huge shear walls just for pure tension instead of tension-compression couple from lateral loads? Because results from RSA are abs (+ or -) but not both. If not then what is the role of RSA in seismic design other than to get the maximum response only to have an idea of total base shear and its distribution.

 

6. How do we say that dynamic effects are not governing rather static seismic forces are governing? By comparing values of base-shear at each story? Most of the times in regular low seismic zones, dynamic analysis does not govern. What is the meaning of "does not govern"? How do we practically specifically check that in ETABS? By comparing forces as I have said?

[UmarMakhzumi]

15 hours ago, Rana said:

2. If RSA is done using ETABS (shifting of mass 5%, then determining acceleration at each node, then multiplying tributary mass to get torsional force), then do we still need to amplify RSA eccentricity by Ax (Amplified torsion)? In my understanding you need to only amplify static seismic cases.

The consideration of horizontal torsion is the same as for the static procedure. Because the forces applied at each story, the story shears, and the overturning moments are separately obtained from the summing procedure, the results are not statically compatible (that is, the moment calculated from the story forces will not match the moment from the summation). Early recognition of this will avoid considerable problems in later analysis and checking.

Quote

6. How do we say that dynamic effects are not governing rather static seismic forces are governing? By comparing values of base-shear at each story? Most of the times in regular low seismic zones, dynamic analysis does not govern. What is the meaning of "does not govern"? How do we practically specifically check that in ETABS? By comparing forces as I have said?

For structures that are very uniform in a vertical sense, the two procedures give very similar results. The modal analysis method is better for buildings having unequal story heights, stiffnesses, or masses. The modal procedure is required for such structures in higher seismic design categories. Both methods are based on purely elastic behavior and, thus, neither will give a particularly accurate picture of behaviour in an earthquake approaching the design event. Yielding of one component leads to redistribution of the forces within the structural system. This may be very significant; yet, none of the linear methods can account for it. So "does not govern" doesn't mean anything and comparison wouldn't yield anything useful as both methods provide different results for different framing.

I will be posting to other questions one by one and modifying this reply..

[WR1]

6 hours ago, UmarMakhzumi said:

Because the forces applied at each story, the story shears, and the overturning moments are separately obtained from the summing procedure, the results are not statically compatible (that is, the moment calculated from the story forces will not match the moment from the summation). Early recognition of this will avoid considerable problems in later analysis and checking.

I guess you are talking about modal super-position, but that is not my question.

 

6 hours ago, UmarMakhzumi said:

The consideration of horizontal torsion is the same as for the static procedure.

Yes and according to SK Gosh (http://skghoshassociates.com/SKGAblog/viewpost.php?id=5), we need to amplify dynamic torsion because;

"....  accidental torsion is not determined as part of the dynamic analysis, but as the result of a separate static load applied at an eccentricity. The only way we can use the exception [to ignore amplification in dynamic] is to incorporate the accidental torsion effects into the building model itself by defining a floor mass distribution that is not uniform so that the center of mass has a 5% offset from the centroid of the floor area."

Agreed. Now, the next step is to how to do it practically. We are not just talking about the concept but to actually do it.

Now, see CSi ETABS Wiki (https://wiki.csiamerica.com/display/etabs/Accidental+eccentricity)

1. In the first method, accidental torsion is included in dynamic analysis by actually shifting CM as SK Gosh suggests that would change the dynamic properties, natural characteristics and stiffness matrices for each eccentricity and so we do not need to amplify further, because accidental torsion has been calculated through dynamic analysis.

Con: The main drawback is that as the properties of model change for each eccentricity, hence 4 separate eigenvalues analyses must be performed for each eccentricity and then finding a way to envelope the maximum response of these 4, which is not possible in majority of software. What is the simple solution? See point #3.

2. Second way is to model a static torsional load [or a static force applied at an eccentricity] at each story for each eccentricity to approximate these effects. Then static + dynamic response is combined. This is where we need to amplify accidental torsion. Because accidental torsion has not been calculated dynamically.

3. An "efficient and practical" approach is adopted in ETABS. After the analysis of MRSA cases;

a. Acceleration at each node is multiplied by tributary mass and given eccentricity so the result is a torsional force = m.a.e = F.e

b. A static response is generated under these torsional loads and added to MRSA dynamic results.

Now, strictly speaking, eccentricity was not directly analyzed in dynamic analysis in method 3 but atleast there is a satisfying globally used practice. So we dont need to increase accidental torsion by this method.

 

4. There is another method developed by  Fahjan et al. and quoted by CSi wiki. It also contains good background information. You can view the paper from csi wiki page.

[Wajahat Latif]

This topic troubled me a lot the last few months so I came across this post while doing my research. A quick update to the consideration of accidental torsion effects in RSA: the dynamic mass shifting procedure has been prohibited by Supplement # 2 to ASCE 7-16. Latest research found that buildings designed with this procedure were more susceptible to collapse.

Now we're only left with the static method of accounting for accidental torsional effects in RSA (including amplification). To accomplish this in ETabs, we can find the amplified eccentricities along both X and Y axes from the regular ELF analysis. These amplified eccentricities are input in the RS-X and RS-Y load cases respectively. I confirmed this approach with Dr. Justin Marshall, the co-author of "Guide to Seismic Provisions of ASCE 7-16", and Engr. Aung, Director AIT Solutions. 

As WR-1 said, Etabs (link) will obtain accidental torsional moments from story forces obtained from the combined RSA, then add these forces to the combined RSA results. This is the procedure prescribed in the "Guide to Seismic Provisions of ASCE 7-16" as well, snippet attached.

Omission of consideration of amplified accidental torsional effects in RSA results in very weak designs, and this is prescribed in both ASCE and UBC-97.

Note: the dynamic mass shifting analysis is still applicable for linear response history analysis. However, for response spectrum analysis it is prohibited.

 

Edited April 21, 2021 by Wajahat Latif