Question: I am currently working in a Consultancy firm in Islamabad and have few queries regarding torsional Irregularity explained as follows:
1) As per UBC torsional irregularity exists if “Maximum story drift, computed including accidental torsion, at one end of the structure transverse to an axis is more than 1.2 times the average of the story drifts of the two ends of the structure”.
In our general practice, we compare the ratio of maximum displacement to average displacement with 1.2 to confirm if the torsional irregularity exists or not. But as per the above stated UBC Statement, we should consider the story drift instead of displacement. What could be then the possible reason for considering displacements instead of Story drift?
2) If the ratio of Story drifts is to be considered for torsional irregularity check, then In ETABS 2016 there are two types of tables for drifts, one is ” Story Max/Avg Drifts” and the other is “Diaphragm Max. / Avg. Drifts”(Pic Attached). Which is to be considered and what is the difference in between story drifts and diaphragm drifts?
3) What does accidental torsion mean in the above statement and how it is calculated?
I would be thankful to you if you could help me in this regard.
Muhammad Arslan Umar
Dear Arslan Umar
Several codes require to consider an “accidental torsion” in addition to inherent torsion in the structure. The inherent torsion is caused by the actual geometry (i.e. the actual eccentricity existing between the center of mass and venter of stiffness). However, the accidental torsion is a minimum amount of torsion which should anyways be considered [in addition to inherent torsion] for (a) accounting the uncertainties in the distribution of mass and stifness in the structure, (b) accounting for possible variabilities in live loads during the intended life span of the structure, (c) accounting for the torsional component in an anticipated ground motion which can hit the structure during its design life, (d) accounting for any other unforseen cause of torsion moments.
This accidental torsion can be considered in analysis in two ways.
1) Directly applying a static torsional moment at the center of mass of each story level. That torsional moment can be determined by just multiplying the assumed eccentricity (typically in the range of 5% to 10% of the building dimension perpendicular to the direction of application of equivalent static earthquake force) with equivalent static earthquake force at each story. This option is generally used with rigid diaphragms assumption.
2) Changing the location of center of mass to 5% (or any assumed eccentricity up to 10%) left and right (in perpendicular direction to the direction of application of lateral load) relative to the actual location of center of mass. In this case, you have to perform multiple analysis (ELF or RSA) for each shifted/modified mass source.
If you are using option 1 and if you are following UBC 97, you may need to check for an additional check on torsional irregularity. Your structure is torsionally irregular if the maximum story drift, computed including accidental torsion, at one end of the structure transverse to an axis is more than 1.2 times the average of the story drifts of the two ends of the structure. Please note that the story drift (i.e. relative displacement between two consecutive storeys) is a significantly improved indicator of seismic response and a more meaningful damage indicator compared to the story displacement. Therefore the check on torsional irregularity should be based on story drift instead of displacement.
If the structure is found to be torsionally irregular, it has the tendency to amplify aby accidental torsion. This is also sometimes referred to as the dynamic amplification of seismic responses. To empirically account for that amplification, UBC 97 have defined an amplification factor Ax. In short, if the torsional irregularity exists, the effects shall be accounted for by increasing the accidental torsion at each level by an amplification factor, Ax, determined as follows.
Ax = (d_max/1.2d_avg)^2, where d_avg is the average of the displacements at the extreme points of the structure at any level. While d_max is the maximum displacement at that level. The value of Ax should not exceed 3.
If you are using option 2, which is relatively more tedious approach (i.e. actually changing the locations of center of mass and then caryying out a series of analysis), then there is no need of considering this amplification. Any possible dynamic amplification in this case is expected to be captured by the change in mode shapes (due to a modified mass matrix).
I hope this explanation will help.