Amplification of Accidental Torsion (Ax) ASCE-7-05 (Eq 12.8-14) Structures assigned to Seismic Design Category C, D, E, or F, Where Type la or lb torsional irregularity exists as defined in Table 12.3-1 shall have the effects accounted for by multiplying M, at each level by a torsional amplification factor (Ax) Determined from the following Equation. In other words if torsional irregularity exists and A x is greater than 1.0 at any level (or levels), a second torsional Analysis must be performed using the new accidental eccentricities.
How to apply the previous equation in Etabs: From Etabs when assigning (Qx with eccentric ratio 5%) to a structure. I. II. III.
Run the model Go to file > print tables > summary report. Go to this paragraph:
STORY MAXIMUM AND AVERAGE LATERAL DISPLACEMENTS STORY
LOAD
STORY4 STORY3 STORY2 STORY1
QX QX QX QX
DIR
MAXIMUM
AVERAGE
RATIO
X X X X
0.0026 0.0020 0.0013 0.0005
0.0021 0.0015 0.0009 0.0003
1.272 1.310 1.356 1.414
For every story from the previous paragraph do the following to get A x:
1-divide the ratio by 1.2 then square the answer Story 4: Ax = (1.272/1.2)2 = 1.1236 Story 3: Ax = (1.310/1.2)2 = 1.1917 Story 2: Ax = (1.356/1.2)2 = 1.2769 Story 1: Ax = (1.414/1.2)2 = 1.3884 Note: Ratio obtained by Etabs = (∂max / ∂average) however if we checked story no 4 for our case Ratio = 0.0026/0.0021 is not equal to 1.272 this is due to that values given in summary report for ∂max & ∂average are approximate if you want to check the exact values refer to the model and it will lead to the value obtained in summary report (1.272) In other words values given for ratio in summary report are exact and can depend on for Ax calculations.
Condition to apply in Etabs Ax > 1 (If Ax < 1 for all stories no need to apply Ax at all) (If Ax < 1 for a story use Ax=1 ) Ax not greater than 3 (if it exceeds 3 use 3) To apply in Etabs calculate the perpendicular width of building per every story (L) to the applied seismic force (in our example Q x). Say L = 15 m Story 4: absolute Ecc. = 0.05x15x1.1236=0.8427 Story 3: absolute Ecc. = 0.05x15x1.1917=0.8937 Story 2: absolute Ecc. = 0.05x15x1.2769=0.9576 Story 1: absolute Ecc. = 0.05x15x1.3884=1.0413
Go to define > static load case > Qx > show lateral load
Run the model again then you will have all eccentricity corrected. General note regarding the previous consideration in Etabs program: However, it is not required to find the resulting new Ax values and repeat the process a second or third time (Until the Ax Converges to a constant or reaches the limit of 3.0). The results of the first analysis with the use of Ax are sufficient for design purposes.
