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The program now implements NBC Structural Commentary J 178, which says.
Structures with flexible diaphragms are designed so that their loads, including the effects of accidental torsion, are distributed to the vertical elements using the tributary area concept. Accidental torsion should be taken into account by moving the center of mass by +/- 0.05Dnx and using the largest seismic loads for the design of each vertical element.
Note that the 2010 Wood Design Manual (WDM) Example 1, Seismic Design Considerations (p470) includes this force by adding 5% to the total shearline force.
Calculation Procedure
Noting that to direct (non-torsional) component of the shearline force should be that determined by tributary area distribution, this can be achieved by setting the rigidities K to the flexible shearline force, seeing that
Fdi = F * Ki / Σ Ki ,
using the notation in the Log file, F being the total force. In that case, the center if mass CM = Centre of rigidity CR, and we are including just the accidental eccentricity ea and not the eccentricity of the structure or loads. We also do not consider the torsional moment J in the other direction, as none of the loads are in the other direction. The torsional component on each line is then
Fti = T * Ki * di / (Jx)
where di is the distance of the shearline from the centre of load and
Jx = Σ Ki * di 2 ; T = F * ea
Shearlines already heavily loaded get higher contributions of accidental torsion, rather than those that are stiffer as in the case of rigid analysis. With seismic analysis, the distribution of load is proportional to the distribution of the mass of building material, which itself is proportional to the “area” that the NBC commentary is referring to. So with this method, the torsional component is distributed using the tributary area concept as the NBC mandates.
Verification of Calculation Procedure
To show that a simple case of uniform load on a rectangular building is consistent with the WDM example, consider a 20 m wide building with 1 kN/m force the diaphragm.
F = 20 kN; Fd1 = Fd2 = 10 kN; K1 = K2 = 10 kN; ea = 1 m; di = 10 m; T = 20 kN-m; J = 2000 kN-m2
Ft1 = Ft2 = 20 kN-m x 10 kN x 10m / 2000 kN-m2 = 1kN
= 5% F
Log File Output
The title of the entire section of the log file for torsional analysis has been changed from “RIGID DIAPHRAGM ANALYSIS” to “TORSIONAL ANALYSIS” , in recognition that some of the output now pertains to flexible analysis. A section is added at the top of the results called, FLEXIBLE SEISMIC DESIGN. The assumptions given in section a), above, are shown first, then the results are given as they are for rigid diaphragm analysis. The source of the accidental eccentricity is given as NBC Structural Commentary J 178.