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Reasons for New Iterations
Stiffness Analysis
Now that load distribution can be affected by the stiffness due to deflection analysis, it is no longer possible to predict ahead of time which wall segment will be critical design, and an iterative procedure is required.
Rigid Analysis
It is an improvement to the program to redesign walls for rigid analysis based on the stiffnesses from the rigid analysis. This improvement became especially important because of the variations in wall rigidity that result from deflection analysis.
Therefore, on each level, first for rigid, and then for flexible, the program runs through two iterations of shearwall design.
Iteration1
The first iteration is used to design shearwalls to determine rigidities and capacities for load and force distribution for the second, final design iteration.
Distribution to Shearlines
For flexible analysis, distribution to shearlines is independent of shearwall design, and is the same for both iterations.
For rigid analysis, if Shearwalls have equal rigidity or Manual input of relative rigidity is selected, then the relative rigidity of the shearlines is also independent of shearwall design, and is calculated by the sum of the wall lengths multiplied by either 1 or the manual input.
For the other rigid analysis options (Use shearwall capacity or Use shearwall rigidity), the rigidities of the shearwalls designed on the second iteration of flexible design are used as the rigidities for the first iteration of rigid design.
Distribution within Line
With shearline forces established, on the first iteration, for both flexible and rigid design:
If Distribute forces to wall segments based on rigidity is not selected, or if Shearwalls have equal rigidity is selected, the program distributes equal force per unit foot to segments within the line.
If Manual input of relative rigidity is selected, then the user input rigidities are used to distribute forces to each shearwall.
Otherwise, the force is distributed each shearwall using the relative capacities of the shearwalls. Since walls are not yet designed, the deflections are not known at this point, and the selection of Use shearwall deflection to calculate rigidity must use the capacity method on the first iteration.
Shearwall Design
With possibly different forces distributed to each wall, the walls are designed. This shearwall design is used to determine rigidities for the second iteration.
Iteration 2
Force distribution
If Shearwalls have equal rigidity or Manual input of relative rigidity is selected, there is no reason for a second iteration, and the program stops at the first iteration, and delivers design results for the shearwall design for the first iteration.
Otherwise, using the walls designed with iteration one, the program determines the force distribution using rigidities derived from either shearwall capacity or deflection analysis, according to the design setting selected. The force distribution is for distribution of loads to shearlines using the rigid diaphragm method, and distribution to forces within shearlines using both methods.
Distribution to Shearlines
The rigidity of a shearline is estimated using the capacity method by the capacity of the designed wall on that shearline, in lbs/in, and by the deflection method by
Σ Fi/DI,
where Fi and DI, are the forces and deflections on each segment. If forces are also distributed within the line based on deflection, so that deflections are equalised, this is just F/D, the total force over the common deflection. Loads are then distributed to the lines using the torsional rigid diaphragm method.
Distribution within Shearlines
If the setting Distribute forces to wall segments based on rigidity is selected, for both the rigid and flexible method, then the program calculates the force distribution on the line based on relative rigidities of segments on the line. Otherwise equal force distribution is assumed.
If Use shearwall deflection to calculate rigidity is selected, then different forces are placed on all full-height segments.
If Use shearwall capacity is selected, the different forces can be placed on each shearwall. At this stage, the program distributes loads based on the actual factored capacity of the walls from the last iteration.
Design
Each shearwall is again designed.. Note that these walls may have different deflections and possibly capacities than those used to distribute forces to design the walls; this is dealt with by the Final Design Check, below.
Number of Iterations
It would have been possible to continue this process to further iterations. This was not done because:
Distribution of Loads to Shearlines
An iterative procedure for rigid diaphragm analysis would tend to concentrate loads on a particular shearline. That is, a heavily loaded line would require more capacity, would become more stiff, would draw more load, and so on. This is not a desirable shearwall design for other reasons.
Final Design Check
The final design check described below now traps and indicates to the user those rare cases where walls passing on the second iteration failed the final design check. This was deemed preferable to the increased processing time that would be needed for all designs if there were more iterations.
Non-convergence
If we established the condition for ending the iterations that shearwall design did not change from one iteration to the next, it would be possible for the procedure to oscillate from one solution to another without ending.