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RE: Accidental Torsion
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- Subject: RE: Accidental Torsion
- From: Johnny Drozdek <jdrozdek(--nospam--at)keymark.com>
- Date: Wed, 05 Jul 2000 16:14:29 -0600
Bill, some of the questions you've raised are quite penetrating. In the development of KeyLat(TM), Keymark struggled long and hard to find solutions to these issues that made sense. My response here is intended to share with the community at large what direction our interpretation took. This is also an attempt to verify the basis of some of the functions that exist within KeyLat's rigid diaphragm analysis. We welcome all feedback. REGARDING A-SUB-X: Ax is based on drift calculations that do not include the redundancy factor "rho". KeyLat's rigid analysis consists of four steps: STEP 1: KeyLat performs one analysis that distributes forces to shear walls based on relative wall rigidity.** STEP 2: Once the wall materials have been selected, KeyLat performs a second analysis, using rho=1.0, to calculate drift. STEP 3: If torsional irregularity exists, KeyLat performs a third analysis, augmenting accidental torsion by Ax. STEP 4: Finally, KeyLat performs a fourth analysis to recalculate the deflection of the walls (which could have changed during step 3). **Note that each step 1-4 occurs on every level of the structure, with upper-level shear and torsion being transferred to lower levels. Holddown forces are also transmitted as point loads to lower levels. KeyLat can analyze up to 5 levels. REGARDING 5% +/- EFFECTS OF ACCIDENTAL TORSION: We feel we account for all possibilities by running the seismic loads in four directions (N,S,E,W). Picture a multi-story building, each level for which a center of rigidity and a center of mass has been computed. These physical locations are fixed. The third story might see a cancellation of "nominal" torsional shear effects from the fourth and fifth stories if they in fact were algebraically opposite to each other because of the centers of mass and rigidity for each level. The "accidental" torsional shears for levels three to five, however, are accumulated and held in reserve by KeyLat on an absolute value basis, and then given a sign to match the sign of the design cumulative torsional shears for the level in question. In this way, the accidental torsion does its best to hurt the structure at every level down through the building. Since some users might feel this to be overly conservative, KeyLat includes the option of combining the accidental torsion from each level not as an algebraic sum, but using SRSS (square root of the sum of the squares) much as is frequently done for response spectrum analysis. In a typical rigid diaphragm analysis performed by hand, one "pass" is made for a given direction (North/South or East/West) and the worst case solution for a particular wall is computed directly. The engineer may intuitively understand which way to move the accidental eccentricity to get the highest load on a particular wall. In contrast, KeyLat performs this calculation in four passes: load to the North, load to the South, load to the East, and load to the West. This may be performed for wind, earthquake, or both, implying a possible eight passes in total. For each pass, the accidental eccentricity is given a sign that will tend to increase the computed torsion for that level. In this way, the program brackets the solution of worst case for each wall without having to use 'judgment.' REGARDING HOW TO ITERATE ON A SOLUTION During an analysis, up to eight passes may be performed (N,S,E,W for wind and seismic). Each pass may consist of up to 5 levels. It is possible that a particular design from the first pass may survive through all the other passes and control. However, if on the eighth pass one wall on the last level requires "bumping" to a higher capacity material, this negates the validity of the first seven passes, since the distribution of relative stiffness has changed. Therefore, if on any pass a wall material is bumped, the entire process starts over. This cycle of passes and "bumping" occurs during STEP 1 and STEP 3 (above). REGARDING HOW KEYLAT DEFINES SUCCESSFUL CONCLUSION TO AN ITERATION The stiffness of the wall depends on the amount of force on the wall (e-sub-n in the 4-part wall deflection equation). But the amount of force on the wall depends on the relative stiffness of the wall. KeyLat assumes that this iterative-type solution has "converged" if (1) no wall required "bumping" of materials since the last iteration and (2) the force on any wall in the current iteration is less than X plf compared the amount of force on the wall during the previous iteration. The value of "X" is called a "convergence tolerance" and is under the control of the user. Generally, we have found that a tolerance of 50-80 plf works well and generates reasonable results (i.e. equilibrium is satisfied, all forces are accounted for, etc). Higher tolerances tend to yield results that are suspect. We have observed most of our solutions converge within 20-100 iterations. We allow the user to specify an upper limit on number of iterations (to avoid an endless loop). However, systems that require more than 100 iterations can generally be improved by adding/subtracting/relocating shear walls. I hope this gives some insight about how KeyLat performs the rigid diaphragm calculations. The obvious conclusion is that this process is very cumbersome, and brain-straining. We believe we have thought through the issues and automated a solution that makes sense. Verification is tricky but possible with a sharp pencil (and lots of extra paper). There are other issues involved, for example KeyLat currently implements Ax on a level-by-level basis. Is this really appropriate? Are the effects of torsional irregularity level-specific or should Ax somehow be applied to the structure as a whole? As always, your comments are welcome. Sincerely, Johnny Drozdek, E.I.T. Keymark Enterprises, Inc. ******* ****** ******* ******** ******* ******* ******* *** * Read list FAQ at: http://www.seaint.org/list_FAQ.asp * This email was sent to you via Structural Engineers * Association of Southern California (SEAOSC) server. To * subscribe (no fee) to the list, send email to * admin(--nospam--at)seaint.org and in the body of the message type * "join seaint" (no quotes). To Unsubscribe, send email * to admin(--nospam--at)seaint.org and in the body of the message * type "leave seaint" (no quotes). For questions, send * email to seaint-ad(--nospam--at)seaint.org. Remember, any email you * send to the list is public domain and may be re-posted * without your permission. Make sure you visit our web * site at: http://www.seaint.org ******* ****** ****** ****** ******* ****** ****** ********
- References:
- Re: Accidental Torsion
- From: sscholl2
- RE: Accidental Torsion
- From: Bill Allen
- Re: Accidental Torsion
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