Two Stage Equivalent Lateral Force Procedure

[KootK]

Where a flexible structure is placed atop a relatively rigid structure, ASCE permits the use of a two stage equivalent lateral force procedure.

One of the requirements for using the two stage procedure is that the stiffness of the rigid base has to be 10 times that of the flexible upper structure (ASCE clause). I'm having difficulty interpreting that particular clause however. As read, I interpret the clause as follows:

1) Take the flexible upper structure and treat it as though it were fixed at the junction between it and the stiff lower structure. Apply a dummy force to the top of the upper structure, calculate the resulting deflection at the level of the applied force, and work out k = F/d.

1) Take the stiff lower structure on its own, taking no account of the presence of the flexible upper structure. Apply a dummy force to the top of the stiff lower structure, calculate the resulting deflection at the level of the applied force, and work out k = F/d.

3) Compare the stiffnesses calculated in steps #1 & #2 to see if the rigid base is 10X as stiff as the flexible upper structure.

Unfortunately, this method of comparing stiffnesses doesn't make sense to me.

Suppose, hypothetically, that you had a 30 story building with uniformly stiff moment frames from top to bottom (i.e. no rigid 'base' or 'podium'). If you performed this same analysis (steps #1, #2, & #3), you should be able to justify using the bottom story of the building as a rigid base. This, even though the building clearly doesn't meet the intent of the ASCE clause.

So... what's up with that? Have I misinterpreted the clause somehow?

Note: the fictional example that I gave above may well fail the period test for using the two stage analysis. That doesn't really alleviate my concerns regarding the stiffness test however.

Thanks for your help.

KK

 

[paddingtongreen]

One thirty story building of uniform stiffness doesn't meet the criteria of two elements of very different stiffness. An appendage of much lower stiffness is not likely to reinforce the vibration of the stiffer element but all of the thirty stories of uniform stiffness will work together.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[vandede427]

30 stories?

The real life example that came to mind would be a mixed use structure: three story wood residential on top of a one story platform (shearwall or steel x-brace).

 

[KootK]

Paddington / Vandede,

I realize that my 30 story building example doesn't meet the intent of a flexible structure on a rigid base. That's precisely my point.

The ASCE provision prescribes tests to be applied to determine (one would presume) when a rigid base is rigid enough. I argue that my uniformly stiff 30 story building may pass these tests, despite the fact that the building obviously shouldn't qualify for the two stage procedure.

To simplify, let's further assume that my 30 story building is a perfect shear building with columns that are infinitely rigid axially (not flexurally). Using the analysis that I described in my original post, the roof of the building would experience 30X the deflection of the first story and, therefore, the first story would be 29 times as stiff as the structure above. So the building passes requirement 12.2.3.1a of ASCE.

As a crude approximation, let's say that the upper, 29 story building has a period of 0.1 x 29 = 2.9 s. Similarly, the combined 30 story building has a period of 0.1 x 30 = 3.0 s. Since 3.0/2.9 = 1.03 < 1.10, the building also passes 12.2.3.1b of ASCE.

So, other than judgment, what's to stop me from considering this fictional structure to be a 29 story flexible building on top of a rigid base?

I'm obviously missing something important in my understanding of this provision. I'd like to get it figured out before I apply it.

KK