P-Delta Effect ASCE 12.8.7

[elinwood]

I have a question regarding the application of ASCE 12.8.7. Equation (12.8-16) in ASCE 7-10 is as follows:


Theta = (Px) * Delta
----------------
Vx * hsx * Cd

Px = Total Vertical Design Load at and above level x
Delta = Story drift occurring simultaneously with Vx
Vx = Seismic Shear at level x
hsx = story height
Cd = deflection amplification factor

Calculation of Theta max is based on Equation (12.8-17):

Theta(max) = 0.5 / (Beta * Cd)

Beta = Ratio of Shear Demand to Shear Capacity for the story
ASCE also noted that theta should not exceed 0.1, which is around Theta(max)

Assuming Beta = 1.0 as permitted and Cd = 5.5, I have my Theta(max) = 0.091

I have the following sample of data from my coworker:

Level 30: P = 140 746 kN, V = 3758 kN, Delta = 6.653mm, h = 3200mm
Level 20: P = 257 772 kN, V = 4579 kN, Delta = 6.659mm, h = 3200mm

Plugging in these data, I get:
Level 30: Theta = 0.0142 < 0.091 [OK]
Level 20: Theta = 0.0213 < 0.091 [OK]

However, my coworker insists on following SEAOC Seismic Design Manual Example 17, where they ignored the Cd in calculating Theta getting the following results:
Level 30: Theta = 0.078 < 0.091 [OK]
Level 20: Theta = 0.117 < 0.091 [NG]

Why did we ignore the Cd value in SEAOC ?

 

[KootK]

I agree with your assessment. Are you looking at the 2012 manual? I have the 2006 manual in which this problem is #16 I think. And in that example, they do include Cd. So perhaps there has been a misprint.

Rationally, [V/[Delta * I / Cd]] is meant to represent the elastic, lateral spring stiffness of the story under consideration (kip/in). If Cd is ignored, that estimate would be off, by a lot. [Delta * I / Cd] needs to represent the elastic drift associated with the applied story shear.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[DaveAtkins]

P delta effects are based on deflection due to factored load, WITHOUT deflection amplification. It has never made complete sense to me, but that is what the Code says. In my mind, if you must have amplified deflection to relieve/reduce seismic load, wouldn't this mean the P delta increase should be based on vertical load times amplified deflection?

DaveAtkins

 

[KootK]

In my mind, if you must have amplified deflection to relieve/reduce seismic load, wouldn't this mean the P delta increase should be based on vertical load times amplified deflection?

I think that I know the answer to this one. Keep in mind, however, that this is just based on my understanding of the fundamentals. I did't find it in a published code interpretation or anything like that.

Firstly, evaluating p-delta effects in the post-yielding range doesn't do much for us as there's really no mechanism available for resisting the additional moments. We really have to rely on the dynamic character of the motion to restore balance.

Contemporary seismic design procedures assume that, once the designer selects a system ductility level, the structure will remain elastic for a certain portion of its load history and be plastic-ish for the remainder. If p-delta effects in the elastic range are significant, then the duration of the elastic load history will be shortened and important assumptions will start getting messed up.

I believe that this is why the ASCE provision assess P-delta magnification using elastic drift response. The antidotes to P-delta effects shortening the duration of elastic response are:

1) verify that the p-delta effect is small enough to be of little consequence or:
2) strengthen the structure in response to p-delta amplification to effectively extend the duration of elastic response.



I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[RPMG]

Eq 12.8-15: Delta = Cd * deflection / I
Eq 12.8-16: Theta = (Px * Delta) / (Vx * Hsx * Cd)

Therefore: Theta = (Px * deflection) / (Vx * Hsx)

In summary, Use Delta and Cd, but understand that this is actually excluding Cd.

 

[rogerheadford]

Not sure how this compares to the manual assessment, but if you use direct analysis (using STAAD for instance) this automatically includes for p-delta response.

 

[DaveAtkins]

rogerheadford,

True--and many engineers do include P-Delta in the analysis, since the software does it for you. The theta factor in ASCE 7 is just a means of deciding if it MUST be included, or if it can be ignored.

DaveAtkins