ASCE7-02 Table 9.5.2.8 vs Section 9.5.5.7.2

[dbockoven]

Hello

I have a 7-story concrete structure with a combined lateral resisting system in the x direction of shear walls and ordinary moment resisting frames.

based on section 9.5.5.7.2 of ASCE 7-02 my thetamax = 0.1
which also happens to be the limit at which you should consider p-delta effects.

My issue stems from the theoretical limit on my inter story deflections now set at hsx/1188-2865, in order to meet a thetamax =0.1, which is considerable higher than the limit from table 9.5.2.8 of hsx/100.

Can anyone provide any guidance on how to procede because as it stands now I am at h/400, considering p-delta, but my stability coeeficient, theta, exceeds theta max by a considerable amount. Is the structure really going to be unstable under these circumstances?

thank you for any help

 

[JAE]

Can you clarify what you mean by:

hsx/1188-2865

??

Tell us your ratio of Px/Vx and your Cd value.

If you take a Table 9.5.2.8 allowable story drift [Δ] = 0.01hsx and a Cd = 4.5 (I'm guessing here) and then plug it into the [Θ] equation:

((Px/Vx)(0.01hsx)) / ((hsx)(4.5)) <= 0.10

The hsx value cancels out and you get:

Px/Vx <= 45

[&Theta;]max = 0.5 / (0.8 x 4.5) = 0.139 using [&beta;] = 0.8

or if Cd = 2.5 then [&Theta;]max = 0.25.

According to ASCE 7, yes - if you exceed [&Theta;]max you are unstable.

Verify your calculation values.

 

[dbockoven]

By hsx/1188-2865 I mean to meet theta max my inter story drifts must be of magnitude hroof/1188 to hbottom story/2865 or 0.14" at the roof to 0.08" at the bottom level.

My Px/Vx ratios vary from 119 at the roof to 287 at the lowest level and Cd = 5

 

[JAE]

With a very high Px to Vx ratio, perhaps you should calculate an exact [&beta;} for the [&Theta;]max. Don't know if this would do you any good or not.

Those ratios seem to imply you have a very low seismic demand.

 

[dbockoven]

I think I may be calculating Vx wrong reading the code it sounds like Vx should be the sum of the applied seismic story shear at level x up to level n, n being the highest level.

I am comparing my results with a ram frame analysis and it appears ram frame is only considering the the applied story shear for its theta calcs.

Can anyone confirm that Vx should be the sum as oulined in the first paragraph of this post?

Either way I will need to do further investigation at the very least at my upper levels to make sure beta is such that theta max is higher than theta.

 

[JAE]

Yes, Vx is the shear at that story, which would be the sum of shears for all stories above the story in question.

 

[dbockoven]

thank you for all your help JAE