Static vs Dynamic Earthquake Load Case: When Do We Use Either or Both?

So will it be dynamic only, or both?

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Do we always have to use both the static and dynamic earthquake load cases for design? When can we use the dynamic case only?

There is no exact rule as to when can we exclude the static and consider only the dynamic case only. And as far as I know there are no codes to regulate this, because the prompting situations cannot be generalized and because it really depends on the situation.

I was fortunate enough to encounter this situation in one of my projects. Fortunate because even if it gave me a hell of a headache in trying to solve the issue, I learned a ton in exchange.

The project is located in the middle east. Seismic code is UBC 97, zone 2B with soil type Sc. It is a 24-storey building with a bearing wall lateral load resisting system. The placement of the walls in my judgement is “odd” – a very eccentric layout of walls favoring the right side and a lot of horizontal elements resisting the shear along X direction and fewer walls on the north-south direction.

plan.JPG
Odd ain’t it? All columns except the 6 columns in the middle are engaged or participates with the wall in resisting lateral loads. Told you…

True enough the walls were a pain in the ass. Nothing’s working!

With my project lead and design manager, we desperately tried to find ways to make the walls work, since the current arrangement of walls and columns was the only arrangement that was allowed by the current architectural layout. The possible solutions that we explored were to add link beams to tie the lateral system. And the other is we cracked the walls that exceeded the modulus of rupture due to tensile stresses brought about by tensile forces and in-plane bending due to lateral loads. The last solution worked, albeit the resulting wall thicknesses were insanely huge for a 24 storey building and reinforcement ratios were still very high – ranging from 2% minimum to the highest requirement of 3.95% (limit is 4% based on the ACI 318M-11). Aside from that, it’s very odd cracking almost all the walls because almost all walls are in tension, I am not exaggerating on this one! It’s as if I’ve cracked all the walls such that redistribution is simply impossible.

 

elevation.JPG
The gray walls are “cracked walls” i.e. property modifiers for f11, f22, m11, m22, and m12 are reduced from 0.70 to 0.35. Can you believe that a large portion of the wall base is in tension?!

When I looked at the governing load combinations, I found out that governing load combination for most of the walls are the static earthquake load combinations. In an effort to understand why, I decided to plot the storey shear. True enough, there is a great disparity between static and dynamic, no wonder everything is struggling!

 

Shear X.jpg
See the gap between static (EQX – orange line) and dynamic (RSX – gray) for the X – direction …
shear-y
See the gap between static (EQY – orange line) and dynamic (RSY – gray) for the Y – direction …

I’ve tried to exclude the load combinations containing the static earthquake load and lo and behold, the largest reinforcement percentage is 2.5% which occurred at the bottom. So that’s the culprit!

I presented this to my design manager and he was convinced also that we can use the design forces using dynamic earthquake loads only or else nothing will work (wind loads and gravity loads were included too although the resulting storey shears for wind loads are way below the storey shears generated by earthquake hence it was not critical.)

Aside from design, this static-vs-dynamic dilemma have profound impacts when calculating the storey drifts and required building separations. A friend told me that they don’t use static earthquake load cases because it’s not realistic. I can see his point. Deriving the earthquake loads via the static force procedure gives only an estimate of the earthquake forces ideal for buildings with very regular layouts. But as the building layout gets complicated, a more complicated and rigorous structural analysis is needed to capture the real behavior of the building. This is done by employing the dynamic analysis which accommodates all combinations of translational and torsional motion due to ground acceleration that is produced during a seismic event.

So will it be dynamic only, or both? Without any code regulating this, it really depends on the results. If the resulting design and wall sections are over the top from expectations, removing the static earthquake load combinations can be an option. Otherwise if both will yield acceptable results based on the calculations and wise engineering judgment, it never hurts to use both dynamic and static earthquake load cases.

Author: The Romantic Alpha

Aside from physical and intellectual strength, a man is also given a heart to feel and share love and value. Dive into the mind of the alpha, feel his heart beat, and let me carry you with my strong yet gentle hands. I'm continuously innovating myself to be a better man, husband, father, friend, and structural engineer. Love's not overrated. The world needs the true essence of which.

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