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# Distribution of Base Shear in a 9-story building

## Distribution of Base Shear in a 9-story building

(OP)
Greetings,

I am doing the analysis of a 9-story building using a dynamic analysis. The building is a residential complex, built using steel. In one direction, concentrically-braced frames (limited ductility) are used and in the other direction, excentrically-braced frames.

In the principal vibration mode for a given direction (X for example), the distribution of base shear for each story seems a bit odd. As I understand it, the shear for a given story is the ratio between (Story weight*Story elevation) / (sum of (Story weights*Story elevations)), am I right?

In other words, for the same weight, the higher level will have a higher story shear than the lower one.

Here is my lateral shear distribution (sorry for the bad formatting):
Story Shear(kN)
9 462.23
8 540.02
7 140.84
6 -19.10
5 89.41
4 214.98
3 295.47
2 347.92
1 422.89
Base 2494.65

Is this a reflection of the effect of the building height? When I look at the story drifts, I can't understand really well what's happening:

Story Average Total Drift (mm)
9 156.022
8 134.312
7 111.825
6 90.1913
5 70.9514
4 52.2582
3 35.9953
2 21.6847
1 10.9419

With this drift distribution, I would expect the story shears to be at least all in the same direction. Am I missing something here? How can one level have little to no shear?

### RE: Distribution of Base Shear in a 9-story building

If these are results from one mode of vibration, the weird values would be expected. You need to perform a response spectrum analysis, combining the modal analysis by way of SRSS or CQC methods. What program are you using for this analysis?

### RE: Distribution of Base Shear in a 9-story building

(OP)
I am using Advance Design America. I just spoke with a colleague, and he confirmed me these are the results from the entire response spectrum analysis, meaning those shear numbers are for all the vibration modes, and not only the principal mode.

Is this right?

### RE: Distribution of Base Shear in a 9-story building

I guess this would be possible, but generally they are all in the same direction when combined. It may be worth checking end conditions for elements within the model to make sure they are defined properly. Also the design spectrum used should be confirmed to be appropriate for the site and soil conditions. I know some programs have built in response spectra, but some need adjustment to be correct.

Your average displacements seem reasonable though, so it is odd. And i would expect a negative story shear only if the displacement of that level is opposite relative to the story above or below.

The code equation for vertical load distribution is an approximate value, which assumes a stiffness relation, and is made to be conservative. You can use that equation for a sanity check too, looking at displacement as well.

### RE: Distribution of Base Shear in a 9-story building

(OP)
Thanks for the answer. I also checked with the software developer, my assumption about including all the vibration modes in the results table was right.

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