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# Calculating Bending stiffness of entire section of a building

## Calculating Bending stiffness of entire section of a building

(OP)
Hi,

I have to carry out a seismic analysis for an existing multi storey building and I have to use engineering judgement to calculate the bending stiffness EI of the entire section of the building ( 20 storeys, 2 bays, one bay is "X" braced. Any ideas?

I will appreciate any of your help.

### RE: Calculating Bending stiffness of entire section of a building

I hope you are doing this as an approximation to get a rough, ballpark idea of the behavior. Not sure where you are located, but the proper thing to do is perform a full blown structural analysis.
In any case, you could do the following:
1. Calculate the moment of inertia of a cross section (plan) of the building based on the column size and location. Then simply calculate the deflection of the building as if it were a beam cantilevered at the base. (The beam consisting of all of the columns)
2. Similar to 1 above, but neglect contribution of the columns. Look at it as if the braced bays form a vertical truss and calculate the deflection at the tip of the cantilevered truss.
3. Combine the effects of 1 and 2 above

Note that this is a very crude method and more of a classroom exercise.

### RE: Calculating Bending stiffness of entire section of a building

Yes, and the I will vary as you proceed down the building as the column sizes change. Very rough indeed...

Mike McCann, PE, SE (WA)

### RE: Calculating Bending stiffness of entire section of a building

I realize this is a bit late, as the question is a few weeks old, but do you have any 3D Analysis tools available? I work at a company that has tools that could help with this.

### RE: Calculating Bending stiffness of entire section of a building

Under lateral loads, both flexural and axial stiffness's of the elements intervene. Also please note that the stiffness cannot be calculated as a property. We talk about the stiffness in a point of the bar, not just about the "stiffness". Because it varies along the height of the building.

Kamal Safa, PhD
Ecole Polytechnique

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