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# Calculate Building Stiffness

## Calculate Building Stiffness

(OP)
i have a real building model (two story) and i do a free vibration test for the building (floors acceleration had been measured)then i get the frequency for the first and second mode. what shall i do to calculate stiffness of the building?

### RE: Calculate Building Stiffness

That's a pretty wide-open question. Sometimes this is code prescribed, and it nearly always depends on a litany of details you haven't included....

### RE: Calculate Building Stiffness

(OP)
its a reinforced concrete model (no special details) i want to know the methodology of calculating stiffness for this building

### RE: Calculate Building Stiffness

Alright, so do you mean the stiffness of the full building? Normally one finds the stiffness of the individual walls/parts, then solves for a centre of stiffness, and applies torsional loading due to the eccentric effects on the building.

This depends greatly on the type of structure; Are you talking about a concrete shear wall or concrete moment frame structure?

### RE: Calculate Building Stiffness

(OP)
building is concrete moment frame and symmetric .The model structure was displaced (pulled back) by 2mm at the second floor level using a steel wire. The wire was then suddenly released and the structure was allowed to vibrate freely. Acceleration and displacements were measured at each floor level until the structure motion damped out.

### RE: Calculate Building Stiffness

Then you can calculate the actual stiffness directly from the spring force formula using fundamental principles, and you also know the true period of the structure as it is the inverse of the first modal frequency measured.

What purpose are you going to apply this to? I presume you know the precise force used to pull the building to the 2mm reflection, or is that the problem?

### RE: Calculate Building Stiffness

(OP)
No, there is two modes (two story building) and there is a damping (R.C model), so i can't calculate it directly .

### RE: Calculate Building Stiffness

(OP)
the purpose is to calculate the change in modulus of elasticity

### RE: Calculate Building Stiffness

Since it's a two story building there are two modes of vibrations. Natural frequency for the first mode will be lower than the 2nd mode, hence the effective stiffness of the building will be lower for the 1st mode as well. since, the stiffness is directly related to structure mass and frequency of vibration, it is important to correctly define the mass for a given mode to calculate structure stiffness for that mode. For a multimodal system, complete mass of the structure doesn't participate with any of the modes of vibrations, actually mass participation reduces for higher modes of vibrations. Modal analysis gives as output also modal mass participation factors. Modal mass participation factor times actual mass is the mass participating in a given mode. This participating mass should be used to determine structure stiffness for that mode.

### RE: Calculate Building Stiffness

I don't think it's as simple as that, I went to a course on the building code in Canada, and the idea they taught is to design the building for the a type of seismic limit state. You may use the weak beam, strong column approach. The seismic load must be directed (designed) to a dedicated load path.

### RE: Calculate Building Stiffness

Moreover, the first mode may be torsional and mot translational.

Biaxial Analysis and Design of arbitrary cross sections
Reinforcement design to all major codes
Moment Curvature analysis

http://www.engissol.com/cross-section-analysis-des...

### RE: Calculate Building Stiffness

Is this for a college course or design practice? I am assuming the former.

I would assume that types of materials in your model is consistent. Therefore, your modulus of elasticity (a material property) does not change in the model.

The stiffness of the building (in this example anyway)is a linear value that you can calculate directly from your pull test. K = Force / Deflection. If you know that your pull force deflected your model 2mm...then you should be all set.

Now, if you are trying to model the behavior of an actual building (that will contain actual people), I doubt that this model testing will be able to provide for a safe, code compliant structure.

"We shape our buildings, thereafter they shape us." -WSC

### RE: Calculate Building Stiffness

number of modes = number of masses for a spectral response analysis, but you can use more if you use other methods. That's my understanding from various dynamic books (Chopra for example) that I have. Usually, if you need more modes than the number of masses, you have local modes moving out of the intent of your design, so you have to look at the deflected shape of each mode to make sure you're on track and make careful assumptions.

### RE: Calculate Building Stiffness

^^ should say response spectra, not spectral response...

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