Part 2: Structures under earthquake. Calculation example using a FEM program

Decembre , 12th 2019 | Author: Prontubeam
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**1.
****Preeliminary
information**

In our article, “Structures under earthquake effects-Calculation example” (Read article) Prontubeam did a hand-made calculation of a simplified two level storey structure under earthquake. It was calculated the vibration modes, maximum displacements and the reactions on the foundation. At the end of the article we wondered if the simplified model used in that example would lead to the same results as a more accurate one using FEM. We decided to do an accurate model and study/compare the results.

It is reminded here below the simplified model used and the results obtained:

Picture 1. Simplified model.

Picture 2. Vibration modes

Figura 3. Results – Reaction on the foundation

**2.
****Calculation
of the model using a more accurate finite element model**

To calculate this example it has been used the finite element program STAAD.Pro. We remind that any other finite element program would give us similar results. In this list (click to open the list in a new tab) it can be found the most important finite element programs voted by our readers. The structure has been modelled with the same hypothesis that the ones used in the hand-made calculation example. This means that the weight of the columns has been neglected and the floor slab is infinitely rigid. This last hypothesis has been modelled providing a very high Young modulus to the floor slab material (to increase its stiffness).

The following picture shows the FEM model used for this example:

Picture 4. FEM model

The hand-made calculation model considered only two degrees of freedom: the horizontal displacement of each level of the Storey. To try to reproduce similar conditions (no vertical displacement of the structure) it has been used sliding supports on the structure nodes blocking the vertical displacement. However, it has been checked that, as expected, this hypothesis has to impact on the results as only the horizontal earthquake is studied (it has not been combined with any vertical load). The connexion between the beams is stiff (bending moments are transmitted). The total mass of the structure is 350kN, which is the same as the one used in the hand-made simplified model (15tons+20tons). We remind that the mass of the columns has been neglected to use the same hypothesis as the ones used in the hand-made simplified model.

The following picture shows the floor response spectra used, which is the same as the one used in the hand-made simplified model:

Picture 5. FRS applied on the structure

**3.
****Results**

The following picture shows the displacement of the structure under the seism, to verify that seems to be as expected:

**Picture ****6****. Displacement of the structure**

Here below it is presented the results. At the end there is a comparison between both, the handmade calculation and the FEM ones.

Vibration modes frequencies of the structure and their associated vibration periods:

**Picture ****7****. 3.1. Vibration modes frequencies of the
structure and their associated vibration periods**

The following table shows the maximum reactions on the supports due to the earthquake:

Figura 8. Support reactions

Results comparison: Hand-made calculation – FEM calculation

Conclusion:

After analyzing the results of both calculations, we can conclude that both models behave in a similar way and the results are close enough to validate the behavior our hand-made calculation.

**4.
****References
to other documents**

**[1] Article from Prontubeam: **Structures under
earthquake effects. Calculation example. https://www.prontubeam.com/articles/2019-07-11-Structures-under-earthquake-effects-Calculation-example/

**[2] Calculation program: STAAD.Pro: ***www.bentley.com/es-mx/Products/STAAD.Pro/*

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