For an engineering project in school, we are checking the stability in the longitudinal direction of an apartment building, taking into account the dynamic effect of earthquakes. For this, we are making a two-dimensional finite element model in Matlab. We have to assume that:
- There is a plane stress condition in the columns
- There is plane strain condition in the floors and walls.
The stability of the building is guaranteed:
- In the transverse direction: membrane action in the columns and the walls.
- In the longitudinal direction bending stiffness of the connections between the columns, the floors and walls.
The picture attached shows an apartment building with properties:
- Nine bays (each 5 m width and 0.25 m thick)
- Six floors (each 3.5 m height and 0.25 m thick)
- Depth of the building is 12 m.
- The building is supported by twenty columns (each 1.6 m width and 5 m height)
- The thickness of the columns has still to be determined but should lie between 0.2 m and 0.8 m.
- E = 35 GPa
- Coefficient of Poisson = 0.25
- Mass density = 2500 kg/m³
- Finishing layer of 350 kg/m²
Plane strain and plane stress can be modeled by means of beam elements, provided that in the elements with plane strain condition adjusted values E' and ν' for the Young’s modulus and the coefficient of Poisson are provided:
E'=E/(1-ν^2) and ν'=ν/(1-ν)
We are struggling with the implementation of the plane stress and plane strain conditions. We have tried to model this as follows:
- Plane strain: We modelled the building with a thickness of 1 m for the superstructure. Therefore, we adjusted the mass density from 2500 kg/m³ to 12 m*2500 kg/m³. In this way the mass of each element is obtained by multiplying by the thickness and length of the element.
- Plane stress: We doubled the stiffness of the column to include both columns at the base.
This implementation gives not the results we are hoping for. Are there any suggestions for improvement?