rc section analysis
Last updated
Last updated
In this page, the analysis of a rectangular reinforced concrete section of a 2D beam is performed to compute the full plastic moment. This is achieved by using the SingleSection2D
element. There is no need to create a larger model.
The model can be downloaded. rc-section-analysis.supan
The section configuration is shown as follows.
The SingleSection2D
element is NOT a connector element. Only one node is required to define the element. First, we define an arbitrary node.
For material models, we use a simple concrete model that adopts Tsai's backbone ConcreteTsai
and the MPF
steel model.
To combine those independent sections into a whole, we use the Fibre2D
section. It is a wrapper that wraps all valid sections into one piece. Accordingly, a SingleSection2D
element can be defined.
Before defining steps, we first create two recorders to record nodal reactions and displacements.
Users with a relative background may help to justify the result.
In this case, a positive moment makes the unreinforced region in tension. This decreases the moment capacity. However, a negative moment does not change the moment capacity significantly.
Interested readers can try to apply both positive and negative rotation and verify the results.
With the above definition, we have , , , , and . For detailed material definitions, please refer to the corresponding pages.
Now we define a rectangular concrete section with the dimension of and nine integration points along section height. Since it is a 2D section, it is meaningless to define multiple integration points along axis. All 2D sections only use 1D integration schemes along axis.
Now define some rebars. The eccentricities are and .
If the axial deformation shall be suppressed, the first DoF needs to be restrained. Here, instead of doing that, we apply an axial force of section capacity, which is .
Now in the second step, a rotation of is applied on the second DoF.
Perform the analysis, the rotation versus moment can be plotted. The maximum moment under such a loading configuration is about .
If the layout is asymmetric, say, for example, the rebars at are removed.