rc section analysis
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
Section Definition
The section configuration is shown as follows.

Model Development
The SingleSection2D
element is NOT a connector element. Only one node is required to define the element. First, we define an arbitrary node.
node 1 0 0
For material models, we use a simple concrete model that adopts Tsai's backbone ConcreteTsai
and the MPF
steel model.
material ConcreteTsai 1 30. 3. 2. 2. 2. 2. .2 2E-3 1E-4
material MPF 2 2E5 400 .01
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.
section Rectangle2D 2 400. 500. 1 9
Now define some rebars. The eccentricities are and .
section Bar2D 3 900. 2 220.
section Bar2D 4 900. 2 -220.
section Bar2D 5 600. 2 0.
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.
section Fibre2D 1 2 3 4 5
element SingleSection2D 1 1 1
Before defining steps, we first create two recorders to record nodal reactions and displacements.
hdf5recorder 1 Node RF 1
hdf5recorder 2 Node U 1
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 .
step static 1
set ini_step_size 1E-1
set fixed_step_size 1
set symm_mat 0
cload 1 0 -6E5 1 1
converger AbsIncreDisp 1 1E-10 20 1
Now in the second step, a rotation of is applied on the second DoF.
step static 2
set ini_step_size 1E-2
set fixed_step_size 1
set symm_mat 0
displacement 2 0 1E-4 2 1
converger AbsIncreDisp 2 1E-10 20 1
Result
Perform the analysis, the rotation versus moment can be plotted. The maximum moment under such a loading configuration is about .
Users with a relative background may help to justify the result.
Asymmetric Layout
If the layout is asymmetric, say, for example, the rebars at are removed.
section Rectangle2D 2 400. 500. 1 9
section Bar2D 3 900. 2 220.
# section Bar2D 4 900. 2 -220.
section Bar2D 5 600. 2 0.
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.
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