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rc section analysis

Previousnotched beam under cyclic loadingNexttruss roof

Last updated 1 year ago

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 element. There is no need to create a larger model.

The model can be downloaded.

Section Definition

The section configuration is shown as follows.

Model Development

node 1 0 0
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 fc=30 MPaf_c=30~\text{MPa}fc​=30 MPa, ft=3 MPaf_t=3~\text{MPa}ft​=3 MPa, εc=0.002\varepsilon_c=0.002εc​=0.002, εt=0.0001\varepsilon_t=0.0001εt​=0.0001, E=200 GPaE=200~\text{GPa}E=200 GPa and fy=400 MPaf_y=400~\text{MPa}fy​=400 MPa. For detailed material definitions, please refer to the corresponding pages.

Now we define a rectangular concrete section with the dimension of 400 mm×500 mm400~\text{mm}\times500~\text{mm}400 mm×500 mm and nine integration points along section height. Since it is a 2D section, it is meaningless to define multiple integration points along zzz axis. All 2D sections only use 1D integration schemes along yyy axis.

section Rectangle2D 2 400. 500. 1 9

Now define some rebars. The eccentricities are ±220 mm\pm220~\text{mm}±220 mm and 0 mm0~\text{mm}0 mm.

section Bar2D 3 900. 2 220.
section Bar2D 4 900. 2 -220.
section Bar2D 5 600. 2 0.
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 10%10\%10% section capacity, which is 600 kN600~\text{kN}600 kN.

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 10−410^{-4}10−4 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 350 kNm350~\text{kNm}350 kNm.

Users with a relative background may help to justify the result.

Asymmetric Layout

If the layout is asymmetric, say, for example, the rebars at y=−220 mmy=-220~\text{mm}y=−220 mm 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.

The 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 and the steel model.

To combine those independent sections into a whole, we use the section. It is a wrapper that wraps all valid sections into one piece. Accordingly, a element can be defined.

SingleSection2D
ConcreteTsai
MPF
Fibre2D
SingleSection2D
SingleSection2D
rc-section-analysis.supan
model
rotation versus moment