Hello,
For my master thesis i am studying the effect of rearranging the rebar layout of reinforced concrete shell structures following the principal stress lines, compared to the orthogonal grid.
But at this moment, I am focused on analyzing the influence of the rebars in a shell structure.
Noticing that Karamba does not have many features about this matter, I thought in a way of doing it using the shell as a simple concrete element and the rebars (beam elements) as reinforced steel material.
Firstly, I was following the Karamba3D TidBits #26 (Ribs from Principal Moments) video to prepare the structure and link the beam elements with the shell elements and it seems to be correct as the displacements are the same for both elements. However, the real problem is happening on the utilization of the structure, I was expecting to see the shell tension utilization to be reduced when comparing with simple concrete shell structure (I started analyzing a slab structure for the simplicity).
Is it possible to see the effective change in the utilization of this kind of mixed element structure?
If not, how would be the best way to make this comparison (effect of rebars in a concrete shell)?
I will upload my GH file here, any help would be appreciated.
I don’t think you can achieve great accuracy by mixing concrete shells and rebar beams together. That would require the cross-sections to stay uncracked which is unlikely?
Some random thoughts:
with concrete, you have to consider the cracked/non-cracked state of the cross-section
utilization of concrete slabs under bending deals with design bending moment resistance which is obtained using the ultimate limit state material and load coefficients (this is Eurocode 2 talk, but you might have a different design code. However, the main idea stays the same.).
to give different bending stiffness considering reinforcement in different parts of the slab, you would need to calculate the effective bending stiffness using equations (can be widely found or derived yourself) and applying those modified stiffnesses to Karamba’s shell elements. You would need to discretize the slab to smaller parts where each has a unique cross-section → unique bending stiffness
adding the amount of reinforcement will increase the beforementioned bending stiffness leading to smaller deformations
“utilization” in both SLS and ULS are two different things: the Serviceability Limit State would have a utilization considering the total deflection, concrete stress, rebar stress and so on. The Ultimate Limit State would be more about the resistance of the cross-section like bending resistance and shear resistance.
Using Karamba for more thorough concrete analysis I think you would need to:
script Karamba (there is a scripting guide available) to modify the cross-sections of each shell element to consider the actual reinforcement
this can then be used to run some non-linear analysis on the structure → increase load iteratively, and in each step, calculate the stiffnesses of each element based on the load → update the stiffnesses → increase the load again and so on. Keep going until you hit the full load level.
Using a simpler approach would be something like:
apply different cross-section to each shell element to illustrate the reinforcement in that part (calculate the stiffness using reinforced concrete theory)
modify the reinforcement orientation (principal stresses or something like that)
compare deformation of the whole structure with different reinforcement scenarios
obtain bending moments and shear forces (straight from Karamba) and calculate the cross-section “utilizations” against those
Hello @Vinícius_Gamboa,
the reason why the addition of the reinforcement has little effect on the utilization of the concrete plate is, that the stiffness of the reinforcement bars is small as compared to that of the uncracked concrete cross section.
In your definition the steel bars show a utilization of only about three percent. They would get activated when the concrete cracks. In the attached definition one can see how the steel utilization increases with increasing eccentricity of the bars: PrincipalStressLines_Shell_cp.gh (136.5 KB)
Karamba3D V3 does not include material non-linearity like cracking. A workaround could be to estimate the thickness of the compressive zone in a first step, use this as the plate thickness and place the reinforcement relative to the uncracked compressive zone.
– Clemens
