Missing experimental data for comparison, is there a way analytically to get the compression/tension

[drennon236]

The assembly consists of a steel and concrete plate, the top plate (steel) is loaded with a uniform pressure load of 1000 Pa. I then wish to check if the compressive and tensile stress data I get from Abaqus is correct, however I dont have any experimental data. I would assume the output is correct since its a very simple model, but is there any way for me to calculate what the tensile/compressive stress should be analytically?

The assembly:

Compressive/Tensile stress:

Ultimately I wish to do the same with a cylinder model - outer steel cylinder and inner concrete cylinder. Apply uniform pressure to steel cylinder and see what the compressive/tensile stresses are in the concrete and compare with analytical data.

Is there a way for me to find the compressive/tensile stresses analytically? Is there something else I could compare if this is not possible to see if my model is accurate?

 

[FEA way]

In the case of two blocks the analytical value of compressive stress will be simply 1000 Pa. For cylindrical shell with uniform radial pressure the hoop stress is equal to qR/t.

 

[drennon236]

So hoop stress is along the circumference:

When I apply pressure like shown above (100 Pa) to the steel part, I will also get 100 Pa on the inner concrete part if I understand correctly. I get the following S, max principle.

And focus on the circled element gives:

I am having trouble relating hoop stress to Abaqus results. I found this on wikipedia: "The vertical, longitudinal force is a compressive force. The hoop stress is tensile". Say we want to look at tensile stress (S, Max.principal) in circled element and try to compare it with hoop stress which is tensile in nature. What exactly would we compare in this case? And also, hoop stress formula is only valid for internal pressure, or can we use it for external pressure aswell? Using hoop stress formula I get: qR/t = 100Pa*4.43m/0.070m = 6328 Pa. So tensile stress should be as high as 6328 N/m2?

 

[FEA way]

In this case I wouldn’t use principal stress but rather stress tensor components. You can create a cylindrical coordinate system and transform results using it to get the hoop stress.

The formula is valid for external pressure as well.

 

[drennon236]

So for one element, these are the tensor stresses I get. Which one of them would I compare to the hoop stress - would it be S33 as it acts along the circumference. However it is negative so I assume it means its not in tension, and cant be compared to hoop stress as hoop stress is tensile? So I would have to use formula for vertical longitudinal force, and compare it with S22 as the arrow in that picture is vertical aswell?

 

[FEA way]

When you transform the results to cylindrical coordinate system, S22 stress component becomes hoop stress. S11 will be radial stress while S33 will be axial one.