Nonlinear Frame Modeling of Statically Indeterminate HBV Slabs

[Daniel_SO]

Hello everyone,

I am currently writing my master's thesis, in which I examine the negative moment region of timber-concrete composite (TCC) structures. For this purpose, I am modeling a TCC slab using a frame model based on the "Rautenstrauch" theory. To realistically include the structural behavior in the calculation, the effect of tensile stiffening must be considered and the entire calculation must be performed nonlinearly. I have adjusted the material laws accordingly. I have set the load steps for the nonlinear calculation to 10.

As expected, the concrete cross-section experiences a large tensile force above the internal support. Here a major problem arises for me:

The deflection is significantly greater than in reality (a test series from TU Braunschweig). This can be traced back to the fact that the concrete cross-section in the support area in my model does not transfer internal forces and generally no longer provides any load-bearing effect in the overall cross-section. However, this makes no sense to me, since the reinforcement should at least transfer the normal force which brought it to the tensile limit (plasticity theory). The only conclusion for me is that in the model the reinforcement and the concrete fail, and then the moment is carried only by the remaining timber cross-section.

The question now is: how would it be possible in the modeling for the concrete cross-section at least to transfer the tensile force of the reinforcement (50.0 kN/cm² * 2.26 cm² = 113 kN)? A strain in the reinforcement of 25 per mille should not actually occur, since the timber cross-section counteracts the strain/curvature. In the test series, the beams failed due to tension failure of the timber cross-section in the span area.

What I have already tried:

1. Points in stress-strain diagrams at a strain of 50 per mille with a stress of 0.022 N/mm² for concrete and 500 N/mm² for reinforcement
2. Inserted a plastic hinge above the internal support (did not work because the material is nonlinear)

[juliane.stopper]

Hi Daniel_SO,

Welcome to our community! And thank you for your message!

For the nonlinear analysis, it is necessary that the reinforcement is already considered in the static analysis. This can be realized by means of structural modification. The procedure to activate the reinforcement is described in the linked manual chapter below:

Consideration of Reinforcement.

If the problem still occurs, the model file would be very helpful to analyze the problem more precisely:

Click on File → Save As and select the following settings to reduce the file size:

Then upload the file here (e.g. *.rf6, *.rs9) – so the community can also contribute to the solution.

Do you not want to share the file publicly? No problem – send it to me via direct message: click on my profile picture or my username → Message.

Best regards
Juliane

[Daniel_SO]

Hello Ms. Stopper,

Thank you very much for your response and the link regarding the consideration of reinforcement. After I have now adjusted the structural modification, the concrete cross-section possesses a tensile force in the support area. Thus, my previous question would be answered.

For further information:

If someone sees this post and also wants to calculate moment redistribution of composite structures, this would be an approach for the model that outputs the internal forces determined in a test. However, in this case, the deformation is significantly larger than the deformation determined in the test.

To also bring the deformation to the level of a test, I would choose a different approach, in which a substitute cross-section is defined for the concrete cross-section in the support area (at 20% of the span length on each side). The substitute cross-section should have the same dimensions as the original cross-section. A new material must be created as the material, in which a new stress-strain diagram is defined. I created this diagram from a superposition of the stress-strain curves of concrete and reinforcement depending on their stiffnesses (Iy, Eigen + Iy, Steiner). Thus, I determined the modulus of elasticity for each strain segment of the diagram as follows:

EI_Concrete + EI_Reinforcement = EI_Total
EI_Total / Iy,SubstituteBar = E_SubstituteBar

With the substitute bar, I not only achieve the same moment redistribution as when considering the reinforcement but also a very small deviation of the deformation from the actual value.

Kind regards,
Daniel_SO