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# Undertaking nonlinear materials analysis using beam elements

Question:

Hi, I'm undertaking some checks on a simple model to make sure I understand how the nonlinear material analysis works, I'm using the nonlinear material function in conjunction with multi-linear elastic links to model the behaviour of a pile under seismic loads where liquifaction occurs .

With reference to the attached file, I initially undertook an analysis of a simply supported steel beam with an elastic material for the steel beam. From this analysis I had a maximum deflection of 127mm at mid span, a maximum combined stress (=Sbz) at mid span of 493N/mm2 and reaction at the supports at the other end of the elastic links of 23.8kN. I then assigned a plastic material  with an Initial Uniaxial Yield Stress of 450N/mm2 to the steel, so trying to start the beam to yield and restribute some load into the elastic links.

I ran a non-linear analysis with geometric and material nonlinearity but there was no difference to the level of deflection, max combined stress (Sbz governs) in the beam nor reaction at the ends of the links, which I would have expected as a plastic hinge is formed in the beam, so there is greater rotation, greater deflections and . I tried running without the geometric nonlinear component, but this didn't change anything.

Once I changed the Initial Uniaxial Yield Stress of the steel to 425N/mm2 I did see a change in line with the expected behaviour, but the the max stress is signficantly higher than the Initial Uniaxial Yield Stress (480N/mm2 vs 425N/mm2). On reading the on-line help manual, I understand that the stress-strain curve is linear elastic/perfectly plastic (i.e. zero hardening), so I don't see how the stress can be any higher than the limit set.

Additionally, how can I determine the curvature of the beam, there doesn't seem to be a strain output for a beam in a non-linear analysis?

Many thanks,

Hi,

This is the stress resultant beam model, which means that the yield criteria is forces (axial force and bending moments) instead of stress. The yield axial force and yield moment are determined as follows:
- Yield axial force = yield stress x area
- Yield moment = yield stress x plastic section modulus

The online help provides the plastic section modulus for the wide-flange section.

In your model, Z is calculated as 2649211 mm3 and when the yield stress is specified as 450 MPa, the yield moment will be 450 x 2649211 = 1192 kN-m. Thus, in order to see the plastic hinge at the middle, the moment should exceed 1192 kN-m.

When plastic material is not included, the bending moment is 1155 kN-m which is lower than yield moment. This is why there was no change in the results when plastic material is included and the yield stress is 450 MPa.

When the yield stress is 425 MPa, the yield moment is 1126 kN-m. In this case, you can see the plastic hinge at the middle as shown below.

Lastly, the curvature is not provided in the stress resultant beam model.

Regards,
DK Lee
Creation date: 5/15/2019 10:50 PM (dklee@midasit.com)      Updated: 5/16/2019 8:21 AM (dklee@midasit.com)