Cantilever beam scenario

[akim]

Hello all,
Here is my problem, I trying to simulate a chair arm being loading horizontally (from the center of the chair out). The Arm consists of a steel insert which is attached to the lower arm which connects to the bottom of the seat. Suffice to say the lower arm is quite stiff and will not deflect much. Therefore the insert should behave like a cantilever beam problem. The insert is a 1/2" diameter 6" length rod (exposed length) that is made of 1010 cold drawn steel (what I have been told). From hand calculations and using the ultimate stress value for the material, the insert should fail at around 100lbf, however in a physical test it goes well beyond that (been tested at 250lbf) and did not plastically deform or very little. I initially ran the static problem in mechanica and the deflection was so small that I didn't run it as a large deformation analysis, and the stresses evident in the rod were well above yield and ultimate. So my question is, is there something obvious I'm missing in my analysis or my theory.
Any help would be appreciated.

Thanks
Al

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[jholst-2]

I would need to look at the stress plot to give a good opinion however, one of the biggest misconceptions about FEA stress results is that if you see stresses anywhere in the model that are over yield, then you have a failure. This is not true for ductile materials like 1010. Local high stress may result in a very local yield that would never be detected during a physical test. Local high stresses are important for brittle materials or fatigue analysis because this is when and where cracks will start. In your case you need to look at the general linearized stress level through the entire cross-section. It is likely that there is sufficient cross-section to carry a much higher load without failure during a physical test. Not much else can be said without looking at the stress plots.

Some professional society Codes and Standards limit the pure bending outer fiber stresses to be 1.5 times the material allowable while pure membrane stresses are limited to 1 times the allowable. The higher limit in bending is because not all of the cross-section is at the highest stress level and there is still more load capacity left in the section.

Another common mistake is to compare a linear stress calculation to material ultimate stress. In a pure sense, once you allow parts to load past yield stress calculated by a linear code (like Mechanica) the stress calculated using that linear analysis is no longer valid especially in those local areas. In a practical sense, you can still use linear stress calculations if you scrutinize the calculations in those very localized areas. Stresses in other areas of the model are most likely valid. Sometimes, depending on the problem, it is better to look at the strain calculated and compare that to the materials maximum elongation. This is only valid for very localized high stresses. In a real physical test when a local area of a part is stressed over yield the stress does not continue to increase at a linear rate as would be calculated by a linear analysis. The local area will go plastic and strain will continue to increase until the part fails do to the strain limit not a stress limit. If you are designing the part to ultimate loads rather than yield, it is going to very difficult using a linear stress calculation.

---Jim Holst