## Robot Structural Analysis

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# Plastic ratio

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I would like to ask a question that concerns the elasto-plastic analysis.

I modeled an element with a standard section, HEA200, having an elastic-perfectly plastic behavior subjected in pure bending. An unjustified result that I noticed is that when the moment at a node of a member reaches the plastic moment resistance of the section (Mpl,Rd), the corresponding plasticity ratio is never equal to 1.0 but is less (much as I increase the discretisation along the element or/and the number of layers in the cross section).

Is this because of the deficiency of the used formulation (DBE) ?

Thank you.

# Re: Plastic ratio

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Hi

Full plasticity of a section - Value of the plastic ratio equals 1.0

Example:

**Rafal Gaweda**

# Re: Plastic ratio

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Thank you for the reply.

In your example there is no moments at the member with plastic properties. If there is only axial force then the value of plastic ratio is o.k indeed.

Take a look at the attached picture, the plastic resistance moment is reached at the base node of the member but the corresponding plastic ratio isn't equal to 1.00. (I have done anything in order to model the member more precisely: number of cross-section division 25/25, the element is divided in 12parts and each of them has 4 intermediate integration points, load increment number 30..).

Thank you,

# Re: Plastic ratio

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It is more sensitive for bar length than discretization of cross section.

Example attached.

**Rafal Gaweda**

# Re: Plastic ratio

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* *When i run your .rtd file (with your settings), the message "instability of type 3" occurs continiously and only if i select "cancel" the calculations end.

But even if we ignore that message i think that it is not rational at all to choose as 0.005m (=5mm...) the max length of member's division for the simpliest of simple cases (just a cantiliver), what would happen if we have a normal structure...?

# Re: Plastic ratio

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Either lower results accuracy or much denser discretization (number of bar fes along bar)

**Rafal Gaweda**

# Re: Plastic ratio

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That is general rule for structural analysis anyway, i am just "worrying" about Robot's accuracy because it is not easy for me to justify such kind of results for a so simple model.

I just wanted to keep in mind the same worry too..

Thank you