Non-linear hinges.

[Anonymous]

Does anybody knows if the rotations described at the non-linear hing model are the chord rotations (θ) ?

Thank you.

[Rafal.Gaweda]

Function defined in hinge definition (moment-rotation) describes interaction between moment and rotation (bar rotation) in point where hinge is defined. If it is not the rotation you mean in your post please describe it more precisely.

[Anonymous]

Rafal, thank you for the reply.

I 'm trying to understand if the rotation used by robot when defining a non-linear hinge  is the chord rotation (see attachement) used by various codes (like FEMA, EC8 etc).

[Rafal.Gaweda]

Take a look at attached screen shot - green lines and arrows indicate the hinge rotation angle

[Anonymous]

That's probably it. Thank you.

It's a different quantity than nodal rotation, right?

I mean for a member 1,2 the chord rotation at the end 1 is given by thιs equation : θ1=(U1+U2)/L+φ1 , where U1,U2 are displacements, L is the lenght of the member  and φ1 the nodal rotaion. Can you confirm if this is what robot considers as a chord rotation?

Are those rotations (at the point where the non-linear hinge is located) demonstrated  anywhere  in table form within robot?

[Rafal.Gaweda]

Robot does not calculated anything like chord rotation.

Displacement \ rotation results for hinges are displayed as results in calculation points in Displacement table.

Look at attached screen shot.

[Anonymous]

I see, that means that it's impossible to use (at least directly) any of the relations given in various codes for the non - linear models, right?

For example at the following attachment there is a relation taken from EC8-part3 regarding ultimate chord rotations, This quantity "θum" can't be inserted in the related field in robot because robot doesn't calculates any chrod rotations.

[Rafal.Gaweda · Accepted solution]

Yes you are right, program does not calculate chord rotation as given by EC8 code.

[Anonymous]

I see, thank you very much.

[Tuctas]

  Hi,

  I would like to express my opinion about this issue.

  Non linear hinge curves in Robot (must) have a physical meaning otherwise they would be useless and push over analysis in Robot wouldn’t have any sense.

  First of all, in case of steel structures, where Robot calculates automatically the parameters of those curves (that represent the behavior of the member), the rules of FEMA273 are used (as it is mentioned in Robot’s help topic). The tables 5.4 and 5.8 of FEMA273, that Robot is referring to, are talking about chords rotation so the “rotation (Rad)” in the one axis of the diagram-model is the chord rotation indeed (In steel members the parameters are given in a relative manner instead of RC members that should be inputted in absolute values).

  The hinge rotation angle, as it is well described in Rafal’s attached picture, shows that it is equal with the difference of the chord rotation values after and before the hinge (these values correspond to the automatically generated calculation nodes on both sides of the hinge obtained from the tables as it is shown in Rafal’s other attached picture). The total rotation “after” the hinge (that is obtained from the table) is the sum of the value “before” the hinge plus the hinge rotation value that corresponds to the diagram of the non linear hinge according to the current step-increment. The value of the hinge rotation is not displayed directly at the displacements table.   

  The initial slope of the diagram (non linear hinge curve) corresponds to the elastic stiffness of the member. If the diagram was modeled in such way that in point B the corresponding rotation was equal to zero, so the initial slope was vertical (that is not able to be done in Robot but it could be approximately modeled only by assigning a large value to the stiffness), then it would represent (only) the plastic rotation of the hinge so the total rotation (“after” the hinge) obtained from the table would be representative and realistic for the current increment. If the diagram is modeled in a way that its initial slope corresponds to the real elastic state (by assigning the proper values of My and θy) then the real rotation is just equal to the corresponding hinge rotation value of the diagram (the non linear hinge curve) and should not be obtained from the table.

[Tuctas]

  I would like to add a comment (to myself..) and also I think that it will be helpful all users that have been involved with push over analysis in Robot (and used non-linear hinges for that reason) to take place and express any opinion about this issue.

  The correct modeling of non-linear hinges, if they are used to model concentrated plasticity in a member (steel, RC) is to set the initial slope of the response curve of it as vertical (i.e the point “B” in the definition of the non-linear hinge model to be placed on the vertical -moment- axis). This can be done approximately as we are not able in Robot to set zero value at the yielding rotation, so it will have a very small value (see attached screen capture “plastic rotation”).

  After we run the push over analysis, the value that we are interested in is the one that correspond to the current point on the diagram (i.e to the current step-component of analysis, see again the attached “plastic rotation”). This value of this point of the diagram (the non-linear hinge model) unfortunately is not obtained directly, but it is equal to the difference between the two calculation points that are automatically generated by the program and are viewed in the table of node displacements. This value is equal to the “plastic hinge rotation” or “plastic hinge chord rotation” of the section and it should be compared to the acceptance criteria that (again) unfortunately is not implemented yet in Robot (although the acceptance criteria are defined in the parameters of the non-linear hinge model, see the attached screen capture “Acceptance criteria”, but finally are not calculated !).

  If we don’t give that very small value in the non-linear hinge model at the yielding rotation (“point B”), then after the (push over) analysis the total hinge rotation will include the elastic part of rotation twice (one time by the yielding rotation of the non-linear hinge model that we have already assigned and a second time by the actual rotation of the elastic member’s length that is taking place out of the hinge).

  Thank you,

  P.S There are other (unresolved) issues too when using push over analysis in Robot but at least as concerns the current issue I think that it must be cleared.

[Tuctas]

  So, I suppose that very few are using push over analysis in Robot so nobody is taking place in such a critical issue..

[Anonymous]

I am trying very hard to understand the application of this nonlinear hinge but I am clueless to its application. Could you be so kind as to explain when, why and how to use the nonlinear hence and subsequently, the pushover analysis?

Thank you so much...