## Robot Structural Analysis

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# Non-linear hinges.

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

Thank you.

Solved! Go to Solution.

# Re: Non-linear hinges.

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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.

**Rafal Gaweda**

# Re: Non-linear hinges.

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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).

# Re: Non-linear hinges.

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

**Rafal Gaweda**

# Re: Non-linear hinges.

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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?

# Re: Non-linear hinges.

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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.

**Rafal Gaweda**

# Re: Non-linear hinges.

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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.

# Re: Non-linear hinges.

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

**Rafal Gaweda**

# Re: Non-linear hinges.

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I see, thank you very much.

# Re: Non-linear hinges.

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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.