Tri-linear Rotational Springs in the Beam

[wardak21]

Hello everyone,

I try to model a beam element using rotational springs at the two ends and elastic element between the two.

I am told to compute Moment-vs-Rotation diagrams of the springs. I am not very confident of my knowledge about this.

Can anybody share a more detailed explanation/or address a reference to read? Please, kindly refer to the attached file for further understanding of my question.

looking forward to your response.

 

[johnbridge231]

You are talking about the "concentrated at the joints plasticity" method which is popular and easy to work with. In this case, you should calculate the Moment vs. Rotation (or curvature) of the cross section of the beam, then find the equivalent tri-linearized diagram of that and assign it to the springs at their edge nodes.
The difficult part is the calculation of the moment vs. curvature diagram, as the single materials (steel, reinforcement or concrete) all have non linear uniaxial strees-strain relationship.s
A good software that could help you a lot to produce such diagrams can be found here.

Regards.

 

[jdgengineer]

Which code are you using for this design? ASCE 41 has guidance as to how to construct Force-Deformation diagrams.

As an example for a steel beam, see Section 5.4.2.2.2 and Table 5-6.