Deformation

 

 

 

Q1. How the value 0.01172 for Load Case type PO is calculated.

The total rotation at node consists of elastic rotation and plastic rotation.

The yield moment of this hinge is 87.275 kN-m and the applied moment is 90 kN-m. So, in this case plastic rotation occurs.

1)      Elastic rotation at node 2: ML/EI = 87.275 x 5 / (32308000 x 0.002133) = 6.331e-3

2)      Plastic rotation at node 1: 0.002683

3)      Plastic rotation at node 2: 0.002703

 

              

          Total rotation at node 2:     1) + 2) + 3) = 0.01172

This is how the value 0.01172 for Load Case type PO is calculated.

 

Q2. If this is the rotation of the node, how it is possible that it is less than the rotation of the hinge in J-end, which is 0.015129 ?

         

As I mentioned in the web board, the “Pushover Hinge(Deformation)” table shows the rotation of pushover hinge,  which is different from the rotation of the node. The hinge rotation is calculated based on the hinge property curve. The elastic rotation of hinge at the yielding moment of 87.275 kN-m is calculated by dividing moment by initial stiffness of the curve.

Moment=87.275 kN-m, Initial stiffness=7023.3957 kN-m

Thus, elastic hinge rotation = 87.275/7023.3957 = 0.012426 rad.

Total hinge rotation = elastic hinge rotation + plastic hinge rotation

     i-end: 0.012426 + 0.002683 = 0.015109

     j-end: 0.012426 + 0.002703 = 0.015129

Hinge rotation of Eurocode corresponds to the chord rotation like FEMA as shown below.

                                   

 

So, the initial stiffness of hinge in case of cantilever subjecting uniform moment along the member should be 2EI/L.                   

You can do this using “User Input” in the hinge property dialog or using FEMA type hinge as shown below.

               

Then, the total rotation for the pushover load case is 6.739e-003 which is slightly higher than the rotation (6.529) of static load case as expected.

                     

 

Total hinge rotation:

              

 

Plastic hinge rotation: