# Moment curve for prestressed two spand bridge

Question:

Dear Midas

I am trying to design a two span concrete bridge which is post stressed using 9 cables. The bridge is to be build 1 m above its final position and to be lowered in place, after prestressing. Durring prestressing, the bridge superstructure i placed in the form. At this stage (cs01), I want to model the deck as vertically supported at the two end supports (ends are free to sway laterally). At the mid support, the bridge is assumed to be fixed in x-, y- and z-direction and also rotationally about the vertical axis (creates statically determined system). At cs01 I have tried to achieve the degrees of freedom at the mid support, by releasing beam end for the top of the supporting columns (frame element 220 - node 220). This seems to create an unexpected moment curve in the super structure. Instead of releasing the beam end at node 220, I have tried to included elastic links between the bridge deck and the top of the supports. By releasing (reducing stiffnesses) in the links, I have been able to release the supports according to what I am after. The only problem is that, when lowering the rotational stiffnesses SRy and SRz in the elastic link 3 (from node 23 to 220)  under the center support, in order to release moment transfer between the superstructure and the center support column, I get a moment curve My for the Deadload case at cs01 "Last step" in the super structure, that differs considerably from the expected moment curve. The expected moment curve is achieve by increasing the values of SRy and SRz to values that approaches a fully stiff connection. I have attached two different plots showing both the expected moment curve (at fixed mid support) and the abnormal moment curve (at released center support). I hope that you may be able to help explain why the release of the moment stiff connection between superstructure and substructure, results in the unexpected moment curve My in the superstructure. I have attaced two versions of the same model. Model 1, where the superstucture and substructure are fixed to one another (correct moment curve) and model 2 with the released moments between superstructure and center substructure (abnormal moment curve).

Model 1 above with expected moment curve (positive max moment 12470 kNm, max negative moment -20474 kNm). This moment curve matches the theoretical moment curve that is achieved by hand calculations.

Model 2 with the unexpected moment curve.

Best regards

Hello,

Sorry I couldn't write back to you sooner.
Actually owing to the way the elastic link stiffness have been provided in model 2, the behaviour is quite different as compared to model 1.  I believe this can be checked quite easily be comparing the DY displacements in both the models.  Now, from what I can gather depending on the modelling done, I believe that though the structure is stress 1m above the actual position, it is still resting on the intermediate pier.  Considering this, I believe model 2 is the right way to go.  With that done, lets discuss about stiffness, since thats the main reason for discrepancy.
1.  The structure is fixed in X,Y and Z at mid for translation.  Thus, SDx, SDy and SDz should be high at middle link.
2.  At the end locations, only the vertical direction is restrained.  Thus, SDx should be high at end links.  SDy and SDz should be given nominal values to avoid singularity errors.
3.  The structure is simply supported, so SRy should be nominal for all the links.
4.  I believe the support system would be such that the bridge definitely won't topple off.  To ensure this, the rotational stiffness of the bridge support about the bridge axis should be high at all link locations.  This can be done by providing high rigidity to SRz at all the link locations.
5.  Also, the bridge ends are free to sway, but the mid support is restrained.  Thus SRx should be high at middle link and nominal at end supports as these are free to sway.
Also, I am not sure on this, but if the bearings are aligned along the curvature, then the links have to be provided beta angle as well.  This has been done in the attached modified model 2.
Hope this helps.  Kindly let us know if further assistance would be required.

Regards,
Nandeep
Technical Manager, MIDAS

Hi Nandeep,

Thanks a lot for the answer. I will proceed with model 2.

Best regards

Creation date: 10/17/2018 10:59 PM (dklee@midasit.com)      Updated: 10/18/2018 8:29 AM (dklee@midasit.com)