Post tensioned concrete plastic hinge

[ludvik]

I am currently trying to perform either a pushover analysis or non-linear time history of a bridge with precast post tensioned piers. Plastic hinges will form at the base of the piers under high seismic loads, and I am trying to determine the properties of this hinge.

There is plenty of guidance out there for determining the properties for a normally reinforced concrete plastic hinge, however, I've had trouble with a post tensioned structures. The plastic hinge will develop at the joint between the bottom segment of the pier and the pilecap. This is effectively zero length, so the normal procedure of assuming a hinge length does not apply. Can anyone give me any guidance as to how to proceed?

 

[ishvaaag]

If I understand the question well, a first stage of your problem is to ascertain the moment-rotation behaviour of your pier at the sections of interest. For the cases where compatibility of deformations still stand, the analyses of the respective transversal sections gives a moment-rotation relationship, since this is a necessary output of the compatibility of deformations method. This can also be used for confined concrete as long as you use for the concrete a stress-strain law corresponding to the case.

What above is where the section is allowed at much to fail on the tensile sides at any time. Other thing is for the cases where the strength of the concrete has been overpowered by the shakeout, and the degradation of the section that has crushed/spalled concrete needs be represented, on which I have not guide to give.

 

[ludvik]

Ishvaag: As you guessed, all that i need is a method of calculating the moment-rotation relationship. Is there some way of using an assumed plastic hinge length? If not, is it related to the bond length of the strand? I can calculate the moments at which the section will yield and the ultimate moment, but the rotations at which these occur are harder to determine.

Once i figure this out, the next level of sophistication would be to figure out the axial force/ moment/displacement interaction relationship.

 

[ishvaaag]

I made a number of worksheets in Mathcad for compatibility of deformations analyses of RC and PC concrete sections (in fact this project was the thing I bought Mathcad for). As long the strands are grouted, the PC ones might serve you, and if not, at least as an approximation. If I remember well, I made them for Box, Pipe and Double Tee sections, and a variety of other full sections. I also made an example for fully general sections with structural shapes, passive rebar and prestress that can be reformed to cover any shape by the device of decomposing it in trapecial components. I think all are freely available from the Collaboratory for Mathcad 2000, Civil Engineering Folder. Were a bit slow in the 166 MHz processors of then but not in the present 3000 MHz. It also can use a variety of steels and you can modify the sheet to hold your preferred stress-strain law for concrete. If you don't find the thing, describe your pier section and provide an e-mail address and I will send you a sheet if one matches more or less what you require.

Respect the length of the "plastic hinge" the compatibility of deformation analyses will give you the height along the pier by what by the standing moments all or part of the passive or active rebar may have yielded. I recently read some literature about plastic hinges in shear walls in buildings and think to remember 1 to 3 stories tall plastification under Earthquake might be used in the model.
1 to 1 or 2 to 1 to the width of the pier maybe also sound reasonable, I think, yet the compatibility of deformations if feasible to follow apeace with the progression of the anlysis will give you more information of the actual behaviour, since all stresses in every concrete and steel component and separately given and charted as output.

 

[dik]

Not knowing the application, you may have to be careful in considering 'hinges' in post-tensioned concrete... they may not have any ductility to be useful...

 

[ludvik]

ishvaag: I can't find the mathcad document you are refering to. It sounds good though, so if you could email it to me at mludvik@hardesty-hanover.com, I would appreciate it.

dik: You make a good point about the applicability of plastic hinges to my structure. One thing i would like to establish is the exact amount of ductility in my section. My understanding is that precast, post tensioned piers tend to have significantly less ductility than a normal reinforced section. I am anticpating that by quantifying the exact moment rotation relationship of the member I will get an answer to the question.

 

[dik]

Prestressed stuff often approaches a balanced or over reinforced condition... just a caution... I recall the PCI having some information on ductility... but memory fades with time <Sigh>... You may want to search their website...