strut and tie model for bent cap under seismic loads

[cwrugrad]

Has anyone else done a strut-and-tie model for a concrete bridge crossbeam (bent cap) under earthquake loads?

Did you use the results in your design of the reinforcing? If not, what did you use for the structural design of the crossbeam for seismic loads?

The column joint-region design recommendations in Priestley & Seible's book "Seismic Design and Retrofit of Bridges" never really made sense to me (seem arbitrary and don't address what happens outside the immediate joint region), so I wanted to see what a strut and tie approach would show.

When I finally got around to doing a strut-and-tie model, for a two-column bridge bent (with 5-girder superstructure) under combined dead loads and seismic loads, I found that I don't like my results.

My boss wanted the crossbeam/bent cap to be an integral two-stage type, with the girders set on top of part 1 of the crossbeam and then part 2 would be cast around the ends of the girders and up to the top of deck to make one big blob of concrete providing moment continuity in both directions.

That made the crossbeam a deep beam, so I followed the AASHTO LRFD recommendation to use the strut-and-tie method.

I wound up with huge forces in the diagonal strut and vertical tie that connect directly to the tension and compression side of each column. The amount of vertical steel supposedly needed for the tie member is more than 1.5 x the total column longitudinal rebar. Given that you can only consider about half the column rebar as effective on the tension side of the column, that means you'd have to provide a tension capacity in the tie member of 3x what the column steel alone provides.

In a way that makes sense, since the crossbeam concrete isn't under the same compressive stress as the column so you don't get the benefit of the interaction diagram. But I didn't expect to need THAT much rebar!

Thoughts, anyone?

 

[civilperson]

There are an infinite number of strut-and-tie models that can represent any given reinforced concrete structure. The more refined the model, the less the required steel. The steel in ALL the models is greater than the actual need. Try a different configuration of struts and ties and see if the amount of steel is going up or down. If the amount is less, use as a guide for a second iteration. Try confining the ties and ends with hoops for a larger usable stress.

 

[cwrugrad]

Thanks! This is only my 2nd serious attempt at strut-and-tie design (not counting a couple of really simple situations), and both times I find my thinking gets in a rut once I've come up with one that "works," and it gets hard to come up with a different one.

With this structure I feel trapped by the requirement for joint equilibrium at the joint where the column tension is applied.

I didn't want to open the constructibility can of worms I think would result from using diagonal tension ties, so that forced me into a vertical tie right there at the column quarter-point. Other than exploring diagonal ties, I can't see a way out of this predicament.

 

[Qshake]

From your description you seem to be looking at a concrete diaphragm (encasing the girder ends) over the bent cap beam.

If this is true, I've not seen a integral detail yet for the diaphragm that ensures composite action with the cap beam. They're called integral based on the monolithic nature with the concrete deck and not the bent beam below. Most integral diaphragms are only pin connected with the beam cap as rotation at the intermediate supports is favorable. As a result, the deep beam assumption doesn't pan out.

If the deep beam isn't correct, then I don't see the point in using strut/tie methods.

Regards,
Qshake

Eng-Tips Forums:Real Solutions for Real Problems Really Quick.

 

[cwrugrad]

Hello, Qshake,

Some of my columns are quite tall (86' clear height). I wanted to ensure double bending in both directions to keep KL reasonable, both so I wouldn't have to figure out how to combine nonlinear second-order P-delta analysis with elastic seismic analysis (AASHTO allows use of approximate moment magnification method for KL/r < 100) and to reduce the risk of asymmetric column behavior due to P-delta effects discussed in Priestley & Seible's book.

The longitudinal-bending problem is quite simple, and I was able to get pretty good agreement between a simple strut-and-tie model and a traditional bending design approach with the diaphragm considered as a vertical cantilever beam supported by the lower crossbeam at the construction joint and subjected to forces at the deck level and girder bottom-flange level.

The amount of reinforcing needed according to both methods was fairly substantial, but not as large as what I'm getting for that vertical tie in my model for bending in the plane of the bent.

For me, the big question is: is there a real problem in ensuring that column seismic moments are effectively carried "around the corner" from the column to the crossbeam, a problem that is revealed by strut-and-tie analysis, or is the strut-and-tie method flawed for this situation (if so, why?), or is MY strut-and-tie model flawed in some way?

 

[Qshake]

I've analyzed and designed some similar height columns and so I'll make some general comments...

The columns I designed were for a three column bent and were about 80' tall. The point of using three columns was to distribute the inplane reactions (moments, shears etc) thereby reducing their impact on any one single column. The columns were formed in three sections with diameters of 1.5m, 1.25m and finally 1m. At each section where the columns changed diameters, a tie beam was placed in the plane of the bent. In my case, the bridge was little over 600' but was integral and so the longitudinal movement was minor.

The usual details for SPC C were used in detailing the concrete frame though the bridge was in SPC B. No specific analysis was done for the beam/column area.

The superstructure above the bent was monolithic but the diaphragm was constructed so as to allow rotation on the top of the bent cap beam. This aides in the over structural analysis of the bridge to be pinned on the intermediate supports.

Not necessarily helpful for strut-tie methods but it affords a look at an arrangement for a similar bent in SPC B/C.

Regards,
Qshake

Eng-Tips Forums:Real Solutions for Real Problems Really Quick.