What is the effect of end diaphragms on prestressed girder forces/deflections?

Question

I'm encasing the abutment ends of prestressed concrete bridge girders in concrete before the deck pour. (For lateral stability and to prevent the soil from spilling through.)

Discussion of intermediate diaphragms for prestressed girders abounds, but I haven't found information on structural behavior of end diaphragms.

For purposes of a consulting engineer

My gut / engineering judgment is telling me the effect is negligible, but I prefer to understand what's actually going on before making simplifying assumptions.

Conceptually (versus a girder without the diaphragms):

1. Does this change deflections during the deck pour? What about long-term deflections?
2. Does this change the live load moments &/or shears?
3. Is there any logic by which the encased length should be a function of girder depth or span length?

I've put a sketch below since terminology and typical bridge configurations vary around the world.

Answer 1

I have no resources to point to in regards to this, but I'm fairly certain your gut-feeling is correct. In fact, end diaphragms exist in bridges primarily to hold the soil on the approach. They can also be useful for temporary lateral stability of the beams, but if that were the only reason, temporary metallic bracing would be much easier and cheaper. Lateral instability (buckling) in the final structure is usually not a controlling factor, especially given the (partial) bracing that is the slab.

Mid-span diaphragms help with transverse load distribution and stop the primary beams from "opening" along with the slab deflection. The same applies to some extent to end diaphragms, but to a much lesser extent since the load is transmitted almost immediately to the bearings. The bearings also help to impede the beams from "opening". This is probably why you've found no resources in regards to end diaphragms: no one's really bothered to think too much about them.

Now, answering your specific questions:

1. This would change deflections somewhat, since the end diaphragm is going to change load distributions from your slab to your beams. This will be most relevant if your bridge has a small distance between diaphragms (less than twice the distance between primary beams, according to classic slab methods such as Rüsch). If the diaphragms are more spread out, then they will have almost no influence in the load distribution and therefore will not influence deflections. This also applies to long-term deflections.

   Long-term deflections are, however, influenced by one more factor, and that is the prestress' differed losses. Over time, the primary beams are going to try to shrink. This is due not only to the concrete's natural shrinkage, but also due to the prestress' compressive creep. If all the beams were exactly the same, the creep and shrinkage should progress similarly along all of them. In that case, the end diaphragm would not have an effect since all the beams would "pull" it the same amount, implying in a simple rigid-body translation, without any deformation on the diaphragm.

   That, however, would be in the perfect world, and that ain't ours. Creep and shrinkage are mysterious and unstable, with a lot of scatter. So even exactly similar beams would probably result in different creeps and shrinkages, meaning that the end-diaphragms would be deformed. The diaphragms deformations (which would appear as horizontal shear forces on the diaphragm) will create tensile forces in the primary beams over time and these tensile forces will influence the creep behavior of the beams over time, leading to a recursive effect.

   Also, the beams would never be exactly the same because the loading in each beam is different (perhaps the central beams have similar loads, but they will certainly not be similar to those at the transversal extremities of the bridge), which is sufficient to generate (slightly) different creep behaviors in the beams.

2. As mentioned in the beginning of item 1, this will change the stresses suffered in the beams since the load distribution from the slab to the beams is modified by the existence of the end diaphragms. If the diaphragms are sufficiently far apart, however, the effect is almost certainly negligible.

3. Here I have a bit less to go on. I can say, however, that at the firm where I work we usually embed the primary beam only a few centimeters (3-5 cm, usually) into the end diaphragms. This allows the end diaphragms' crack-control reinforcement to pass without much fuss. The primary beams are designed with all their reinforcement sticking out at both ends in order to anchor into the diaphragms. Obviously, if your beam is unusual or if is a deep beam, the behavior might be different.