Baisc Prestress Loss Question

[Perception]

Hello,

I feel kinda silly for asking this, but I have a basic conceptual question about losses in prestressed concrete. Shrinkage, creep, elastic shortening, etc. will cause a concrete member to reduce in volume. This reduction in volume leads to the development of forces in the concrete and thus the strands (PL/AE).

What I don't understand is why this added force reduces the prestressing force in prestressed strands. My understanding is strands are in a state of compression, and conceptually it seems like reducing the volume of a concrete member would only add to that compression (like squeezing a ball between your hands). Losses due to steel relaxation on the other hand make sense to me; the strands are in compression and are trying to stretch back out to its original state. What am I conceptually missing here?

Thanks,

 

[BridgeSmith]

Actually the strands are in tension, which produces compression in the concrete. When the concrete shrinks due to elastic shortening, drying shrinkage, and creep under sustained load, the prestressing strands get shorter and therefore have less tensile stress in them. This shortening creates camber and causes tension on the opposite side of the concrete section. When subsequent loading is applied, the strands stretch back out and can produce concrete tension around the strands, as well.

 

[rapt]

HotRod10,

Close but not quite.

The shortening will reduce the tension force in the strands as you suggest as they are shorter, but it will cause deflection towards the face that the tendons are closest to, not camber in the other direction.

Bonded steel will reduce the compression in the concrete at that face thus making that concrete face slightly longer that the other face, meaning that deflection caused by restraint to shortening is towards the face with the bonded steel. Unbonded tendons would have little effect but there would normally still be bonded reinforcement at the face the tendons are closest to.

 

[BridgeSmith]

Not sure if we're actually disagreeing or just misunderstanding each other, rapt. Let me try again.

Generally, the prestressing strands are in the bottom of the beam (at midspan, at least, but sometimes harped so they are higher at the ends). For prestressed beams, they are stretched and the concrete is poured and cured around them. After curing, the strands are released and some of the tension in the strands is transferred to the concrete, compressing it. The bottom of the beam gets shorter, morethan the top due to the greater compression near the strands, resulting in an initial upward camber and relieving some of the tension in the strands. The upward cambering continues, due primarily to creep (plastic deformation) which shortens the bottom of the beam even further and relieves more of the pretension of the strands. The reductions in stress in the strands due to their shortening are the prestress losses, which are dependent primarily on the concrete properties.

When the beam is placed spanning between supports and loaded, the selfweight and superimposed loads bend the beam back down somewhat, stretching the strands and the surrounding concrete which the strands are bonded to. If the superimposed loads are light, which for a bridge girder they usually are, the beam will continue to camber up, but at a progressively slower pace, as the concrete continues to gain strength, decreasing the creep, and the moisture level stabilizes, reducing the rate of shrinkage.

When transient loads are applied, the beam bends down, increasing compression in the top of the beam and decreasing the compression at the bottom of the beam. If the load is large enough, the concrete in the bottom of the beam goes into tension. If the tension exceeds the modulus of rupture for the concrete, the concrete cracks. This is typically considered a serviceability failure.

 

[rapt]

HotRod10

I was simply commenting on your statement in the first post, repeated below, which is probably not what you really meant to say!

"the prestressing strands get shorter and therefore have less tensile stress in them. This shortening creates camber"

Yes, the scenario you have stated in your second post would be correct for highly prestressed members with low extra loading, except that you have left out the effect of shrinkage which happens at about the same rate as creep and has the opposite effect and is dependent on the amount of bonded steel as well as the concrete properties. Many prestressed members have much lower levels of prestress and will not behave like this as the initial uplift from the prestress is less than the self weight of the member, so there is no initial upward camber and the concrete around the strands may be in tension.

In more modern prestress design (the last 50 years in some countries, and much longer in reality as Freyssinet's early PT design in the 1930's (I think) was partially prestressed), cracking is not really considered serviceability failure. It normally means you have a partially prestressed member and it is necessary to consider crack widths and crack control measures in the design as you would for RC member design.

 

[BridgeSmith]

rapt, my experience with prestressed concrete members is limited to bridge girders, which I assumed (apparently incorrectly) was typical of prestressed concrete for other applications. Thank you widening my understanding of the subject.

I'm still not seeing what was incorrect about my statement you quoted. I did not include any discussion of what was going on in the concrete, but as far as it went, what did I get wrong?

 

[IDS]

The problem is, if you want to look at the effect of creep and shrinkage on section curvature (and hence deflection), you need to look at the strains in the concrete at both faces, rather than just the prestressing strand.

It is true that creep in concrete in compression will reduce the tensile strain in the prestressing strand, but the effect of that on curvature will depend on the creep strain at the top face, and the reinforcement density. Usually creep tends to magnify the existing deflection, but that is not always the case.

In the case of shrinkage, the direct effect on the bottom strands will be the same, but for a symmetrical un-cracked section there will be no effect on curvature because the top face strains change by exactly the same amount (assuming uniform shrinkage). In practice the bottom face (at mid-span) will normally have more bonded reinforcement, which reduces the shrinkage strain in the bottom face, resulting in nett downwards deflection. After cracking this effect is amplified, and the effects of shrinkage have a similar magnitude to creep, even in a symmetrical section.

Finally, a simple way to way to calculate the effects of shrinkage and creep is to apply the strain as a virtual compressive prestress force to all the reinforcement, then calculate the section curvature as you would normally. This works for un-symmetrical reinforcement, with or without cracking.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[rapt]

HotRod10

The shortening of the prestress strands does not cause camber. In fact, the shortening of the prestress strands reduces the force in them so it reduces camber due to the prestress as P is reduced and camber due to prestress is related to P.e. The camber due to creep is caused by the shortening of the concrete at the bottom which is under higher compression stress than the top so it shortens more creating upward curvature.Then there is (normally downward) camber due to shrinkage restraint caused by bonded reinforcement.

 

[BridgeSmith]

"The shortening of the prestress strands does not cause camber."

Technically, it's the shortening of the concrete and prestressing strands, as they are bonded and move together.

"...the shortening of the prestress strands reduces the force in them so it reduces camber due to the prestress as P is reduced and camber due to prestress is related to P.e."

Well, the rate of the cambering due to creep slows as the strands relax and the concrete gains strength and becomes less susceptible to creeping. However, creep of concrete is plastic; once the concrete shortens due to creep, it does not rebound. Elastic rebound due to reduced compression is not creep. Typically, our bridge girders are expected to have half an inch to 2 inches of camber when they are put into service. They are usually anticipated to double the initial camber over their design life. This can be minimized by increasing the time to transfer.

"Then there is (normally downward) camber due to shrinkage restraint caused by bonded reinforcement."

That is a separate effect from camber due to creep. The sag (what we call 'downward camber') due to shrinkage and permanent load on our bridge girders is typically much less than the camber.

 

[hokie66]

Sounds to me like you know a thing or two about bridge girders, HotRod10. Improving rideability in pretensioned bridges is a noble effort. Ever drive across the Chesapeake Bay Bridge Tunnel? The trestle spans make you think you are in a boat, riding the waves up and down.

 

[BridgeSmith]

"Sounds to me like you know a thing or two about bridge girders, HotRod10."

I should after 17 years as a bridge design engineer at a DOT, where other departments handle much of the ancillary work, like contracts, construction oversight, etc. This does leave me out of my depth when it comes to construction practices and such, but I try to keep up on that through conversations with our field guys and reading questions and answers here. I do always try to keep in mind the poor guy who has to build what I design, since there was a brief era in my life when I was that poor guy.

My experience with prestressed girders is also somewhat limited, due to the fact that we defer the actual prestressed design to the contracted fabricator. We review the designs, so we get to see what they did.

"Improving rideability in pretensioned bridges is a noble effort."

And a difficult one. Unless the bridge is on a crest vertical curve to match the final camber, keeping it down to a manageable level usually requires more harped strands than the precasters would like. We mostly do prestressed girders on lower speed and lower traffic roadways. We do mostly steel plate girders, which are usually pretty good for rideability if they are erected properly.

"Ever drive across the Chesapeake Bay Bridge Tunnel?"

Never been that far east in the US, except the Accelerated Bridge Construction Conference in Miami a couple years ago, but I didn't get to do much sightseeing.