Prestress Load Combinations 1

[youngstruct23]

Hi guys,

I have a question regarding the load combinations used for determining ultimate bending moments in prestressed concrete. For arguments sake, just assume a rectangular beam carrying a uniform distributed load, with a parabolic PT cable that is stressed to balance out the deadload. In all the references I have seen, the load combination of 1.2G + 1.5Q is used (in Australia anyway). Now I am probably missing something here, but I have always thought of post tensioning as an applied external force, with in the case of a simple parabolic tendon a uniform uplift force along the length of the tendon which is cancelled out by downward forces at the anchorage and stressed ends. If this is in fact the case, why cant the primary moments caused by post tensioning be included in the load combinations for strength (for example 1.2G + 1.5Q + P)?. This would make quite a difference when the level of stressing is such that it balances the deadload. I know the secondary hyperstatic moment is to be included in the strength combination, but I cant understand why the primary moments induced are not included.

Now before I get a serving for not properly understanding PT just know that the limited work I have done with it I have never deducted the primary moments and I will continue to design that way until I read something definite to show otherwise. This question is moreso just for interest and my personal understanding.

 

[struggle66]

Youngstruct23,

I was always confused about this PT balanced moments until I found out that PT is not a sky-hook.

You must not include uplift PT moments in ultimate strength calculation because gravity still exists and the dead load is still there. The only action you should include in your ultimate strength calculation is PT secondary moment. You can include uplift PT moments in serviceability and deflection calculations.

 

[rowingengineer]

I am so very confused, are you suggesting you can reduce the moments due to Pt then use these same moments for strength of the concrete. or maybe I am not following? Struggles66's "uplift moments" is also causing my head to hurt, I don't see the different between ultimate and serviceability for analysis and what uplift moments would be.

http://www.nceng.com.au/

"Programming today is a race between software engineers striving to build bigger and better idiot-proof programs, and the Universe trying to produce bigger and better idiots. So far, the Universe is winning."

 

[youngstruct23]

Rowingengineer,

I reread my original post and dont blame you for being confused, I didn't really translate my thoughts into words very well.

Basically what I am suggesting is that the PT force is physically there and causes a hogging moment in the beam/slab. As such I dont understand why this hogging moment is not included in the limit state load case for "downward loading" (1.2G + 1.5Q). In the case of a transfer check we ensure that the beam/slab has ample capacity to resist this same hogging moment before full deadload is applied (or losses occur) with the load case 1.15P + 0.9G. Then when we check the "downward loading" condition with 1.2G and 1.5Q we disregard this same hogging moment as if it doesnt exist.

Struggle66, that is the same thing I was thinking, you cant beat gravity and the deadload will always be there. But when considering the PT as an external load acting on the beam/slab, the curvature of the tendon generates an upward loading which is cancelled out at the ends by the downward loadings arising from the slope in the cable at the anchorage/stressing point. As such, no net uplift is generated and the deadload reactions are exactly the same as if the beam/slab wasnt stressed (provided there are no hyperstatic effects). Although no net uplift is generated, there is still a physical hogging moment due to the prestress and eccentricity of the cable, and I cant understand why we cant use this moment to reduce our ultimate design moments.

I just reread all of that and completely understand if you cant follow my ramblings, the written word is not my strong point. Anyway I think an Easter beer is overdue, have a good weekend all

 

[asixth]

If it is beneficial to the design actions it shouldn't be included at ultimate limit state. If it is detrimental than it should be included.

 

[cooperDBM]

Youngstruct23,

The ultimate flexural strength of a section isn't dependent on loading. The flexural strength is the bending moment consistent with the section straining in rotation about a neutral axis to the point that, ideally, the tensile steel has yielded (or close) and the concrete in compression is at, or below, it's safe crushing strength (say strain = 0.003). If the steel was prestressed then at that point it has strained beyond the effective prestress stress so that the original prestress force at the section no longer exists. That's why the ultimate force in the tendon is higher than the prestress force. The resulting flexural strength is then checked against the factored external loads that still exist in that state.

Serviceability checks occur at a point where the tendon hasn't strained beyond the level of prestress.

 

[youngstruct23]

CooperDBM,

I wasn't talking about calculating the ultimate capacity of the section, I was talking about determining the ultimate design moment that is to be checked against the ultimate capacity of the section. I actually have written a spreadsheet that iteritavely calculates the final strains and stresses in a PT section with regular reinforcing, based on the initial strain in the prestress and the general principles you outlined above, to give me my ultimate capacity.

 

[struggle66]

Rowingengineer,

I mentioned balanced moment as uplift moment and I think OP is suggesting to reduce the balance moment from the total factored moments for ultimate strength calculation.

youngstruct23,

Below my understandings of PT effects on serviceability and ultimate strength calculations.

For serviceability limit state, the balanced moment induces compression at the bottom of the section. When the member is under service, the external stresses have to overcome that compression. So balance moment can be included for serviceability calculation. I think that is understood by everyone.

For ultimate conditions, after stressing, we think that full dead load or a portion of the dead load is balanced due to PT moment. But it does not actually balance (eliminate) the dead load because gravity still exists. What I am trying to say is even though the balance moment does lift up the member, dead load can not actually eliminated because of gravity.

I dont know how to say it more clearly but you can not include the balance moment for ultimate strength calculation. For ultimate strength, we think that PT moment help balance the dead load but it is not. Ultimate strength calculation is about the change in N.A.

 

[cooperDBM]

Youngstruct23,

The assumptions for the sectional flexural capacity and the applicable loading (design moment) which you're comparing it to have to match. As stated in my explanation the prestress force no longer exists at the level of rotational strain that the capacity is based on, therefore it's not a load at the ultimate limit state.

 

[KootK]

I think that it is a matter of not double dipping. One way to go is to consider the impact of the pre-stressing forces in your sectional analysis. In this context, the pre-stressing forces help to resist the applied moments and shears just as rebar does. Alternately, it would be perfectly rational, although perhaps not overtly code compliant, to use the balancing force to offset your gravity load instead.

What you can't do is both of these things simultaneously. The pre-stressing has to be considered to either balance the load OR resist the flexure and shear in a sectional sense. These models are, of course, two sides of the same coin. But you still only have one coin to spend. And you're definitely not reduced to having zero coins to spend.

I disagree with the skyhook comments to some degree. The load balancing takes some of the load off of the element traditionally conceived of as the "beam" (concrete & rebar) and drops it at the columns (or other supports). IMHO, this is almost as frickin' cool and magical as a sky hook.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[struggle66]

KootK

"The load balancing takes some of the load off of the element traditionally conceived of as the "beam" (concrete & rebar) and drops it at the columns (or other supports). "

Are you talking about the secondary moment?

 

[KootK]

Struggle,

Both really. When I think of it in my head, I envisage it exactly as YS23 seems to. That is, as a largely externally applied load (save buckling / compression). YS23's explanation of the load path in his original post is entirely consistent with my understanding.

I see the issue as not entirely different from a suspension bridge like the Golden Gate. The reason that the trusses under the bridge deck at Golden Gate get to be so slender is because the suspension cables are dealing with most of the gravity load and taking it out to the piers. Same thing for PT, just with the cables on the inside of the beam and the drape nowhere near as optimal.

My PT experience is almost entirely unbonded floor slabs constructed in North America. All those 7", largely unreinforced slabs wouldn't have a prayer if we couldn't count on balancing load effect to do its thing in the strength limit state.

Kootenay Kid



The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[Ingenuity]

...why cant the primary moments caused by post-tensioning be included in the load combinations for strength (for example 1.2G + 1.5Q + P)?. This would make quite a difference when the level of stressing is such that it balances the deadload...

It sure would.

So, if you balanced 100% of G, and there was no other applied external loading other than G, then your factored design moment would be 0.2G, (i.e 1.2G - P, where P is equal to 100% of G). Similarly, using the same logic, if you balanced 120% of G, (and there was no applied live load, or other loadings), the factored design moment would be ZERO! (1.2G - P, where P = 120% of G)

Gravity defying. I do not think so, but nice try!

 

[KootK]

I have worked on at-grade post-tensioned transfer beams where a good portion of the PT couldn't be stressed until the dead load of most of the building above was in place to balance out the PT uplift forces. Analytically, the consequence of not staging the PT stressing would have been that the PT "balancing" loads would have snapped the beams upwards with hogging moment. As I understand it, bridge engineers often need to examine similar load cases when employing staged (girder/slab) construction.

These are both examples where PT balancing forces are clearly capable of more than offsetting 100% of the gravity loads in play at the time of consideration.

Of course, there's no such thing as a free lunch and gravity can't just be wished away Gandolf style. If one considers "the beam" to be the entire system (concrete, rebar, PT), then the gravity loads are still very much on "the beam". However, if one considers the beam (concrete, rebar) and the PT cables to be two separate systems, then a portion of the gravity loads -- perhaps in excess of 100% -- have been reassigned from the "beam" to the cables. And nothing about this reassignment would fall into the "something for nothing" category. The concrete/rebar beam system would be propped up by a second system (the PT) at the cost of all the extra material and human effort required to install that second system. And structurally, there would be a bunch of additional new consequences to consider:

1) PT anchorage checks.
2) Net upward load cases.
3) Additional compression in the concrete.
4) PT relaxation and corrosion issues...

No magical free lunch here; just a clever use of materials.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[rapt]

As others have said, the prestress effect P * e is included in the capacity side of the calculations, increasing the capacity. It cannot also be included in the applied actions side and reduce the applied moments.

 

[struggle66]

Youngstruct,

Ignore my comment above. Now I realized that my comments were based on the wrong imagination. P x e (balanced moment) will always be there like gravity.

 

[struggle66]

Hi guys,

I was confused after reading this post. So I looked into a few example calculations. In those examples, unbalanced moment is used for serviceability limit state but only secondary moment is included for the strength calculation (ultimate limit state). But in the ultimate limit state total applied moment is not deducted(balanced) by the primary PT moments (P*e). Is that correct?

Thanks

 

[rapt]

Struggle,

Secondary prestress only is included in any calculations relying on strain compatibility. This would include Ultimate calculations and service calculations on cracked sections used to determine stress conditions in the steel and concrete post cracking.

Full prestress is only included in service stress calculations based on gross properties. This is a historical thing. See below

stress = P/A + M/Z
where M = Mdl + Mll + Mprestress
where Mprestress = P.e + Msec

This could also be written as
stress = P/A + M/Z + P.e/Z
where M = Mdl + Mll + Msecondary

So now even at service, M does not include P.e. It is a separate term as it is in cracked section calculations. You could then rearrange the equation so that P.e is on the stress side and that is how we do cracked section calculations.