Strand7 and eccentric prestressed slab 5

[diacivil]

There is a proposal suggests that if we used post tensioned slab on expansive soil with zero eccentricity straight tendons, this design can work in both cases of doming and dishing slab in dry and wet condition respectively. The proposal suggest that once the doming and dishing occur, that means we will get some effect of the post tensioned steel. However, I modeled the proposal in Strand7 non-linearly and I got no effect of the post tensioned steel. Once I apply eccentricity, the prestress works perfectly. I am looking to hear from you.

 

[KootK]

I appreciate it if anyone has more info about concentric slabs.

I'll leave the software idiosyncrasies to others. Some practical tips:

1) concentric prestressing like this gets you just one thing of any real value: initial compression strain in what will eventually be tensile fibres in the loaded cross sections.

2) #1 implies grater moment capacity, cracking later in the load history and uncracked section stiffness longer in the load history.

3) While #2 will mean less dishing deflection, it's unlikely to meaningfully affect doming deflection. Expansive soils, like frost lenses, expand as they like and are relatively unaffected by SOG stiffness. As such your doming deflection should be unaffected by the post tensioning.

4) Presumably it is top surface cracking caused by doming that is of greatest concern. Because of #3, I would not expect cracking to be greatly improved. The slab will assume the curvature imposed by the expansive soil and cracks will form to facilitate that curvature, just as would be the case in the absence of the post tensioning. Post tensioning will, of course, reduce ordinary temperature and shrinkage cracking.

5) because of points 1-4, I'd be tempted to model the concentric prestressing effect as simply an increase in the modulus of concrete rupture. Depending on the results that you're interested in, and whether or not you have mild reinforcing, it may not even be necessary to perform a non-linear analysis.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[BAretired]

I don't feel that any retraction was necessary. While the effect that you described may not be significant in this instance (small displacements), there was nothing in your statement that was technically flawed. The phenomenon that you described is in fact the very reason why post tensioned members do not buckle under the axial loads applied by the tendon anchors.

I'm afraid there was something in my statement which was technically flawed, KootK. A concentric prestress in a prismatic member creates uniform compression at every cross section throughout the length of the member except in the immediate vicinity of the end anchorages. This is true whether the member is straight or curved.

If an unstressed slab is subjected to external forces causing bending moments along the center line, the fiber stress at point x,y will be M_xy/I where M_x is the moment at x and y is the distance above the c.g. Deflection can be calculated based on the magnitude of the moment and the magnitude of I. If the section remains uncracked, I is the uncracked moment of inertia.

If the slab is pre-stressed concentrically, the only difference is that a compressive stress is added to the fiber stress in all locations. Thus the deflection is identical whether it is pre-stressed or not, provided the non pre-stressed slab does not crack.

BA

 

[KootK]

I'm not buying it BA. All of your last post works for me with one exception: you've chosen to ignore the second order load balancing effect that was the subject of your original, retracted comment. Deflection would be slightly less for the post tensioned member because, when deflected, the induced curvature in the tendons would create an upwards balancing load identical in concept to how intentional drape in suspended slabs does.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[KootK]

Here's some related info supporting the notion that second order balancing load effects are what keep prestressed axial members from buckling under their own prestress.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[diacivil]

I totally agreed what you have posted Kootk for column only. However, I am still not sure how to make the concrete to behave non-linearly in Strand7.

 

[hokie66]

A post-tensioned slab on ground differs from a column. The ground imparts a tensile force on the slab, which is at the bottom, and thus eccentric.

 

[IDS]

I totally agreed what you have posted KootK. However, I am still not sure how to make the concrete to behave non-linearly in Strand7.

Then why don't you provide some information about your analysis, so we can provide some useful advice?

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[diacivil]

Hi IDS,
I model 8 metres length of simply supported beam with distributed load and prestressed tendons with zero eccentricity. I model the beam as beam element and as plate element.the tendon was stressed to about 85% of the total strength. Concret strength is 32 mpa. Beam dimensions in both cases are 500 mm depth x 300 mm width. Defelction was same in both cases and no effect of the concentric prestress. I have chosen the nonlinear analysis and plastic materials. However, the results fom linear and nonlinear analysis are both same. Please let me knew ifI miss anything.

 

[diacivil]

The prestress tendon is modelled as truss element with rigid links to the concrete. The axial egfect of the prestress is appeared as expected. However, no effect of the prestress on the moment capacity at all.

Cheears

 

[BAretired]

The prestress tendon is modelled as truss element with rigid links to the concrete. The axial egfect of the prestress is appeared as expected. However, no effect of the prestress on the moment capacity at all.

What do you mean "no effect of the prestress on the moment capacity at all". Without prestress, the member has no moment capacity. With prestress, it has a calculable moment capacity.

If you meant to say that the prestress has no effect on deflections, I would agree with that finding.

BA

 

[KootK]

However, the results fom linear and nonlinear analysis are both same.

Do all of your models predict concrete cracking?

As was asked above, how are you modelling the soil here.

The prestress tendon is modelled as truss element with rigid links to the concrete.

Can you sketch this for us? The only longitudinal connection between concrete and tendon should occur at the member ends.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[BAretired]

f'c = 32 MPa
Ec = 4500(f'c)^1/2 = 25,450 MPa
L = 8000 mm
I = bd³/12 = 300x500³/12 = 3.12e9 mm⁴
w = 3.6 N/mm (dead weight of beam only)

Δ = 5wL⁴/384EI = 2.5 mm

Under the self weight of the beam, I find the deflection to be 2.5 mm with or without prestressing. This assumes the unreinforced beam does not crack under its self weight.

BA

 

[diacivil]

HI,

thanks all for your responses.

the member has same moment capacity with and without prestress as it can be calculated from wl^2/8.
I modeled the problem as simply supported beam to understand the effect of prestress and then will change to soil support and use winkler model.

 

[diacivil]

distributed load case is only 10 kn/m
combination load case is from distributed load and prestress
note: I applied 1 mm eccentricity to avoid software error (as explained in strand7 manual)

http://s7.postimg.org/xk3e1v9sb/mom.jpg

bending moment of combination load case

http://s12.postimg.org/9cfsxhz1p/NEW_3_2.jpg

bending moment of distributed load case

http://s4.postimg.org/5m689lx3x/image.jpg

deflection of of combination load case

http://s2.postimg.org/3xblnrk89/NEW_3.jpg

deflection of distributed load case

 

[BAretired]

the member has same moment capacity with and without prestress as it can be calculated from wl^2/8.

That is an incorrect statement. The moment capacity is the ability of the member to resist moment. We don't know what that is because we don't know the details of the tendons but the moment capacity without prestress is zero unless you provide some conventional reinforcement.

What you meant to say, I believe, is that the moment is the same whether or not the member is prestressed. That statement is true only if the unstressed member does not crack. If it cracks, it will collapse unless reinforced. If adequately reinforced, it will deflect more because of the cracking.

distributed load case is only 10 kn/m
combination load case is from distributed load and prestress
note: I applied 1 mm eccentricity to avoid software error (as explained in strand7 manual)

With a distributed load of 10 kn/m, the maximum moment is 10*8²/8 = 80 kn-m. If the member is unstressed, an uncracked section would develop a maximum fiber stress of 6.4 MPa or about 928 psi which is far beyond the cracking strength of the concrete.

It is beyond me why a 0 mm eccentricity should produce a software error. That would appear to be a deficiency in the software.

BA

 

[Brad805]

What is the area of prestress rebar?

Any limitations to Strand7 in educational mode?

 

[diacivil]

Dear BAretired
I completely agree with you. but I do not know how to model it correctly.

Dear Brad805
the rebar dia is 10 mm.

and I donot know if there is limitation for student version.

 

[BAretired]

@KootK,

We still have an outstanding issue to be addressed in this thread. Concentric post-tensioning tendons in a curved prismatic member produce pure axial compression throughout the curved member. They produce axial shortening but no deflection.

When a slab is tensioned concentrically and then curved by external forces, the effect of the prestress remains the same. It is still concentric no matter what shape the slab takes. It can produce only pure axial stress in any section normal to the curved axis. Deflection produced by external forces does not result in any load balancing by the tendons.

BA

 

[JAE]

What BAretired is stating (curved beam with concentric presterss = only axial compression) was what a professor friend of mine (Dr. M. Tadros - U of Nebraska Omaha) some years ago.
I had a hard time getting my head around it but I think he (and BAretired) is correct.



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[KootK]

@BAretired/JAE: are neither of you swayed by the column information that I posted above which, in my opinion, clearly shows the effect that I've been espousing? It's from Bazant for goodness sake. You'd be hard pressed to find a more reputable, living source.

A curved tendon, curved by way of drape or deformation, has components of it's tension oriented vertically. Obviously. If those components don't push upwards against the encasing concrete, then what keeps the cable in vertical equilibrium?





I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.