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.

 

[diacivil]

So you agree the proposal is not going to work?

 

[IDS]

Diacivil, I am not sure what proposal you mean, but I can't see that Brad805 suggested that anything would not work, if done properly.

One problem with your latest model is that you have used von mises stress criterion for yielding, which is not appropriate for a brittle material like concrete.

There are probably other problems. I will look tomorrow.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[rapt]

I have been out of contact so have missed the discussion.

Tendon curvature/change in angle causes bending /curvature effects.

Concrete centroid curvature/change in angle when subject to axial load causes bending/curvature effects.

When you combine the 2 of them with a tendon that follows the concrete centroid exactly, the 2 sets of effects, one internal and one external exactly balance each other and you end up with axial compression.

Forget about balanced loads, it is just a nice term. It is all about moments. A parabolic profiled tendon resulting in a balanced load of w over a length L simply represents the moments based on wl2/8 in a much nicer fashion. If the curvature was random, it would be much harder to represent it as a balanced load and much easier as moments.

 

[BAretired]

Augmenting what rapt said above, the attached sketch shows a member with three crank points. If the member is concentrically prestressed from A to E, the blue arrows represent the axial compression in each member. The tension in the tendons is equal and opposite to the axial compression and is not shown. If there are no losses due to friction or other source, the axial compression will be equal in each leg.

The resultant of the two forces acting at each of points B, C or D is the bursting force where the tendons would break out of the concrete if not anchored securely.

If there are friction losses at each of the crank points and stressing is done from point A, axial compression will be greatest in leg A-B. Compression in leg B-C will be diminished by the loss at point B and the compression in each of the remaining legs will be reduced further. Even when there are prestress losses, except for axial shortening, the cranked member retains its shape if concentrically stressed throughout each part.

A curve can be approximated by a series of short straight lines so the same argument holds for a curved member.

BA

 

[IDS]

I have now looked at the Strand7 analysis and made a number of changes:

1. I have changed the 3 rows of plate elements to 2, so I can connect the truss members representing the tendon directly to the plate nodes, rather than using an "attachment" link.

2. I have deleted the vertical rigid links because they weren't doing anything. You can always add them back in if they have a purpose in a later stage of the analysis.

3. I have changed the node restraints to remove all moment restraint, and remove the restraint in the Y direction except for the central node at each end. The other restrained nodes are restrained in the Z direction at both ends and in the X direction at one end only.

4. On the Property-Material tab the plate Material has been changed to elastic, and the Yield Criterion to Max Stress.

5. On the stress-strain table I have adjusted the stresses in the tensile region so that: a) the initial elastic modulus is the same in tension and compression; b) the maximum tensile stress is close to zero, c) the stress-strain slope after cracking has a very small positive slope.

6. I have added rigid links connecting the central nodes to the edge nodes at each end. If you don't do that you get problems with transverse tensile stresses when the pretension is applied, because we aren't modelling the confinement reinforcement.

Note that although concrete has a tensile strength of a few MPa, after cracking it has zero strength, so it should be modelled as close to zero maximum tensile strength, rather than the plastic 2 MPa you had.

After making those changes the deflections look reasonable: 0.76 mm without prestress and 0.26 mm with prestress. Also the stress plots show that the section is all in compression with prestress, and cracked with tension on the bottom without prestress.

Four node plate elements are not a good model for beam bending, so I have also run the analysis with 8 node plate elements (NEW3.st7) which you will see gives a much smoother stress plot. Deflections in this case are 0.83 mm and 0.27 mm.

Finally I would repeat that for this application using beam elements with a moment-curvature table is not only much easier to set up, it is likely to give better results, and will certainly converge much quicker, because modelling reinforced concrete as a composite material with plate and truss elements is fraught with difficulties (see links posted by Brad805, which are really worth reading).

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[diacivil]

Dear IDS,

I do not know how to thank you for your special efforts and time. I really appreciate your knowledge, effort and time.

I will see the models and get back to you.

Thanks a lot.

 

[rowingengineer]

I do believe tracking him down thru his website

https://newtonexcelbach.wordpress.com/,

find a place to send him a carton is required. Doug's response is well above and beyond the call of duty.

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."

 

[IDS]

I only do these things when there is something I find interesting. In this case it has brought to light several things that we take for granted, but are not at all obvious.

diacivil - it looks like you took your stress-strain diagram from one of the Strand7 web-notes (which has the same problem with the initial elastic modulus in tension being much higher than in compression). If you do have access to the web notes have a look at:
ST7-1.20.40.10 Modelling Nonlinear Concrete with Nonlinear Elastic Material
which I think covers the subject better than the other one.

I have had a look at using a beam element to represent the concrete, rather than plates. This makes it easier to set up the model, and if you set the material to elastic it gives the same results as before. If you use elastic-plastic properties it depends on the order of loading. In the attached file New5a.st7 the load is applied with prestress (small deflection), then removed (deflection returns to zero), then load without prestress (large deflection), then removed (only part of deflection recovered), then load + prestress again (large deflection).

Which all makes sense.



Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[Brad805]

What no screenshots for the herd? Just joking of course. You are a heck of a good contributor like several other in the thread.

 

[IDS]

I think a screen-shot might be a good idea.

Also I should expand on the "all makes sense" comment. The results using elastic-plastic properties make sense for an elastic-plastic material, but reinforced concrete is non-linear elastic if the steel doesn't yield. When you remove the load the cracks close up and the beam returns to zero deflection (ignoring creep and shrinkage).

In the attached screen shot the contours show concrete stresses for the load without prestress, and the graph shows curvature along the beam for each load case:

1. Normal load + prestress: Concrete is uncracked and curvature profile is parabolic
2. Load removed: Curvature returns to zero
3. Normal load without prestress: Curvature initially follows the same line as Stage 1, then after concrete cracking, increases rapidly, then again more rapidly as the moment increases. At the moment I am not sure why we are getting this two-stage non-linearity.
4: Load removed: Only the elastic part of the deflection is recovered - this is not how concrete behaves (ignoring creep).
5: Normal Load + prestress: Curvature follows almost the same line as without prestress, because the non-linear deflections of Stage 3 are treated as being locked in. Again, this is not how concrete behaves.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[IDS]

The bi-linear profile of the curvature line after cracking was due to the small number of elements in the beams. Subdividing each beam into 8 I get the attached results, which shows a smooth curvature in the section curvature line.

The deflection (without prestress) increases to 0.81 mm, but note that the model ignores many factors that will have a much more significant effect on the long term stresses and deflections:

1) Creep
2) Shrinkage
3) Tension stiffening
4) Loss of tension stiffening
5) Differential temperature effects
6) Differential shrinkage effects

And we haven't even started on soil-structure interaction effects.



Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/