Concrete Slab Design using STAAD (Polygonal Meshing) 2

[Rainbowtrout]

Hi All,

(This is my first post.)

I have a concrete roof slab with a few circular openings and rectangular openings, and it is framed into concrete walls on all sides. The roof slab needs to be designed for HS-20 (highway truck) loads. I am using Polygonal Meshing in STAAD to create triangular plate elements.

Question:
1) Has anyone used the Global Moment outputs given in STAAD? I couldn't find any documentation on how its calculated, and whether it follows the Wood-Armer formula (add Mxy to Mx and My). If you don't use global moments, how do you design orthogonal reinforcement? Keep in mind triangular plates have their local axes all over the place.

2) Do you typically use plate center stress or plate corner stress? I usually use plate center stress. I think plate corner stress can be over conservative and there is no need to design for the moment occurring at the exact centerline intersections. However, this post (

http://communities.bentley.com/products/structural/structural_analysis___design/f/5932/t/62185.aspx)

makes think twice. What do you use and what is your reasoning?

Thanks!

 

[JedClampett]

Seems like a pain to me, with a lot of layout and stress concentration issues. If you're just worried about meshing to the round holes, why don't you consider them square?
Now if you're just trying to challenge yourself, that's another story.

 

[Rainbowtrout]

I don't object to modelling circular openings as rectangular openings. However, what size should I use? If I use the diameter of my openings, am I being being conservative or not? And how will the answer change as the geometry changes? I can sketch things up and think through for different load cases. However, I thought it would be easier to put everything accurately on STAAD and let STAAD give me a rough idea on what will happen. I will wait a bit to see whether others have better ideas for my problem. If not, I will start simplifying the geometry by hand.

Thanks.

 

[JedClampett]

The circular openings should be modeled as squares with sides diameter by diameter. The fallacy with your reasoning, "it would be easier to put everything accurately on STAAD and let STAAD give me a rough idea on what will happen" is that you still need to reinforce your slab in a roughly orthogonal manner with a limited size and shapes of reinforcing.
Unless the openings approach a large proportion of your slab, you probably will end up replacing the reinforcing cut by the opening evenly on each side of it. For rectangular and square openings, put in #5 corner bars. And if the openings are very large, you should put in a pattern of beams around them.
It's not worth refining these analyses to a very fine level. The guys (and gals) building them are not Swiss watchmakers. They're closer to lowland gorillas. Simple designs are easier to build and less likely to be messed up.
But I don't blame you for wanting to find all this out for yourself.

 

[canwesteng]

STAAD won't include Mxy in the global moment output, so for two way slab design you need to make the local axis and global axis line up for plates, which means using quad plate elements, unless you let STAAD do the ACI concrete design for you, then they claim they allow for it. As above poster noted, best to just model the circles as squares and use the output to do your own design.

 

[Splitrings]

RISA recommends transitioning from rectangular to circular as shown in the attached. I have not had good luck with triangular elements. The local axes don’t coincide. I typically exclude them from the results.

I believe the corner forces are the “exact” solution. The values for the center of the plate are an average of the corner forces. My guess is you will see very high stresses at the corners of your square openings. Large enough forces you can’t reasonably reinforce against. If you look at a plate a couple of inches away from the corner of the opening, the forces/stresses will be more reasonable.

 

[Gumpmaster]

It's interesting the different approach that we in the US have versus our European counterparts. The folks that I've worked with from Europe are very concerned about both including twisting moments and in-plane shears when designing orthogonal reinforcement. They use both the Wood-Armer and Clark-Nielsen methods and then plot everything agains an interaction diagram. Here in the US that would be considered major overkill for most structures.

95% of the time I just use a rectangular mesh and consider local moments like Jed says. The other 5% of the time where you have something screwy it may be worthwhile to consider the more exact approach.

The big negative I see for using the more exact approach, aside from it being more time consuming and difficult, is that it separates the engineer from what's really happening in the structure. You're just plotting a bunch of data points against an interaction diagram. Who know's what's really, physically happening.

 

[JoshPlumSE]

Interesting discussion. Some thoughts on the subject:

1) There are a a couple of different ways that I typically handle reinforcement design for slabs based on a plate element analysis.
a) Using Plate Forces (Mx, My, Mxy, et cetera)
b) Using Corner Forces

2) When using Plate Forces, the effect combination of twisting moment (Mxy) and Mx or My is a excellent theoretical concern. So, Gumpmaster is correct when he cites Wood-Armer as a way to combine these moments together to get a final design moment. I usually simplify this a bit to just Mx_demand = Mx +/- Mxy and My_demand = My +/- Mxy.
a) Now, anyone who tells you that you an always ignore Mxy (or any program that gives you a reinforcement requirement which ignores Mxy) is being somewhat irresponsible.
b) How irresponsible is up for debate though. There are certainly cases where Mx +/- Mxy is going to be dramatically different than just looking at Mx by itself. However, in most common cases, the Mx and the Mxy values will have their maximums at very different locations of the slab. So, the % difference in demand moment when including Mxy is much, much lower than you would think... at least for most common situations. The key is that, if you choose to ignore Mxy, you need to know why you are ignoring it and when you should try to be more exact.
c) Even when you combine Mx and Mxy together to get a demand moment, this is based on an FEM solution and can easily have an un-realistic stress riser. Most of the time, you will "average out" this demand moment over the width of a representative design strip instead of designing for the absolute maximum.

3) When using corner forces to design the plate, there is not as much "plate theory" to slog through. So, it can be easier to arrive at your final design. In RISA (not sure how other programs implement this concept) you're really just looking at the internal forces (not force per unit length) relative to the global axes of your structure. Therefore, you just sum up these forces over a representative width to come up with a total design moment for that width.

4) When done properly, it is my experience that both methods produce approximately the same reinforcement design. In the end the "best" method is really whichever one the engineer feels most comfortable with and whichever one gives him (or her) the best feel for what is actually happening with their slab.

If you look at the RISAFoundation program (or the soon to be released elevated slab design program), the programs are based around the concept that the end user shouldn't have to be an FEM expert to understand the results of their plate element analysis. So, we strive to organize the results and present them in a way which is very intuitive and easy to understand. You still have the nuts and bolts of the FEM solution to dig through should you desire. But, you don't have to. Instead, you will spend most of your time on reviewing design strips and their shear and moment diagrams.

 

[Splitrings]

@JoshPlum,
You mention "averaging out" these stress risers over the width of a design strip. How wide a strip to use has been a cause of uncertainty for me. Around openings and notches, the narrower the strip the higher the average stress! These stress risers certainly don’t appear to be converging on a solution. Lately I have been using displacement convergence as an indicator.

 

[JoshPlumSE]

Well, discussions about what a reasonable design strip width are could go on for awhile. In the end it's a matter of engineering judgment for me. Though I did attempt to "categorize" some methods for establishing a reasonable design strip width as part of the RISAFoundation documentation. We were just getting so many questions about it that we felt like we had to write something down. Though we specifically do not endorse any one method over another. I have included this discussion for your reference below... though this does not have any specific discussion on openings and how those will affect the design strips:

ACI Definition of Strips (Section 13.2 of ACI 318-11)
This section of the ACI code is really intended for elevated slabs. But, the concepts can be extended into mat foundations as well. The requirement for "column strips" is that the width on each side should be set to 25% of the span length or width whichever is smaller. Then the "middle strip" is defined to span between the edges of the column strips.

This method requires engineering judgment for column grids that are not perfectly aligned and rectangular. In addition, when the column strip becomes very small then the middle strip may become very wide so that the entire slab is included in either a column strip or a middle strip.

The ACI strip method listed above is based on essentially 1/2 of the mid-span tributary lines. The hand calculation methods would have you design for the full tributary moments over this smaller width which should be conservative. Computer methods (like RISAFoundation) will design for the average moment over the assumed design width which should result in a more efficient design.

Zero Shear Transfer Method
The Zero Shear Transfer method used the shear force contours perpendicular to the span of the slab to set the design width. This should provide a result very similar to using the mid-span tributary lines, but is a bit more theoretically derived for non-rectangular column layouts. This method is described in greater detail in the PTI publication Design Fundamentals of Post-Tensioned Concrete Floors.
Ideally, this method should give design strips of similar width to the ACI strip method. However, it is more rationally derived and should work better for cases where uneven column spacing makes the strip method difficult to apply.

Zero Moment Method
In a similar fashion to the zero shear transfer method, the Zero Moment method uses the moment contours to identify where the moment changes sign. This can be used to set the design strip width approximately equal to the distance between zero moments.

Shear Perimeter Method
Another basis would be to set the design width equal to the pedestal width plus a distance 'd' or 'd/2' on each side. This will end up being a more conservative assumption for flexure than the other methods listed. As such, it would be more appropriate for situations where shear or punching shear failures are a primary concern. Examples would also include cases where the pedestal is very large such as for a vertical vessel or grain silo. This is similar, though not identical, to a method given in the NEHRP document GCR 12-917-22 (Seismic Design of Reinforced Concrete Mat Foundations).

Hybrid Method / Engineering Judgment
A variation on these methods would be to start off setting the column strip using the ACI strip method. Then, if necessary, the width could be modified based on considering the other methods. This is especially true for situations where the column grid is not aligned or rectangular.

In addition, when the middle strip widths get too large, they could be set to values closer to the column strip width. The middle strip would normally be centered on the area with the highest mid-span moments. This would neglect lower moment regions between the column and middle strips. Hence the strips would designed for a higher moment per unit width. This reinforcement could then be extended into the lower moment regions between strips. Or the user could set up another design strip for these lower moment regions.

 

[Splitrings]

These methods are all geared towards two way slab systems. I am looking more at generic shell and plate structures. Circular tanks with holes and deep notches, etc.

 

[Rainbowtrout]

Thanks for all of your thoughts! Here is what I think.

Stay away from irregularly-shaped plates. Take advantage of rectangular shapes. Check Mxy despite it may not control in most regularly shaped structures unless it has openings, special loads, etc.

If your plate is small enough - I would say <2d (?), you will be OK using the center stress. If you are using larger plates, be careful at corners.