Concrete edge beams 5

[GalileoG]

During a luncheon at work, we had several interesting discussions that I thought I would share with you folks:

One of my colleagues said that a concrete edge beam does NOT need to be designed for torsion if you pin the edges and design the secondary beams and the slab for the moment. However, another colleague stated that the above is simply incorrect and that the edge beam must always be designed for torsion, but did not state why. A third colleague said that it all depends on the rebar detailing? As you can imagine, I was left more confused than when the conversation started. I'm curious as to which side everyone here would take in this debate.

The discussion then jumped on to steel. If we have a secondary beam spanning perpendicularly into the primary beam, with the primary beam supported by a column on each of its end, and the connection between the primary and secondary beam is a clip angle, would we design the primary beam for torsion? The point that was raised is that the double clip angle can experience significant rotation/deformation as long as it is not too thick, and thus the end of the secondary beam can be treated as a pin without any significant torsion on the primary beam. Does that make sense to anyone? Because I don't know if I buy it. What about the stiffness of the primary beam, does that play any role?

Ah what the heck, since I'm posting a thread, I might as well ask another question that's been bothering me: I have a reinforced concrete slab (150 mm thick or 6") with a whole bunch of openings. I am worried that my slab will not act as a rigid diaphragm because of all the openings. How can I calculate and prove that my slab can act as a rigid diaphragm? Also, I was told that my slab has to match the rigidity/strength of my shear wall for it to be effective. What is the rational behind that? I do not understand that statement and have never heard it before until recently. How about you guys?


Clansman

 

[priya15]

Dear All,

This has been an immensely useful thread even though I think my understanding on compatibility and equilibrium torsion just got better. But this thread actually got me thinking further. Say, for example, I have a cantilevered slab with a back span. Now, can I say that the equilibrium torsion due to cantilever is some what nullified by compatibility torsion on the other side and only check the beam for effective torsion (i.e. equilibrium torsion - compatibility torsion)? Pattern live load will cause more grief, but that is a different aspect which we should consider anyway.

In any case I would just design for equilibrium torsion and be glad that the beam may not in reality experience so much torsion. But it would be interesting to know your thoughts on this situation, which happends all the time.

 

[slickdeals]

I think if you have a cantilever with a back span, the edge beam can be designed for compatibility alone. I am curious to see what others think.

 

[ron9876]

If the beam is not required for equilibrium then you can design for redistributed torsion or neglect torsion depending on the condition and your judgement. Don't know what effective torsion is.

 

[rowingengineer]

if you have a cantilever slab with a back span with an external edge beam, this system can be designed as a compatibility system. Because if the edge beam was removed the slab would still be able to function structurally is designed with enough steel.

Rapt,
Why the increase I tie spacing for thermal effects, I wouldn't have thought that thermal effects would have effect shear or torsion. Is this to just ensure that the torion/shear cracks don't open up?


Here is extract from page 37-39 of Concrete international July 2009, it was an article talking about wood and armer but then is started talking about how to handle torsion in FEA programs, have included for information/discussion.

"Design Using Element Nodal Forces

Slab design methods based on element nodal forces
have been widely implemented in FEA software. These
methods are attractive because results are relatively
accurate even for very coarse meshes, can be used for
slabs containing beams or drop panels, and are easily
extended to design prestressed or post-tensioned floors.
In this approach, the critical question facing engineers is
how to account for the total torsion T computed across
the design section, which is separate from the total
primary bending moment M, as illustrated in Fig. 4. (sorry couldn't past the figure)

Principally aligned design sections

The effect of twisting moments can be ignored when design sections are aligned with the principal bending directions at all locations, as the twist on the design section vanishes in this case. A rule of thumb that is sometimes used is that torsion and twist can be ignored if T is less than 10% of M.12 If the torsion is greater than this value, then neglecting the torsion and twist effects may lead to unconservative results. Many commercial FEA programs are capable of plotting vectors corresponding to the directions of principal bending; and after reviewing such results, design sections can be chosen to be orthogonal to these principal bending directions. When these directions do not match with desired reinforcement directions,the components of required reinforcement are determined first with respect to the principal bending directions and then transformed via a simple change of axes into the desired orientations.

Bending modified by torsion

One approach to incorporating T is to directly combine M with ±T, similar to the Wood and Armer approach. From
a mechanics standpoint, however,this concept differs from the Wood and Armer method in that the moments are resultants from the entire design section, not an infinitesimal plate element. In addition, this approach
can lead to highly uneconomical designs when T is significant compared with M.

“Beam” torsion

Another approach that has been implemented in commercial FEA
software is to account for T according to building code provisions for beams in torsion. This approach resists torsion in the slab by hoop stresses, and reinforcement is proportioned to satisfy this load path.

Torsion resolved into transverse shear

The total torsion T in the design section can be decomposed into linearly varying transverse shear per unit length with a maximum value equal to 6T/L2, where L is the width of the design section. By multiplying this maximum shear by the width of the design section, an equivalent (but quite conservative) resultant shear force due to torsion, which is equal to 6T/L, can be considered during the shear design of the section."




When in doubt, just take the next small step.

 

[rapt]

Rowingengineer,

For thermal, it was an increase in the nuymber of ties, so a decrease in the spacing.

RE The FEA quates above,
1 FEA is only accurate for the elastic analysis of the slab. It is generally not "accurate" for the design of the slab, which is normally not elastic.
2 The Mxy moment in FEA analysis for slabs is not actually torsion. To define the moments on an element to match the actual stress state in the element, it is necessary to define 3 moments, Mx, My and Mxy. If you are designing about the principal axes, Mxy is zero. Otherwise there are 3 moments. The longitudinal moments Mx, My and Mxy which defines the twist in the element. As it is not practical to reinforce for the principal axes (as they are at a different rotation at every point in the slab), we reinforce in an orthogonal pattern so have to deal with the 3 moments.
3 So Mxy is NOT compatibility torsion. It is the degree of twist in an element required to define the actual stress state in the element. This twist occurs in just about every element to varying degrees, even a perfectly symetrical, regular slab. In such a slab, the Mxy moments could be as large as 15-20% of the Mx or My values at the peak Mx and My points. For irregular slabs they could be significantly higher.
4 It is unconservative to ignore these moment in design. Several FEA analysis design programs have been ignoring it for many years, and producing under strength designs as a result. Once I heard it quaintly defined as "the effects of 2way action leading to reduced moments". Rubbish, it is under-design by ignoring part of the design actions on the slab.
It is nice for them to suggest that if it is less that 10% you can ignore it, but that is like saying that for a Equivalent Frame analysis you only need to design for 90% of the calculated moments. Convenient for the design but underdesign no matter what. And codes do not allow you do reduce your design moments by 10% because it is easier to calculate!
5 Many codes do not mention Mxy specifically. When I pointed this out to the AS3600 committee, their response was that the code does say to include it as it says that all actions must be included and it is part of the design moments on an element calculated as a result of the calculation method used, FEA. The designer is supposed to understand this and implement it correctly in design. They agree that it is definitely NOT compatibility torsion, as I think you will find the writers of your Concrete International will attest. Otherwise they would not have modified their own program recently to include Wood Ahmer calculations for design.
6 Also, note the "error" in that article where all of the "design strips" are the full width of a column panel, no column/middle strip distribution. I hope no-one in Australia is designing like that. It is not acceptable to AS3600 for RC or PT plat slabs.

 

[rowingengineer]

I post the full article because I do believe that people could be lost if they haven’t read the first part of the article.
I do agree with your comments about Mxy and FEA programs, but i would have thought that there were also torsion moments in slabs. I do believe the last part of this article is talking about torsion, I also think that torsion in slabs can be treated as compatibly torsion, same as beams.
I have many problems with FEA programs As discussed in thread507-249338. but that being said i trust many programs.


When in doubt, just take the next small step.

 

[csd72]

Slickdeals,

A simple way to tell if it is compatability torsion is envision the beam with a torsional swivel at the ends.

If the beam is still stable after you put the swivels in then it is compatability torsion.

In the case of the torsion at the end of the cantilever, with a swivel at the support the cantilever will rotate and therefore this is not compatability torsion.

rapt and rowingengineer,

Some interesting comments. I will not comment on this as my experience with FEM is very limited.

 

[rowingengineer]

please exchange "but that being said i trust many programs"
with "but that being said i DON'T trust many programs".

csd72, your not missing out on much.

When in doubt, just take the next small step.

 

[slickdeals]

Consider the following situation:
If you have an interior beam with 20' long joists framing into one side and 40 ' long joists framing into the other side, which will create an unbalanced moment over the girder. This unbalanced moment will have to be transferred via torsion into the columns.

I realize that this is compatibility torsion which will self-limit itself based on the torsional cracking.

My question is this:
If the (unbalanced negative moment-20% redistribution allowed)exceeds the threshold torsion, should torsional reinforcing be provided in the beam to pick up the difference?

 

[rowingengineer]

I must be having a slow day, I don't see the unbalanced moment.

When in doubt, just take the next small step.

 

[pa4912]

slickdeals,
This is exactly the problem I face. I.e. can you just pin this in your model as you assume it cracks and therefore provide nothing for torsion. OR, still design for the (reduced, since its compatability) torsion as surely it must be in there somewhere.

From reading the above, I'd guess that some engineers are neglecting whilst others are designing for it. With apparently no ill-effects. Has anyone designed for no torsion and subsequently seen lots of cracking?

 

[rowingengineer]

There is a difference in some programs between "pinning" the modal and using zero torsional stiffness for the member. We will discuss assuming zero torsional stiffness just to make sure.

I designed a crash barrier kerb for torsion and saw a lot of cracking nearing ultimate load. Got to do the test on the design so is was kind of cool to see what happens. This was equilibrium torsion, not compatibility which is you direct question, I am yet to see an edge beam crack up such that anyone could notice, if that helps.

The reason many engineers will design with zero torsional stiffness and only supply closed lig ties, is because once you surpass the uncracked torsional strength the stiffness of the beam reduces dramically (about 80-95%), thus it is very hard to get your model to equilibrium, without a few iterations. Using the closed lig arrangement will ensure the torsional cracks are keep to a reasonable size for service loads, for compatibility torsional type loadings.


When in doubt, just take the next small step.

 

[pa4912]

rowingengineer, thanks for that.

I have a torsional question for those who are using the new ACI 318-08 version.

It states (R.10.3.3) that to use 'moment redistribution', the beam must be designed for a Minimum Net Tensile Strain of 0.0075. Does this mean if we want to use compatibility torsion, our edge beam must meet this requirement? Or is it refering to the secondary beam framing into it?

Or both?

 

[rowingengineer]

pa4912,
Please post your question in a new thread, as I doubt that your question will get much notice here. and if you do I will answer your question there.


When in doubt, just take the next small step.