concrete edge beams

huangyhg

concrete edge beams
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
ok, clansman, i'll take a crack at a few:
concrete:
i use aci 318 (you didn't state your own location/code) and within that code the aci explains that if you have secondary beams framing into a primary edge beam, as long as you design the secondary beams for pinned ends, you can then design the primary beam for a minimum torsion loading instead of a full analysis which would assume fixed ends and calculated torsion.  
they even have a couple of 3d sketch-views of two structures showing the difference between a structure which doesn't need the torsional resistance for stability and one that does need the torsional resistance for stability.
for a typical exterior bay of a building, where the interior joists or beams are designed with assumed pinned exterior ends, then the exterior beam's torsional resistance is not theoretically needed for the structural stability of the floor.  
for a beam that has a single cantilevered slab hanging off the edge of it, the torsional strength of that beam is essential for the cantilevered slab to remain cantilevered...thus for that sort of case you must include the torsional aspects of the design.
for my own personal "standard" i almost always will close any type of edge beam stirrups with torsional stirrups instead of open "u" stirrups...just because.
steel
similar condition except that normally your primary beam end connections are not designed to resist torsion - therefore you would get a slight natural twist in the primary beam that is normally neglected.  there is also some minor flexural stiffness in a concrete floor slab that helps minimize this twist as well.  
you mentioned "what about the stiffness of the primary beam, does that play any role".  if you are talking about torsional stiffness, re  
re concrete, jae is correct. if you do not rely on the torsion moment from the connection to the beam in the slab design, you can ignore it for the beam design also, but, the torsion is still there, so you must still detail the beam with minimum torsion reinforcement because you do not want the torsion cracks opening up. the spacing and details of the ties in the beam should conform the to minimum torsiuon reinforcement rules.
i think uk code states you do not have to design for torsion if the frame does not require the beam to resist torsion for stability. i take that as long as the slab takes the moment then you can ignore torsion in beam.
what jae was describing is the difference between compatability and equilibrium torsion. for the cantilevered slab supported by the beam with no backspan (assumption), the beam must work in torsion for the structure to be stable and therefore must be designed accordingly.
compatability torsion will have redundancy to some degree, and if torsion cracking occurs and a reduction in torsional stiffness, stress will be eleviated and alternate load paths used.
all rectangular concrete cross-sections have torsional stiffness to some degree and will attract torsion, deep narrow beams more so the wide flat beams.
as for the steel, the secondary beams spanning onto the edge beam will be stiffen the edge beam if the connection does not allow rotation. however, the edge beam will not take torsion, it will rotate compatibily will the flexural rotations of the secondary beams because of it's lack of torsional stiffness.
as for the 150mm slab, i don't see why it won't work as a rigid diaphram.
what is a wf beam. i'm from australia where our i-beams are designated as ub or universal beams.
to add to what jae said - i generally do not design edge concrete beams for torsion, just pin the ends of the secondary beams and also provide a minimum number of crack control bars at the top of the secondary beam ends (say 3 no. 5s) to keep the cracks under control as they open up when the beam rotates to behave as designed (pin-pin).  also use closed stirrups on perimeter beams.
regarding the steel - i agree with the point that was raised.  all simple shear connections are designed to accommodate the deformations required to behave as a pin (thus not transferring any torsion to your primary beam).
regarding the slab - one way to tell is to span it between two walls on each end.  double the stiffness of one of the walls compared to the other one.  place a lateral load in the center of the slab and run it as a membrane mesh with the actual stiffness properties of the slab (including openings etc).  if the wall with twice the stiffness picks up about twice the load, then its rigid.  if they both pick up half the load, then its flexible.  that being said, i would just assume its rigid and move on.   
regarding to the validity of the voided slab as diaphragm - make sure there is uninterrupt/adequate path to transfer the horizontal shear, you may need to strengthen local areas around the opening to ensure the slab acting as a rigid deep beam, or truss.
i mostly agree with everyone. i think the perimeter concrete beams should be designed for redistributed torsion per aci unless the span of the secondary beams is small.
it seems to me that the torsion in a steel beam is created by eccentricity of load as opposed to an imposed rotation with concrete beams. i have always assumed that the steel torsion is resisted by a couple between the slab and the connection.
asixth,
a wf beam (wide flange) is basically the same as a ub, but they have lots more sections to choose from.
willsv,
i don't think the connection can be considered pinned and no torsion is transfered to the primary beam. if the connection is a welded side plate, the reaction is going to be applied to the beam with an eccentricity introducing torsion. the only way to avoid this is to design the connection so it doesn't allow rotation and the secondary beam is essentially continuous. no torsion will be transfered to the primary beam of a wf section because of the small j value.
regarding to the edge beam with transverse secondary beams -it will rotate with insignificant torsional effect if its end connections can accommodate a small amount of deformation such as in the bolted joints, i will pay attention for beams with moment connections at ends, the combined effects of all reactions could be killer. for concrete edge beam, the compatibility torsion usually is not a big concern, although needs to be addressed, unless the edge beam does not have adequate dimensions for various of reasons. for such case, other issues (bending, deflection) may still outweigh the torsional effect.