Rigid Diaphragm Design 1

[mjohan]

I am analyzing a buildings diaphragm based on computed direct shear and torsional shear.

Scenerio:
8" Hollow core planks with 2" concrete topping.

Question #1:
When designing the chord beam for tension, do you only consider the ultimate moment from direct shear??? Can the torsional moment be neglected when considering this tension reinforcement because of ACI equation 11.6.1 (a) - "It shall be permitted to neglect torsion effects when the factored torsional moment Tu is less than:" ...
which it is (note, this equation does not account for the thickness of concrete, only the area of the building was used... this seemed odd to me, however, a section of beam does not consider its' length using this formula either). I am trying to figure out which to use, neglecting the torsional moment results in area of steel required = .4 in^2, including torsional moment results in 3.5 in^2. (2) #4 bars or (4) #9 bars ??

Question #2:

I further designed some lateral and transverse reinforcement due to shear throughout the diaghragm. Then I asked myself, Do you really need to include this reinforcement if the 2" concrete topping, (analyzed as a deep plain beam) could take the shear. Following this procedure, the required reinforcement is drastically reduced.

Thanks,
Mark

 

[JAE]

Mark:
I'm not so sure that section 11.6.1a has anything to do with diaphragm design. This is the section on torsional shear that single members, like a beam, experience sometimes. I don't believe that it is intended for a full diaphragm.

In fact, the torsional shear you are talking about is really an added STRAIGHT shear due to torsional effects on the whole system, not on a single piece of that system. I'm assuming that you are taking the direct lateral forces and applying them to the structure, which results in straight shear coming into the resisting elements (shearwalls?). Then you are accounting for torsional effects that are due to perhaps seismic offset (5%). This twists the building but does not twist (torque) the diaphragm. The diaphragm is in fact simply rotated in a plane and this is not torsion on the diaphragm.

The chord beam design in tension should include all applicable load combinations. So the lateral forces (both direct loads and torsional offset loads) should be applied to the diaphragm and the resulting tension forces calculated from them. The chord beam also should not be getting torqued unless I'm missing something unique about your structure.

If your diaphragm can take the shear as a plain concrete member (see the back of the ACI code for the chapter on plain concrete) then you can consider it....but if you are in a seismic region, I'd be prudent and ensure some ductility with the use of reinforcing....although the shear failure isn't really ductile, the reinforcing does hold it together.

 

[mjohan]

Thanks JAE,

Your reply was very helpful.

I have one question regarding your last statement. As a brief description, seismic governs the design, the building is located in philly. At one shearwall in this building, the calculated reaction was 150 kips, length of wall = 34'. The 2" topping does not calculate. Would you then consider reinforcing the joints of the 8" plank until the shear force is small enough that the topping would suffice? Or would you not consider the topping at all when designing the reinforcement in the planks?

Thanks again,
Mark

 

[JAE]

Mark:
Let me make sure I understand: "the 2" topping does not calculate".

Do you meant that the 34' of shearwall limits the 2" topping to 34' of length for shear calculations? and the result is the 2" topping doesn't have enough shear capacity to resist the 150k?

If so, what you need to do is create a collector element along the full length of the diaphragm to collect the 2" topping shear (across the full length) and then transfer it to the shearwall across the 34' length.