Shear capacity of trough slabs and stirrups (links) detailing

[lefaveau]

Hi There colleagues,
I have the following questions on shear links (stirrups) that I need assistance on:
1) In trough slabs (one-way ribbed joists-slabs) design- How is the shear capacity of the slabs determined in BS code and ACI-318?
2) I have read and seen calculations where the conclusion from the calculations has been that the shear links are generally not required and are used only to carry the tension reinforcement? -Could this be from the fact that the shear capacity of the concrete exceeds the applied shear force?
3)What is the effect of short detailing links in a T beam.i.e where links have been detailed wrongly and they fall short of going all the way up the beams (ribs) short of cover?
4) Do links need to be detailed like in ordinary beams or can it be sufficient for them to cover the rib and end up in the slab?

Thank you in advance for your assistance.

Aubrey

 

[CELinOttawa]

1) Don't know these codes well enough to comment.
2) I know of no code which allows the base Vc to be used exclusive of stirrups without Vc >= 2* Vf (ie: The factored load applied shear has to be less than half the plain concrete strength). Even then most designers will put in nominal stirrups at d/2. This is never to be done in seismic zones; They always require stirrups.
3) They do not function and should be ignored.
4) Check your hook anchoring provisions of your code. It is always best to terminate around a bar within a compression zone.

 

[JAE]

Answers for ACI 318.

Joists are specifically defined in ACI to meet certain criteria:
They are spaced with pans less than or equal to 30"
They have a certain min. span-to-depth ratio
They are at least 1O" deep (I think)
Then they are "joists" vs. "beams".

So if they qualify as joists then your shear capacity = φVn = φVc + φVs but the Vc value (2 x sqrt(f'c)bd) is allowed to be increased 10% to 1.1 x 2 x sqrt(f'c)bd.

Stirrups in joists over the past decades many times are not used. This is because the pans sometimes are flared at the ends to increase the width b.
If that doesn't work then stirrups are required.
I've used single leg stirrups - vertical bars hooked at each end and spaced as needed to get the Vs value needed. Or I've used what I call a "ladder" stirrup which is essentially one long bar bent into a back-and-forth way to form vertical legs in the joists at a set spacing.

One other aspect of the shear capacity - joist pans typically have a slight slope to the vertical sides (1:12 usually) so this results in a varying width up the height of the joist.
We typically use the average width (width at mid-height) for Vc calculations. I know other engineers use the bottom (minimum) width to be conservative.

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[hokie66]

Agree with JAE. Pan joists usually don't require shear reinforcement, but when they do, my first choice is tapered pans to extend the width at the ends. Then the zigzag stirrups as he described. I haven't used individual stirrups.

 

[lefaveau]

Thank you very much everybody for the responses.
I have a few more questions for clarity:

CEL- In your third response you mention that short detailed stirrpus do not function- Is this specifically to joist slabs or beams in general? Besides anchorage length, curtailing them in compression zone, could that mean that the capacity of the concrete compression for shear capacity needs to looked at in terms of its contribution to the shear capacity of the section?

JAE- What area of the pans is flared? Is there a sketch I can refer to? You talk of using single leg stirrups,calculations point to area of shear steel and spacing, how do you use the single leg stirrup? what assumptions go with this and how do you detail it?

Hokie66
Can you clarify by means of a stetch or something the tapered areas that you would increase in order to increase the shear capacity of the pans?

 

[CELinOttawa]

Well, stirrups may not need to go "all the way up" to be effective, but it really depends on how far they go and what areas they cross.

Fundamentally stirrups work by crossing between the tension and compression zones of a beam. They cross the theoretical cracks which occur in a beam in flexure. There are many models for their design (truss analogy, strut and tie, section stress, cut section capacity, etc) but they can all be thought of as being a "how big, and where" check. You also need to ensure you develop the bar that will do the job.

If you have a bar in the right place, crossing a theoretical crack that is, and that bar stops right after the crack it is not effective. Being in the right place at the right time only gets you points if you have the confidence to hook the guy/gal/deal. In this case the stirrup has to have the strength to do the job; That means a development check (hook, longer length, bar terminator, etc).

 

[CELinOttawa]

Oops: That should be "Fundamentally stirrups work by crossing a theoretical crack, and are detailed between the tension and compression zones for convenience and constructibility." Didn't mean to imply that they work because they go between the tension and compression zones; Stirrups can be entirely in a compression or tension zone, still be crossing a crack and still be doing the job.

 

[JAE]

lefaveau,
See attached. This is a copy of a technical document from CECO - I'm not sure if they still market or sell these forms (you might call them) but these were what I've used in the past.
The forms were about 3 feet long and the taper created 4 to 5 inches of extra shear width, b.

Single leg stirrups are essentially vertical legs (#3 or #4 bars) that have stirrup/tie end hooks at each end. These are placed vertically in the web of the joist and tied to the top and bottom steel.
The hooks of these stirrups are aligned with the top and bottom horizontal bars and should occur a close to the top or bottom of the joists as possible.



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[JAE]

Here's another sketch.


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[TXStructural]

Projects down here are wide module beams/joists (that is, joists are skipped, putting ribs on about 6 ft centers and requiring them to be designed as beams, rather than joists.) We always have stirrups, since they are classified as beams in ACI 318. Typically, these stirrups are V-shaped #3 bars which extend outward and anchor into the slab on each side of the rib, or have a stirrup hook on each side. Bottom bars are dropped into the V. There are also designers using welded wire to form stirrups in narrow members. You can get excellent shear capacity and the small diameter wire results in a thin layer of shear reinforcement, keeping cover thicker or making more room for longitudinal reinforcement.

Ceco provides good resources online and here is a good guide.

http://www.cecoconcrete.com/Resources/Technical/files/concepttocompletion.pdf

and here:

http://www.cecoconcrete.com/Resources/Technical/files/design_main.pdf

CRSI details the placement of bars in our Placing Reinforcing Bars book. We currently do not detail stirrups in joists, but show support details for longitudinal bars.
Sorry I cannot provide an online edition of the book.

https://netforum.avectra.com/eweb/s...?prd_key=2b2d24d2-0d49-4af8-960e-a2df4fe460e9

 

[lefaveau]

Thank so much colleagues. Let me digest the information!