Really it's just basic statics, nothing more, other than the embediment length of the legs of the hairpin to develop the tension force.
The total lateral force is resisted in shear at the cup of the Vee at the anchor bolts. Call that total lateral kick "H". Each leg of the hairpin takes one half of that total force multiplied by the ratio of the incline of the haipin leg. The greater the spread of the hairpin, the greater the force in the rods to resist "H". Then you just have to make sure you have enough length in the legs to develop the force. Simple really.
Are these "hairpins" in a structural slab, or just in a slab on ground? I have seen a few queries about them on this site, but to me it seems questionable practice to use the slab on ground, which is really just a pavement, to resist lateral building forces. What happens when at a later date someone needs to cut a slot in the floor for services installation or something?
You rely on the friction between the slab and the ground to resist the outward thrust. And yes, if someone were to cut out part of the slab you could have a problem. But that is true for any structural element. As a building owner you need to check if it's acceptable to remove or modify any item before you do it.
I am well aware of your concerns and agree, but have used these slabs on the ground for many years to embed the hairpins. Generally, they extend less than 8 feet into the slab proper from the mainframe anchor bolts. I also spec WWM which (1) extends the amount of slab you are picking up in dead load, and (2) provides continuity between the hairpins in case one is cut. I would have a problem though if the owner wanted to use fibermesh in lieu of the WWM.
Remember though that one of the driving forces in the footing sizes is the uplift. If you make the footing deeper rather than larger to add the extra weight required to resist the uplift, then you get the added benefit of lateral bearing against the footing to help resist the spreading. I never rely on this force unless the owner does not want a slab or tie beam installed, but know it is there as a redundancy in case any hairpin is cut.
I would like to add a question to this discussion. Do you guys use a steel angle against the anchor bolts that the hairpin is placed against? If so, is the purpose of the angle to provide a direct force transfer from the bolts to the hairpin, thereby avoiding any need to involve ACI 318 Appendix D? Or am I way off here?
Never have used a steel angle, and as to the placement of the hairpin, it is behind the anchor bolts, allowing 2" of cover from the edge of the concrete slab to the hairpin. The anchor bolts are usually a mimimuum of 3 to 4 inches away then.
