Mild Reinforced Concrete Beam Shear Capacity H>35", but not a deep beam (ACI 318-14 9.7.2.3)

[Celt83]

Diving deeper into running strain-compatibility analysis on some beams to verify some computer results I stumbled on the condition of relatively deep beams as defined in ACI 318-14 9.7.2.3 having a depth greater than or equal to 36" and the consideration or lack thereof of the provided skin reinforcement to the capacity of the beam and more generally beams with layers of steel in tension much higher in the cross section than anticipated when looking at shear strength of the cross section.

I looked at a test case of a 12 x 36 cross section with #4 stirrups and (3)#8 main tension face bars and (2)#7 compression face bars which we would typically provide to give the stirrups something to tie too both with and without #4 skin reinforcement spaced per ACI 318-14 24.3.2 up to H/2.

Considering the skin reinforcement nets an increase of about 110 ft-kips to the flexural capacity but a decrease to the shear capacity of the beam of about 4 kips. 4 kips isn't all that large of a decrease but if you run the skin reinforcement for the full height of the beam looking at strain compatibility a lot of those bar layers end up in tension and raise the centroid even further.

So the question I am getting at is does anyone have any resources or any insight into the standard ACI shear equations and in conditions like this is the intent really to take d as the distance to the centroid of all of the steel undergoing tension or was the intent of d in those equations, 22.5.5.1, meant for a typical condition up to like 2 layers of tension steel?

Another condition where we have seen this lower shear capacity in computer analysis and verified by a hand strain-compatibility analysis is two-way slabs with drop panels proportioned to help reduce the amount of flexural reinforcement, ACI 8.2.4, and the existence of a bottom reinforcing mat. Per ACI 318-14 8.7.4.2.1 the bottom steel in the column strip should be continuous or have a class B splice, the problem being in a lot of conditions based on strain compatibility the "bottom" mat at the deeper drop sections is actually in tension thus reducing the tension steel centroid location and the one-way shear capacity.

I have seen this rationalized away as designing the section only considering the steel you need for flexure but my hesitation with this is if the bars are present the response of the cross section will not match the analysis and potentially have a significantly lower shear capacity based on the standard equations.

 

[KootK]

I don't know the answer to your question with much certainty but, since nobody else seems to either, I'll give it my best shot.

THE CODE & WHAT SHOULD BE DONE

My code, the Canadian one, lets us use the maximum of 0.9 x d or 0.72 x h for the shear depth of the member. Most country's codes have a similar provision and, in that way, keep designers to from having to use unrealistically small values for the shear depth. Easy.

THE THEORY AS IT PERTAINS TO CONCRETE WITHOUT SHEAR REINFORCING

Without shear reinforcing, we're essentially assuming that our members have cracked flexurally but not in shear (diagonal tension). We're looking for the maximum value of elastic shear stress to compare to our limit for diagonal tension. Shear stress on a cracked reinforced concrete section starts at zero on the tension face and jumps upwards at the vertical location of each group of reinforcing bars. The maximum value is reached at the neutral axis, as usual. With regard to side face bars, I believe that this implies that:

1) If you wanted to be able to use the flexural capacity of your member including all of the side face bars, then your shear depth and your shear capacity would drop just as you've described.

2) If you only wanted to be able to use the intended flexural capacity of of your tension face bars, and not the side face bars, your shear depth and your shear capacity would again drop, but not nearly as much. Essentially, with the side face bars straining under flexure, you reach your intended capacity with:

- a deeper neutral axis begetting;
- a reduced flexural lever arm begetting;
- greater aggregate rebar tension begetting;
- higher peak shear stress at the neutral axis.

So yeah, you're on to something there.

THE THEORY AS IT PERTAINS TO CONCRETE WITH SHEAR REINFORCING

With shear reinforcing, we are assuming a section that has cracked in diagonal tension and is left with the following shear resisting mechanisms:

1) Shear friction across the compression block. Since the side face bars will lower the neutral axis, they would also deepen the compression block and increase the shear capacity of this mechanism.

2) Aggregate interlock across the diagonal crack. Side face bars will limit the width of shear cracks and thus increase the shear capacity of this mechanism.

3) Dowel action of the rebar. Side face bars will increase the shear capacity of this mechanism as each side face bar will act as an additional dowel.

So, for members with shear reinforcing, side face bars will improve shear capacity in all respects.



I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[Celt83]

Thank you for the reply KootK.

I'll need to dig more into the US code. I know for pre-stressed/post-tensioned sections you are allowed to use 0.8*H but no such allowance exists for mildly reinforced sections.