What about Biaxial Shear in RC? 1

[Mainu]

Let´s take a rectangular RC column subjected to an action with components along both axes. Here we have the common issue of biaxial bending that we can solve routinely and about what we can find numerous references. But... What happens with shear? How do we deal with the biaxial shear? In this case, references (even in the most reputed books about concrete design) dissapear...

Some people have their own thumb rules. Ones decide to design the reinforcement for Vx and Vy and later add both numbers to obtain the required steel. Other ones think that it is possible and reasonable to design for sqrt([Vx]^2+[Vy]^2) along the main direction. But... Is there nowadays some scientific paper, code, or research to support our designs about this topic?

I would be glad to hear your thoughts about this and, of course, if any of you have some good reference about this topic and he/she wish to share it with the community, it will be highly appreciated.

Thanks in advance.

 

[r13]

Japanese concrete design specification has adopted the "ellipse function", since 1996, for combining V_c and V_s in capacity resisting biaxial shears. In 2003, Hansapinyo C. published research paper indicating the ellipse function underestimates the concrete capacity, and overestimates the strength contributed by shear reinforcement. A latest paper published on "Journal of Engineering and Development", Iraq 2014, has reached similar conclusion after conducting experiments on biaxial shears, and biaxial shears with torsion. The conclusion is shown below for information. (Note the comparison of ACI was through importing the JSCE formula and imposing on ACI provisions)

4. Conclusions :
The ultimate capacity in this study is discussed separately in terms of the concrete and the shear reinforcement contributions based on the current design method using ellipse interaction formula (JSCE code 2007). From experimental results of the tested reinforced concrete beams, the following conclusions can be drawn.

1. The comparison of ultimate capacities from experimental results with the calculated values from the ellipse formula using the ACI and JSCE codes indicates that these codes gives quite conservative values of ultimate capacity where reductions of about (30 to 76)% and (7 to 20)%, respectively, are observed.

2. The ellipse formula underestimates the capacity of concrete part by about (119 to 188%) and about (43 to 50%) for ACI and JSCE design, respectively. This is due to the increase of shearing area along diagonal crack plane. Tilting of the specimen significantly increases the effective depth while shear span remains constant; hence the shear span-to-depth ratio is decreased, especially with the high reinforcement ratio used in the tested specimen.

3. For the contribution of shear reinforcement, the calculations using ellipse formula overestimate the shear reinforcement part by (-21) to (-6) % and by (-25) to (-11) % for the ACI and the JSCE codes, respectively. Therefore the experimental results have exposed weakness in existing ellipse formula.

4. When transverse steel ratio is stepwise increased from zero to 0.00377, 0.00502 and 0.00754, the ultimate load is increased by 47.5%, 63% and 101% respectively. While when transverse steel ratio is increased from 0 .00377 to 0.00502 and 0.00754, shear reinforcement contribution is increased by 47.7% and 136% respectively. Also by increasing the transverse steel ratio from 0.00377 to 0.00502 and 0.00754 the ratio of (experimental /calculation) was increased by 10.6% and 18.6% respectively.

 

[IDS]

retired13 - is that quoted from?:

https://www.iasj.net/iasj?func=fulltext&aId=86700

Behavior Of Rectangular Reinforced Concrete Beams Subjected To Bi-Axial Shear Loading; Journal of Engineering and Development, Vol. 18, No.2, March 2014, ISSN 1813- 7822

The conclusions are a bit hard to follow, but I'll read the paper.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[r13]

Yes. I don't think it is an excellent paper, but as a period on my brief introduction of the available researches. Here is another paper you might want to read. Link

 

[Agent666]

Agent666 - do you know if bi-directional shear was a significant cause of failure in the Christchurch earthquake?

I don't recall it ever being raised as an issue with respect to framed structures. Our modern codes (1970s onwards) are based on capacity design principles are intended to protect against a shear failure (especially in column). Ultimately this is intended to ensure a dependable flexural based failure occurs well before a brittle shear type failure. As noted also our codes require the design for biaxial shear.

The CTV building which collapsed and killed over 100 people has an almost criminally low amount of shear/confinement reinforcement in the columns, 400 diameter columns with G300 R6 spirals at 200 ctrs (read never complied with the standard of the day), and I still don't think they failed purely in shear. But it probably didn't help matters, there were a lot of compounding problems that contributed.

One thing they did change in the latest amendment which may or may not have come out of the royal commission recommendations and/or research since 2011 was to revise the maximum allowable shear stresses.

Reducing them for columns and walls, it was previously min of 0.2f'c and 8MPa for walls and columns & beams. Now for beams it's 0.2f'c & 10MPa, for walls 0.16f'c & 6MPa, for columns 0.2f'c & 6MPa. Our wall detailing requirements were revised quite a lot as they didn't perform particularly well.

No significant changes to beam and columns, but we've typically had much more onerous detailing requirements than other recognised international standards for beams and columns.

Even, in seismic zones, I would consider Vc = 0.

The degree to which the concrete contributes is ultimately dependant on the curvature at hinge regions. In NZS3101 for example at higher levels of curvature its certainly zero, but for moderate curvatures 50%Vc can be used. Outside of hinge regions 100%Vc can still be used for comparison. I'm not sure what ACI says on the matter.

I believe, design for the larger, or dominate, shear force of the two will satisfy the requirement for both directions.

Please don't anybody do this!

 

[r13]

Obviously ACI is late to the party. I don't recall it has addressed biaxial shear forces in the code until now. Even up to the latest development, ACI still assigns concrete strength V_c = 2√f'_cb_wd in each direction as usual. The biaxial shear forces phenomenon is not limited to columns only. On my brief research, only Japanese has provide provisions address biaxial shear in its design code since the 90's, I am not aware any other country has similar provisions up to this point of time.

 

[IDS]

Thanks Agent666. It occurred to me after posting that question that we are here discussing the combination of separate perpendicular forces, whereas the seismic force is a single force that may be resolved into perpendicular directions, so it's rather a different situation.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[r13]

The new ACI provision on controlling biaxial shar bring up an interesting question, which can be demonstrated by the example below:

Assume V_uy = 0.45 V_ux, and V_n = V_ux = 10√f'_c. In this case, V_uy < 0.5V_n, so shear reinforcement will be designed for V_s = V_ux - V_c = V_ux - 2√f'_c. Now the question is, though not required to consider for biaxial shear, but V_uy = 0.45 V_ux = 0.45V_n = 4.5√f'_c > V_c, what is the available strength to resist the force beyond the concrete strength?

Note that for simplicity, strength reduction factor is ignored on the expressions above.

 

[Settingsun]

Retired13, the ACI code requires you to design for the y-direction shear force the same as for uniaxial shear, so the concrete contribution gets counted for both directions. If the ellipse interaction is correct, ACI is a bit unconservative with the greatest unconservatism being when one direction is maxed out and the other is approx half capacity (as in your example).

 

[r13]

ateveh,

I think the example presents a question that needs to be explored more deeper into it. As far as I could tell, except very few exceptions, I have never pay attention to Vy, but fully design Vx as specified by the code. Most of our calculations were checked through layers, without any objection, I think my practice was accepted by many. It left no doubt, that there would have cases similar to the example, then, the question remains, what is the strength accounted for Vy which was left unchecked? I rather think ACI has underestimated the concrete shear capacity, either unknowingly, or conservatively. I think the conclusions of researches cited above aligns with this thought, and hope to see/have more insight on this hidden capacity.

 

[Agent666]

Retired13, clearly you provide shear reinforcement in both directions.... Edit - just to be clear this was in response to your previous example.

 

[Agent666]

what is the strength accounted for Vy which was left unchecked

This is the point, you should be checking it. In this day and age of spreadsheets and automated design there is no excuse for not checking it.

 

[r13]

Agen666,

Yes, obviously

 

[Settingsun]

I think your question is too general. Did your beams have closed stirrups so they had y-direction shear reinforcement even though you didn't explicitly design it? Is the y-direction force just an artefact of a computer frame analysis that is actually resisted by a slab in-plane? Were the beams wider than deep, so the smaller y-direction shear force was OK 'by inspection' and the reviewers saw no need to comment on it? Did your structure ever actually experience its design loads? Did large y-direction shear ever occur in your designs, since you don't seem to be sure? There could be any number of reasons which can't be ruled out without something specific to look at.

 

[r13]

So, this goes a full circle back to my previous statement "I believe, design for the larger, or dominate, shear force of the two will satisfy the requirement for both directions." which has been in step with the ACI code up to the latest development see Agent666's quote on ACI318-2019 code provisions). And the latest development leads to the question in my example.

 

[Agent666]

Let´s take a rectangular RC column....

From the OP's original post.... Why are beams even being talking about here!?

 

[r13]

ACI is even weaker on shear on columns.

 

[Settingsun]

Beam-column then...

 

[Trenno]

Beam... Column... all the same thing.