Interpretation of 7.3.2.6(c) of TMS 402-16 1

[EngineerRam]

Hi,

How does everyone interpret the following from 7.3.2.6(c)?:

"The sum of the cross-sectional area of horizontal and vertical reinforcement shall be at least 0.002 multiplied by the gross cross-sectional area of the wall, using specified dimensions."

Is the gross cross-sectional area taken about the horizontal or vertical section, or both? I am currently taking it about both in order to be most conservative.

I believe it can be one of 4 options

(Asv = vertical steel; Ash = horizontal steel; Agv = vertical concrete gross section; Agh = horizontal concrete gross section)

1) Asv/Agh + Ash/Agv >= 0.002 (this is a sum of reinforcement ratios, not reinforcement, so technically not correct)

2) (Asv + Ash)/Agv >= 0.002

2) (Asv + Ash)/Agh >= 0.002

4)(Asv + Ash)/max(Agv,Agh) >= 0.002 (most conservative, and the one I take)

Which of these is correct to you?

 

[engineering_patrol]

The cross section of an element is independent of its orientation. So, I don't see any point to define Agv and Agh. Use A=width x height of the cross section.

 

[JoshPlumSE]

EngineerControl -

We're talking about walls here, not beams. Here's my interpretation:

Agh = Wall cross section when looking at horizontal reinforcement = thickness of wall times height of wall
Agv = Wall cross section when looking at vertical reinforcements = thickness of wall times length of wall

I agree with the OP that this is not a very well written provision in the code. I tend to think interpretation #1 is the most rational interpretation. I believe if you take a look at the SEAoC Seismic Design Manual Volume 2 Example 4 they do it this way. I'm looking at the 2015 version of this manual though.

Asv/Agh + Ash/Agv >= 0.002

 

[Blackstar123]

My vote also goes to interpretation No. 1. This is basically what we do. We calculate area and spacing of reinforcement for cross section of unit meter (or unit ft) width and then provide the same spacing along the total length.

 

[Agent666]

Yeah we have a similar provision in the NZ masonry code, we interpret it similar to using #1.

But it is really saying 0.002xAg/m > Ash/m + Ash/m, I don't think its phrased that badly in code, but I think you are interpreting it slightly incorrectly using the entire wall length and height, as this averages out any reinforcement ratios.

It's fairly clear if considered on a per meter basis for Ag & reinforcement areas then it simply becomes the sum of reinforcement ratios being greater than 0.002 (0.2%) on a per meter basis in each direction. So #1 effectively applies.

If the reinforcement changes over the height or length, then you still need to satisfy this relationship locally. It is not considered over the entire wall length or height as some averaging will occur and you may have isolated areas where the sum of both ratios is less than 0.002Ag. Where Ag is a unit length x thickness.

Our provision, but written in terms of ratios as intended:-

 

[JoshPlumSE]

But it is really saying 0.002xAg/m > Ash/m + Ash/m, I don't think its phrased that badly in code, but I think you are interpreting it slightly incorrectly using the entire wall length and height, as this averages out any reinforcement ratios.

Good point, the SEAoC seismic design manual does use the spacing of the reinforcement in their calculations. I may have overly focused on the overall length and overall height when I was refuting Engineer_Patrol's comment about the areas being the same.

 

[EngineerRam]

Thank you all!

JoshPlumSE: Would you also interpret the minimum requirement of vertical reinforcement > 1/3 horizontal reinforcement as a reinforcement ratio? I see that the SEAOC does it this way, but have seen other examples that the total reinforcement is taken. The second approach seems like it could get ridiculous with the amount of vertical reinforcement required if the wall has a high aspect ratio.

Agent: Does the New Zealand code have anything similar to the above requirement? If so, is it also taken as reinforcement ratio?

 

[Agent666]

I don't believe our concrete code has a similar requirement.

Our minimum ratios in each individual direction summed up are a lot higher than 0.2% I believe, about 0.14% for horizontal reinforcement and 0.27% vertically (based on 30MPa concrete). So minimum sum would be 0.41% for non seismic detailing. Double the 0.2% you've noted.

So the sum being higher than 0.2% was probably just seen as being redundant for concrete. For masonry they left it in I guess.