tension controlled section question

[geo321]

I was reading some of the topics and thinking of an elementary topic that would like to share with you.

Regarding the flexure in beams or slabs, we usually design our section to be tension controlled (strain in steel should be higher than 0.005) which will guarantee a ductile behavior since reinforcement will yield and have excessive deformations before concrete will break in compression.

However, many engineers like the fact of being conservative so they will always have tendency to increase the required steel area and here comes my question.

Tension controlled means that fs ≥ fy. When As (steel area) will increase, the neutral axis will do the same and fs will decrease. Let us suppose that the section, for a reason or another, has been reduced and the acting moment is requiring a certain amount of steel and is tension controlled (strain in steel is slightly above the required 0.005).

In this particular case, being conservative and adding more than required (or for some deflection purpose) will result in the fact that steel will not yield and we will not get the required ductile behavior since the strain in the steel will be less than 0.5%.
Is there something I am missing ?
thank u

 

[jayrod12]

Perhaps I'm missing something, but yield strain for steel is .002.

 

[structSU10]

If by code you are no longer a tension controlled section your phi factor reduces in accordance with the steel strain to account for the concrete crushing being more 'undesirable' (see ACI 318-05 figure R9.3.2). Generally it means you hit a plateau for you section capacity.

 

[geo321]

Jayrod12, yield strain in steel is fy/Es which is 0.002 for 420Mpa. But tension controlled condition states that strain in the steel should be higher than 0.005. In other words, The design has to be based on steel strain larger than 0.002 to ensure ductile performance

 

[allgoodnamestaken]

I cannot say anything about US Code, but in Canada in 99% of conditions the balanced condition (steel yields just as concrete crushes) is the maximum reinforcement allowed.

 

[jayrod12]

Agreed with allgood. As long as the steel yields, it's ok, there's no 0.005 requirement that I'm aware of.

 

[Hokie93]

ACI 318-11 Section 10.3.4 requires a minimum net tensile strain equal to 0.005 in the extreme tension reinforcing steel in order for a flexural member to quality as "tension-controlled". The minimum net tensile strain for a non-prestressed flexural member per ACI 10.3.5 is 0.004. If the section in question has a net tensile strain between 0.002 (for a compression-controlled section with Grade 60 reinforcement) and 0.005, the phi factor is linearly interpreted between 0.65 (tied) and 0.90 or between 0.75 (spiral) and 0.90. So Geo, for your scenario, the phi factor would slightly less than 0.90 because of the "additional" reinforcing steel.

 

[ARS97]

ACI requires that the steel strain be a minimum of 0.005 for tension-controlled sections - this results in a maximum allowable amount of steel area, in order to maintain that minimum strain. (Most concrete design textbooks show the procedure for determining this max steel area.) So, yes, you can add too much steel to where it won't be a ductile failure. As long as you maintain than minimum steel strain of at least 0.005, it's a tension-controlled section. Maybe I'm misunderstanding......

 

[jayrod12]

As both allgood and I said, we are not intimately familiar with the ACI codes, but rather the CSA codes. I do not believe I've heard tension-controlled sections before. I'm also not well versed in seismic design so perhaps it is under the seismic requirements.

Where's Koot when needed to lend a good blend of CSA and ACI knowledge? Is this one of the few times the CSA and ACI codes differ slightly?

 

[structSU10]

It appears that CSA is different if you don't have the adjusting phi factor

it slides to use a phi more 'appropriate' for a more brittle failure.

 

[jayrod12]

Ah, yes, no sliding phi factor here. Straight up 0.65.

 

[rapt]

The difference in the Canadian code is that it uses partial factors for concrete and reinforcement. Rather than a single capacity factor at the end of the calculation as ACI uses.

So the Compression force is already reduced by its factor in the calculation of the section strength and the reinforcement is reduced by its factor. Then you get C and T to be equal.

Because the reduction factor on the concrete is much higher than the one on the reinforcement, this automatically increases the neutral axis depth and reduces the design lever arm in the strength calculations depending on the level of compression/ductility.

And all comparisons are then done with Balanced Condition.

Because the neutral axis depth etc in ACI code is calculated from forces based on the full material strength, the zone between .75Balanced and Balanced has to be allowed for and this is done by fudging the capacity reduction factor as mentioned above by others.

 

[jayrod12]

Thanks for the clarification rapt.