Strain at 0.002, ACI 318, 10.3.3 2

[MGMtulsa]

I am interested in some discussion.
Section 10.3 states the general principles for sections subject to flexure and axial loads and per ACI 318-11, 318-08...-02.
Section 10.3.3 states that "...it shall be permitted to set the compression-controlled stain limit equal to 0.002."
Questions:
1. Is this stain of 0.002 applied to the tension steel?
2. Or, is the 0.002 strain applied to the concrete which is in compression?

Notes:
10.3.2 notes BALANCED strain when steel yields simultaneous with concrete at an ultimate strain of 0.003. (For steel with Fy=60 ksi, the strain equals 0.00207.)
10.3.3 notes COMPRESSION CONTROLLED section when tension steel strain is less than or equal to 0.003 (the strain for compressed concrete).
10.3.4 notes TENSION CONTROLLED section when tension steel strain is 0.005 or greater. Also, the TRANSITION region is noted (between 0.003 and 0.005).
10.3.5 notes NOMINAL STRENGTH with a requirement for strain to equal or exceed 0.004.

[please limit discussion to the two questions. I intend to start a 2nd thread for a variation of this problem. thanks]

 

[techiestruc]

The strain limit 0.002 is applied to the extreme tension steel. This strain limit was based on yielding of Grade 60 reinforcement (ey = fy/Es = 60/29000 = 0.002). Determining the strain values of tension steel for concrete subjected to flexure is significant for obtaining the appropriate reduction factor (i.e. 0.90 for tension-controlled and 0.65 for compression-controlled). It is desirable to have under-reinforced concrete beams so that the tension steel will yield first before the concrete crushes (you will have time to run!) which is the reason a limit of 0.004 was set to assure that the beam will be under-reinforced.

 

[MacGruber22]

Regarding question 2, usable strain in concrete is always .003 in/in.

 

[rapt]

Macgrubber,

It is only always .003 if you use ACI code and the rectangular stress block. If you use a real stress strain curve for concrete, it is often as high as .0035 (Eurocode, BS8110) for lower strength concrete and can drop to .0028 (Eurocode) for higher strength concretes.

 

[MGMtulsa]

I appreciate the responses.
Can we focus on the subject of the two questions, i.e. "...it shall be permitted to set the compression-controlled stain limit equal to 0.002."
Let's add a question.
0. To what is the 0.002 strain applied?
Then the original questions #1 and #2 follow.
Thanks.

 

[jdgengineer]

janssenbrian already answered the question...

Section 10.3.3 of ACI 318-08 says "Sections are compression-controlled if the net tensile strain in the EXTREME TENSION STEEL, et, is equal to or less than the compression-controlled strain limit when the concrete in compression reaches its assumed strain limit of 0.003. The compression-controlled strain limit is the net tensile strain in the reinforcement at balanced strain conditions. For Grade 60 reinforcement, and for all prestressed reinforcement, it shall be permitted to set the compression-controlled strain limit equal to 0.002"

Therefore, if the net tensile strain in the extreme tension steel is less than 0.002 then the section is compression controlled.

 

[UcfSE]

The 0.002 is the tensile strain in the steel. Less tensile strain, or compressive strain, is compression controlled.

 

[MGMtulsa]

In talking with other engineers, I have found that there is a difficulty in understanding the wording in the ACI Section 10.3.3. The difficulty results in the lack of distinction or understanding between limits and conditions.

For example, there is a limit called "compression controlled section". And, there are conditions called compression, also tension. The limit is defined using the terms "compression" and "tension". And of course, the condition of compression or tension is the result of a force applied to a sectioned area of resisting material, i.e. concrete and/or steel.

Consider the compression limit. Concrete and reinforcing form a couple to resist flexure. The reinforcing has a tension force, and the concrete has a compression force as it opposes the reinforcing in flexure.

ACI 10.3.3 defines the compression limit. That limit is defined in terms of the amount of strain in the reinforcement (tension). As noted in 10.3.3 for Grade 60, the limit is stated at 0.002.

Per the definition in ACI 10.3.3, the beam in flexure is compression controlled when the tension reinforcement is at a strain of 0.002 or less. The "compression limit" recognizes the threshold at which the concrete could fail in crushing compression -- the result of too much reinforcing.

ACI 10.3.4, 10.3.5, and others continue to define other limits, i.e. tension controlled, control for maximum steel, etc.

I started this discussion for the purpose of listening to the explanation given by more engineers. The engineers who have participated to date have shown their understanding in terms of the ACI code. And yes, Janssenbrian is right on target.

To promote understanding, I found a diagram that gives a good graphical summary of the ACI 318, Section 10.3, including 10.3.3. The graphic is taken from a text book, the chapter attributed to Mr. Murat Saatcioglu, Professor and University Research Chair, Dept. of Civil Engineering, University of Ottawa, Ottawa, CANADA. I have altered the graphic to convert the phi equation from metric to U.S. Customary Units. See attachment.

The Saatcioglu graphic is an expansion of that found in the PCA notes ACI 318-08, see Section 9.3.2, page 5-10.

Hope this helps others to read the ACI Section. I appreciate the input from each of you to date.

If others have had difficulty with this ACI section, please add to the thread and say so, speak up, ask questions. It will help.