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RE: Concrete Crack Width

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The object is to limit the crack width at the surface.  After a crack reaches a certain size (which is the implied limit of "Z") it is considered not acceptable.  The maximum allowable crack width considered is in the elastic range of the section whether it is designed with 40 grade, 60 grade, ultimate or working strength.

Consider a 12" section #9 @ 12" that has 1 1/2" of cover, d = 10", and a calculated crack width of 0.013" (Z=145) at the surface.  Assuming concrete takes no tension, and all of the tension is resisted in the rebar.  Consider now that you increase the cover to 2".  The increase in cover decreases the d to 9 1/2".  The stress profile changes and the crack width increases to 0.016" (Z=178).

The concrete section will leak relative to the surface crack width.  Protection of the rebar is not quite the same issue.  The thicker covers tend to remain alkaline at the rebar level and passivates the rebar better, but that is a bit of a different issue than leaking. 

You may wish to look at ACI 350 for a better explanation.

ACI 318 does not have the same leak considerations as ACI 350 and considers once you are operating at the lower stresses of 40 grade rebar, the Z is not as great an issue and will generally not govern.  The modulus of elasticity of rebar is the same regardless of what grade of rebar you have.  ACI 350 has the same observation and illustrated in Fig 2.6.7(a) and (b). 

Plane sections remain plane and Hooke's Law is still in force.

I hope that this helps.

Harold Sprague, PE
Krawinkler, Luth & Assoc.

-----Original Message-----
From:	Roger Turk [SMTP:73527.1356(--nospam--at)]
Sent:	Tuesday, July 28, 1998 10:25 AM
To:	seaint(--nospam--at)
Subject:	Fw: LRFD, ASD, and USD

I have a problem understanding the crack control requirements of the ACI 
code.  I understand the stated theory about the crack control requirements, 
but don't understand why additional cover will require more reinforcing.  If 
the width of the crack at the surface is the limiting factor, then increased 
cover should have less effect on the exposure of the reinforcing to corrosive 
environments.  After all, we are still dealing with "plane sections remain 
plane" and "Hooke's Law applies," aren't we?

Since the crack control requirements do not apply if Grade 40 steel is used, 
that is the maximum amount of reinforcing that I will use in a footing, 
regardless of whether or not Grade 60 reinforcing is used.

A. Roger Turk, P.E.(Structural)
Tucson, Arizona

T. Eric Gillham wrote:

. > Bill:
. > 
. > It sounds like the foundation sections you were reviewing were 
. > overdesigned (for strength), perhaps as the result of minimum steel
. > requirements?
. > 
. > USD ASSUMES an ultimate state when computing the strength of a member.  
. > The steel is assumed to be yielding, the concrete is assumed to have a 
. > strain of .003. When designing using USD, if one were to design a member
. > "exactly", it would have just the right amount of steel such that when 
. > the steel is yielding, the moment manifested in the member matches the 
. > imposed moment (factored). Therefore, it sounds strange to me that the 
. > strain in the concrete was way below .002. It would seem that if the 
. > ultimate stength of the example foundation section was calculated, it 
. > should be greater than that required by the factored loads.
. > 
. > For example, computing the strength of a 12x24 beam, 2#8 tension steel,
. > d=22", f'c=4ksi, fy=60ksi using USD gives an ultimate strength of 165k-ft.
. > 
. > Using a moment curvature program, no strain hardening in the steel, gives:
. > 
. > concrete strain=.0008   steel starts yielding, moment is 154.5k-ft
. > 
. > concrete strain=.003     steel strain is .0234, moment is 160k-ft  (about
. > 3% different from USD).
. > 
. > Max moment is 160k-ft, with concrete strain maxing out at .004.
. > 
. > The MC program (SEQMC) takes into account the cracking of the section, and
. > of course is based on equilibrium, and uses the Mander model for concrete.
. > 
. > 
. > T. Eric Gillham PE
. >