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RE: ACI 10.5.3 Minimum Flexural Reinforcement

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> ACI318-02    10.5.3 (Minimum reinforcement of flexural members)
> "The requirements of 10.5.1 and 10.5.2 need not be applied if
> AT EVERY SECTION the area of tensile reinforcement provided is
> at least one-third greater than required by analysis."
> 
> 1.	If phi Mn >= 1.33 Mu, don't I need any flexural
> reinforcement at all? How about temperature and shrinkage
> reinforcement? (if I can ignore 21.3.2.1)

You still need flexural reinforcement.  It says "10.5.1 and 10.5.2 need not
be applied"; it does NOT say that sections 7.12, 7.13, 10.2.5, and 22.2 need
not be applied.

This section simply allows you to use LESS than the minimum values
calculated in 10.5.1.and 10.5.2.  You are not allowed to use completely
un-reinforced concrete except in the specific situations listed in section
22.2.


> 2.	If some portion of a flexural member has phi Mn >= 1.33 Mu
> and other portions have phi Mn < 1.33 Mu, can't I apply 10.5.3
> to the areas of phi Mn >= 1.33 Mu?

Yes, 10.5.3 can be applied to isolated parts of beams.

 
> 3.	What's the relationship 10.5.3 and cracking moment?
> (In my opinion, Eq 10-3 is related with Mcr, which is
> dependent upon section and material properties.) If
> phi Mn >= 1.33 Mu and Mu < Mcr, no flexural reinforcement
> is required.  How about if phi Mn >= 1.33 Mu and Mu > Mcr,
> so phi Mn > 1.33 Mcr?  In this case, 10.5.3 says that
> minimum reinforcement is not required for phi Mn >= 1.33 Mu.
> But, its load Mu > Mcr says it will crack.  Isn't this a
> contradiction?

Yes, eq. 10-3 is based on cracking moment.  Basically, 10-3 is there to
PREVENT the case where the un-reinforced section (cracking moment) is
stronger than the reinforced section (Mcr > phi Mn).  If the beam DOES crack
in this situation (an accidental overstress, for example) all of the tension
is applied to the reinforcing steel which fails suddenly with no warning. 

The exception (paragraph 10.5.3) is for when you can prove that the maximum
applied moment is much less than the cracking moment.  Even then you have to
provide enough steel to give the reinforced section 133% of the required
strength.  


> Do I need reinforcement smaller than minimum reinforcement, 
> which will resist Mcr?  If this is true, I need small amount
> of flexural reinforcement  although I do not need minimum
> flexural reinforcement. Correct?

Exactly.

-----
Jason W. Kilgore, P.E., S.E.
Leigh & O'Kane, LLC
Kansas City, Missouri



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