Precast Concrete Beam Design for Flexural Capacity

[astructurale]

Using computer software to generate precast and prestressed concrete beam designs is a usefull tool, but it seems that for some particular cases the design becomes too conservative.

I've run across the following when designing simple span uniformly loaded beams,

ØMn < 1.2Mcr and ØMn < 2.0Mu

This case happens at in the first 1/4 of the beam span each end under a uniform dead and live loading. I realize that the design is following the code, but does this take it a step too far. When designing a beam by hand this condition would never be found, but the software finds it becuase it evaluates the loading at smaller length intervals.

I am creating beam tables for our sales department to use, and I've found that when looking at the maximum loading on varying spans for the same cross-section & same strand pattern that as the spans shorten this becomes an issue and limits the loading capacity when using prestress alone, or it requires that developed re-bar be added near end 1/4 spans to generate the capacity requried . In my opinion this is conservative because you will never get a full uniform live load along the full length of the beam to create that exact loading scenario.

Some progams to do not even take this into account (not sure why), but it is a real design issue I've been told by the software company. I am using Concise Beam (

http://www.blackmint.com).

The first time I ran across it they said that this is a common design flaw missed when doing the calculations by hand. Is there a way to get around this. I've been doing beams for years and never had to increase my steel (or decrease my capacity) to deal with this, so it seems a little "picky" to me.

Anyone have any opinions on this or have you run across this before in your designs?

 

[rapt]

astructurale,

Looks like your approximate hand design methods have been wrong for years then. The checks are necessary.

 

[rowe]

Are you (and the software co.) using ACI? If so, what article(s) refers to that particular restraint and what does the code commentary say?

While software for complex design is extremely useful and time saving, it is the design engineer's responsibility to ensure that the design is safe (and code compliant). Software is a human product and subject to human error. I have received several updated software versions to fix "bugs" or code related errors. The discovery of these "bugs" and errors are often the result of USER research of the designs produced by the particular software.

I strongly suggest you review those prestressed code checks with which you are not familiar and develop your engineering experience and judgement. I hope you will find an answer to your question and add to this thread again.

Good luck.

 

[astructurale]

rapt - I don't know anyone who would do a hand check for a beam at every 200th of section of a beam to find this. And it is not really a case of right/wrong, but code intrepretation I think.

***
Yes, I am using ACI 318-02, and so does the software. I also know that it is the designer's responsiblity to ensure the deisgn is safe and code compliant. The designs are safe, and based on my research on the program it is also code compliant.

OK the rest is going to be long, but I want to more clearly explain what I am asking, and give a bit more detail into what I do already know,

I must add that ØMn > Mu for these cases. This is not an issue where the design could fail.

From what I have found the applied moment, (wul^2)/8, rises faster than the cracking moment, Sbc[(P/A)+(Pe/Sb)+fr]-Mnc[(Sbc/Sb)-1]. So there is a point in the beam where ØMn < 1.2Mcr, and also ØMn < 2.0Mu. At ØMn > 2.0Mu the cracking moment criteria is waived. In the beams I have run across this on ØMn is very close to 2.0Mu, but does not exceed it.

Also, PCI 6th ed handbook states in 4.2.1.4 that the "code requires that the total prestressed and nonprestressed reinforcement be adequate to develop a design strength at least 1.2Mcr" and that the "provision is genearlly assumed to apply only at critical flexural sections, and is waived for members with shear and flexural streenght at least 2.0Mu..."

To futher narrow down my question...

Is it reasonable to say that since the non-compliance, ØMn < 1.2Mcr and ØMn < 2.0Mu, occurs at 0.20*L, and is not located at the point of maximum flexural requirement (the center of the beam), which would be the "critical" flexural section, then the beam still satisfies the requirement of PCI, and it therefore acceptable?

I cannot find in ACI where the requirement is spelled out as plainly as in PCI. It may be that other software are making this assumption, but this particular program is taking a more conservative route by not doing so. I am also going to ask the program technical person this specific question, but I wanted to know if anyone had any opinions or code interpretations on this particular requirement.

Thank you for for posts thus far,
astructurale

 

[rowe]

The basic cracking moment req'ment is a means of ensuring that cracking will occur before flexural strength is reached, and by a large enough margin (1.2Mcr) so that significant deflection will occur to warn that the strength Mn is being approached.

It doesn't matter where the max. flex. req'ment is in regard to this Mcr req'ment. If the flexural strength Mn is below Mcr at any point, then there is no warning if Mn is reached. ACI says it's OK if there is no warning crack if you reinforce the section for twice what is needed (2Mu).

My opinion is that since the strength of the beam varies along its length, the requirement applies throughout the beam length.

Good Luck

 

[astructurale]

Good point rowe.

Well, I have already heard back from technical support for the software. (One of the pluses of this program is fantastic techincal support). Apparantely this is debated topic. He pointed out that other codes (Canadian for example) provide more explicit information on this check than ACI. Since ACI does not provide explicit informaiton PCI has made some futher assumptions for designers, which I now belive allows me to consider my design as acceptable since my capacity is close to 2.0Mu and the warning does not occur at critical sections as defined in 4.2.1.5 by PCI. In other codes, where it explicitly states that the check must be made for all sections instead of critical sections, the comparision is to 1.3Mu or 1.5Mu when 1.2Mcr is exceeded, which is much less stringent than the 2.0Mu set by ACI.

Thanks for the discussion. I still welcome more comments.

 

[haynewp]

"In my opinion this is conservative because you will never get a full uniform live load along the full length of the beam to create that exact loading scenario."

How do you know this for sure?


"I must add that ØMn > Mu for these cases. This is not an issue where the design could fail."

I'm not sure that is exactly true, you're abruptly going from an uncracked to a cracked section in a dynamic fashion. Hence the 1.2Mcr requirement.


"Is it reasonable to say that since the non-compliance, ØMn < 1.2Mcr and ØMn < 2.0Mu, occurs at 0.20*L, and is not located at the point of maximum flexural requirement (the center of the beam), which would be the "critical" flexural section, then the beam still satisfies the requirement of PCI, and it therefore acceptable?"


I would say no, you should be satisfying ACI, not a discussion in PCI. In the PCI quote, note the words "generally assumed".

Be aware you are also required to check that your available shear strength is also > 2*Vu to waive the 1.2Mcr provision. And the critical location for shear is not going to be at midspan.

 

[rapt]

The interpretation I have received from the Australkian code committee on this (it says to check at critical sections) is that any section where the capacity is less than 1.2 Mcr is a critical section for minimum capacity and that it therefore needs to be chcecked at all points in a concrete member.

 

[haynewp]

Yes, that is the way I think ACI should be applied as well. I think he was trying to take the critical section as just being at midspan.

 

[apsix]

rapt
Is it just me, or is that an illogical definition of critical section? They should then just state the minimum capacity is required for the full length of the member.

Did you get an explaination where the clause 'This requirement may be waived at some critical sections .....provided....will not lead to sudden collapse...' is appropriate to use?

I have assumed that it could be appropriate in cases such as ground beams where the displacement of a member after cracking is limited.

I'll finish by quoting from AS3600 Supp1-1994;"The intention of this clause is to ensure overall ductile failure of the member and this can be achieved without satisfying the requirement for min. reinf't at every cross-section".
Is this still valid?

Apologies to those not using AS3600.

 

[rapt]

apsix,

I think the definition is logical if you consider why minimum reinforcement is required and the failure type it is trying to negate. Yes, the clause probably should have said it was needed everywhere except for the need to define the extra part of the clause you then quote.

Yes, the explanation for this part of the clause is that you do not need to supply minimum reinforcement on one face of the beam as long as reinforcement on the other face is sufficient to carry the full load. e.g. you do not need to supply minimum reinforcement over the columns as long as the beam can carry the full loading as a simply supported member, ignoring all comntinuity effects at the columns. THis is only to satisfy ultimate loading. This solution would not work for crack control in the negative moment areas.

 

[cooperDBM]

I'm in the camp that every section where minimum strength is required should be checked. The problem for ACI prestressed concrete users is that the limit below which minimum strength is required, strength greater than 2 times moment, is much higher than many other codes, and ACI non-prestressed beams, which use strength greater than 1.33 times moment. Therefore longer lengths of a prestressed beam requires minimum strength under ACI. This may be why PCI focuses on critical sections only - though as pointed out above the definition of critical section is open to debate.

As far as Concise Beam is concerned it checks every section by default, since it supports Canadian and Australian codes as well as ACI. In recognition of this debate there is an option in Concise Beam to force the program to only check the critical section (minimum moment to strength ratio).

 

[astructurale]

Thanks cooperDBM. When I had discused this with Concise, they pointed me in the direction of the optional check box, and also reminded me about the other codes it checks and what their standards are.

To all:
Thanks for discussing this topic. That's a great part of these forums. These discussions can test your understanding of topics. And it can either confirm your understanding or point out things you had not considered. I've gotten a little of both this time.