Cracking moment larger than moment of resistance? 1

[Woody1515]

Hello,

Is it possible for the cracking moment of a reinforced concrete beam to be larger than the ultimate moment of resistance? If I run the numbers with an 8” thick by 48” deep 30 MPa concrete beam with 2-15M bars top and bottom (very simple example) - I get a larger cracking moment than moment of resistance. This may be because the formula for the cracking moment has no resistance factors applied to it? Should I apply the 0.65 resistance factor to the cracking moment, since it is applied to the moment of resistance? I am trying to determine if the beam will crack under the factored ultimate loads.

This beam would be for a simple grade beam on piles supporting a new residential addition. The contractor wants to use a 48” deep beam as that is the only form he has available to him. The grade beam will be way stronger than what is required, but I want to know if the beam will even crack under the full design factored loads. Or in more general terms, can I compare the cracking moment (without a factor applied to it) to the factored loads?

 

[Tomfh]

how large a load factor is required to get ride of the nightmare over load concerns?

Ductility (minimum steel) is a separate layer of safety. Like lifeboats. You can't just say your boat is so strong it doesn't need lifeboats.

 

[r13]

Tomfh,

I never said that. Below is my original response posted on 2 Apr 20 18:46:

If you have calculated both and find Mcr > Mu, the intuitive way is to design for the larger moment (Mcr in this case), or go through the code to determine a permissible lower design moment; however, this is not always done (calculate cracking moment), then the code took care of this matter by requiring the section must be reinforced with the specified minimum steel (Asmin), or, in the US, 4/3 times of the steel required by analysis (in another term, 1.33 Mu), whichever is smaller.

 

[IDS]

The precast section above failed in sudden flexural bending during installation. It was 350 mm thick and quite heavily reinforced on the bottom face, which would have been in tension in the completed structure. There is nothing mysterious about the failure mechanism:

[ul]
[li]The load factor during handling is only the dead load factor x whatever is assumed for the dynamic load factor, which is not well defined. It is certainly much less than the load factor on the lifters, even though the consequences of failure are the same.[/li]
[li]Differential thermal stresses can be enough to generate tensile stresses in the concrete of the order of 2 MPa, which will reduce the cracking moment by half.[/li]
[li]When the applied bending moment exceeds the concrete cracking moment the stress and strain in the steel are close to zero. The section deflects and gains significant momentum before the stress in the steel is sufficient to start to restrain the falling concrete.[/li]
[li]The combined static moment (which was sufficient to crack the concrete) and dynamic moment cause sudden failure of the reinforcement.[/li]
[/ul]

In this case the top face reinforcement was low ductility mesh. If it had been normal ductility bar that might have had sufficient ductility to prevent total failure, but the section would have been rendered useless anyway.

The circumstances that combine to cause this sort of failure are fairly rare, but not so rare that the potential consequences can be ignored. In this case luckily no-one was standing undereath when it failed.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[IDS]

rapt - I don't recall if we have discussed this before, but I have always read the minimum strength requirement as saying that the design bending capacity based on a cracked section (Phi.Mu) shall exceed 1.2 x cracking moment. In other words, (Mu0)min should be (M*)min. I shall continue to do so, (and use Phi = 0.8 for this case).

Regarding use of low ductility steel, the requirement only applies to sections where failure might lead to sudden collapse or reduced collapse load, so low ductility steel shouldn't be used at these locations anyway.

But certainly the code wording could be revised to make that point clearer.


Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[rapt]

IDS,

AS3600 specifically says
- clause 1.7 notation defines Muo as the ultimate strength in bending.
- "the ultimate strength in bending Muo" should be greater than 1.2Mcr in 8.1.6 for minimum moment.

In the previous clause. 8.1.5 Design Strength in bending it defines the "design strength in bending" as being phi Muo.

I suggested it be changed to phi Muo about 20 years ago and have been doing so ever since but to no avail!

Unfortunately, the code changed phi to .85, much to my displeasure as you know. However, in this case, it actually increases it to 1.02Mcr, instead of the old .96Mcr, though I doubt the concrete and reinforcement notice the difference!

Retired13

The problem was highlighted in tests on low ductility reinforcement where lightly reinforced sections, often with reinforcement significantly above that required for Mcr, failed suddenly at very low deflections, in the order of 5mm in 3-4m spans, on first cracking.

 

[IDS]

AS3600 specifically says
- clause 1.7 notation defines Muo as the ultimate strength in bending.
- "the ultimate strength in bending Muo" should be greater than 1.2Mcr in 8.1.6 for minimum moment.

Yes that's what it actually says.

What I meant was, I do my designs as though it says something different; i.e. I apply the phi factor even though the code says you don't need to.

Just checking the codes again, there is another thing I do as standard practice that is not actually required by the code. The Bridge Code specifically says "without axial force". AS 3600 has identical wording except for leaving out those three words, but doesn't include axial force in the cracking moment equation. I treat axial force as an effective prestress. I don't see any justification for ignoring it.


Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[rapt]

IDS,

I agree. Unfortunately others using RAPT want it to do what the code says!

I would include axial force if externally applied.

 

[r13]

Rapt,

Do you know the thickness of the test specimen? I am thinking, right or wrong, the slender effect maybe in the play.

I don't know your code, but in the US, the phi factor is applied to the capacity side to prevent over stretch of demand, a safety guard on design. And, the inclusion of axial load is a two edged sword, I include it when it works against my design (increase M), but ignore it when help, but its existence is uncertain at times (can be removed at anytime regardless of duration).

 

[rapt]

No, they were no particularly slender. Normal slab thickness for the spans involved.

 

[IDS]

Do you know the thickness of the test specimen? I am thinking, right or wrong, the slender effect maybe in the play.

What slenderness effect are you talking about here?

I don't know your code, but in the US, the phi factor is applied to the capacity side to prevent over stretch of demand, a safety guard on design. And, the inclusion of axial load is a two edged sword, I include it when it works against my design (increase M), but ignore it when help, but its existence is uncertain at times (can be removed at anytime regardless of duration).

Other than the terminology, the Australian concrete design codes follow the same basic principles as ACI 318, i.e. loads are factored up and/or down (whichever gives the worst case) and section strengths are calculated using the full design material strength, then factored down with a single capacity reduction factor. As discussed above, I don't know why the capacity reduction factor should not be applied when looking at minimum bending capacity, and I always apply it.

For the case of the minimum moment capacity calculation, I use whatever axial load is coexistent with the critical bending moment, even though the code says you don't need to include it.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[r13]

IDS,

I start to second guess the failure at low stress level is similar to slender effect in columns, have no positive linking yet.

Since we don't usually calculate the "minimum moment capacity" in the US, sorry that I didn't get it in the first place. I suggest to think this way "a member must have minimum capacity to support load, but must not too close to the maximum capacity, that might break the member." As the "must" is a mandate to achieve, and the "must not" is a prohibition, so, you shouldn't apply a reduction factor to the minimum strength a member needs to achieve, and lower the bottom limit/line.

 

[BridgeSmith]

In the AASHTO code, the phi factor is applied as a reduction to the capacity, and compared to the factored load, with all the factors, including the 1.33 if applicable for lightly loaded members. The phi factor is not applied in any way to the calculation of Mcr.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[IDS]

I start to second guess the failure at low stress level is similar to slender effect in columns, have no positive linking yet.

No, they are two separate effects. The dynamic load resulting from concrete cracking can occur in sections with no axial load. Obviously they can combine in sections with combined axial load and bending, since the sudden loss of stiffness after concrete cracking will cause a larger deformation than for the same load applied slowly.

Why do you think this dynamic effect is not significant?

Since we don't usually calculate the "minimum moment capacity" in the US, sorry that I didn't get it in the first place. I suggest to think this way "a member must have minimum capacity to support load, but must not too close to the maximum capacity, that might break the member." As the "must" is a mandate to achieve, and the "must not" is a prohibition, so, you shouldn't apply a reduction factor to the minimum strength a member needs to achieve, and lower the bottom limit/line.

In the AASHTO code, the phi factor is applied as a reduction to the capacity, and compared to the factored load, with all the factors, including the 1.33 if applicable for lightly loaded members. The phi factor is not applied in any way to the calculation of Mcr.

No-one is suggesting that a reduction factor should be applied to the cracking moment. The Australian code says that the unfactored bending capacity of the cracked section must be greater than the estimated cracking moment x 1.2. Rapt has said that in his opinion the code should apply the capacity reduction factor to the bending capacity, and I have said that is what I do, but that is not what the Australian codes do require.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[r13]

IDS,

No, I don't discount the dynamic effect. It complicates an issue I want to simplify, which may not be realistic.

 

[IDS]

retired13 - What "may not be realistic"?



Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[r13]

Simplify the dynamic effect, I don't have a focus point yet.

 

[IDS]

Why do you want to simplify it?

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[r13]

Habit

 

[Woody1515]

Thanks for the information everyone! Very interesting discussion. I believe my initial error involved including the “compressive” steel as part of the minimum required steel.